acid-base equilibrium calculations and charts

Version 3.2.3 (for MS-ExcelTM, English)Freeware for educational and non-commercial use

Since 1992 (Turbo-Basic/DOS, Portuguese)

pH and Acid-Base Titration Curves:

Analysis and Simulation

Copyright © 1992 - 2007Prof. Ivano G. R. Gutz

[email protected]

Cite, bookmark for new releases and link to http://www2.iq.usp.br/docente/gutz/Curtipot_.html

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil

Head of the Chemistry Department of IQ-USP (2004-2006; 2006-2008)

Member of the Editorial Boards of Talanta and Electrochemistry Communications

Coordinator of the Chemistry Olympiad in Sâo Paulo (2 million high school students)

Fellow of IUPAC

Research interests:

CV, Publications, see: www2.iq.usp.br/docente/gutz

Dr. Ivano Gebhardt Rolf Gutz - Full Professor (since 1992)

This freeware is a courtesy of

F41

Gutz: a) Invention, development, miniaturization, automation and application of analytical devices, systems and methods, with preference for electroanalytical, electrophoretic and spectroeletroanalytical flow systems, including microfluidics. b) Research in environmental chemistry with emphasis on the liquid phase and related chemistry of the atmosphere in the São Paulo megacity – the largest “laboratory” of ethanol use as fuel; development of sampling, speciation and determination methods.

» generation of curves with equally spaced data in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison

Read the License first (place mouse on red dot at left); if you agree with all terms, you can use CurTiPot in educational and non-commercial applications

The Regression module becomes operational after activation of the Solver supplement; you can do this later

Regularly check for updated releases at the author’s site www2.iq.usp.br/docente/gutz (University of São Paulo, Brasil)

Experimental pH values are assumed free of calibration, junction potential and alkaline errors of the sensor (to be corrected previously for most accurate results)

The author reserves the right not to be responsible for the correctness, completeness, accuracy and bug-free operation of the freeware CurTiPot

Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10)

Read local instructions in comment boxes by placing the mouse on cells with red marks (like in Q2, Q13, Q15 and Q21 in this page);

Some features and uses of CurTiPot (hover on red mark at Q2 to read about the name and origins of the program)

• pH calculation of aqueous solutions (>30 species in equilibrium)

• Simulation of simple and complex acid-base titration curves - Virtual Titrator

• Data analysis of real and simulated curves

» Evaluation of curves by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKas by non-linear regression

• Distribution of species and protonation of bases vs. pH and vs. volume

Configure Microsoft Excel to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

Ionic strength and activity coefficient corrections available in pH calc but not yet in other modules

Click on the pH_calc tab, at the botton of the page; If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

Click on Calculate pH; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

Switch to the preloaded Simulation of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;

Version 3.2.3 (for MS-ExcelTM, English)Freeware for educational and non-commercial use

Since 1992 (Turbo-Basic/DOS, Portuguese)

Applications

Installation

Limitations

Fast Start

pH and Acid-Base Titration Curves:

Analysis and Simulation

Cite, bookmark for new releases and link to http://www2.iq.usp.br/docente/gutz/Curtipot_.html

Q2

The acronym CurTiPot means Potentiometric Titration Curves (in reversed order). The software was originally written in Turbo Basic for DOS and first demonstrated and distributed during the 15th Annual Meeting of the Brazilian Chemical Society, in 1992. Since 1997, the software is avaiolable for download at http://allchemy.iq.usp.br CurTiPot for DOS, versions 1 and 2, was not translated do English, but became widely used in Brazil. The Excel version was launched in 2006 and presents some extra features, like the powerful Regression module and a separated pH calc module. Activity coefficient and ionic strength calculations (implemented in the Turbo Basic version since 1992) are available in the pH calc module. Sitemeter tracks over 1,000 downloads of the freeware to more than 90 countries monthly from my site http://www2.iq.usp.br/docente/gutz/Curtipot_.html. More copies of CurTiPot are downloaded from over 80 download sites. Feedback by e-mail with criticism and suggestions is appreciated (although I not always find time to answer). If you are really satisfied with CurTiPot, what about linking to http://www2.iq.usp.br/docente/gutz/Curtipot_.html in your homepage? Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

Q13

End user license agreement Thank you for your interest in the CurTiPot version 3 freeware, a workbook of spreadsheets for Excel (proprietary software of Microsoft), authored by Dr. Ivano G. R. Gutz, Professor of the Institute of Chemistry of the University of São Paulo, São Paulo, Brazil, now on referred as Author of CurTiPot. Please examine the License Agreement before you start using CurTiPot. Personal or Educational Use Only The Author grants you a non-exclusive and non-transferable freeware license of CurTiPot for your personal or educational use at home, in classroom or in academic laboratories. If you intend to make commercial use of CurTiPot, including but not limited to any profitable non-educational activity or selling or distributing CurTiPot for payment, you must obtain a written permission from the Author in advance. Restrictions You may introduce modifications in the spreadsheets to suit your needs, but you are not allowed to remove the original notices about the intellectual property of the workbook and macros, in special but not only from the front page. You shall not distribute copies of modified versions without approval by the Author of the clearly identified changes. Distribution You may share unmodified copies of CurTiPot with students and colleagues that do not have access to the Internet, if they agree to be bound to these Terms and Conditions and as long as you take all reasonable precautions to avoid exposure of your copy to viruses. To minimize risks, it is highly advisable, to use only updated copies obtained from the Author’s download page. Changes to Terms and Conditions The author reserves the right to update CurTiPot and to modify these Terms and Conditions at its sole discretion, without notice or liability to you. You agree to be bound by these Terms and Conditions, as modified. Please download updated versions of CurTiPot from time to time and review the Terms and Conditions. Disclaimer of Warranties The Author disclaims any responsibility for any harm resulting from your use (or use by your colleagues or students) of CurTiPot and third party software used in conjunction with it. CurTiPot is provided "AS IS," with no warranties whatsoever, express, implied, and statutory, including, without limitation, the warranties of merchantability, fitness for a particular purpose, and non-infringement of proprietary rights. The author also disclaims any warranties regarding the security, reliability, accuracy, stability, convergence and performance of CurTiPot. You understand and agree that you download and/or use CurTiPot at your own discretion and risk and that you will be solely responsible for any consequences of incorrect information or results obtained with CurTiPot. This license does not entitle the Licensee to receive from the Author any extra documentation not contained in the program file, support or assistance by any means, or enhancements or updates of CurTiPot other than those made available for download at the Author’s site. Limitation of Liability Under no circumstances shall the Author or his employer be liable to any user on account its use or misuse of CurTiPot. If you accept the terms and conditions given above, you are entitled to use CurTiPot free of charge for unlimited time and number of uses. The Author will enjoy your comments, error reports and suggestions by e-mail.

Q15

Gutz: If you intend to use the Regression module, check if Solver figures in the Tools list. If not, close CurTiPot, open a blank page and install the Solver: Tools/Supplements/check the Solver box, find it and install. If the supplement is not pre-loaded on the HD, insert the Office® installation disk and upload the file This installation is required only once on a PC. Open CurTiPot again and start using the regression module.

Q21

End user license agreement Thank you for your interest in the CurTiPot version 3 freeware, a workbook of spreadsheets for Excel (proprietary software of Microsoft), authored by Dr. Ivano G. R. Gutz, Professor of the Institute of Chemistry of the University of São Paulo, São Paulo, Brazil, now on referred as Author of CurTiPot. Please examine the License Agreement before you start using CurTiPot. Personal or Educational Use Only The Author grants you a non-exclusive and non-transferable freeware license of CurTiPot for your personal or educational use at home, in classroom or in academic laboratories. If you intend to make commercial use of CurTiPot, including but not limited to any profitable non-educational activity or selling or distributing CurTiPot for payment, you must obtain a written permission from the Author in advance. Restrictions You may introduce modifications in the spreadsheets to suit your needs, but you are not allowed to remove the original notices about the intellectual property of the workbook and macros, in special but not only from the front page. You shall not distribute copies of modified versions without approval by the Author of the clearly identified changes. Distribution You may share unmodified copies of CurTiPot with students and colleagues that do not have access to the Internet, if they agree to be bound to these Terms and Conditions and as long as you take all reasonable precautions to avoid exposure of your copy to viruses. To minimize risks, it is highly advisable, to use only updated copies obtained from the Author’s download page. Changes to Terms and Conditions The author reserves the right to update CurTiPot and to modify these Terms and Conditions at its sole discretion, without notice or liability to you. You agree to be bound by these Terms and Conditions, as modified. Please download updated versions of CurTiPot from time to time and review the Terms and Conditions. Disclaimer of Warranties The Author disclaims any responsibility for any harm resulting from your use (or use by your colleagues or students) of CurTiPot and third party software used in conjunction with it. CurTiPot is provided "AS IS," with no warranties whatsoever, express, implied, and statutory, including, without limitation, the warranties of merchantability, fitness for a particular purpose, and non-infringement of proprietary rights. The author also disclaims any warranties regarding the security, reliability, accuracy, stability, convergence and performance of CurTiPot. You understand and agree that you download and/or use CurTiPot at your own discretion and risk and that you will be solely responsible for any consequences of incorrect information or results obtained with CurTiPot. This license does not entitle the Licensee to receive from the Author any extra documentation not contained in the program file, support or assistance by any means, or enhancements or updates of CurTiPot other than those made available for download at the Author’s site. Limitation of Liability Under no circumstances shall the Author or his employer be liable to any user on account its use or misuse of CurTiPot. If you accept the terms and conditions given above, you are entitled to use CurTiPot free of charge for unlimited time and number of uses. The Author will enjoy your comments, error reports and suggestions by e-mail.

Save your data, settings and results in Curtipot_anyname.xls files to preserve the original software (optionally deleting unused spreadsheets, but not the this first one);

The software CurTiPot, version 1.0 for DOS (Disk Operating System, Microsoft), was created in 1991 in Turbo Basic and launched in 1992.

Version 2 appeared in 1992. It is not limited to volumetry, accepting data from titrations with coulometric generation of reactants.

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil

Head of the Chemistry Department of IQ-USP (2004-2006; 2006-2008)

Member of the Editorial Boards of Talanta and Electrochemistry Communications

Coordinator of the Chemistry Olympiad in Sâo Paulo (2 million high school students) Countless copies are downloaded from over one hundred software distribution sites

CurTiPot was written almost during weekends and holidays, in São Paulo and, sometimes, at the beach:

Version 3.0 for Excel is na evolution of the DOS version. A new Regression module is the highlight. It was released in 2006 (in Portuguese).

Version 3.1 was translated to English and launched in May 1st, 2006, in the site www2.iq.usp.br/docente/gutz/Curtipot_.html.

Interest in CurTiPot is growing: in November 2006, over 2000 copies were downloaded from the author's site.

Version 3.2, released in December 2006, includes a separate pH_cal module.

HistoryThis freeware is a courtesy of

Q34

CurTiPot é um acrônimo das palavras Curvas de Titulação Potenciométrica, cunhado em 1991 durante o desenvolvimento do programa de simulação e análise de curvas de titulação ácido-base em linguagem Turbo Basic (Boreland), compatível com o DOS da Microsoft. O lançamento oficial se deu em 1992, em comunicação e mini-curso com aula prática, durante a 15ª Reunião Anual da SBQ: "Análise de dados experimentais e simulação de curvas de titulação ácido-base com CURTIPOT", GUTZ, I.G.R., 15ª Reunião Anual da SBQ, Caxambú, 1992, Livro de Resumos, pag. QA-062; "Quimiometria em equilíbrio químico", mini-curso, 15ª RASBQ Disponibilizada gratuitamente para download em http://allchemy.iq.usp.br, a versão para DOS se disseminou pelo país e está presente no ensino-aprendizagem desde então. As versões para DOS 1 e 2 (que aceita dados coulométricos) funcionam em sucessivas versões do Windows(95/98/NT/Milenium/2000 e XP), mas não responde ao mouse e seus recursos de manipulalção, gravação e impressão de dados e gráficos estão superados. O programa Excel da Microsoft foi escolhido para a versão 3 do CurTiPot por possuir recursos gráficos suficientes, facilitar modificações pelo usuário, comunicar-se de forma transparente com macros escritas em Visual Basic for Applicarions e por estar disponível na maioria dos atuais microcomputadores. O módulo Analise_II para análise de dados por regressão não linear multiparamétrica é o principal marco evolutivo da versão para Excel. O métod permite avaliar amostras mais complexas e/ou diluídas que os métodos gráficos ou de linearização; p.ex. implementação similar no programa Origin da Microcal foi aplicada a água de chuva (COELHO, L.H.G.; GUTZ, I.G.R., "Método simples e efetivo de análise por regressão não linear de titulações potenciométricas de água de chuva", XI Encontro Nacional de Química Analítica, Campinas, SP, 2001. Livro de resumos, pag. EQ-54). Na análise de rotina de séries de amostras similares entre sí, permite determinar rapidamente as concentrações de múltiplos componentes. A adição do módulo pH para cálculo de pH de soluções aquosas simples ou complexas com correção do efeito da força iônica merece registro; também é prática a tabela Constantes de dissociação. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

» generation of curves with equally spaced data in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison


The Regression module becomes operational after activation of the Solver supplement; you can do this later




Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) Use the e-mail:


Some features and uses of CurTiPot (hover on red mark at Q2 to read about the name and origins of the program)

pH calculation of aqueous solutions (>30 species in equilibrium)

of simple and complex acid-base titration curves - Virtual Titrator

Data analysis of real and simulated curves

Evaluation of curves by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKas by non-linear regression

of species and protonation of bases vs. pH and vs. volume

Configure Microsoft Excel to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

Ionic strength and activity coefficient corrections available in pH calc but not yet in other modules

pH_calc tab, at the botton of the page; If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

Calculate pH; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

Switch to the preloaded Simulation of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;




Countless copies are downloaded from over one hundred software distribution sites


Version 3.0 for Excel is na evolution of the DOS version. A new Regression module is the highlight. It was released in 2006 (in Portuguese).

Version 3.1 was translated to English and launched in May 1st, 2006, in the site www2.iq.usp.br/docente/gutz/Curtipot_.html.

CurTiPot is growing: in November 2006, over 2000 copies were downloaded from the author's site.

Version 3.2, released in December 2006, includes a separate pH_cal module.

Z42

Gutz: To see a satelite image of São Paulo, paste the addres in your browser and zoom in and out: http://maps.google.com/maps?hl=en&ie=UTF8&om=1&z=9&ll=-23.684774,-46.024475&spn=1.287779,1.84021&t=h





[email protected]


(hover on red mark at Q2 to read about the name and origins of the program)

to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macros

If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;

; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;

of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

. There are buttons to load the last titration curve from Simulation;

before you advance to the less simple but more powerful Regression to fit concentrations and pKas;





module is the highlight. It was released in 2006 (in Portuguese).

www2.iq.usp.br/docente/gutz/Curtipot_.html.

AD42

Gutz: To see a satelite image of Guaecá, paste the addres in your browser and zoom in and out: http://maps.google.com/maps?hl=en&ie=UTF8&om=1&z=15&ll=-23.822097,-45.464902&spn=0.020101,0.028753&t=h

0.1 pH Calculator Fill out concentration of ingredients; Enter; Click button B18.

EDTA HCl Acetic acid Citric acid Alanine

[B]

[HB] 0.061

0.039

0 0 0.1 0 0 0

0 0 0.139 0 0 0

0 0 -0.161 0 0 0

Electrolyte Na+ K+ Ca++ Cl- NO3- ClO4-

0.161

0.161 0 0 0 0 0

Charge Balance OK

Results at chemical equilibrium Correction of ionic strength effects

Ionic strength 0.2220 0.743 9.865E-08 pH


[B] 1.221E-06

[HB] 6.100E-02

3.900E-02

4.018E-07

0.000E+00 0.000E+00 1.000E-01 0.000E+00 0.000E+00 0.000E+00

at pH = 7.006 and p[H] =


% B 0.53 100.00 0.00 99.58 94.73 0.19

% HB 96.69 0.00 61.00 0.42 5.26 99.81

2.78 39.00 0.01 0.00

0.00 0.00 0.00

0.00

0.00

0.00

Solution composition - reagents added, in mol/LAcid / Base protonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H]

SziCi

Ci (mol/L)

ziCi

g H+ a H+

Equilibrium concentration of species, in mol/L

Acid / Base protonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

Species distribution (fractional composition, in %)


Phosphoric acid

% H2B

% H3B

% H4B

% H5B

% H6B

G1

pH Calculator - Fast start: - Click on the button "Calculate pH ..." (cell B18) and check cell H21 for the solution of the default acid-base chemical equilibrium problem: a mixture of H3PO4 and NaH2PO4. - Change the default concentration of H3PO4 in cell D7; press Enter; click Calculate... - Check the pH of water at 25 ºC: Delete C7 and D7, Enter, Calculate pH. - Compute a NaH2PO4/Na2HPO4 buffer solution: write 0.05 in D5 and D6, and 0.15 in B15, Enter, Calculate pH. - change pKa2 (M6), e.g. 7.2 to 9.2, Enter, Calculate pH. If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - Compare the values of pH, p[H] and "pH" in line 21; have a look at other results in lines 21 to 57 (you don't need to understand all these figures now - some are for advanced users). - formulate multicomponent mixtures and solve them instantly. - load other acid/base systems clicking on Database (J2). This acid-base pH calculator first appeared as a separated module in the 3.2 Excel version of CurTiPot, an evolution of the 1.0 Turbo Basic version launched in 1992. Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

B3

Gutz: Name of the acid or base (of the conjugated acid). To change it, write in cell K3 or load a different system from the Database

A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) added to the solution, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) added to the solution, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) added to the solution, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) added to the solution, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of the base B introduced in the solution: [HB] + [H2B] + [H3B] + ...

A12

Gutz: Maximum H+ concentration available from the full deprotonation of all forms of HiB used in the formulation of the solution: [HB] + 2[H2B] + 3[H3B] + ...

A13

Gutz: Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).

A14

Gutz: Fill out with the concentration of counter-ions of the salts of acids and bases, as well as other electrolytes added to the solution (e.g., to adjust ionic strength). This data is not essential but it will reduce the uncertainty of the estimation of activity coefficients and pH. Note: sulfate, a common divalent anion, is only fully dissociated a pH>4 because of its first protonation constant of 100 (= pKa2 2 of sulfuric acid). To deal more accurately with this acid/base system, load sulfuric acid from the Database (instead of defining it as electrolyte).

B14

Gutz: Name of the ion (strong electrolyte). To change it, write in cell K11.

A15

Gutz: Para adicionar NH4Cl 0,1 mol/L à solução, lançar 0,1 nesta linha, coluna do Cl- e 0,1 na linha 5, coluna do hidróxido de amônio. NaCl 0,1 mol/L, lançar 0,1 em Na+ e 0,1 em Cl-.

A16

Gutz: Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).

A17

Gutz: Electroneutrality is not a must to calculate the pH (by clicking B18). However, there will be some extra uncertainty in the results due to incorrect ionic strength calculation.

F19

Gutz: Definition of pH, see: http://www.iupac.org/goldbook/P04524.pdf Activity coefficient dependence from I, see: http://www.beloit.edu/~chem/Chem220/activity/index.html

A21

Gutz: The amount of electrostatic interaction between ions in solution is related to the ionic strength, I, a parameter used in the Debye Hückel equation for estimation of activity coefficients and extended versions of this equation, suitable for work at I>0.01 mol/L, where the effective hydrated ion size of the species also becomes relevant. As a general trend, the activity coefficient decreases with the increase of I (due to ion-ion interactions like the formation of ion pairs) down to a minimum in the region of I = 0.3 to 0.7 mol/L. At such high values of I, the association constants of each with all other major ions need to be feed to the equations or empirically fitted, to reduce uncertainty in estimates. The Davies equation, based on the average behavior of the ions and used here to deal with in complex mixtures for witch such constants are not readily available, renders estimates with greater uncertainty.

C21

Gutz: This and other activity coefficientes are (uncertain) estimates made with the Davies equation. Read more in cells A21 and K15.

E21

Gutz: This and other activity coefficientes are (uncertain) estimates made with the Davies equation. Read more in cells A21 and K15.

G21

Gutz: This is an estimate of the pH (see definition in http://www.iupac.org/goldbook/P04524.pdf ) that would be measured by a pH meter for a solution with the given composition, at 25ºC (or another temperature specified for the pKa values). The potential of potentiometric sensors (like the glass electrode) changes linearly with the inverse of the logarithm of the activity of hydrated H+ ions, not the concentration (expressed as p[H] in cell L21). The uncertainty of estimated pH values is never lower than the uncertainty of the pKa values in use, and it grows with the ionic strength, I, due to deficiencies of the Davies equation (more about in cells A21 and K15). It can exceed 0.1 pH unit for I>0.05, specially in solutions with highly charged ions (like PO43-).

100.00 100.00 100.00 100.00 100.00 100.00

at pH = 7.006 and I =


0.009 0.743 0.069 0.743 0.069 0.743

0.069 1.000 0.304 1.000 0.304 1.000

0.304 0.743 0.743 0.743

0.743 1.000 1.000

1.000

0.743

0.304

Electrolyte Na+ K+ Ca++ Cl- NO3- ClO4-

0.743 0.743 0.304 0.743 0.743 0.743

at pH = 7.006

Acid / Base EDTA HCl Acetic acid Citric acid Alanine

h 1.022 0.000 1.390 0.004 0.053 0.998

% S[HiB]

Activity coefficient (g) of species


Phosphoric acid

g B

g HB

g H2B

g H3B

g H4B

g H5B

g H6B

gi

Average protonation (h) of (conjugated) basesPhosphoric

acid

read comment

Fill out concentration of ingredients; Enter; Click button B18. Change freely or load values from the database

Acid / Base EDTA HCl Acetic acid

Charge of B -4 -1 -3 -1

10.170 -7.000 12.350 4.757

6.110 7.199

2.680 2.1480

2.000

1.500

SS 0.000

0 1.000E-01 Electrolyte Cl-

0 1.390E-01 Ion charge 1 1 2 -1

0 -0.161 pKw 13.997

- Davies equation parameters Color coding

for activity coefficient estimation D o n o t c h a n g e

0 0.161 A 0.509 C h a n g e c r i t e r i o u s l y

0 b 0.300 Fill out, change or leave blank

7.006 pOH 6.991 p[H] 6.877 p[OH] 6.862

Stepwise apparent constants recalculated for I = 0.22200

Acid / Base EDTA HCl Acetic acid

1.79E-07 Charge of B -4 -1 -3 -1

9.137 -7.258 11.575 4.499

5.335 6.683

1.37E-07 2.164 1.8898

1.742

1.500

SS 0.258

0.000E+00 1.000E-01 pK'w 13.739

6.877

0.10

85.77

14.14

pKas of acids HiB (in inverted order) or pKw-pKb of bases B

Carbonic acid

Phosphoric acid

pKan = logKp1

pKan-1 = logKp2

pKan-2 = logKp3

pKan-3 = logKp4

pKan-4 = logKp5

pKan-5 = logKp6

Na+ K+ Ca++

'-log of ion activities '-log of ion concentrations

Carbonic acid

[H+]Phosphoric

acid

pK'an = logK'p1

[OH-] pK'an-1 = logK'p2

pK'an-2 = logK'p3

pK'an-3 = logK'p4

pK'an-4 = logK'p5

pK'an-5 = logK'p6

Carbonic acid

J1

Gutz: n in pKn is the maximum number of dissociable protons of the acid or maximum number of protonations of a base Books with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976 present the protonation constants of the Bases instead of dissociation constants of the Acids Interconversion is immediate: Kp = 1/Kd or pKd = 1/logKd so pKa = logKp For multiprotic systems, remember that the first pKa is the last logKp The Database spreadsheet lists pKa values of many acids and bases, to be manually copied to this spreadsheet

N2

Gutz: Replace any or all pKa values, names or charges of this spreadsheet at will, or load them from the Database.

J3

Gutz: Attention: the pKas are ordered from the last to the first for computational reasons and in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4. Martell, A. E.; Smith, R. M., Plenum Press: New York, 1976 – listS protonation constants pKp of (conjugated) bases instead of dissociation constants of acids. Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa The index n in pKan is thus the maximum number of dissociable protons of the acid, what is the same as the maximum number of protons accepted by the (conjugated) base.

K3

Gutz: Write a name (or formula) that identifies the conjugated acid-base system. You can indicate the fully deprotonated base e.g., phosphate, acetate, NH3, pyridine EDTA4- (or Y4-); or the neutral form of the system, H3PO4 (or phosphoric), NH3, HCl, etc.

J4

Gutz: Fill out with the charge of the most deprotonated species of acid or base in accordance with the highest pKa for the system, e.g., -2 for carbonate//carbonic acid -3 for phosphate///phosphoric acid -4 for EDTA 0 for NH3 or pyridine

J5

Gutz: Fill out with pK1 of HB (monoprotic acid) or pK2 of H2B (diprotic acid) or pK3 de H3B etc. This is the normal order for protonation or the reverse order for dissociation (see comment about in J3).

J6

Gutz: Fill out with pK1 of H2B (diprotic acid) or pK2 de H3B etc.

J7

Gutz: Fill out with pK1 of H3B or pK2 de H4B etc.

J8

Gutz: Fill out with pK1 of H4B or pK2 of H5B or pK3 de H6B

J9

Gutz: Fill out with pK1 of H5B or pK2 of H6B

J10

Gutz: Fill out with the pK1 of H6B (hexaprotic acid or base like EDTA4-)

I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.

J11


I12

Gutz: Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.

J12


I13

Gutz: Summation of Cizi of all acidic and basic ingredients; if not zero, it shoud be neutralized by counterions in the electrolyte.

J13

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). The program corrects for I variation using the Davies eq. and displays the resulting value in K31.

K15

Gutz: CurTiPot recalculates apparent equilibrium constants at the ionic strength, I, of the solution from thermodynamic constants (I=0) by estimating activity coefficients with help of the Davies equation. The accuracy is good for I<0.05, acceptable for I<0.2 and poor for higher values of I. There is no rigorous means to calculate activity coefficients of individual ions, although there are many equations pursuing the reduction of the uncertainty of the estimates by taking in accountt individual effective ion size parameters and specific ion-ion interactions and/or introducing empirical coefficients fitted to real data. Such parameters are readily available only for the most common inorganic and organic ions, limiting their application range in comparision with the simple and general Davies eq. A compilation of over twenty equations with references to original work is available in the file Ionic St_effects.pdf contained in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip For calculations involving seawater (e.g. ionic strength at different salinities), see: http://ioc.unesco.org/oceanteacher/oceanteacher2/02_InfTchSciCmm/01_CmpTch/05_ocsoft/01_toolbox/OcCalc/OcCalc.htm

I16

Gutz: Summation of Cizi of all electrolytes

J16

Gutz: A and b are parameters of the Davies equation, used for activity coefficient estimation. They depend on temperature, dielectric constant, electrolyte, etc. The recommended values for water at 25ºC are: A=0.509; b=0.300. The Davies eq. does not require the size of different hydrated ions but, to some degree, the A and b parameters may be empirically adjusted to more closely describe a given electrolyte. For example: For NaCl + HCl solutions, A=0.43 and b=0.49 conducts to gH+ values in excellent agreement with those provided (up to 0.5 mol/kg) in http://www.iupac.org/projects/2000/Aq_Solutions.zip on base of more complete equations fitted to experimental data. For phosphate solutions, A=0.51 and b=0.20 seems appropriate at pHs above neutrality.

I17

Gutz: Charge Balance of all Cizi of ingredients added (before equilibrium); if not zero, it shoud be neutralized by adding counterions.

J17

Gutz: Read comment in cell J16 (above) and K15.

K21

Gutz: p[H] = -log[H+], calculated with the apparent pKas (cells K25 to Q30), while "pH" (cell O21) is obtained with the thermodinamic pKas, valid only for I=0 (see comment in cell K15), and pH (cell H21) uses estimated activities to como closer to the measurable pH. Although potentiometric sensors respond to activity of species (see comment in G21), it is possible – but not usual – to calibrate a pH meter (a high impedance voltmeter) with H+ concentration standards at a given value of I (to keep the activity coefficients constant) and measure free hydrated proton concentrations directly a this I. Some other techniques like spectrophotometry respond to concentration and may be used to indirectly measure p[H] (e.g., optodes).

I31

Gutz:

100.00

0.2220

0.304

0.743

1.000

-

1.140

Carbonic acid

Carbonic acid

pKa(n) = -log Kd(HB-->B) = log Kp(1)

Citric acid Alanine Acid / Base EDTA HCl

-3 -1 -2 Charge of B -4 -1 -3

6.396 9.867 10.329 1.48E+10 1.00E-07 2.24E+12

4.761 2.348 6.352 1.91E+16 3.54E+19

3.1280 9.12E+18 4.98E+21

9.12E+20

2.88E+22

2.88E+22

- Kw 1.01E-14

-1 -1

D o n o t c h a n g e

C h a n g e c r i t e r i o u s l y

Fill out, change or leave blank

No ion-ion interaction corrections (unity activity coefficients)

"pH" 7.393 "pOH" 6.604

Overall apparent protonation constants recalculated for I =

Citric acid Alanine Acid / Base EDTA HCl

-3 -1 -2 Charge of B -4 -1 -3

5.621 9.609 9.813 1.37E+09 5.52E-08 3.76E+11

4.245 2.348 6.094 2.97E+14 1.81E+18

2.8698 4.32E+16 1.40E+20

2.39E+18

7.54E+19

1.37E+20

K'w 1.82E-14

Overall protonation constants = bp = SKp (calculated by the program)

Carbonic acid

Phosphoric acid

bp1

bp2

bp3

bp4

bp5

bp6

NO3- ClO4

-

Carbonic acid

Phosphoric acid

b'p1

b'p2

b'p3

b'p4

b'p5

b'p6

O21

Gutz: "pH" is the value found in calculations where concentrations are used in the law of mass action expressions supplied with thermodynamic equilibrium constants – as usual in high school or introductory general chemistry classes and textbooks. Comparison with pH (cell H21) and p[H] (cell K21) reveals that errors are small only for diluted solutions, where ion-ion interactions occur less significant and activities depart less from concentrations (see comments in cells A21 and K15).

Acetic acid Citric acid Alanine

-1 -3 -1 -2

5.71E+04 2.49E+06 7.36E+09 2.13E+10

1.44E+11 1.64E+12 4.80E+16

1.93E+14

Overall apparent protonation constants recalculated for I = 0.22200

Acetic acid Citric acid Alanine

-1 -3 -1 -2

3.15E+04 4.18E+05 4.06E+09 6.49E+09

7.34E+09 9.05E+11 8.06E+15

5.44E+12

(calculated by the program)

Carbonic acid

Carbonic acid

Virtual Titrator – Simulation of curves

Titrand EDTA HCl Acetic acid Citric acid

[B]

[HB]

0.05

0 0 0.05 0 0 0

0 0 0.15 0 0 0

Titrant Strong ac. Strong base Carbonic acid

[B] 0.1 Titrand Water

[HB] Dispensed addedSS 20 0

0 0.1 0 1.00E-01 Titrant max.

0 0 0 0.00E+00 50.00 50

Initial "pH" 1.806

Data ID on curves

Copying curves

Resizing axis

Other graphics

Data analysis

Vadd "pH" Vadd "pH" [H] CHtot = Dill. ratio

(mL) simulated CHcalc

0.000 1.806 1.563E-02 1.500E-01 1.000E+002.157 2.020 9.540E-03 1.354E-01 9.026E-014.096 2.235 5.822E-03 1.245E-01 8.300E-015.754 2.449 3.553E-03 1.165E-01 7.766E-01

Sample (titrand) and standard (titrant) composition (concentrations in mol/L)Phosphoric

acidL-Glutamic

acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]S[H]

Volumes of titrand and titrant (in mL)

[H2B]

S[B] Nº of titrant additions

S[H]

with "error" (do not use)

simulated with "error"

Titrand (sample)

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with NaOH 0.1 mol/L)

Volume of titrant (mL)

p[H

]

G1

"Hands on" the "VIRTUAL TITRATOR": - Click on the button "Clear ret(ained) curves" (cell A32) - all but the last simulated curve will disappear; - click on the button "Titrate with constant volume additions" (A28) - the default tiration of 20 mL of 0.07 mol/L H3PO4 with 0.1 mol/L NaOH will be generated with 50 additions of 1 ml of titrant; - click on "Titrate with constant pH increments" (A24) - notice the difference in data distribution; - click on "Retain curve" (A30); - change the H3PO4 concentration in (C7), press Enter; - titrate again ant retain curve; - change pKa2 (cell M6) from 7.2 to 9.2 (Enter) and titrate; If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - click on the button at M12 to load pKas of other acids and bases ... - observe the effect of CO2 absorption by NaOH solution by writing 0.001 in D16 - add other components to the mixture and calculate the initial pH clicking at A21 - add random experimental error to the curve fillng values in cells J17 and J18 (e.g., 0.03 and 0.1); - titrate a phosphate buffer of Na2HPO4 + NaH2PO4 with strong base, retain the curve and titrate it with strong acid; - user your creativity... Warning: This version of the CurTiPot's Virtual Titrator calculates "pH" or p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not yet correct for the effect of ionic strength, I, on activity coefficients, taken as unity (see cell A20 for more information). This does not change the volume of the inflections, nor the general shape of the curves. Refer to the pH_calc module to calculate the pH of any solution with estimated activity coefficents. The apparent pKas for a given I, computed in pH_calc and pasted in cells K3 to Q10 of Simulation to obtain titration curves with values closer to pH in the ordinates. Copyright: This acid-base titration curve simulator is an expanded Excel version of the original Turbo Basic for DOS program CURTIPOT launched by the Author in 1992 (still available). Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

A3

Gutz: The titrand is the sample to be evaluated by titration with a strong acid or strong base. Tipically, 5 to 25 mL of titrand (cell F16) are carefully measured and placed in a beaker, a combined glass electrode (connected to a pH meter) and a magnetic stirrer bar are introduced and water is added till the electrode is covered (cell G16). Titration is carried out by adding small aliquots of titrant (usually with a buret or motor driven syringe) and registering the pH afterstabilization of the reading.

B3

Gutz: Name of the acid or base (of the conjugated acid) To change, whrite in cell K3

A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) to be considered in the simulation, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) to be considered in the simulation, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) to be considered in the simulation, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) to be considered in the simulation, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])

A12

Gutz: Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])

B14

Gutz: Leave blank - this cell corresponds to the conjugated base of the acid, e.g., Cl- or NO3-.

C14

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2)

D14

Gutz: Leave blank/fill out with de concentration of carbonate used as titrant To simulate the absorption of CO2 in an alkaline titrant, leave blank and fill cell D16

B15

Gutz: Leave blank/fill with de concentration of strong monoprotic acid used as titrant e.g., HCl. For weak or diprotic acids like H2SO4 change charge and pKas first, at cells R4 to R6.

C15

Gutz: Leave blank - this cell corresponds to the protonated of OH- , H2O2, handled as solvent.

D15

Gutz: Leave blank/fill out with de concentration of bicarbonate, if used as titrant. To simulate the absorption of CO2 from the air by an alkaline titrant, leave blank and fill H2CO3 (cell D16)

B16

Gutz: Leave blank or change charge and pKas first, at cells R4 to R6, and fill with the concentration of diprotic acid like H2SO4

C16

Gutz: Leave blank Fill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.

D16

Gutz: Leave blank/fill out to simulate the absorption of CO2 by an alkaline titrant (effect visible on the curve for 1% or more of [H2CO3] relative to the titrant concentration)

F16

Gutz: Volume of the aliquot of titrand (with the composition given above) to be titrated

G16

Gutz: Water is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution. The (undesirable) effect of dillution on the simulated curve may be best appreciated by exagerating this volume, retaining the curve and repeating the titration without added water.

F18

Gutz: Maximum volume of titrant to be added up to the end of the titration (may be less or equal to the capacity of the buret ).

G18

Gutz: Total number of additions of the titrant from the buret (max.: 120; typical: 30 or 50). You can choose constant volume additions (A24) or constant pH increment (A27).

A20

Gutz: Click on button at A22 to calculate the "pH" of the starting solution, before addition of any titrant (but after dillution, if G16 not zero). Refer to the spreadsheet pH_calc to calculate the pH of the same solution and for difinition of pH, p[H] and "pH". These values depart increasingly as the electrolyte concentration (more precisely, the ionic strenght) of a solution increases, due to ion-ion interactions. pH = -log aH+ where aH+ is the proton activity (concentration x activity coefficient) What this Simulation module calculates is p[H], when pK'as (apparent constants at the I of the solution) are available, or "pH" when thermodynamic constants (from the Database) are used instead. p[H] = -log [H+] , where [H+] is the hydrated proton concentration, in mol/L.

B34

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates. To add labels to your graphics, activate the drawing tools of Excel and insert text boxes.

B35

Gutz: To copy graphics with simulated curves and paste them into other documents (e.g.: Word or Excel without links to the original: - Fill out the header of the figure (optional) - Click in the box of the figure near the margins, to select it - Repeat the last simulation of a curve - Press Ctrl+C and wait for processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

B36

Gutz: Click twice on the volume or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

B37

Gutz: - Use the Graphics spreadsheet to plot derivatives by the DpH/DV aproximation and to overlay curves. - Use Evaluation to generate first and second derivative curves with interpolation and smoothig and to accurately locate inflection points of real and simulated titration curves. - Use Distribution to obtain de fractional composition and the mean protonation level of the bases during the titration as well as in function of pH.

B38

Gutz: - Use Evaluation to accurately evaluate well defined inflection points on real and simulated titration curves, assisted by cubic splines smoothing and interpolation - Use Regression to refine the concentrations of analytes and/or pK values of real or simulated titration curves by nonlinear multiparametric regression and to analyse complex curves, with hidden inflections (some learning required) Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D)

A39

Gutz: Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D) - Paste data in columns A and B of the destination spreadsheet

B39

Gutz: This version of the CurTiPot's Virtual Titrator calculates p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not yet correct for the effect of ionic strength, I, on activity coefficients, taken as unity. This does not change the volume of the inflections, nor the general shape of the curves. Refer to the pH_Calc module to calculate the pH and activity coefficents of any solution. The apparent pKas for a given I can be computed in pH_Calc and pasted in cells K3 to Q10 of this spreadsheet to obtain titration curves closer to pH.

C39

Gutz: Do NOT use this column for Evaluation or Regression. Values displayed to ilustrate the simulated dispersion in the volume dispensing by the "buret". This column will remain blank when null dispersion is choosen in J17 and J18.

D39

Gutz: These pH values with dispersion will be overlayed in the graphic This column will remain blank when null dispersion is choosen in J17 and J18

E39

Gutz: Free hydrated proton concentration (or activity)

F39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentration s of line 11 and the pKas given or under refinement.

G39

Gutz: Dillution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume of sample (+water), the factor is 0.5

7.077 2.664 2.168E-03 1.108E-01 7.386E-018.061 2.878 1.323E-03 1.069E-01 7.127E-018.749 3.093 8.073E-04 1.044E-01 6.957E-019.210 3.307 4.927E-04 1.027E-01 6.847E-019.508 3.522 3.006E-04 1.017E-01 6.778E-019.697 3.736 1.835E-04 1.010E-01 6.735E-019.817 3.951 1.120E-04 1.006E-01 6.708E-019.894 4.165 6.832E-05 1.004E-01 6.690E-019.944 4.380 4.169E-05 1.002E-01 6.679E-019.982 4.594 2.544E-05 1.001E-01 6.671E-01

10.014 4.809 1.553E-05 9.995E-02 6.664E-0110.050 5.023 9.474E-06 9.983E-02 6.656E-0110.098 5.238 5.781E-06 9.967E-02 6.645E-0110.170 5.452 3.528E-06 9.944E-02 6.629E-0110.282 5.667 2.153E-06 9.907E-02 6.605E-0110.457 5.881 1.314E-06 9.850E-02 6.567E-0110.730 6.096 8.017E-07 9.763E-02 6.508E-0111.144 6.310 4.892E-07 9.633E-02 6.422E-0111.748 6.525 2.985E-07 9.450E-02 6.300E-0112.577 6.739 1.822E-07 9.209E-02 6.139E-0113.626 6.954 1.112E-07 8.922E-02 5.948E-0114.824 7.168 6.784E-08 8.615E-02 5.743E-0116.044 7.383 4.140E-08 8.323E-02 5.549E-0117.146 7.598 2.526E-08 8.076E-02 5.384E-0118.041 7.812 1.542E-08 7.886E-02 5.258E-0118.706 8.027 9.408E-09 7.751E-02 5.167E-0119.169 8.241 5.741E-09 7.659E-02 5.106E-0119.478 8.456 3.503E-09 7.599E-02 5.066E-0119.677 8.670 2.138E-09 7.561E-02 5.041E-0119.804 8.885 1.305E-09 7.537E-02 5.025E-0119.886 9.099 7.961E-10 7.521E-02 5.014E-0119.941 9.314 4.858E-10 7.511E-02 5.007E-0119.982 9.528 2.965E-10 7.503E-02 5.002E-0120.018 9.743 1.809E-10 7.497E-02 4.998E-0120.059 9.957 1.104E-10 7.489E-02 4.993E-0120.115 10.172 6.737E-11 7.478E-02 4.986E-0120.200 10.386 4.111E-11 7.463E-02 4.975E-0120.333 10.601 2.509E-11 7.438E-02 4.959E-0120.548 10.815 1.531E-11 7.399E-02 4.932E-0120.896 11.030 9.342E-12 7.336E-02 4.890E-0121.459 11.244 5.701E-12 7.236E-02 4.824E-0122.365 11.459 3.479E-12 7.081E-02 4.721E-0123.818 11.673 2.123E-12 6.846E-02 4.564E-0126.155 11.888 1.296E-12 6.500E-02 4.333E-0129.983 12.102 7.906E-13 6.002E-02 4.001E-0136.644 12.317 4.824E-13 5.296E-02 3.531E-0150.000 12.531 2.944E-13 4.286E-02 2.857E-01

read comment

Titrand

EDTA HCl

Charge of B -4 -1 -3

10.170 -7.000 12.350

6.110 7.199

2.680 2.1480

2.000

1.500SS 0.000

0 5.000E-02 pKw 13.997

0 1.500E-01

Change the pKas freely or load values from the database

Sum

(initial vol.)

20.00 Titration speed D o n o t c h a n g e

S pH= 0.000 Slower 0 C h a n g e c r i t e r i o u s l y

S Vol= 0.000 Faster delay (s) Fill out, change or leave blank

Dill. ratio h1 h2 h3 h4 h5

EDTA HCl Acetic acid Citric acid

0.000E+00 2.68739.735E-02 2.57291.700E-01 2.45012.234E-01 2.3331

pKas of acids HiB (inverted order) or pKw-pKb of bases B

Carbonic acid

Acid / BaseName

Phosphoric acid

pKan = logKp1

pKan-1 = logKp2

pKan-2 = logKp3

pKan-3 = logKp4

pKan-4 = logKp5

pKan-5 = logKp6

of titrand and titrant (in mL)

Dispersion simulationNº of titrant additions

Titrant (buret)

Phosphoric acid

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0



p[H

]

J1

Gutz: n in pKn is the maximum number of dissociable protons of the acid or maximum number of protonations of a base Books with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976 present the protonation constants of the Bases instead of dissociation constants of the Acids Interconversion is immediate: Kp = 1/Kd or pKd = 1/logKd so pKa = logKp For multiprotic systems, remember that the first pKa is the last logKp The Database spreadsheet lists pKa values of many acids and bases, to be manually copied to this spreadsheet

K3


J4


J5

Gutz: Fill out with pK1 of HB (monoprotic acid) or pK2 of H2B (diprotic acid) or pK3 de H3B etc. This is the normal order for protonation or the reverse order for dissociation

J6

Gutz: Fill out with pK1 of H2B (diprotic acid) or pK2 de H3B etc.

J7

Gutz: Fill out with pK1 of H3B or pK2 de H4B etc.

J8

Gutz: Fill out with pK1 of H4B or pK2 of H5B or pK3 de H6B

J9

Gutz: Fill out with pK1 of H5B or pK2 of H6B

J10

Gutz: Fill out with the pK1 of H6B (hexaprotic acid or base like EDTA4-)

I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I

J11

Gutz: The ionic dissociation product of water changes with temperature and ionic strength. For pure water at 25ºC, the value is 13.997

I12

Gutz: Maximum concentration of H+ that could be dissociated from the components addet to the solution

H16

Gutz: Total volume before titration (F16+G16)

J17

Gutz: Simulation of titration data with random errors of pH presenting Gaussian distribution with standard deviation specified in J17. For S pH > 0, resulting data is displayed in column D and overlayed on the titration curve.

L17

Gutz: Keep delay = 0 for titration at maximum speed (dictated by the computer performance) Choose delay > 0 to pause between additions of titrant, resembling the time required to wait for pH measurements to sabilize in a real titrations. Press Escape during a titration to ignore the delay, proceeding at max. speed.

J18

Gutz: Simulation of titration data with random errors in volume readings presenting Gaussian distribution and standard deviation specified in J18. For SVol>0, resulting effect on measured pH appears in column D and is overlayed on the titration curve. Observe that the efect of volume reading errors is more severe near the inflections (unbuffered regions!).

H39

Gutz: Dillution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experiment

I39

Gutz: Average number of protons associated with the base B1 at the given pH. For HiB, this is can be seen as a fractionary value of i that reflects the mean of the concentrations of the forms in equilibrium at a pH value.

J39

Gutz: Average number of protons associated with the base B2 at the given pH. For HiB, this is can be seen as a fractionary value of i that reflects the mean of the concentrations of the forms in equilibrium at a pH value.

2.614E-01 2.23362.873E-01 2.15683.043E-01 2.10193.153E-01 2.06473.222E-01 2.04033.265E-01 2.02483.292E-01 2.01493.310E-01 2.00863.321E-01 2.00433.329E-01 2.00113.336E-01 1.99813.344E-01 1.99473.355E-01 1.99003.371E-01 1.98293.395E-01 1.97183.433E-01 1.95433.492E-01 1.92703.578E-01 1.88563.700E-01 1.82523.861E-01 1.74234.052E-01 1.63744.257E-01 1.51764.451E-01 1.39564.616E-01 1.28544.742E-01 1.19604.833E-01 1.12954.894E-01 1.08314.934E-01 1.05244.959E-01 1.03254.975E-01 1.01994.986E-01 1.01194.993E-01 1.00674.998E-01 1.00325.002E-01 1.00045.007E-01 0.99775.014E-01 0.99455.025E-01 0.98995.041E-01 0.98295.068E-01 0.97195.110E-01 0.95455.176E-01 0.92745.279E-01 0.88635.436E-01 0.82625.667E-01 0.74365.999E-01 0.63906.469E-01 0.51927.143E-01 0.3973

Titrant

Acetic acid Citric acid Carbonic acid Strong Acid Strong Base

-1 -3 -2 -2 -1 -1

4.757 6.396 9.950 10.329 -6 15.742

4.761 4.420 6.352

3.1280 2.2300

Change the pKas freely or load values from the database Change carefully, if necessary

Color coding

D o n o t c h a n g e

C h a n g e c r i t e r i o u s l y

Fill out, change or leave blank

h6 h7 h1 titrant h2 titrant h3 titrant

Carbonic acid Strong Acid Strong Base Carbonic ac.

1.00001.00001.00001.0000

or pKw-pKb of bases B

L-Glutamic acid

L-Glutamic acid

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0



p[H

]

O1

Gutz: Replace any or all pKa values of this spreadsheet as needed. Many values are listed in the Database

R3

Gutz: Strong acids like HCl or HClO4 have a negative pKa, estimated as -6 or less.

S3

Gutz: The pKa (=log Kp) of the strong base OH- is usually taken as 15,745 at 25ºC and infinite dillution, but there are other values in the literature.

S13

Gutz: Any three monoprotic or diprotic acid-base systems can be included the titrant. Common practice to titrate with a strong acid or a strong base, having CO2 as unwanted (and difficult to eliminate) interferen. Change this setup manually (pKas are not loadable from the database).

1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99990.99980.99960.9994

Titrand

Carbonic ac. Acid / Base EDTA HCl Acetic acid

-2 Charge of B -4 -3 -2 -1

10.100 1.479E+10 1.000E-07 2.239E+12 5.715E+04

6.300 1.905E+16 3.540E+19

9.120E+18 4.977E+21

9.120E+20

2.884E+22

2.884E+22

Kw 1.007E-14

Change carefully, if necessary

Overall protonation constants = bp = SKp (calculated by the program)

Phosphoric acid

bp1

bp2

bp3

bp4

bp5

bp6

T3

Gutz: CO2 absorption from the air makes this a common interferent in the titrant and the titrand.

U5

Gutz: Attention: the pKas are ordered from the last to the first for computational reasons and in agreement with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976, that list protonation constants pKp of (conjugated) bases instead of dissociation constants of acids. Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa The index n in pKan is thus the maximum number of dissociable protons of the acid, what is the same as the maximum number of protons accepted by the (conjugated) base.

pKa(n) = -log Kd(HB-->B) = log Kp(1)

Titrant

Citric acid Carbonic acid Strong Acid Strong Base Carbonic ac.

0 -1 -2 -1 -1 -2

2.489E+06 8.913E+09 2.133E+10 1.000E-06 5.517E+15 1.259E+10

1.435E+11 2.344E+14 4.797E+16 2.512E+16

1.928E+14 3.981E+16

L-Glutamic acid

Retained curves, formelrly simulated

Vol pH Vol pH Vol pH Vol

1 1 2 2 3 3 4

0 1.838538 0 1.301032.049407 2.050888 3.165531 1.5301373.938869 2.263239 5.551868 1.7592455.618284 2.475589 7.205499 1.988352

7.032329 2.687939 8.285625 2.217468.170884 2.900289 8.964158 2.446567

9.08299 3.112639 9.380021 2.6756759.858687 3.32499 9.631052 2.90478210.60375 3.53734 9.781198 3.1338911.41871 3.74969 9.870507 3.36299712.37769 3.96204 9.923457 3.59210513.50223 4.174391 9.954788 3.82121214.74101 4.386741 9.973306 4.0503215.98032 4.599091 9.984243 4.27942717.09362 4.811441 9.990701 4.50853517.99712 5.023791 9.994512 4.73764218.67074 5.236142 9.996762 4.9667519.14162 5.448492 9.99809 5.19585719.45613 5.660842 9.998873 5.42496519.65993 5.873192 9.999336 5.65407219.78955 6.085542 9.99961 5.8831819.87128 6.297893 9.999772 6.11228719.92293 6.510243 9.99987 6.34139519.95629 6.722593 9.999931 6.57050219.97918 6.934943 9.999971 6.7996119.99705 7.147293 10 7.02871720.01421 7.359644 10.00004 7.257825

20.0348 7.571994 10.00008 7.48693220.06374 7.784344 10.00015 7.7160420.10787 7.996694 10.00026 7.94514720.17736 8.209045 10.00045 8.17425520.28762 8.421395 10.00076 8.40336220.46167 8.633745 10.00129 8.6324720.73226 8.846095 10.00218 8.861577

21.1421 9.058445 10.0037 9.09068521.7385 9.270796 10.00627 9.319792

22.55746 9.483146 10.01063 9.548923.59709 9.695496 10.01802 9.77800724.79377 9.907846 10.03054 10.0071126.02813 10.1202 10.0518 10.2362227.17152 10.33255 10.0879 10.4653328.14247 10.5449 10.14927 10.6944428.93161 10.75725 10.25386 10.9235429.59039 10.9696 10.43277 11.1526530.21046 11.18195 10.74088 11.3817630.91664 11.3943 11.27756 11.6108731.88401 11.60665 12.23125 11.8399733.38986 11.819 13.98773 12.0690835.93712 12.03135 17.44677 12.2981940.57981 12.2437 25.25432 12.5273

50 12.45605 50 12.7564

pH Vol pH Vol pH Vol pH Vol pH

4 5 5 6 6 7 7 8 8

Vol pH Vol pH Vol pH Vol pH Vol

9 9 10 10 11 11 12 12 13

pH

13

Degree of smoothing

(0 to 100%) 90

Interpolated points 100

Volume pH Interp. Vol. Fitted pH dpH/dV

0.000 2.201 0.0000 2.1986 0.0608 0.00002.498 2.392 0.5051 2.2297 0.0631 0.00464.617 2.697 1.0101 2.2631 0.0701 0.00926.278 2.878 1.5152 2.3013 0.0817 0.01387.499 3.054 2.0202 2.3464 0.0980 0.01848.354 3.207 2.5253 2.4010 0.1189 0.02238.934 3.462 3.0303 2.4660 0.1367 0.01299.318 3.631 3.5354 2.5375 0.1450 0.00369.569 3.790 4.0404 2.6108 0.1439 -0.00589.734 4.077 4.5455 2.6812 0.1333 -0.01519.844 4.162 5.0505 2.7447 0.1187 -0.01209.922 4.275 5.5556 2.8020 0.1092 -0.00689.984 4.759 6.0606 2.8559 0.1050 -0.0016

10.042 5.169 6.5657 2.9089 0.1058 0.002910.109 5.083 7.0707 2.9635 0.1108 0.007010.198 5.113 7.5758 3.0216 0.1211 0.025410.329 5.443 8.0808 3.0975 0.1962 0.123210.526 5.606 8.5859 3.2372 0.3810 0.268210.826 5.840 9.0909 3.5153 0.7595 0.507411.281 6.024 9.5960 4.0530 1.4053 0.697811.956 6.174 10.1010 4.8852 1.6911 -0.406212.930 6.377 10.6061 5.5927 1.0708 -0.648314.273 6.628 11.1111 5.9863 0.5300 -0.399516.015 6.820 11.6162 6.1745 0.2516 -0.173218.100 7.032 12.1212 6.2735 0.1661 -0.031920.372 7.268 12.6263 6.3520 0.1503 0.000422.606 7.433 13.1313 6.4305 0.1631 0.013124.592 7.652 13.6364 6.5147 0.1676 -0.004026.205 7.800 14.1414 6.5969 0.1549 -0.021127.423 7.972 14.6465 6.6691 0.1316 -0.020528.292 8.210 15.1515 6.7309 0.1144 -0.013528.888 8.339 15.6566 6.7859 0.1043 -0.006529.286 8.641 16.1616 6.8375 0.1010 -0.001229.548 8.756 16.6667 6.8883 0.1004 0.000029.721 8.943 17.1717 6.9391 0.1009 0.001129.837 9.366 17.6768 6.9904 0.1027 0.002329.919 9.456 18.1818 7.0430 0.1055 0.002729.984 9.778 18.6869 7.0967 0.1066 -0.000730.045 9.947 19.1919 7.1500 0.1042 -0.004130.117 9.873 19.6970 7.2013 0.0983 -0.007530.213 10.151 20.2020 7.2488 0.0891 -0.010930.354 10.421 20.7071 7.2909 0.0785 -0.008030.571 10.688 21.2121 7.3291 0.0735 -0.0019 How to change the axis of a curve30.907 10.880 21.7172 7.3662 0.0746 0.0042 How to copy/paste a curve31.430 11.062 22.2222 7.4055 0.0819 0.0102 Data ID on curves

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation

Interpolation and smoothing by cubic splines

d2pH/dV2

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

smoothed data derivative 2nd derivative

Volume (mL)

dp

H/d

V0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

0.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

14.0000rough data smoothed data

Volume (mL)p

H

F2

Gutz: Interpolation with smoothing is a valuable tool to rapidly and precisely locate well defined inflections on titration curves. Up to 1000 points can be interpolated (select in cell I4) Sucessive inflections may correspond to the stepwise deprotonation of a multiprotic acid like phosphoric (or protonation of a multiprotonable base like ethylenediamine) or be originated by various acids or bases contained in a sample. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression). It is wise to compare the experimental curve with the simulated one based on the suposed interpretation of the results (this can be done with Simulation and Graphs or better, for skilled users, with the Regression module). Although Regression is far superior for hidden or overlaped inflections, no chemometrics tool can extract accurate results from poor data (insufficient measurements, data with high scatter, etc.).

A3

Gutz: Click Clear and paste or fill out with up to 300 data points from a real titration, or Copy previously simulated data using one of the buttons.

H3

Gutz: The smoothig factor is selected empirically. Start with 80% and try other factors until you find the best compromise between desired dispersion reduction and undesired curve flattening/dostortion. 0% - minimum filtering, cubic pline curve passes though all points 100%- maximum filtering; the fitted curve approaches linearity.

H4

Gutz: Defines the number of points to be interpolated from the initial to the final volume Minimum: 4 Typical: 100 Maximum 1000

A5

Gutz: Delete existing data (or click the Clear button) before you write or paste experimental data, or copy data from Simulation by clicking on the buttons above. Volume values in mL are expected, but mass of titrant or number o coulombs (coulometric titration) can be used instead.

B5

Gutz: Copy or paste pH values, experimental or simulated, with our without dispersion (simulated random errors). Uncalibrated pH electrodes do not impair the determination of concentrations at sharp inflections, but will offset pKa values estimated graphically. Electrode potentials can replace pH values when evaluating data from other ion selective electrodes.

C5

Ivano Gebhardt Rolf Gutz: The number of interpolated points can be chosen from 4 to 1000 in cell I4.

32.243 11.134 22.7273 7.4500 0.0950 0.013333.501 11.428 23.2323 7.5008 0.1052 0.006935.430 11.597 23.7374 7.5551 0.1089 0.000538.375 11.822 24.2424 7.6097 0.1062 -0.005942.886 11.958 24.7475 7.6614 0.0977 -0.008250.000 12.199 25.2525 7.7092 0.0930 -0.0012

25.7576 7.7565 0.0953 0.005826.2626 7.8067 0.1047 0.012526.7677 7.8631 0.1197 0.017327.2727 7.9284 0.1396 0.022127.7778 8.0064 0.1771 0.062728.2828 8.1166 0.2686 0.118528.7879 8.3040 0.5180 0.378729.2929 8.6824 1.0185 0.603329.7980 9.3568 1.6264 0.386130.3030 10.1812 1.4747 -0.551630.8081 10.7658 0.8374 -0.587631.3131 11.0589 0.3674 -0.330231.8182 11.1804 0.1482 -0.118132.3232 11.2416 0.1239 0.040032.8283 11.3118 0.1493 0.010133.3333 11.3873 0.1444 -0.019833.8384 11.4535 0.1178 -0.024334.3434 11.5076 0.0974 -0.016134.8485 11.5533 0.0852 -0.008035.3535 11.5950 0.0813 0.000135.8586 11.6363 0.0818 -0.000336.3636 11.6774 0.0806 -0.002236.8687 11.7174 0.0775 -0.004137.3737 11.7553 0.0724 -0.006037.8788 11.7902 0.0654 -0.007938.3838 11.8210 0.0564 -0.009738.8889 11.8471 0.0473 -0.008439.3939 11.8690 0.0395 -0.007039.8990 11.8872 0.0330 -0.005740.4040 11.9026 0.0280 -0.004340.9091 11.9157 0.0243 -0.003041.4141 11.9273 0.0219 -0.001641.9192 11.9381 0.0210 -0.000342.4242 11.9487 0.0213 0.001142.9293 11.9599 0.0231 0.002343.4343 11.9721 0.0253 0.002143.9394 11.9855 0.0274 0.002044.4444 11.9998 0.0293 0.001844.9495 12.0150 0.0310 0.001645.4545 12.0311 0.0326 0.001545.9596 12.0479 0.0340 0.001346.4646 12.0653 0.0352 0.001146.9697 12.0834 0.0363 0.001047.4747 12.1019 0.0372 0.000847.9798 12.1209 0.0379 0.000748.4848 12.1402 0.0385 0.000548.9899 12.1598 0.0389 0.000349.4949 12.1795 0.0391 0.0002

50.0000 12.1993 0.0392 0.0000

Volume dpH/dV

Initial volume 0.000 Maximum 9.9698982 1.75260684

Final volume 50.000 Minimum

How to change the axis of a curveHow to copy/paste a curve

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation Optional: ---->

Fitting range (zoom)Inflection

auto-finder

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00


Volume (mL)

dp

H/d

V

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.00000.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000


Volume (mL)

pH

Titration with 0.100 mol/L NaOH of 20 mLof sample containing 0.05 mol/L H3PO4 and 0.05 mol/L NaH2PO4 with simulated dispersion (sV=0.05 mL and spH=0.05)

O1

Gutz: The spreadshhet at column R can be used or adapted to assist trivial stoichiometric calculations. Copy and paste the volumes of all inflections to R6, R7, etc. and inform the required other parameters

P1

Gutz: The spreadshhet at column R can be used or adapted to assist trivial stoichiometric calculations. Copy and paste the volumes of all inflections to R6, R7, etc. and inform the required other parameters

L2

Gutz: The program calculates the maximum and the minimum of the first derivative in the region bracketed by the initial and final volumes. Thus, inflections are to be evaluated one at a time. For the titration of acids with bases, inflections correspond to the maxima. For bases titrated with acids, the inflections are given by the minima. Precision of the inflection point by interpolation with smoothing is better than for the conventional dpH/dV calculation suggested in textbooks (and quite independent of the selected number of interpolated points). Of course, good data near the inflections is decisive. The Regression module may provide superior results, due to fitting to a general equation describing the entire curve instead of empirical splines fitted with an arbitrary smoothing factor (that influences the result for poor data or undefined inflections).

N2

Gutz: Maximum value of the first derivative of the curve at the inflection, as calculated from the fitted cubic spline. Precision is higher than for the conventional dpH/dV calculation suggested in textbooks. The Regression module may provide superior results, due to fitting to a general equation describing the curve instead of empirical splines. Of course, good data near the inflections is decisive for all approaches.

J3

Gutz: Starting volume for the smoothing/interpolation process. Zero is OK unless there are various inflections; in such case the initial and final volumes should bracket one inflection at a time, in order to auto-detect the interpolated volume of one inflection.

L3

Gutz: The maximum reveals the volume of an inflection of a titration performed with a base as titrant. (ignore the excess of digits of the results)

J4

Gutz: Maximum volume of titrant to be considered for the smoothing/interpolation process. For curves with various inflections, the initial and final volumes should bracket one inflection at a time.

L4

Gutz: The minimum reveals the volume of an inflection of a titration performed with an acid as titrant

J48

Gutz: Click twice on the dpH/dV or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

J49

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic (optional) - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

J50

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates.

Concentration of

Sample Water Total

20 0 20 0.1

Vol. Inflection n (mols) delta n [species]1ª 9.97 0.000997 0.000997 0.049852ª 29.96 0.002996 0.001999 0.099953ª4ª5ª6ª7ª8ª9ª

10ª

Assisted calculation of concentrations (optional)

Vol. of titrand (sample)

titrant (mol/L)

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00


Volume (mL)

dp

H/d

V

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.00000.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000


Volume (mL)

pH

R5

Gutz: Fill out with the volumes of the inflections (in mL)

S5

Gutz: Calculated number of mols of titrant added up to the inflection

T5

Gutz: Number of mols of titrant added between inflections

U5

Gutz: Concentration of a titrated species (em mol/L) in the sample as calculated from the titrant consumed to reach an inflection. Sucessive inflections may correspond to the stepwise deprotonation of a multiprotic acid like fosforic (or protonation of a multiprotonable base like ethylenediamine) or to various acids or bases mixed in the same sample. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression) It nontrivial samples, is wise to compare the experimental curve with the simulated one based on the suposed interpretation of the results (this can be done with Simulation and Graphs orbetter (for skilled users) with Regression.

Distribution Diagrams and Protonation Curves

Acid-base system selection

Simulation setup EDTA HCl Acetic acid Citric acid

Regression setup Citric acid Ascorbic acid Acetic acid Ammonia

The curves plotted aginst Volume are significant only for acids/bases present in the titration (including traces of visual indicator)

To follow color transition of a visual indicator, fill out their pKa(s) and right click "new HiB"

Hover the mouse on any curve to identify it (e.g., "alfa 2" corresponds to the diprotonated base)

Click with right mouse button on any gray cell to generate curves

Phosphoric acid

Phosphoric acid

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80

1.00 Distribution of HiB species

pH

ai

<— aHiB aB—>

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80

1.00 Distribution of HiB species during titration

Volume (mL)

ai

<— aHiB aB—>

pH

7

0

14

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Average protonation (h) of the (conjugated) base

pH

Pro

ton

ati

on

of

B

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80


Volume (mL)

ai

<— aHiB aB—>

pH

7

0

14

n=3 pKa - invert order constants

Carbonic acid 12.3500 b1

HCl Carbonic acid 7.1990 b2

fill out the pKas 2.1480 The curves plotted aginst Volume are significant only for acids/bases present in the titration (including traces of visual indicator) for new HiBs

How to change the axis of a curveHow to copy/paste a curveData ID on curves

pKa or log Kp for all plots Overall protonation

mouse button on any gray cell to generate curves

L-Glutamic acid

new HiB à pKn = logKp1

new HiB à pKn-1 = logKp2

pKn-2 = logKp3 b3pKn-3 = logKp4 b4pKn-4 = logKp5 b5pKn-5 = logKp6 b6

a B

a HB

a H2B

a H3B

a H4Ba H5B

a H6B

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80

1.00 Distribution of HiB species

pH

ai

<— aHiB aB—>

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80


Volume (mL)

ai

<— aHiB aB—>

pH

7

0

14

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00Distribution of HiB species

pH

log

ai

<— aHiB aB—>

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Average protonation (h) of the (conjugated) base

pH

Pro

ton

ati

on

of

B

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80


Volume (mL)

ai

<— aHiB aB—>

pH

7

0

14

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5

3.0 Average protonation (h) during titration

Volume (mL)

Pro

ton

ati

on

of

B 14

pH

7

0

2.24E+12

3.54E+19

4.98E+21

Molar fraction of each species as a funciton of pH

alpha 0 alpha 1 alpha 2 alpha 3

pH h B HB0.000 2.993 0.0000 0.0000 0.0071 0.99290.200 2.989 0.0000 0.0000 0.0111 0.98890.400 2.982 0.0000 0.0000 0.0176 0.98240.600 2.972 0.0000 0.0000 0.0275 0.97250.800 2.957 0.0000 0.0000 0.0429 0.95711.000 2.934 0.0000 0.0000 0.0664 0.93361.200 2.899 0.0000 0.0000 0.1013 0.89871.400 2.848 0.0000 0.0000 0.1516 0.84841.600 2.779 0.0000 0.0000 0.2207 0.77931.800 2.690 0.0000 0.0000 0.3097 0.69032.000 2.584 0.0000 0.0000 0.4156 0.58442.200 2.470 0.0000 0.0000 0.5299 0.47012.400 2.359 0.0000 0.0000 0.6411 0.35892.600 2.261 0.0000 0.0000 0.7390 0.26102.800 2.182 0.0000 0.0000 0.8177 0.18223.000 2.123 0.0000 0.0001 0.8767 0.12333.200 2.081 0.0000 0.0001 0.9184 0.08153.400 2.053 0.0000 0.0002 0.9468 0.05303.600 2.034 0.0000 0.0002 0.9657 0.03413.800 2.021 0.0000 0.0004 0.9778 0.02184.000 2.013 0.0000 0.0006 0.9855 0.01394.200 2.008 0.0000 0.0010 0.9902 0.0088

How to change the axis of a curve 4.400 2.004 0.0000 0.0016 0.9929 0.0056How to copy/paste a curve 4.600 2.001 0.0000 0.0025 0.9940 0.0035

4.800 1.998 0.0000 0.0040 0.9938 0.00225.000 1.995 0.0000 0.0063 0.9923 0.0014

5.200 1.991 0.0000 0.0099 0.9892 0.0009

5.400 1.985 0.0000 0.0156 0.9838 0.0006

5.600 1.976 0.0000 0.0246 0.9751 0.0003

5.800 1.962 0.0000 0.0384 0.9614 0.0002

6.000 1.941 0.0000 0.0595 0.9404 0.0001

6.200 1.909 0.0000 0.0911 0.9088 0.0001

6.400 1.863 0.0000 0.1371 0.8629 0.0000

6.600 1.799 0.0000 0.2011 0.7988 0.0000

6.800 1.715 0.0000 0.2852 0.7148 0.00007.000 1.613 0.0000 0.3874 0.6126 0.00007.200 1.499 0.0000 0.5006 0.4994 0.0000

bp

H2B H3B

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00Distribution of HiB species

pH

log

ai

<— aHiB aB—>

M34


M35

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

M36


7.400 1.386 0.0000 0.6137 0.3863 0.00007.600 1.284 0.0000 0.7157 0.2843 0.00007.800 1.200 0.0000 0.7996 0.2004 0.00008.000 1.136 0.0000 0.8634 0.1365 0.00008.200 1.091 0.0001 0.9092 0.0907 0.00008.400 1.059 0.0001 0.9407 0.0592 0.00008.600 1.038 0.0002 0.9616 0.0382 0.00008.800 1.024 0.0003 0.9753 0.0244 0.00009.000 1.015 0.0004 0.9840 0.0156 0.00009.200 1.009 0.0007 0.9894 0.0099 0.00009.400 1.005 0.0011 0.9926 0.0062 0.00009.600 1.002 0.0018 0.9943 0.0039 0.00009.800 1.000 0.0028 0.9947 0.0025 0.0000

10.000 0.997 0.0044 0.9940 0.0016 0.000010.200 0.994 0.0070 0.9920 0.0010 0.000010.400 0.990 0.0111 0.9883 0.0006 0.000010.600 0.983 0.0175 0.9821 0.0004 0.000010.800 0.973 0.0274 0.9724 0.0002 0.000011.000 0.957 0.0428 0.9571 0.0002 0.000011.200 0.934 0.0661 0.9338 0.0001 0.000011.400 0.899 0.1009 0.8991 0.0001 0.000011.600 0.849 0.1510 0.8490 0.0000 0.000011.800 0.780 0.2199 0.7801 0.0000 0.000012.000 0.691 0.3088 0.6912 0.0000 0.000012.200 0.586 0.4145 0.5855 0.0000 0.000012.400 0.471 0.5287 0.4712 0.0000 0.000012.600 0.360 0.6401 0.3599 0.0000 0.000012.800 0.262 0.7381 0.2619 0.0000 0.000013.000 0.183 0.8171 0.1829 0.0000 0.000013.200 0.124 0.8762 0.1238 0.0000 0.000013.400 0.082 0.9182 0.0818 0.0000 0.000013.600 0.053 0.9468 0.0532 0.0000 0.000013.800 0.034 0.9657 0.0343 0.0000 0.000014.000 0.022 0.9781 0.0219 0.0000 0.0000

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5

3.0 Average protonation (h) during titration

Volume (mL)

Pro

ton

ati

on

of

B 14

pH

7

0

Molar fraction of each species during titration

alpha 4 alpha 5 alpha 6 alpha 0 alpha 1

Vol pH h B HB0 1.805933 2.687322 3.61E-17 1.26E-06

2.157614 2.02049 2.572874 1.33E-16 2.83E-064.096958 2.235047 2.45005 4.59E-16 5.98E-065.755102 2.449604 2.333024 1.49E-15 1.19E-057.078253 2.664161 2.233499 4.61E-15 2.24E-058.061853 2.878718 2.156713 1.36E-14 4.03E-058.750105 3.093275 2.101796 3.9E-14 7.04E-059.210199 3.307832 2.064602 1.09E-13 0.000129.508298 3.522389 2.040308 3E-13 0.0002029.697834 3.736947 2.024774 8.2E-13 0.0003369.817529 3.951504 2.014913 2.22E-12 0.000557

9.89385 4.166061 2.008575 6.01E-12 0.0009179.944514 4.380618 2.004302 1.62E-11 0.0015089.981636 4.595175 2.001075 4.35E-11 0.00247510.01425 4.809732 1.99811 1.17E-10 0.00405510.05032 5.024289 1.994684 3.13E-10 0.00663510.09858 5.238846 1.989968 8.39E-10 0.01083310.17046 5.453403 1.982848 2.24E-09 0.01763810.28233 5.66796 1.971702 5.95E-09 0.02859110.45808 5.882517 1.954153 1.57E-08 0.046023

10.7315 6.097074 1.926826 4.09E-08 0.07327811.14655 6.311632 1.88533 1.05E-07 0.1147311.75153 6.526189 1.824839 2.63E-07 0.17519512.58207 6.740746 1.741789 6.35E-07 0.25822913.63273 6.955303 1.636726 1.46E-06 0.36328114.83232 7.16986 1.516771 3.19E-06 0.483228

16.05155 7.384417 1.394852 6.55E-06 0.605137

17.15269 7.598974 1.284745 1.27E-05 0.715231

18.04606 7.813531 1.195418 2.34E-05 0.804536

18.70999 8.028088 1.129041 4.15E-05 0.870876

19.17208 8.242645 1.082861 7.16E-05 0.916996

19.47944 8.457202 1.052169 0.000121 0.947589

19.67823 8.67176 1.032364 0.000203 0.967231

19.8052 8.886317 1.019787 0.000337 0.97954

19.88687 9.100874 1.011817 0.000556 0.98707119.94159 9.315431 1.006668 0.000916 0.99150119.98222 9.529988 1.003134 0.001504 0.993858

H4B H5B H6B

20.01859 9.744545 1.000365 0.002467 0.994720.05964 9.959102 0.997685 0.004042 0.99423120.11549 10.17366 0.99444 0.006612 0.99233620.19992 10.38822 0.989844 0.010795 0.98856620.33362 10.60277 0.982812 0.017575 0.98203720.54905 10.81733 0.971745 0.028489 0.97127720.89774 11.03189 0.95428 0.04586 0.95421.46139 11.24644 0.927058 0.073025 0.92689222.36894 11.461 0.885698 0.114351 0.88560123.82454 11.67556 0.825373 0.174655 0.82531826.16296 11.89012 0.742504 0.257512 0.74247329.99273 12.10467 0.637593 0.362415 0.63757736.65195 12.31923 0.517711 0.482293 0.517703

50 12.53379 0.395758 0.604244 0.395754

Molar fraction of each species during titration

alpha 2 alpha 3 alpha 4 alpha 5 alpha 6 scaling scaling

pH/14 n*pH/14 [H]0.312675 0.687323 0.128995 0.386986 0.000.427121 0.572876 0.144321 0.432962 -0.200.549938 0.450056 0.159646 0.478939 -0.400.666952 0.333036 0.174972 0.524915 -0.600.766456 0.233521 0.190297 0.570892 -0.800.843207 0.156753 0.205623 0.616868 -1.000.898063 0.101867 0.220948 0.662845 -1.200.935158 0.064722 0.236274 0.708821 -1.400.959288 0.04051 0.251599 0.754798 -1.600.974553 0.025111 0.266925 0.800774 -1.800.983974 0.01547 0.28225 0.846751 -2.00

0.98959 0.009493 0.297576 0.892727 -2.200.992682 0.00581 0.312901 0.938704 -2.400.993975 0.00355 0.328227 0.98468 -2.600.993779 0.002165 0.343552 1.030657 -2.800.992046 0.001319 0.358878 1.076633 -3.000.988365 0.000802 0.374203 1.12261 -3.200.981876 0.000486 0.389529 1.168586 -3.400.971116 0.000293 0.404854 1.214563 -3.600.953801 0.000176 0.42018 1.260539 -3.800.926618 0.000104 0.435505 1.306516 -4.000.885209 6.07E-05 0.450831 1.352492 -4.20

0.82477 3.45E-05 0.466156 1.398469 -4.400.741752 1.89E-05 0.481482 1.444446 -4.600.636708 9.92E-06 0.496807 1.490422 -4.800.516764 4.91E-06 0.512133 1.536399 -5.00

0.394854 2.29E-06 0.527458 1.582375 -5.20

0.284755 1.01E-06 0.542784 1.628352 -5.40

0.19544 4.22E-07 0.558109 1.674328 -5.60

0.129083 1.7E-07 0.573435 1.720305 -5.80

0.082932 6.67E-08 0.58876 1.766281 -6.00

0.05229 2.57E-08 0.604086 1.812258 -6.20

0.032566 9.75E-09 0.619411 1.858234 -6.40

0.020124 3.68E-09 0.634737 1.904211 -6.60

0.012373 1.38E-09 0.650062 1.950187 -6.800.007583 5.16E-10 0.665388 1.996164 -7.000.004638 1.92E-10 0.680713 2.04214 -7.20

H2B H3B H4B H5B H6B

0.002832 7.17E-11 0.696039 2.088117 -7.400.001727 2.67E-11 0.711364 2.134093 -7.600.001052 9.92E-12 0.72669 2.18007 -7.800.000639 3.68E-12 0.742015 2.226046 -8.000.000388 1.36E-12 0.757341 2.272023 -8.200.000234 5.01E-13 0.772666 2.317999 -8.40

0.00014 1.83E-13 0.787992 2.363976 -8.608.31E-05 6.62E-14 0.803317 2.409952 -8.804.84E-05 2.36E-14 0.818643 2.455929 -9.002.75E-05 8.18E-15 0.833968 2.501905 -9.201.51E-05 2.74E-15 0.849294 2.547882 -9.407.92E-06 8.75E-16 0.864619 2.593858 -9.603.93E-06 2.65E-16 0.879945 2.639835 -9.801.83E-06 7.53E-17 0.895271 2.685812 -10.00

-10.20-10.40-10.60-10.80-11.00-11.20-11.40-11.60-11.80-12.00-12.20-12.40-12.60-12.80-13.00-13.20-13.40-13.60-13.80-14.00

logarithm of molar fraction of each species as a funciton of pH

alpha 0 alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 alpha 6

[OH] B HB-14.00 -49.96628 -21.52935 -4.95304 -0.007087-13.80 -48.58885 -20.61244 -4.496645 -0.011209-13.60 -47.21379 -19.6979 -4.042626 -0.017707-13.40 -45.84246 -18.78708 -3.592322 -0.02792-13.20 -44.47688 -17.88202 -3.147782 -0.043897-13.00 -43.12014 -16.9858 -2.712074 -0.068706-12.80 -41.77669 -16.10287 -2.289658 -0.106807-12.60 -40.4527 -15.23939 -1.886703 -0.164369-12.40 -39.15609 -14.4033 -1.511127 -0.24931-12.20 -37.89593 -13.60366 -1.171999 -0.370699-12.00 -36.68088 -12.84913 -0.877988 -0.537205-11.80 -35.51694 -12.1457 -0.635076 -0.754811-11.60 -34.40537 -11.49465 -0.444541 -1.024792-11.40 -33.34227 -10.89207 -0.302478 -1.343247-11.20 -32.31997 -10.33028 -0.201212 -1.702497-11.00 -31.32934 -9.800169 -0.131614 -2.093417-10.80 -30.36178 -9.293128 -0.085091 -2.50741-10.60 -29.41027 -8.802136 -0.054616 -2.937452-10.40 -28.46958 -8.321956 -0.034952 -3.378306-10.20 -27.53602 -7.848917 -0.02243 -3.826301-10.00 -26.60714 -7.380556 -0.014586 -4.278974

-9.80 -25.68135 -6.915278 -0.009825 -4.73473-9.60 -24.75765 -6.452096 -0.00716 -5.192582-9.40 -23.83548 -5.99045 -0.006031 -5.65197-9.20 -22.91462 -5.530101 -0.006199 -6.112655-9.00 -21.99509 -5.071085 -0.0077 -6.574673

-8.80 -21.0772 -4.613719 -0.010851 -7.038341

-8.60 -20.16163 -4.158662 -0.016311 -7.504318

-8.40 -19.24949 -3.707043 -0.02521 -7.973733

-8.20 -18.34259 -3.260658 -0.039341 -8.448382

-8.00 -17.44367 -2.822254 -0.061454 -8.931012

-7.80 -16.55678 -2.395883 -0.0956 -9.425675

-7.60 -15.68763 -1.987246 -0.147481 -9.938072

-7.40 -14.8437 -1.603834 -0.224585 -10.47569

-7.20 -14.03387 -1.254524 -0.335792 -11.04742-7.00 -13.26711 -0.948283 -0.490069 -11.66221-6.80 -12.55032 -0.692005 -0.694307 -12.32697

H2B H3B H4B H5B H6B

-6.60 -11.88608 -0.488286 -0.951106 -13.04428-6.40 -11.27176 -0.334478 -1.257815 -13.81151-6.20 -10.70042 -0.223655 -1.607509 -14.62172-6.00 -10.16309 -0.146841 -1.991212 -15.46594-5.80 -9.650894 -0.095166 -2.400053 -16.3353-5.60 -9.156365 -0.061154 -2.826559 -17.22232-5.40 -8.673816 -0.039122 -3.265043 -18.12132-5.20 -8.199204 -0.025027 -3.711466 -19.02826-5.00 -7.729788 -0.016128 -4.163084 -19.9404-4.80 -7.263771 -0.010628 -4.618101 -20.85593-4.60 -6.800016 -0.00739 -5.075379 -21.77373-4.40 -6.337843 -0.005734 -5.534241 -22.6931-4.20 -5.876902 -0.00531 -5.994334 -23.61372-4.00 -5.417105 -0.00603 -6.455571 -24.53547-3.80 -4.958603 -0.008045 -6.918103 -25.45852-3.60 -4.501821 -0.01178 -7.382355 -26.38329-3.40 -4.047541 -0.018017 -7.849109 -27.31056-3.20 -3.597045 -0.028038 -8.319647 -28.24161-3.00 -3.152341 -0.043851 -8.795977 -29.17846-2.80 -2.716467 -0.068494 -9.281137 -30.12414-2.60 -2.293854 -0.106398 -9.779558 -31.08308-2.40 -1.890645 -0.163706 -10.29738 -32.06142-2.20 -1.514737 -0.248315 -10.84251 -33.06706-2.00 -1.175189 -0.369285 -11.424 -34.10906-1.80 -0.880685 -0.535297 -12.05053 -35.19611-1.60 -0.637241 -0.752371 -12.72812 -36.33422-1.40 -0.446187 -1.021833 -13.4581 -37.52471-1.20 -0.303664 -1.339828 -14.23661 -38.76374-1.00 -0.20202 -1.6987 -15.056 -40.04365-0.80 -0.132128 -2.089325 -15.90714 -41.35531-0.60 -0.085375 -2.503089 -16.78142 -42.69011-0.40 -0.05471 -2.932941 -17.67179 -44.04099-0.20 -0.034866 -3.373615 -18.57298 -45.40270.00 -0.02214 -3.821406 -19.48129 -46.77153

Titration curves and first derivatives overlay Source of data to plot/overlay

0 0 0 0

1 1 0 0 How to change the axis of a curve

1 0 0 0 How to copy/paste a curve

Update curve(s) after any change in the Simulation, Evaluation or Regression modulesSimulation dpH/dV Simul. with dispersion dpH/dV

Evaluation

Regression

dpH/dV Eval. with smoothing dpH/dV

dpH/dV Regression fit dpH/dV

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-2

0

2

4

6

8

10

12

14 Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

A3

Gutz: Ao marcar: Simulador, dados são importados das coulnas A e B (a partir da linha 41) da planilha Simulador

A4

Gutz: Ao marcar: Analise Inicial, dados são importados das coulnas A e B (a partir da linha 41) da planilha Analise Incial

A5

Gutz: Ao marcar: Analise dados são importados das coulnas A e B (a partir da linha 41) da planilha Analise

How to change the axis of a curve Data ID on curves

How to copy/paste a curve

Vol

Update curve(s) after any change in the Simulation, Evaluation or Regression modules

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-2

0

2

4

6

8

10

12

14 Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

K4


N4


K5

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

Simulation Simulation with dispersion (random errors) EvaluationpH Vol_ dpH/dVol Vol pH Vol_ dpH/dVol Vol pH

0 2.2006762.498198 2.3916794.616751 2.697066.277554 2.8781417.498631 3.0535838.354143 3.2070168.933581 3.461699.317551 3.631131

9.56914 3.7903079.734098 4.0767249.844382 4.1623039.922234 4.274979.983755 4.75871910.04184 5.16872310.10871 5.08267810.19827 5.11261510.32876 5.44318510.52583 5.60588610.82611 5.8399811.28062 6.02350511.95617 6.17387612.93028 6.37654314.27344 6.62754316.01474 6.82005718.09986 7.03231720.37165 7.26773

22.6057 7.43313624.5918 7.651831

26.20529 7.79973527.42289 7.97231728.29176 8.21049628.88767 8.338675

29.28587 8.641195

29.54825 8.75646829.72093 8.94260529.83671 9.36637429.91868 9.4556129.98368 9.77810130.04534 9.94660330.11674 9.87264730.21301 10.1513630.35449 10.42055

30.5708 10.6880430.90661 10.8796531.42984 11.0622632.24327 11.1336633.50071 11.4275135.43031 11.5968738.37481 11.8219442.88566 11.95825

50 12.19936

Evaluation Evaluation with smoothing/interpolation Regression raw dataVol_ dpH/dVol Vol pH Vol_ dpH/dVol Vol pH Vol_

0 2.2721.249099 0.076457 0.896 2.4743.557475 0.144146 1.862 2.6755.447152 0.109032 2.958 2.8766.888092 0.143678 4.196 3.0787.926387 0.179347 5.547 3.2798.643862 0.439519 6.971 3.489.125566 0.441285 8.444 3.6829.443345 0.632687 9.964 3.8839.651619 1.736297 11.538 4.084

9.78924 0.775983 13.154 4.2869.883308 1.447195 14.783 4.4879.952995 7.863233 16.371 4.689

10.0128 7.058186 17.858 4.8910.07528 -1.28681 19.192 5.09110.15349 0.334265 20.359 5.29310.26352 2.533248 21.387 5.494

10.4273 0.825602 22.342 5.69510.67597 0.779606 23.293 5.89711.05336 0.403782 24.285 6.098

11.6184 0.22259 25.318 6.29912.44323 0.208055 26.339 6.50113.60186 0.186873 27.272 6.70215.14409 0.110557 28.056 6.904

17.0573 0.101798 28.665 7.10519.23575 0.103624 29.109 7.30621.48867 0.074039 29.417 7.50823.59875 0.110112 29.624 7.70925.39854 0.091667 29.76 7.9126.81409 0.14174 29.849 8.11227.85732 0.274124 29.906 8.31328.58971 0.215099 29.943 8.514

29.08677 0.759708 29.969 8.716

29.41706 0.439343 29.988 8.91729.63459 1.077902 30.004 9.11829.77882 3.660004 30.021 9.32

29.8777 1.088741 30.042 9.52129.95118 4.961495 30.072 9.72330.01451 2.732474 30.118 9.92430.08104 -1.035869 30.19 10.12530.16487 2.895103 30.301 10.32730.28375 1.902699 30.474 10.528

30.46264 1.236593 30.742 10.72930.7387 0.570578 31.151 10.931

31.16822 0.349009 31.763 11.13231.83655 0.087774 32.664 11.33332.87199 0.233693 33.962 11.53534.46551 0.08777 35.824 11.73636.90256 0.076436 38.547 11.93840.63024 0.030217 42.767 12.13946.44283 0.033891 50 12.34

Regression fitted curvedpH/dVol Vol pH Vol_ dpH/dVol

Database of dissociation constants of acids / protonation constants of bases

Setup 1 2 3

Name EDTA HCl

Charge of B -4 -1 -310.170 -7.000 12.3506.110 7.1992.680 2.1480

2.0001.5000.000

Last loaded setups 1 2 3

pH calculator EDTA HCl Phosphoric acid

Simulation EDTA HCl Phosphoric acid

Regression Citric acid Phosphoric acid Ascorbic acid

Acid or Base Charge, fully

Selection Frequently used systems deprotonated

Hydroxide ion -1 15.7452 HCl -1 -73 Phosphoric acid -3 2.148 7.1994 Acetic acid -1 4.7575 Citric acid -3 3.128 4.761

Ammonia 0 9.2447 7 Carbonic acid -2 6.352 10.3291 EDTA -4 0 1.5

Alphabetical order Insert new lines anywere to add more systems

Acetamide 0 0.63

Acetic acid -1 4.757Acetoacetic acid -1 3.58Acrylic acid -1 4.25Adipic acid -2 4.43 5.41

Alanine -1 2.348 9.867Aminobenzene = aniline 0 4.62-Aminobenzoic acid -1 2.108 4.9464-Animobenzoic acid -1 2.501 4.8742-Aminobutanoic acid -1 2.29 9.836-Aminohexanoic acid -1 4.373 10.8045-Aminopentanoic acid -1 4.27 10.766

2-Aminophenol -1 4.78 9.97-1 3.55 10.24

Ammonia 0 9.244Aniline 0 4.63

Arginine -1 1.823 8.991

pKas or logKps of acids HiB (i=0 to n) or pKw-pKb of bases B

Phosphoric acid

pKan = logKp1

pKan-1 = logKp2

pKan-2 = logKp3

pKan-3 = logKp4

pKan-4 = logKp5

pKan-5 = logKp6

pKa1 pKa2

b-Alanine

A3

Gutz: Having loaded the choosen constants, click to transfer all values of the setup to any spreadsheet: pH_calc, Simulation or Regression. The 7th system must be carbonic acid or another monoprotic or diprotic acid-base for Regression, where it is shared by the titrand and the titrant.

C3

Gutz: The index n in pKan is the maximum number of dissociable protons of the acid, what is the same as the maximum number of protons accepted by the (conjugated) base. Books with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976 present the protonation constants of the Bases instead of dissociation constants of the Acids. Interconversion is simple: Kp = 1/Kd or pKd = 1/logKd so pKa = logKp For multiprotic systems, remember that the first pKa is the last logKp, when adding pKas to this database.

D4

Gutz: Write this number in column A of the line of the Acid/Base pKas you want to load automatically and press "Load pKas from database"

C6

Gutz: Charge of the most deprotonated (dissociated) form of (conjugated) base considered in the equilibria of an acid-base system with given constants

C7

Gutz: Attention: in this setup, the pKas are ordered from the last to the first for computational reasons, and in agreement with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976, that list protonation constants pKp of (conjugated) bases instead of dissociation constants of acids. But pKa = logKp for a monoprotic acid (because Kp = 1/Kd and 1/logKd = pKd = pKa ) For multiprotic systems, the first logKp is the last pKa The index n in pKan is the maximum number of dissociable protons of the acid, what is the same as the maximum number of protons accepted by the (conjugated) base.

C8

Gutz: pKa1 of H2B (diprotic acid) or pKa2 of H3B etc.

C9

Gutz: pKa1 of H3B or pKa2 of H4B etc.

C10

Gutz: pK1 of H4B or pK2 of H5B or pK3 of H6B

C11

Gutz: pKa1 of H5B or pKa2 of H6B

A12

Gutz: Before loading, write the numbers from 1 up to 7 (or less) in front of the Acids/Bases you want to include in the setup. Warning: Regression acepts only mono- or diprotic acid/base as system 7; as a rule, carbonic acid is chosen (this system is shared by the titrand and the titrant). Unexpected system loaded? Check for repeated numbers down-list (forgoten from a previous selection). Uncertain pKa values in gray or red.

C12

Gutz: pKa1 of H6B (hexaprotic acid or base like EDTA4-)

D13

Gutz: Write this number in column A of the line of the Acid/Base pKas you want to load automatically and press "Load pKas from database"

D18

Gutz: Charge of the most deprotonated (dissociated) form of (conjugated) base considered in the equilibria of an acid-base system with given constants

E19

Gutz: Uncertain pKa values are displayed in gray; very uncertain values, in red.

B27

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. The pKa1 for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa of 3.58 is found.

E27

Gutz: This is the aparent pKa. By considering that only a part of the dissolved CO2 is converted in H2CO3 and part remains as CO2(aq), the "true" pKa would be 3.58

A29

Gutz: Insert lines as needed to add your most frequently used acid-base systems

Arsenic acid -3 2.24 6.96Arsenous acid -1 9.22Ascorbic acid -2 4.1 11.79

Asparagine -1 2.14 8.72Aspartic acid -2 1.99 3.9Barbital 0 7.43Barbituric acid -1 4.01Benzenesulfonic acid -1 0.7Benzoic acid -1 4.19Benzylamine 0 9.332-Benzylpyridine 0 5.13Betaine -1 1.83

Boric acid -3 9.236 12.74Butanoic acid -1 4.833-Butenoic acid -1 4.34Butylamine 0 10.77sec-Butylamine 0 10.56tert-Butylamine 0 10.68Cadaverine 0 10.05 10.93

Carbonic acid -2 6.352 10.329Catechol -2 9.4 12.8Chloroacetic acid -1 2.8652-Chloroaniline 0 2.653-Chloroaniline 0 3.464-Chloroaniline 0 4.152-Chlorobenzoic acid -1 2.923-Chlorobenzoic acid -1 3.824-Chlorobenzoic acid -1 3.983-Chlorophenol -1 8.854-Chlorophenol -1 9.182-Chlorophenol -1 8.49Choline 0 13.9

Chromic acid -2 –0,2 6.51Citric acid -3 3.128 4.761Codeine 0 8.21Creatinine 0 4.83 9.2m-Cresol -1 10.01O-Cresol -1 10.2p-Cresol -1 10.17

Cupferron -1 4.16Cyanic acid -1 3.46Cysteine -2 1.71 8.36Decylamine 0 10.642,4-Diaminobutanoic acid -1 1.85 8.24

Dichloroacetic acid -1 1.32,3-Dichlorophenol -1 7.46

Diethylamine 0 10.933Diisopropylamine 0 11.05

Dimethylamine 0 10.774Dimethylgloxime -2 10.66 12,0 12,3-Dimethylpyridine 0 6.582,4-Dimethylpyridine 0 6.992,5-Dmethylpyridine 0 6.42,6-Dimethylpyridine 0 6.65

E68

Gutz: This is the aparent pKa. By considering that only a part of the dissolved CO2 is converted in H2CO3 and part remains as CO2(aq), the "true" pKa would be 3.58

3,4-Dimethylpyridine 0 6.463.5-Dimethylpyridine 0 6.15Dinicotinic acid -1 2.8Diphenylamine 0 0.79Dipicolinic acid -2 2.16 4.76Dopamine -1 8.9 10.6d-Ephedrine 0 10.139Ethanolamine 0 9.5

Ethylamine 0 10.636Ethylenediamine 0 6.848 9.928Ethylenediaminetetraacet -4 0 1.5Ethyleneimine 0 8.012-Ethylpyridine 0 5.89Formic acid -1 3.745Fumaric acid -2 3.053 4.494

6 L-Glutamic acid -2 2.23 4.42L-Glutamine -1 2.17 9.13L-Glutathione -2 2.12 3.59Glyceric acid -1 3.52Glycerol -1 14.15

Glycine -2 2.35 9.778Glycolic acid -1 3.831Glyoxylic acid -1 3.18Heptanedioic acid -1 4.71Heptanoic acid -1 4.89Heptylamine 0 10.67Hexamethylenediamine 0 11.857 10.762Hexanoic acid -1 4.85Hexylamine 0 10.56Histamine 0 6.04 9.75

Histidine -1 1.7 6.02Hydrazine 0 8.07Hydroazoic -1 4.72Hydrogen bromide -1 -9Hydrogen chloride -1 -7

Hydrogen chromate ion -1 6.52

Hydrogen cyanide -1 9.21Hydrogen fluoride -1 3.17Hydrogen peroxide -1 11.65Hydrogen selenate ion -1 1.66

Hydrogen sulfide -2 7.02 13.9Hydrogen thiocyanate -1 0.9Hydroquinone 0 10.35

Hydroxylamine 0 5.96m-Hydroxybenzoic acid -2 4.06 9.92p-Hydroxybenzoic acid -2 4.48 9.323-Hydroxypropanoic acid -1 4.51

8-Hydroxyquinoline -1 4.91 9.81Hypobromous -1 8.63Hypochlorous -1 7.53Hypoiodous -1 10.64Imidazole 0 6.953

Iodic acid -1 0.77Isocitric acid -3 3.29 4.71

Isoleucine -1 2.319 9.754Lactic acid -1 3.86l-Ephedrine 0 9.958l-Leucine -1 2.328 9.744Lysine -1 2.04 9.08Maleic acid -2 1.91 6.332Malic acid -2 3.459 5.097

Malonic acid -2 2.847 5.696Melamine = 1,3,5-triazine- 0 5Methionine = (S)-2-amino- -1 2.13 9.27Methylamine 0 10.63

2-Methylaniline = o-touid 0 4.4474-Methylaniline = p-tolui 0 5.0842-Methylbenzimidazole 0 6.192-Methylbutanoic acid -1 4.83-Methylbutanoic acid -1 4.77Methylmalonic acid -2 3.07 5.76Methyl-1-naphthylamine 0 3.674-Methylpentanoic acid -1 4.841-Methylpiperidine 0 10.08

2-Methylphenol = o-cresol -1 10.284-Methylphenol = p-cresol -1 10.262-Methylpyridine 0 5.973-Methylpyridine 0 5.684-Methylpyridine 0 6.02Morphine 0 8.21Morpholine 0 8.331-Naphthol -1 9.342-Naphthol -1 9.51Nicotine 0 8.02 3.12

Nitrilotriacetic acid -3 1.1 1.652-Nitroaniline 0 -0.263-Nitroaniline 0 2.4664-Nitroaniline 0 1

2-Nitrobenzoic acid -1 2.1792-Nitrophenol -1 7.213-Nitrophenol -1 8.394-Nitrophenol -1 7.15

3-Nitrobenzoic acid -1 3.4494-Nitrobenzoic acid -1 3.442Nitrous acid -1 3.15Noradrenaline -1 8.64 9.7Octadecylamine 0 10.6Octanedioic acid -1 4.52Octanoic acid -1 4.89

Oxalic acid -2 1.252 4.266Oxaloacetic acid -2 2.22 3.89Papaverine 0 6.4Pentanoic acid -1 4.84Perchloric acid -1 -10p-Periodic acid -2 1.55 8.281,10-Phenanthroline 0 4.84m-Phenetidine 0 4.18o-Phenetidine 0 4.43

Phenol -1 9.98Phenylacetic acid -1 4.28Phenylalanine -1 2.2 9.31Phenylethylamine 0 9.84Phenylglycine -1 1.83 4.39

Phosphoric acid -3 2.148 7.199m-Phthalic acid -2 3.54 4.6

o-Phthalic acid -2 2.95 5.408p-Phthalic acid -2 3.51 4.82Picolinic acid -2 1.07 5.25Picric acid -1 0.38Pilocarpine 0 6.87Piperazine 0 9.83 5.56

Piperidine 0 11.123 7.53p-Phenetidine 0 5.2

Proline -1 1.952 10.64Propanoic acid -1 4.874Propylamine 0 10.566Purine 0 2.3 8.96

Pyridine 0 5.2293-Pyridinecarboxylic acid -1 4.854-Pyridinecarboxylic acid -1 4.96Pyrimidine 0 6.35Pyrocatechol -2 9.4 12.8Pyrophosphoric -4 1.52 2.36Pyrrolidine 0 11.27Pyruvic acid -1 2.39Quinine 0 8.52 4.13Quinoline 0 4.9

Resorcinol -2 9.3 11.06Saccharin -1 11.68

Salicylic acid -2 2.97 13.74Selenic acid -1 1.92Selenous acid -2 2.64 8.28Serine -1 2.19 9.05

o-Silicic acid -2 9.66 11.7m-Silicic acid -2 9.7 12Strychnine 0 8.26

Succinic acid -2 4.207 5.636Sulfuric acid -2 -3 1.99Sulfurous acid -2 1.91 7.18d-Tartaric acid -2 3.036 4.366meso-Tartaric acid -2 3.22 4.82Terephthalic acid -1 3.51Thiazole 0 2.44Thioacetic acid -1 3.33

Thiosulfuric acid -2 0.6 1,6 3Threonine -1 2.088 9.1m-Toluic acid -1 4.27o-Toluic acid -1 3.91p-Toluic acid -1 4.36

Trichloroacetic acid -1 0.66Triethanolamine 0 7.762Triethylamine 0 10.715

Trimethylacetic acid -1 5.03

Trimethylamine 0 9.8Tris(hydroxymethyl)- amin 0 8.075Tryptophan -1 2.35 9.33Tyramine 0 9.74 10.52Tyrosine -1 2.17 9.19Urea 0 0.1Uric acid -1 3.89Valine -1 2.286 9.718

Database of dissociation constants of acids / protonation constants of bases

Davies equation, used in CurTiPot 4 5 6 7 for activity coefficient estimation:

Acetic acid Citric acid References-1 -3 -2 -2 Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976.

4.757 6.396 9.950 10.329 Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972.4.761 4.420 6.352 Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979.

3.1280 2.2300 Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963. Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981.Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.Dissociation constants of inorganic and organic compounds (compliation with 33 pages)

4 5 6 7 Dissociation constants of organic compounds (~600 compounds)Acetic acid Citric acid Alanine Carbonic acid Visual Indicators for acid-base titrationsAcetic acid Citric acid L-Glutamic acid Carbonic acid Tutorial on acids and bases Acetic acid Ammonia HCl Carbonic acid Properties of acids and bases

Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002)

Temperat. Ionic

ºC strength Formula

25 0 NaOH

12.35 25 0 H3PO425 0 CH3COOH

6.396 25 0 H3C6H5O7

25 0 NH325 0 H2CO3

2 2.68 6.11 10.17 25 0.1 C10H16N2O8

Insert new lines anywere to add more systems Find more values in the references and links

25 0 C2H5NO

25 0 CH3COOH18 0 C4H6O3 25 0 C3H4O2 25 0 C6H10O4

25 0 C3H7NO225 0 C6H7N25 0 C7H7NO2 25 0 C7H7NO2 25 0 C4H9NO2 25 0 C6H13NO2 25 0 C5H11NO2

20 0 C6H7NO25 0 C3H7NO2

25 0 NH325 0 C6H7N

12.48 25 0 C6H14N4O2

pKw-pKb of bases B

L-Glutamic acid

Carbonic acid

pKa3 pKa4 pKa5 pKa6

M19

Gutz: The structural formula of most of the acids and bases listed here can be found in the Wikipedia, en.wikipedia.org

11.5 25 0 H3AsO4 0 H3AsO3

24 0 C6H8O6

25 0.1 C4H8N2O3

10.002 25 0 C4H7NO4 25 0 C8H12N2O3 25 0 C4H4N2O3 25 0 C6H6O3S 25 0 C7H6O2 25 0 C7H9N 25 0 C12H11N 0 0 C5H11NO2

13.8 20 0 H3BO325 0 C4H8O2 25 0 C4H6O2 20 0 C4H11N 25 0 C4H11N 25 0 C4H11N 25 0 C5H14N2

25 0 H2CO325 0 C6H4(OH)225 0 ClCH2COOH25 0 C6H6CIN 25 0 C6H6CIN 25 0 C6H6CIN 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C5H14NO

20 0 H2CrO46.396 25 0 H3C6H5O7

25 0 C18H21NO3 25 0 C4H7N3O 25 0 C7H8O 25 0 C7H8O 25 0 C7H8O

25 0.1 C6H6N2OHCNO

10.77 25 0 C3H7NO2S 25 0 C10H23N

10.44 25 0 C4H10N2O2

25 0 Cl2CHCOOH25 0 C6H4Cl2O

25 0 (CH3CH2)2NH25 0 C6H15N

25 0 (CH3)2NH25 0 C4H12O2N225 0 C7H9N 25 0 C7H9N 25 0 C7H9N 25 0 C7H9N

25 0 C7H9N 25 0 C7H9N 25 0 C7H5NO4 25 0 C12H11N 25 0 C7H5NO4 25 0 C8H11NO2 10 0 C10H15NO 25 0 C2H7NO

25 0 CH3CH2NH225 0 H2NCH2CH2NH2

2 2.68 6.11 10.17 25 0.1 C10H16N2O825 0 C2H5N 25 0 C7H9N 20 0 HCOOH25 0 C4H4O4

9.95 25 0 C5H9NO4 25 0 C5H10N2O3

8.75 9.65 25 0 C10H17N3O6S 25 0 C3H6O4 25 0 C3H8O3

25 0 H2NCH2COOH25 0 HOCH2COOH25 0 C2H2O3 25 0 C7H12O4 25 0 C7H14O2 25 0 C7H17N 0 0 C6H16N2

25 0 C6H12O2 25 0 C6H15N 25 0 C5H9N3

9.08 25 0.1 C6H9N3O2

30 N2H4HN3

HIHCl

25 0 HCN25 0 HF25 0 H2O2

25 0 H2S25 0 HSCN20 C6H6O2

25 0 NH2OH19 0 C7H6O3 19 0 C7H6O3 25 0 C3H6O3

25 0

25 0 HOBr25 0 HOCl25 0 HOI25 0 C3H4N2

25 0 HIO36.4 25 0 C6H8O7

HCrO4-

HSeO4-

25 0 C6H13NO2 HC3H5O3

10 0 C10H15NO 25 0 C6H13NO2

10.69 25 0.1 C6H14N2O2 25 0 C4H4O4 25 0 C4H6O5

25 0 HOOCCH2COOH25 0 C3H6N6 25 0 C5H11NO2S 25 0 CH5N

25 0 C7H9N25 0 C7H9N25 0 C8H8N2 25 0 C5H10O2 25 0 C5H10O2 25 0 C4H6O4 27 0 C11H11N 18 0 C6H12O2 25 0 C6H13N

25 0 C7H8O 25 0 C7H8O 20 0 C6H7N 20 0 C6H7N 20 0 C6H7N 25 0 C17H19NO3 25 0 C4H9NO 25 0 C10H8O 25 0 C10H8O 25 0 C10H14N2

2.94 10.334 20 025 0 C6H6N2O2 25 0 C6H6N2O2 25 0 C6H6N2O2

25 0 C7H5NO4

25 0 C6H5NO3

25 0 C6H5NO3 25 0 C6H5NO3

25 0 C7H5NO4 25 0 C7H5NO4

25 0 HNO225 0 C8H11NO3 25 0 C18H39N 25 0 C8H14O4 25 0 C8H16O2

25 0 C2H2O4 13.03 25 0 C4H4O5

25 0 C20H21NO4 25 0 C5H10O2

HClO4H5IO6

25 0 C12H8N2 25 0 C8H11NO 28 0 C8H11NO

25 0 HC6H5O 18 0 C8H8O2 25 0 C9H11NO2 25 0 C8H11N 25 0 C8H9NO2

12.35 25 0 H3PO425 0 C8H6O4

25 0 C8H6O4 25 0 C8H6O4 25 0 C6H5NO2

C6H3N3O7 30 0 C11H16N2O2 23 0 C4H10N2

25 0 C5H11N28 0 C8H11NO

25 0 C5H9NO225 0 CH3CH2COOH25 0 CH3CH2CH2NH220 0 C5H4N4

25 0 C5H5N25 0 C6H5NO2 25 0 C6H5NO2 20 0 C11H8N2 20 0 C6H6O2

6.6 9.25 H4P2O7 25 0 C4H9N 25 0 C3H4O3 25 0 C20H24N2O2 20 0 C9H7N

25 0 C6H6O2 18 0 C7H5NO3S

25 0 C7H6O3 25 0 H2SeO4

0 H2SeO3 25 0 C3H7NO3

H4SiO4H2SiO3

25 0 C21H22N2O2

HOOCCH2CH2COOH25 0 H2SO4 25 0 H2SO325 0 C4H6O6 25 0 C4H6O6 25 0 C8H6O4 20 0 C3H3NS 25 0 C2H4OS

25 0 H2S2O325 0 C4H9NO325 0 C8H8O2 25 0 C8H8O2 25 0 C8H8O2

25 0.1 Cl3CCOOH25 0 (HOCH2CH2)3NH25 0 (CH3CH2)3NH

25 0 C5H10O2

25 0 (CH3)3NH25 0 (HOCH2)3CNH325 0.1 C11H12N2O2 25 0 C8H11NO

10.47 25 0 C9H11NO3 21 0 CH4N2O 12 0 C5H4N4O3 25 0 C5H11NO2

Davies equation, used in CurTiPot Over twenty equations for activity coefficient estimation, see: Ionic St_effects.pdf

for activity coefficient estimation: in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip

Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976.Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972.Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979.Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963. Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981.Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.Dissociation constants of inorganic and organic compounds (compliation with 33 pages)Dissociation constants of organic compounds (~600 compounds)Visual Indicators for acid-base titrationsTutorial on acids and bases Properties of acids and bases Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002) http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf

Molecular mass

g/mol

97.97660.052

192.027

17.026

292.09

59.067

60.052102.089

72.063146.143

89.09493.13

137.138137.138

17.026

http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf

http://www.zirchrom.com/organic.htm

http://www.beloit.edu/~chem/Chem220/indicator/

http://achpc50.chemie.uni-karlsruhe.de/Cours%20de%20Chris%20Anson/OHP8acids.doc

http://ptcl.chem.ox.ac.uk/MSDS/msds-searcher.html






N18

Gutz: Molecular weight calculator Java Applet: http://www.ch.cam.ac.uk/magnus/MolWeight.html

184.19128.09

110.1

153.18165.23

116.07147.13146.15

75.07

68.08

131.18

165.23

31.1

107.17107.17

108.14108.14

180.3

166.14166.14

208.259

85.15

115.13

120.11

79.1

110.1177.98

88.06324.42129.16

110.1

138.12

105.09

334.41

118.0998.0882.07

150.09150.09

119.12

Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer

Over twenty equations for activity coefficient estimation, see: Ionic St_effects.pdf http://nvl.nist.gov/pub/nistpubs/jres/081/1/V81.N01.A03.pdf

in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip Primiary standard buffer solutions pH at various temperatures

http://nvl.nist.gov/pub/nistpubs/jres/066/2/V66.N02.A06.pdf

Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963.

Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.

http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf











Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer


Primiary standard buffer solutions pH at various temperatures


Titration Data Analysis - Multiple Regression

Titrand Citric acid Acetic acid Ammonia HCl

[B] 1.181966E-09 0 1.2978E-13 0 0 0

[HB] 1.588244E-05 0 0.000439863 0 0 0

0.0048880063 0 0.029625122 0 0 0

0.0350858302 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

S[HiB] 0.03998972 0 0.03006498 0 0 00.1150493855 0 0.059690106 0 0 0

max. free H 0.0049197747 0 0.000439863 0 0 0

Titrant Strong Acid Strong base Carbonic acid Vol. Tittrand (mL)

[B] 0.1 Sample Water Total

[HB] 20 0 20.00

[H2B] SS

S[HiB] 0 0.1 0 0.1 SS[HiB]S[H] 0 0 0 0

Vad "pH" "pH" [H] delta^2

(mL) real or simul. fitted mol/L mol/L mol/l

0.000 2.2720 2.2728 5.35E-03 3.736E-10 -1.933E-05 1.80E-010.896 2.4740 2.4739 3.36E-03 2.220E-12 1.490E-06 1.72E-011.862 2.6750 2.6749 2.11E-03 7.210E-12 2.685E-06 1.65E-01

Fitted total Bj concentrations (in gray) and equilibrium conc. at initial pH (in mol/L)

Phosphoric acid

Ascorbic acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[H] bound

SS [H]

CHRNL-CHcalc CHRNL

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00 Titration with 0.100 mol/L NaOH of 20.0 mLof a mixture of 0.040 mol/L citric acid

+ 0.030 mol/L ascorbic acid

Volume (mL)

pH

G1

Gutz: This module employs multiparametric nonlinear regression (MPNLR) to assist you in the determination of the concentration of acidic and basic components by volumetric acid-base titration; optionally, pK’a values can be determined or refined. MPNLR is a powerful alternative to the graphical evaluation of titration data, being faster and, in general, more accurate. It is the method of choice for complex mixtures and/or very diluted samples; valuable also to detect (and, possibly, quantify) the presence of minor components, perhaps overlooked in the graphical evaluation. Some learning is required to understand and use this module properly (the red dot comments cover essential aspects). The supplement Solver of the software Excel MUST be previously installed. Se instructions in comment M17. Differently from the pH_calc module, Regression does not (yet) correct for ion-ion interactions. Consequently, thermodynamic constants from the Database (valid strictly at I=0) may not generate the best possible fit to experimental curves. More coincident curves will be obtained by fitting the pKas too (viable when their values fall within the pH region explored during the titration). The returned “constants” may be described as pK’as (=conditional or apparent pKas), valid at the effective I of the solution (not calculated in this version and frequently variable during a titration). The parameter denoted as pH in this module is closer to “pH” when using pKas for I=0 and to p[H], after fitting pK’as. The more diluted the solutions, the closer "pH" and p[H] come to pH (see definitions in pH_calc). Warning: no chemometric tool can extract accurate results from poor data (insufficient measurements, data with high scatter, systematic errors, etc.). Before you analyze difficult titration data with Regression, collect the best data you can in the laboratory, after careful planning (assisted by Simulation) and well executed experiments with calibrated instrumentation and high purity well standardized reagents. The program fits the user-selected parameters based on the least squares of the difference of calculated and fitted total dissociable H+ concentrations. The macro may be modified to minimize the pH differences instead, or to consider data weighting.

B3

Gutz: Name of the acid or base. To change it, write in cells K3 to K10 (to P10), or load other systems from the Database As a rule, do NOT disturb colored cells, not ot overwrite the resident equations.

A4

Gutz: Fitted equilibrium concentration of the deprotonated (conjugated) base at the initial pH (I19); The fitted global concentration of all forms of the acid-base system, [B]+[HB]+[H2B]+... appears in line 11

B4

Gutz: Do NOT overwrite this cell or any other one of the same color, not to corrupt the equations.

A5

Gutz: Fitted equilibrium concentration of the monoprotonated (conjugated) base at the initial pH (I19); The global concentration [B]+[HB]+[H2B]+... appears in line 11

A11

Gutz: Total concentration of the acid or base identified in line 3, obtained by summing up the contributions of all forms in equilibrium: [B]+[HB]+[H2B]+... This concentration is a parameter fitted by regression with help of the Solver for acids/bases with all considered pKas in the pH region covered by the titration. The more a pKa departs from this region, the more inaccurate the result, as is the case for strong acids, to be excluded from the regression and calculated from the excess of H+ (cell I14) Convergence is accelarated with good initial guesses but, in general, zero is an acceptable starting value

B11

Gutz: You may write 0 (zero) as starting value in all cells of line 11 (B11 to H11). During least squares fitting, the values of the cells specified by you in the Solver setup will be adjusted accordingly. An initial guess, based on graphical evaluatian, will help and speed up Solver's convergence.

G11

Gutz: Do not include the concentration of HCl or any other strong acid as an unknown to be fitted by the Solver. The pH data of a titration is to far from the pKa of these acids ( below zero, impossible to reach in aqueous medium) thus the fitted value will be meaningless. The concentration of HCl or other strong acids should be obtained indirectly, from cell I14. As a check, write the value of I14 in cell G11; the result shoul be compatible.

A12

Gutz: Dissociable H+ concentration still bound to each (conjugated) base at the initial pH

A13

Gutz: Free H+ originated from each acid or (conjugated) base at the initial pH, supposing that it was added to the sample protonated to neutrality, and not as a salt (e.g., H3PO4 but not H2NaPO4). As this is frequently not the case, the value can be zero or negative (e.g., NH3 (= NH4OH) will not only provide no protons but will take them from acids with lower pKa, if present, or even from water) The undissociated H+ at the initial pH is not computed here; it appears in line 12.

D14

Gutz: This column has pKas shared with the Titrand, cells H3-H6. Carbonic acid is the default system, but any other diprotic or monoprotic acid-base system may be chosen instead.

C15

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2)

B16

Gutz: Leave blank/fill with the concentration of strong monoprotic acid used as titrant e.g., HCl (or twice the concentration of a H2SO4)

E16

Gutz: Volume of the aliquot of titrand (sample)

F16

Gutz: Water (or electrolyte solution) is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution.

G16

Gutz: Total volume before titration

D17

Gutz: Leave blank/fill out with the concentration of CO2 that may have been absorbed by the the titrant. CO2 absorption is most relevant for dilluted alkaline titrants. It is advisable to titrate the dilluted base against a strong standardized acid to determine this concentration of bicarbonate/carbonate with help of Regression before using the base as a titrant for the titration of unknown samples.

A39

Gutz: Click on the Clear button. Type or paste experimental pH vs. Volume data from real titrations or Click on one of the Simulation buttons in line 38 to copy previously simulated curves (with or without random errors).

B39

Gutz: Copy "pH" data from the simulation (click B38 for "clean" data or D38 for data with dispersion ) or type or paste real pH data.

C39

Gutz: Click on button K19 to calculate the fitted curve and overlay it on the experimental data in the graph.

D39

Gutz: Free hydrated proton concentration (or activity)

E39

Gutz: Squared value of the residues given in column F, minimized by the Solver by ditting the selected parameters.

F39

Gutz: Diference of H+ concentrations adjusted by the Solver (column G) and calculated by the general equation

G39

Gutz: Value of the H+ concentration fitted by the Solver by minimization of the squares of the residues (column E), taking dilution in consideration.

D41

Gutz: Do NOT write in this colored region! You will corrupt the equations.

2.958 2.8760 2.8760 1.33E-03 1.605E-13 -4.007E-07 1.57E-014.196 3.0780 3.0773 8.36E-04 3.435E-10 1.853E-05 1.49E-015.547 3.2790 3.2786 5.26E-04 9.690E-11 9.844E-06 1.41E-016.971 3.4800 3.4801 3.31E-04 8.773E-12 -2.962E-06 1.34E-018.444 3.6820 3.6817 2.08E-04 6.671E-11 8.168E-06 1.27E-019.964 3.8830 3.8831 1.31E-04 1.080E-11 -3.287E-06 1.20E-01

11.538 4.0840 4.0846 8.24E-05 2.613E-10 -1.617E-05 1.14E-0113.154 4.2860 4.2859 5.18E-05 4.245E-12 2.060E-06 1.09E-0114.783 4.4870 4.4873 3.26E-05 5.777E-11 -7.600E-06 1.04E-0116.371 4.6890 4.6886 2.05E-05 7.326E-11 8.559E-06 9.90E-0217.858 4.8900 4.8899 1.29E-05 2.450E-12 1.565E-06 9.51E-0219.192 5.0910 5.0911 8.11E-06 5.501E-12 -2.345E-06 9.19E-0220.359 5.2930 5.2926 5.09E-06 3.471E-11 5.892E-06 8.92E-0221.387 5.4940 5.4938 3.21E-06 6.984E-12 2.643E-06 8.70E-0222.342 5.6950 5.6952 2.02E-06 5.933E-12 -2.436E-06 8.51E-0223.293 5.8970 5.8967 1.27E-06 1.336E-11 3.655E-06 8.32E-0224.285 6.0980 6.0980 7.98E-07 7.933E-14 2.817E-07 8.13E-0225.318 6.2990 6.2995 5.02E-07 3.150E-11 -5.613E-06 7.95E-0226.339 6.5010 6.5009 3.16E-07 8.295E-13 9.108E-07 7.77E-0227.272 6.7020 6.7022 1.99E-07 2.527E-12 -1.590E-06 7.62E-0228.056 6.9040 6.9036 1.25E-07 9.858E-12 3.140E-06 7.49E-0228.665 7.1050 7.1050 7.85E-08 7.623E-17 8.731E-09 7.40E-0229.109 7.3060 7.3065 4.94E-08 4.226E-12 -2.056E-06 7.33E-0229.417 7.5080 7.5078 3.10E-08 3.644E-13 6.037E-07 7.29E-0229.624 7.7090 7.7089 1.95E-08 2.698E-14 1.643E-07 7.26E-0229.760 7.9100 7.9097 1.23E-08 8.985E-14 2.998E-07 7.24E-0229.849 8.1120 8.1122 7.73E-09 1.902E-14 -1.379E-07 7.22E-0229.906 8.3130 8.3125 4.86E-09 4.707E-14 2.170E-07 7.22E-0229.943 8.5140 8.5104 3.06E-09 1.211E-12 1.100E-06 7.21E-0229.969 8.7160 8.7154 1.92E-09 1.520E-14 1.233E-07 7.21E-0229.988 8.9170 8.9199 1.21E-09 2.269E-13 -4.763E-07 7.20E-0230.004 9.1180 9.1205 7.62E-10 1.585E-13 -3.981E-07 7.20E-0230.021 9.3200 9.3230 4.79E-10 2.953E-13 -5.434E-07 7.20E-0230.042 9.5210 9.5208 3.01E-10 3.020E-15 5.496E-08 7.20E-0230.072 9.7230 9.7201 1.89E-10 1.158E-12 1.076E-06 7.19E-0230.118 9.9240 9.9224 1.19E-10 8.110E-13 9.005E-07 7.19E-0230.190 10.1250 10.1261 7.50E-11 9.265E-13 -9.626E-07 7.18E-0230.301 10.3270 10.3270 4.71E-11 3.337E-15 -5.776E-08 7.16E-0230.474 10.5280 10.5283 2.96E-11 3.226E-13 -5.680E-07 7.13E-0230.742 10.7290 10.7299 1.87E-11 8.711E-12 -2.951E-06 7.10E-0231.151 10.9310 10.9315 1.17E-11 4.725E-12 -2.174E-06 7.04E-0231.763 11.1320 11.1325 7.38E-12 1.237E-11 -3.517E-06 6.96E-0232.664 11.3330 11.3339 4.65E-12 8.224E-11 -9.068E-06 6.84E-0233.962 11.5350 11.5350 2.92E-12 5.993E-14 -2.448E-07 6.67E-0235.824 11.7360 11.7363 1.84E-12 2.195E-11 -4.685E-06 6.45E-0238.547 11.9380 11.9375 1.15E-12 1.879E-10 1.371E-05 6.15E-0242.767 12.1390 12.1388 7.26E-13 7.746E-11 8.801E-06 5.74E-0250.000 12.3400 12.3401 4.57E-13 3.092E-11 -5.561E-06 5.14E-02

1.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-01

1.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-011.00E+00 1.80E-01

read comment

Use Database or literature values as estimates and refine as needed

Name Citric acid Acetic acid

0 Charge of B -3 -3 -2 -1

0 6.400 12.350 11.8021 4.7570

0 4.760 7.199 4.1003

3.128 2.148

SS

0 7.005E-02

0 1.747E-01

0 5.360E-03

-3.332E-05

CHcalc 1.801E-01 CHcalc

1.801E-01

1.871E-12 [OH]=Kw/[H] 1.856E-09

5.346E-03 [H]=10^-"pH"

2.272 initial "pH"

CHcalc Dill. Titrant Dil Titrand h1 h2 h3 h4

mol/L Citric acid Acetic acid

1.80E-01 0.0000 1.0000 2.8770 2.4291 1.9854 0.99671.72E-01 0.0429 0.9571 2.8167 2.3207 1.9769 0.99481.65E-01 0.0852 0.9148 2.7357 2.2291 1.9638 0.9918

pKas of acids HiB (reverse order) or pKw-pKb of bases B

Carbonic acid

Phosphoric acid

Ascorbic acid

pKan = logKp1

pKan-1 = logKp2

pKan-2 = logKp3

pKan-3 = logKp4

pKan-4 = logKp5

pKan-5 = logKp6

SS[bases]

SS[H] bound

SS[H] max.free H+ (negative results are possible)

Excess of H+ (if any), from an HiB not included in the MPNLR (e.g., a strong acid)

CHRNL <---- To be fitted with Solver, besides concentrations (cells in gray) and/or pKas

Minimize with Solver ---->

Phosphoric acid

Ascorbic acid

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00 Titration with 0.100 mol/L NaOH of 20.0 mLof a mixture of 0.040 mol/L citric acid

+ 0.030 mol/L ascorbic acid

Volume (mL)

pH

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-2.5E-05

-2.0E-05

-1.5E-05

-1.0E-05

-5.0E-06

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05Residues (CH, RNL - CH, calc)

Volume (mL)

CH

RN

L-C

Hc

alc

H3

Gutz: This header will appear also in the Titrant, cell D14. To change it, write in cell Q3. Carbonic acid is the default system, but any other diprotic or monoprotic acid-base system may be chosen instead.

J5

Gutz: Attention: the pKas are ordered from the last to the first for computational reasons and in agreement with the most extensive compilations of equilibrium constants, e.g., Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976, that list protonation constants pKp of (conjugated) bases instead of dissociation constants of acids. Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa The index n in pKan is thus the maximum number of dissociable protons of the acid, what is the same as the maximum number of protons accepted by the (conjugated) base.

I12

Gutz: Summation of the undissociated H+ at the initial pH for all bases

I13

Gutz: Summation of the free H+ of each base, supposing that it was added to the sample protonated to neutrality, and not as a salt (e.g., H3PO4 but not H2NaPO4). As this is frequently not the case, the value can be zero or negative (e.g., NH3 or NH4OH will not only provide no protons but will borrow them from acids with lower pKa if present, or even from water) The H+ undissociated at the initial pH does not appear here but in I12.

I14

Gutz: A positive value indicates that, after satisfying the protonation needs of the bases included in the regression, there is H+ available from the dissociation of a (relatively) strong acid (possibly not included in the regression due to low pKa). Writing this concentration in line 11 (G11 for HCl) shoul result in a null value for this field by repeating the regression. A negative value will be observed for NaH2PO4 (ou de NH3), if there is no simultaneous excess of HCl. Necessary to say that a null value is obtained, for example, for 0.1 mol/L H3PO4 as well as for 0.1 HCl + 0.1 NaH2PO4 ou 0.2 HCl e 0.1 Na2HPO4. There is no way to distinguish the initial formulation of the sample on base of the titration (it would be necessary to measure the conc, of Cl- ou Na+).

I16

Gutz: Read comment in cell M17 first. In the field for variable cells of the Solver, write B16; and the index of cells of the concentrations of acids/bases in the sample to be fitted (B11-H11, in gray). Refinement of pKa values can e considered in a second pass. In special cases, the concentration of components of the titrant may be also refined. A sample with just one relatively strong acid (with a pKa far below the the region of pH covered by the titration), I16 is the only one cell to be fitted. When other acids/bases with pKas in the explored region (or near it) are supposed to be present, the corresponding cell(s) in line 11 (B11-H11) must be listed in the Solver, besides I16. In case of convergence problems, use Escape to interrupt the regression. Start again including the smallest possible number of most relevant components, providing reasonable initial estimates of the concentrations and pKas. Convergence criteria can be changed in the Solver setup. 200 iteractions and 50 seconds is a good start.

M17

Gutz: Select the blue cell N17, open Tools/Solver and configure the second line of the setup box: Equal to: Value: 0 (zero). Check if N17 figures as destination cell (to be minimized) In the variable cells, introduce I16 and those cells of line 11 that correspond acids/bases supposedly present in the sample, separated by a comma (or semicolon). You can also hold down Ctrl and click on all cells to be fitted. If the Solver is not listed in Tools of Excel, proceed as follows: - Close CURTIPOT - Open a blank form - Click Tools/Supplements - Mark the Solver box and install it - If the file is not on the hard disk, locate it on the Office installation CD - Once Solver appears on the Tools list, load Curtipot again This procedure is required only once on a computer.

H39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentration s of line 11 and the pKas given or under refinement.

I39

Gutz: Dilution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume ofthe sample (+water), the factor is 0.5

J39

Gutz: Dilution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experiment

K39

Gutz: Average number of protons associated with the base B1 at the given pH

1.57E-01 0.1288 0.8712 2.6335 2.1575 1.9437 0.98701.49E-01 0.1734 0.8266 2.5139 2.1051 1.9133 0.97951.41E-01 0.2171 0.7829 2.3871 2.0687 1.8689 0.96781.34E-01 0.2585 0.7415 2.2619 2.0443 1.8067 0.94981.27E-01 0.2969 0.7031 2.1434 2.0281 1.7238 0.92241.20E-01 0.3325 0.6675 2.0323 2.0176 1.6226 0.88211.14E-01 0.3658 0.6342 1.9228 2.0107 1.5094 0.82491.09E-01 0.3968 0.6032 1.8073 2.0060 1.3947 0.74731.04E-01 0.4250 0.5750 1.6827 2.0026 1.2910 0.65069.90E-02 0.4501 0.5499 1.5487 1.9998 1.2050 0.53919.51E-02 0.4717 0.5283 1.4125 1.9969 1.1396 0.42409.19E-02 0.4897 0.5103 1.2814 1.9934 1.0927 0.31678.92E-02 0.5044 0.4956 1.1596 1.9885 1.0603 0.22548.70E-02 0.5168 0.4832 1.0474 1.9811 1.0388 0.15498.51E-02 0.5277 0.4723 0.9389 1.9699 1.0248 0.10348.32E-02 0.5380 0.4620 0.8265 1.9527 1.0157 0.06768.13E-02 0.5484 0.4516 0.7070 1.9267 1.0100 0.04367.95E-02 0.5587 0.4413 0.5810 1.8883 1.0063 0.02797.77E-02 0.5684 0.4316 0.4547 1.8331 1.0040 0.01777.62E-02 0.5769 0.4231 0.3393 1.7585 1.0025 0.01127.49E-02 0.5838 0.4162 0.2417 1.6636 1.0016 0.00717.40E-02 0.5890 0.4110 0.1662 1.5539 1.0010 0.00457.33E-02 0.5927 0.4073 0.1111 1.4387 1.0006 0.00287.29E-02 0.5953 0.4047 0.0726 1.3293 1.0003 0.00187.26E-02 0.5970 0.4030 0.0469 1.2361 1.0002 0.00117.24E-02 0.5981 0.4019 0.0300 1.1628 1.0000 0.00077.22E-02 0.5988 0.4012 0.0191 1.1088 0.9999 0.00047.22E-02 0.5992 0.4008 0.0121 1.0713 0.9997 0.00037.21E-02 0.5995 0.4005 0.0076 1.0460 0.9995 0.00027.21E-02 0.5998 0.4002 0.0048 1.0293 0.9992 0.00017.20E-02 0.5999 0.4001 0.0030 1.0184 0.9987 0.00017.20E-02 0.6000 0.4000 0.0019 1.0113 0.9979 0.00007.20E-02 0.6002 0.3998 0.0012 1.0066 0.9967 0.00007.20E-02 0.6003 0.3997 0.0008 1.0033 0.9948 0.00007.19E-02 0.6006 0.3994 0.0005 1.0006 0.9917 0.00007.19E-02 0.6009 0.3991 0.0003 0.9981 0.9869 0.00007.18E-02 0.6015 0.3985 0.0002 0.9953 0.9794 0.00007.16E-02 0.6024 0.3976 0.0001 0.9913 0.9676 0.00007.14E-02 0.6038 0.3962 0.0001 0.9856 0.9495 0.00007.10E-02 0.6058 0.3942 0.0000 0.9769 0.9221 0.00007.04E-02 0.6090 0.3910 0.0000 0.9635 0.8814 0.00006.96E-02 0.6136 0.3864 0.0000 0.9430 0.8239 0.00006.84E-02 0.6202 0.3798 0.0000 0.9123 0.7465 0.00006.67E-02 0.6294 0.3706 0.0000 0.8673 0.6491 0.00006.45E-02 0.6417 0.3583 0.0000 0.8044 0.5380 0.00006.15E-02 0.6584 0.3416 0.0000 0.7209 0.4224 0.00005.74E-02 0.6814 0.3186 0.0000 0.6191 0.3152 0.00005.15E-02 0.7143 0.2857 0.0000 0.5058 0.2247 0.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.0000

1.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.00001.18E+00 0.0000 1.0000 2.9993 2.9929 1.9999 1.0000

Use Database or literature values as estimates and refine as needed pKa(n) = -log Kd(HB-->B) = log Kp(1)

Ammonia HCl Citric acid Acetic acid Ammonia

0 -1 -2 2.51E+06 2.24E+12 6.34E+11 5.71E+04 1.75E+09

9.2440 -7.0000 10.329 1.45E+11 3.54E+19 7.99E+15 0.00E+00 0.00E+00

6.352 1.94E+14 4.98E+21 0.00E+00 0.00E+00 0.00E+00

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

pKa Str. Ac. pKa OH pKw Kw

-6.0000 15.7447 14.0000 1.00E-06 5.55E+15 1.00E-14

h5 h6 h7 hAcForte hBaForte

Ammonia HCl

1.0000 0.0000 1.9999 0.00 1.001.0000 0.0000 1.9999 0.00 1.001.0000 0.0000 1.9998 0.00 1.00

or pKw-pKb of bases B Overall protonation constants = ß Prot

Carbonic acid

Phosphoric acid

Ascorbic acid

b Str. Ac. b OH

(if any), from an HiB not included in the MPNLR (e.g., a strong acid)

To be fitted with Solver, besides concentrations (cells in gray) and/or pKas

S(CHRNL-CHcalc)2

Carbonic acid

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-2.5E-05

-2.0E-05

-1.5E-05

-1.0E-05

-5.0E-06

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05Residues (CH, RNL - CH, calc)

Volume (mL)

CH

RN

L-C

Hc

alc

Q3

Gutz: The pKas of this column are shared by the titrant (for fitting or setting D15-D17) and the titrand (for calculalting H11)

1.0000 0.0000 1.9997 0.00 1.001.0000 0.0000 1.9995 0.00 1.001.0000 0.0000 1.9992 0.00 1.001.0000 0.0000 1.9987 0.00 1.001.0000 0.0000 1.9979 0.00 1.001.0000 0.0000 1.9966 0.00 1.001.0000 0.0000 1.9946 0.00 1.001.0000 0.0000 1.9915 0.00 1.001.0000 0.0000 1.9865 0.00 1.001.0000 0.0000 1.9787 0.00 1.001.0000 0.0000 1.9666 0.00 1.000.9999 0.0000 1.9480 0.00 1.000.9999 0.0000 1.9197 0.00 1.000.9998 0.0000 1.8782 0.00 1.000.9997 0.0000 1.8195 0.00 1.000.9996 0.0000 1.7403 0.00 1.000.9993 0.0000 1.6421 0.00 1.000.9989 0.0000 1.5304 0.00 1.000.9982 0.0000 1.4149 0.00 1.000.9971 0.0000 1.3086 0.00 1.000.9954 0.0000 1.2187 0.00 1.000.9928 0.0000 1.1495 0.00 1.000.9886 0.0000 1.0991 0.00 1.000.9820 0.0000 1.0638 0.00 1.000.9717 0.0000 1.0397 0.00 1.000.9557 0.0000 1.0231 0.00 1.000.9313 0.0000 1.0111 0.00 1.000.8951 0.0000 1.0013 0.00 1.000.8430 0.0000 0.9918 0.00 1.000.7713 0.0000 0.9805 0.00 1.000.6798 0.0000 0.9654 0.00 1.000.5720 0.0000 0.9438 0.00 1.000.4564 0.0000 0.9119 0.00 1.000.3457 0.0000 0.8660 0.00 1.000.2492 0.0000 0.8019 0.00 1.000.1728 0.0000 0.7178 0.00 1.000.1162 0.0000 0.6155 0.00 1.000.0763 0.0000 0.5012 0.00 1.000.0494 0.0000 0.3875 0.00 1.000.0317 0.0000 0.2848 0.00 1.000.0201 0.0000 0.2000 0.00 1.000.0128 0.0000 0.1360 0.00 1.000.0081 0.0000 0.0902 0.00 1.000.0051 0.0000 0.0586 0.00 1.000.0032 0.0000 0.0377 0.00 1.000.0020 0.0000 0.0240 0.00 1.000.0013 0.0000 0.0153 0.00 1.000.0008 0.0000 0.0097 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.00

1.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.001.0000 0.0000 2.0000 0.00 1.00

HCl

1.00E-07 2.13E+10

0.00E+00 4.80E+16

0.00E+00

0.00E+00

0.00E+00

0.00E+00

Carbonic acid

acid-base equilibrium calculations and charts

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