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A Comprehensive Application To Assist in Acid−Base TitrationSelf-Learning: An Approach for High School and UndergraduateStudentsDavid Gonzalez-Gomez,*,† Diego Airado Rodríguez,*,‡ Florentina Canada-Canada,*,§ and Jin Su Jeong*,∥

†Department of Science and Mathematics Education, Training Teaching School, University of Extremadura, Avenida de laUniversidad s/n, Caceres, Caceres, Spain 10003‡Nofima AS, Osloveien 1, NO-1431 Ås, Norway§Department of Science and Mathematics Education, Education School, University of Extremadura, Badajoz, Badajoz, Spain 06071∥Department of Graphic Expression, University Center of Merida, University of Extremadura, Calle Santa Teresa de Jornet 38,Merida, Badajoz, Spain 06800

*S Supporting Information

ABSTRACT: Currently, there are a number of educationalapplications that allow students to reinforce theoretical ornumerical concepts through an interactive way. More precisely,in the field of the analytical chemistry, MATLAB has beenwidely used to write easy-to-implement code, facilitatingcomplex performances and/or tedious calculations. The mainobjective of this research is to present an ad hoc open MATLABcode toolbox, named AChemTitri, aimed to construct acid−basetitration curves in an interactive format. The software has been designed by the means of pop-up windows where students only needto be acquainted with a basic or elementary knowledge of MATLAB. With this application, students will be able to practice withcomprehensive titration options such as the titration of strong, weak, or polyfunctional acids and bases and, for each titration, differentconcentration of each compound as well as the titration volume can be selected. As a result, the software plots the titration curve(pH vs volume) and the first and second derivative of this former curve as well, together with the numerical results. Thus, studentswill have the opportunity to calculate the final point and pH of the titration graphically and numerically. In addition, concentrationdiagrams are also displayed (log of the species participating in the titration vs pH); thus, it will be easy to follow how the acid−basetitration is progressing. In conclusion, this application is a feasible way to improve the basic concepts of acid−base titration throughoutthe practice of numerical exercise assisted by computer calculation. The possibility of changing all the chemical parameters and thegraphic visualization of results could ease the learning process of students facing the titration concepts for the first time.

KEYWORDS: Analytical Chemistry, First-Year Undergraduate/General, Computer-Based Learning,Distance Learning/Self Instruction, Acids/Bases, Inquiry-Based/Discovery Learning

■ INTRODUCTION

Chemical equilibrium in general and acid−base equilibrium inparticular play a major role in chemistry education. It is a fact thatacid−base chemistry is and has been a common feature in generalchemistry curriculum for a number of years. Also, titration curveshave been traditionally the most common approach to understandacid−base equilibrium, both in theoretical and practicalapproaches. The teaching of titration curves has been lately acontroversial topic among the teaching communities; however, sofar, in 2014 it is contemplated in the curriculum in manyuniversities and even in the last year of high school education.Harris1 and Hawkes2 maintained an interesting correspond-

ence, published in the Journal of Chemical Education, in the frameof “what textbooks should contain” and what chemistry teachersshould teach. This conversation reflects well the two mainpositions of teachers with regard to titration curves. Among theteaching communities, there are defenders1 and detractors2 at

teaching calculation of titration curves to undergraduatestudents. Harris1 supports the inclusion of acid−base titrationcurves in analytical chemistry textbooks, as well as its teaching inclass. This author claims the value of learning the theory beyondtitration curves, in spite of the fact that most chemists will notbring titrations curves into practice. He defends that studyingtitrations curves will make students learn chemical equilibrium.Titration curves are normally studied by breaking them intoregions, i.e., initial point, before equivalence point, at theequivalence point, and after equivalence point, and theknowledge of proper chemical processes taking place in eachregion will provide students a better understanding of chemicalequilibrium. For instance, it would be a wise way to understandhow buffers work. He also states the usefulness of titration curvesin the calculation of equilibrium constants.3 Some authors defend

Article

pubs.acs.org/jchemeduc

© XXXX American Chemical Society andDivision of Chemical Education, Inc. A DOI: 10.1021/ed5005646

J. Chem. Educ. XXXX, XXX, XXX−XXX

pubs.acs.org/jchemeduc

http://dx.doi.org/10.1021/ed5005646

as well the usefulness of titration curves to aid in the selection ofthe right indicator.1,4

Harris stated that the performance of buffers can beunderstood through titration curves. Under this point of view,buffer capacity has to be understood like the variation of pH withthe volume of titrant. Thus, a simple look at titration curves ofpolyprotic acid or base would allow students to locate themaximum buffer capacity of a given buffer. The intermediateform of a diprotic acid is sometimes considered las a buffer sinceit always has a pH ≈ (1/2)(pK1 + pK2); however, just by lookingat its titration curve it would be easy to understand that itpresents a minimum buffer capacity.1

On the other hand, Hawkes2 is not in complete agreementwith teaching titration curves calculation. He defends focusingteaching on more “needed knowledge”. He states that confusioncould be created in “sub-average” students, for instance, whenrelating buffers to titrations. He claims that calculating titrationcurves is a complicated way to understand buffers and isunneeded to choose the right indicator. In his opinion,equilibrium calculations have been in general overemphasizedin the curriculum.2,5 It has been reported by this author in his10 peer-reviewed publications that the standard curriculum forintroductory chemistry includes much that is valueless and evenmisleading and does not reflect the needs of students. Heproposes a revision of the curriculum taking into account the realneeds and interests of students and states that prestigiousorganizations such as The International Union of Pure andApplied Chemistry (IUPAC) or the American Chemical Society(ACS) should lead the change.5

The usefulness of computer-assisted experiments and the so-called virtual laboratories for acid−base teaching has been recentlyreported by Hernandez-Espinoza and Astudillo-Saavedra.6

Hernandez and Czerwinska demonstrated applicability ofapplicability of an online module to teach key concepts withinacid−base such as hydrolysis of salts, conjugate acids and bases,and strength of acids and bases.7 Different examples of computergenerated acid−base titration data and curves can be found in therelated literature.8,9 However, probably the most related back-ground to our work, in the field of computer-generated acid basetitration curves, is the one recently published by Smith et al.10

enabling the generation of 3-D surfaces to visualize howpHbehaves during titration and dilution procedures. Nevertheless,in this article, equimolar concentrations of the target species andtitration agent are always considered, while with “chemistry”, thosevariables can be freely varied, giving rise to a more open andgeneral view of the influence with all the involved variables.In this article, the application “AChemTitri” is presented as a

tool aimed to assist students in the learning process of acid−basetitration. The application is framed in MATLAB and it has beendesigned to be used by means of pop-up windows where the finaluser only needs to have basic or elementary knowledge ofMATLAB. The benefits of using new technology tools topromote learning have been already proved. In fact, the currentvirtual courses using collaborative web tools such as aLF,Moodle, or WebCT are already used in most universities andeducational institutions.11 Beside these web tools, theimplementation of user-friendly coding systems and interactivee-Learning or m-Learning applications allows instructors todevelop ad hoc pieces of software or applications to reinforce theconcepts that students have already learned from textbooks orlectures, especially in those subjects with sophisticated contentsof mathematical calculations applied to chemical data.12,13 Thebenefits of these e-learning methodologies include the means for

creation of motivational environments significantly enhancingstudents’ meaningful learning. Different reported studies14,15

indicate that students achieve better comprehension, retain theinformation longer, and enjoy classes more effectively when e-learning methodologies are employed, empowering andenhancing their construction of a more cohesive understandingwith the interconnected facets of a discipline.“AChemTitri” has been conceived to be useful for students at

different levels and with different degrees of knowledge in thestudy of acid−base equilibria and titration curves. When themainobjective is to teach calculation and drawing of titration curves,“AChemTitri” can be used by the students as excellent feedbackto their calculations and plots. On the other hand, the applicationcan be also employed in a more holistic way since titration curvesunder different experimental conditions can be produced for thefurther study of the influence of the main variables. This secondpractice is intended for a more critical and practical interpretationof titration curves through the actual influence study of theinvolved variables, namely, the nature of the titrant and theproblem to be titrated, initial volume of problem solution andrelative concentrations of titrant agent and target species.

■ BACKGROUND

Educational Framework

Acid−base titration can be taught by using different approaches.In the most traditional procedures, teaching relies primarily onpassive-student lectures with algorithmic-problem exams. Occa-sionally, scripted lab classes follow theoretical titration lectures,where students have the chance to practice their observationalskills and make links between theory and practice.16 In contrast,inquired-based learning (IBL) puts emphasis on the learner as anactive agent in the process of knowledge acquisition.With the useof IBL,17 students have the opportunity to practice how scientistsdo science, in this way acquiring a significant learning of thechemistry key concepts, as it is the acid−base titration. On theother hand, the use of computer technologies in scienceeducation has been extensively reviewed. For instance, Ruttenet al.18 mentioned in their review that the use of computationaltools in the science classroom has the potential to generatehigher learning outcomes,19 since students have the chance to doauthentically inquiry activities. Besides, with the use ofcomputational tools in science teaching, students can explorehypothetical situations, interact with a simplified version of aprocess or system, change the time-scale of events, and practicetask and solve problems in a realistic environment withoutstress.18 Thus, motivated by this teaching methodology, in thisresearch, we propose an acid−base titration computerapplication used in IBL methodology as acid−base titration labsimulator. Thus, to work with this application, each group ofstudents will have a real-case titration experiment, where they willbe asked to find the answer through the experimentation with theapplication. Typical examples could be the study effect of theexperimental conditions, such as the initial volume of the acid/base to be titrated, chemical concentrations, and acid or basedissociation constant.Software Description

To achieve the teaching aims established before, an innovativecomputer application was developed in MATLAB environment.The application, named “AChemTitri”, has been designed toprovide students with a powerful tool that will allow them tounderstand through the self-practice and experimentation withthe main concepts of acid−base titration. AChemTitri is a group

Journal of Chemical Education Article

DOI: 10.1021/ed5005646J. Chem. Educ. XXXX, XXX, XXX−XXX

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of MATLAB text-code files that are freely available from theauthors upon request. The targets of this application are bothsenior high school students and undergraduate students inscience. To switch from one mode to the other, users will need toselect the proper option in the main menu (Figure 1). (Videotutorials on how to use AChemTitri are available as SupportingInformation.)In both cases, the application has three sections: check before

start (section one), titration curves (section two), and post-tasksurvey (section three). The first and third sections are common forboth types of users. The first section (“Check before start”)contains practical information about the application, like the userguide, theoretical contents, HTML-5 multimedia tutorial andonline questionnaires, in order to assess whether the user is readyto use the application in order to have significant learning. Theother common section (“Post-task survey”) is dedicated to surveythe overall experience with this application, where users areallowed to comment or submit feedback in order to improve futureversions of this application. The “Titration curves” sectioncontains the different scenarios where students might practiceand learn about pH titration curves. High school students will beable to titrate strong acid/base with a strong base/acid or a weakacid/base with a strong base/acid. Undergraduate students will beadditionally able to titrate polyfunctional acid/base with strongbase/acid and also the undergraduate student view includes moresophisticated experiments related to the concentration/dilutioninfluence in the titration curve (Figure 2).

To construct the titration curve, users first need to decide thetype of solution to titrate (strong acid/base, weak acid/base orpolyfuntional acid/base), its concentration (expressed as molar)and the initial solution volume. After making this first selection,students will have to select the concentration of the acid/baseknown solution. Once all variables are selected, the applicationshows the result of titration curve (pH vs known solution volumeof titrant); in addition, students might have the possibility to plotthe first and second derivative in order to get some graphicalassistance for selecting the equivalence point (Figure 3).In the case of polyfunctional acid/base in the results windows

the concentration diagram is also plotted. This concentration dia-gram represents the evolution of the concentration in all chemicalspecies involved in the titration. In addition, the numerical resultsof the equivalence point (strong orweak acid/base) or equivalencepoints (polyfunctional acid/base) and equivalence pH are alsodisplayed in the results windows (Figure 4).At this point, it is possible to change all experimental conditions,

the identity of the weak or polyfunctional acid/base and theconcentration of the known acid/base solution. Finally, the lastoption displayed in the undergraduate students view is the “acid/base advance studies”. Here students will have the chance toexperience how the titration curve is affected by the solutionconcentration. The users will be able to observe in the same plotup until five different concentration scenarios and therefore willhave the possibility to study the different titration curves as well asthe concentration diagrams (see detail in Figure 5).

Figure 1.This figure represents the main screen of the application AChemTitri (undergraduate view). This main screen is divided into three sections: inthe first section (“Check before start”), the student will have access to practical information such as video tutorials or theoretical contents; the secondsection (“Titration curves”) constitutes the main part of the application and is dedicated to the titration calculations; and, finally, in the third section(“Post-task survey”), an online survey is implemented to evaluate the usability of the software.



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The Supporting Information of this manuscript includes a setfour video instructions about how to use AchemTitri. The firstvideo tutorial shows how to titrate a strong acid, in the secondone how to titrate a weak acid, the third one is dedicated topolyfunctional acids, and finally, the last video explains how touse the advance studies options.

Acid−Base Theory

The acid−base theory constitutes one of the major concepts thatstudents must learn during their science education training. Allgeneral chemistry syllabuses include the acid−base concept, notonly in undergraduate courses but also in the last year of the high

Figure 3.Example result windows for the titration of a weak acid (acetic acid). In the result windows, the graphical and numerical results are displayed. Inthis window, students will have the possibility to change all the experimental conditions and to evaluate the different results.

Figure 2.Close-up view of pop-up windows that support students will have to carry out a titration of a weak acid (A) or a simultaneously comparison ofdifferent experimental conditions (B).



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school education. Among the different theories, the Brønsted−Lowry acid−base model forms a practical and useful compromisebetween other approaches as the Arrhenius, Lewis and Usanovich

concepts.20 Thus, the application developed in this research usedthe Brønsted-Lowry acid−base concept as theoretical frameworkto provide students a computer tool for better understanding of

Figure 4. Example result windows for the titration of a polyfunctional acid (maleic acid). For this type of titration, the concentration diagram is alsoincluded to provide students with more information about the evolution of the different chemical species involved in the acid−base equilibrium.

Figure 5. Images of the titration curves and concentration diagrams obtained with AChemTitri advance studies option. In column A, the influence of theinitial volume of the solution to titrate is assessed (initial maleic acid solution). In column B, the influence of the molar concentration of the titrant(sodium hydroxide concentration) is shown. Finally, in column C, the influence of the molar concentration of the target analyte (maleic acid solution) isstudied.



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this concept, which causes many questions and takes a toll onstudents grade, as it was mentioned before.21

According to Brønsted−Lowry theory, an acid is defined as thesubstance able to donate a proton, and a base as the substanceable to gain a proton.22 Considering this definition, a Brønsted−Lowry acid behaves as an acid when there is another substanceable to gain the lost proton from the acid (Brønsted−Lowrybase).As a consequence, when an acid substance loses a proton, it

forms a conjugate base and, in the opposite way, when a basesubstance gains a proton, it forms a conjugate acid of a base. It isalso important to consider that the strongest a Brønsted−Lowryacid is, the weaker the corresponding conjugate base and viceversa. In addition, the solvent nature is another factor to beconsidered, since they can act as a proton-donor or proton-acceptor, and as a consequence, they influence the acid−basebehavior of the solute solved. According to this, a strong acid orbase is that substance that undergoes a complete dissociationwhen reacting with other acid/base, and in contrast, for a weakacid/base, the dissociation reaction proceeds to only a smallextent. The equilibria constant of this reaction constitutes aquantitative measure of the acid/base strength.On the other hand, an acid−base titration could be defined,

from an analytical point of view, as the action of counting theaverage number of analyte particles in solution through thereaction with a known number of standard particles.23 Titrationcalculation, using conventional equivalence point detection, canonly be applied accurately when the neutralization reactionproceeds to a large extent; therefore, it is not appropriate for thetitration of very weak acids/bases. For this reason, thecalculations compiled in AChemTitri application do not includevery weak acids/bases. Tables 1 and 2 summarize some of thecalculations coded in the software to determine the titrationequivalent points as well as the concentration of the differentspecies existing in the solution during the titration.

■ DISCUSSION

Description andDiscussion of theObtained Titration Curves

Case I: Titration of a Strong Acid with a Strong Base.Initial pH of the solution will correspond to a hydronium ionconcentration, exactly equal to the molar concentration of theacid to be titrated, since it is completely ionized. The solution willpresent acid character until the equivalence point and basiccharacter after that. The solution will be neutral at theequivalence point. The hydronium ion concentration at everymoment before the equivalence point will correspond to themolar concentration of non-neutralized acid; in the same way,the hydroxide ion concentration after the equivalence point willbe equal to the molar concentration of the titration agent inexcess. Under equimolarity conditions, i.e., molar concentrationof titrant equal to molar concentration of analyte, the equivalencepoint will be reached after adding a volume of titrant equal to theinitial volume of analyte solution.Graphically, the equivalence point corresponds to the

inflection point of the titration curve in this kind of system. Itis also possible to obtain the first and second derivative plots ofthe titration curve for a more easy localization of the equivalencepoint. The equivalence point will appear like a maximum and acut with the x-axis in the first and second derivative plots,respectively. It is a fact that a maximum or a cut with abscises ismuch more easy to be unequivocally located in a plot than aninflection point. Table1.ChemicalReactions

andListofEqu

ations

UsedToCon

structtheTitration

ofStrong

Acids

intheInitialPoint,beforetheEqu

ivalence

Point,intheEqu

ivalence

Point,and

aftertheEqu

ivalence

Point

TitrationType

InitialConditio

nsBeforetheEq

uivalencePo

int

EquivalencePo

int

AftertheEquivalence

Point

Titrationof

astrong

acidwith

astrong

base

HCl+

H2O

→H

3O++Cl−

HCl+

NaO

H→

H2O

+NaC

lHCl+

NaO

H→

H2O

+NaC

lNaO

H+H

2O→

HO

−+Na+

HCl+

H2O

→H

3O++Cl−

HCl+

NaO

H→

H2O

+NaC

l[H

3O+ ]

=[C

HCl]=Ci

=×

−×

++

HC

VC

VV

V[

O]

ii i

3H

Cl

HC

lN

aOH

adde

d

HC

lad

ded

[H3O

+ ]=[O

H−]

=×

−×

+−

CV

CV

VV

[OH

]i

iHl

adde

dad

ded

CiH

Cl

HC

l

adde

d

Titrationof

aweakacidwith

astrong

base

HOAc+H

2O→

OAc−

+H

3O+

HOAc+NaO

H→

NaO

H+H

2OOAc−

+H

2O→

HOAc+OH

−NaO

H+H

2O→

HO

−+Na+

HOAC+H

2O→

OAc−

+H

3O+(K

a)=

×−

K[H

OAc

][O

H]

[OAc

]b

=×

−×

+−

CV

CV

VV

[OH

]i

i

adde

dad

ded

CiH

Cl

HC

l

HC

lad

ded

=+

KC

[HO

]3

aH

OAc

=×

−×

+C

CV

CV

VV

ii i

HO

AcH

OAc

HO

AcN

aOH

adde

d

HO

Acad

ded

[HOAc]

=[O

H−]

=× +

CC

VV

Vi

i

iN

aOAc

HO

AcH

OAc

HO

Acad

ded

=×

+

−K

CV

VV

[OH

](

)/(

)i

ii

b

2

HO

AcH

OAc

adde

d

=×

+K

CC

[HO

]a

NaO

Ac3

HO

Ac



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To discuss the effect of the concentration of analyte andtitration agent on this type of titration curves, it is necessary toconsider equimolarity, in order to make things easier tounderstand. Then it will be observed that the more dilutedthey become, the less pronounced the pH change around theequivalence point will be.Case II: Titration of a Strong Base with a Strong Acid. In

the titration of a strong base with a strong acid, initial pH willcorresponds to a hydroxide concentration equal to the molarconcentration of the base to be titrated. The solution will remainstrongly alkaline close to the equivalence point, neutral at theequivalence point and acid beyond it. Again, like in Case I, pH iscalculated along the whole titration through hydroxide andhydronium ion concentrations, which are equal o molarconcentrations of base and acid, respectively.The effect of concentration will be exactly the same as in Case

I: the intensity of the pH jump around the equivalence point willincrease with the concentrations of analyte and titrant.Case III: Titration of a Weak Acid with a Strong Base.

Calculations in this case are not that straightforward as in CasesI and II, since it is necessary to take into account the presence ofthe acid itself, its conjugated base and the possible mixtures ofboth species. The pH of those mixture solutions will depend onthe relative position of two competitive equilibria: the ionizationof the acid and the hydrolysis of the conjugated base. Thus,pH depends, on the one hand, on the relative values of theirionization (Ka) and hydrolysis (Kb) constants and, on the otherhand, the ratio between the concentrations of weak acid and itsconjugate base. These solutions containing a weak acid and itsconjugated base are known as buf fer solutions and their mainfeature is that they present a remarkable resistance to changesin pH as a result of either dilution or small additions of acidsor bases.22 Maximum buffer capacity is reached at equal

concentrations of weak acid−conjugated base, but it alsodepends on their total concentration. pH calculations in thesekind of systems have to be done considering different regions:before starting the titration, the solution contains a weak acid andthe extent of its dissociation is given by its dissociation constant(Table 1); when adding increasing volumes of titrant, beforereaching the equivalence point, different buffers are generated,which pH depends on Ka and the ratio between the con-centrations of weak acid and conjugated base. We shouldmention that when 50% of the acid is neutralized, pH is equal topKa; at the equivalence point the only sample present in solutionwill be the conjugated base and pH will be calculated through itshydrolysis constant,Kb (Table 1); after the equivalence point, thepH will be determined by the excess molar concentration ofstrong base used as titrant. The shape of this curve in the regionbeyond the equivalence point becomes identical to that for astrong acid (Case I).To discuss the effect of concentration, it is necessary to

consider again analyte and titrant solutions of the same strengths.The initial pH value will increase and the pH at the equivalencepoint will decrease with the dilution. For intermediate titrantvolumes, pH will not be very affected by the dilution due to thepresence of buffers, since it is a fact that pH of buffered solutionsis largely independent of dilution.With respect to the effect of the dissociation constant of the

acid on the shape of the titration curves, the pH jump around theequivalence point will become smaller as the acid becomesweaker. This is due to less quantitative completion of the reactionbetween analyte and titrant. This fact, together with the effect ofthe concentration, makes more limited the choice of indicator forthe titration of weak acids with respect to strong ones.

Case IV: Titration of a Weak Base with a Strong Acid.Deduction of the titration curve for a weak base titrated with a

Table 2. Chemical Reactions and List of Equations Used To Construct the Titration of Polyfunctional Acids in the Different Stagesof the Acid−Base Equilibrium

Reaction 1: H2M + H2O → H3O+ + HM− K1

Reaction 2: HM− + H2O → H3O+ + M2− K2

Initial Point Before First Equivalence Point First Equivalence Point

[H3O+] = [HM−]

≈ =− ×+C [HM ] C V

V VNaHM i

NaOH added

H2M added[H2M] + [HM−] = CiH2M

= =−

+ +

+KC

[H O ][H M]

[H O ][H O ]i

13

2

2

32

H M 32

≈ =× − ×

+C

C V C V

V V[H M] i i

iH M 2

H M H M NaOH added

H2M added2

2 2 =+

+ K C[H O ]

1 CK

32 NaHM

NaHM

1

=

=× +

−

+ −

+ +

+

K

CC

[H O ][HM ][H M]

[H O ] ( [H O ])[H O ]

13

2

32

NaHM 3

H M 32

Before Second Equivalence Point Second Equivalence Point After Second Equivalence Point

=× − ×

+C

C V C V

V Vi i

iNa M

NaOH added H M H M

H M added2

2 2

2

M2− + H2O → OH− + HM− =− ×

+− V V C

V V[OH ]

( )

i

added 2ndEP NaOH

H M added2

=× − − ×

+C

C V V V C

V V

( )i i

iNaHM

H M H M added 1stEP NaOH

H M added

2 2

2

× =− −

−KK

[OH ] [HM ][M ]2

w

2

[OH−] ≈ [HM−]

=×+

KC

C

[H O ]2

3 Na M

NaHM

2 =× ×

VC V

C

2 i i2ndEP

H M H M

NaOH

2 2

=×+

− C VV V

[M ]( )/2

i

2 NaOH 2ndEP

H M 2ndEP2



G


strong acid is analogous to Case III. Again, it is indicated to breakthe curve into regions to perform calculations: initial pH will beobviously alkaline and will depends on the base concentrationand its hydrolysis constant (Table 1); different buffers will begenerated after increasing volumes addition of titrant up to theequivalence point; the conjugated acid of the analyte will be theonly sample in solution in the equivalence point and thus pH willdepend on its concentration and dissociation constant (Ka); theexcess of added titrant after the equivalence point will determinethe pH in that region.The effect of concentration and hydrolysis constant of the base

will be analogous to that in Case III. That is, initial pH willdecrease, the pH at the equivalence point will increase with thedilution and the magnitude of the pH decrease around theequivalence point will decrease with the hydrolysis constant ofthe analyte.Case V: Titration of a Polyprotic Acid with a Strong

Base, Advanced Studies.Multiple end points can be observedin this kind of titration, as long as the acidic groups of the analytediffer sufficiently in strength. In general, two individualequivalence points of practical value will be observed for anacid with two protons when the ratio between the two dissoci-ation constants (Ka1/Ka2) is

22 at least 104. The main assumptionor approximation that is done in such cases consists in neglectingthe second dissociation in the early part of the curve. The sameapproximation also implies that shortly beyond the firstequivalence point, the first equilibrium can be also not takeninto account at any extension. For higher values of the ratioKa1/Ka2, the introduced error by considering these assumptionsis minimized. From the educational point of view, it is advisableto consider the cases of acid with huge differences amongsuccessive ionizations, but in the same way, it would be alsointeresting to compare with acids with not that big of a differencein successive Ka values to make the student aware of thelimitations of the approximations and the subsequent limitationsin the choice of a suitable indicator.Once the above referred approximations are assumed, the

development of the titration curve is not that different from thecorresponding curve of a weak acid in each of the possibledissociations of the polyprotic one of interest.“AChemTitri” gives also students the possibility of studying

the effect of three experimental variables: initial volume ofsolution to be titrated, molar concentration of the target analyteand molar concentration of titrant. Figure 5 shows the obtainedtitration curves when studying the effect of each one of thesevariables.Case VI: Titration of a Polyfunctional Base with a

Strong Acid as Advanced Studies. The calculation of thetitration curve for a polyfunctional base follows the sameprinciples as those stated in Case V.In this case, also, the effect of the same variables can be studied.

In all the presented cases, “AChemTitri” provides alsocomposition diagrams as a function of pH in order to make iteasy to the student to understand compositional changes takingplace in the presented titrations.Assessment of Application Usability

Knowing the limitations of computer software supports toevaluate the capability and functionality of the application design.The evaluation procedure should include a complete assessmentof how well the programs functions on users’ computer hardwareand this capability and functionality must be tested on all possibleequipment.24 Then, the review of usability requirement is relatedto the evaluation of software components to see if they conformto the evaluation guide for engineering software. Likewise, theapplication interface included with these features is a significantcomponent that could impact the capability and functionality ofsoftware and the efficiency of users. Before permitting publiconline access, the proposed application was verified by authors toperform all its tasks correctly after all application capabilities hasbeen tested. Then, to test the usability of the AChemTitriapplication, an online survey was conducted among differenttype of users (professors, professionals, undergraduate students,graduate students and high-school students). The survey wasconsisted in three blocks of questions: in the first one, basicinformation about the user was asked; the second block wasdedicated to collect information about the usability ofapplication; and finally, the third part of the survey was intendedto find how satisfied were the students after using AChemTitri.A total of 50 participants completed the online survey: among

them, 39% were professors, 11% were graduate students, 33%were undergraduate students, 5.5% were high school studentsand the remaining 11% were professionals not related with theeducation field. The results of this survey, expressed aspercentage, are summarized in Table 3.In general, users did not experience trouble with setting up the

application in their computers (over 70% of the participants wereeither satisfied or very satisfied with the installation process).Regarding the video tutorial implemented in the software, allparticipants found them very useful to learn how to use theapplication and to exploit all the potentialities from it. Inaddition, almost all the participants found the application user-friendly and self-explanatory. With regard of the calculationsprocesses, students were in general satisfied or very satisfied.Finally, around 7% of the participants were neutral about thequality of graphical results, while 85% of the participants weresatisfied or very satisfied. On the other hand, users were alsosurveyed about which function of the application would be themost useful from them. The results show that the majority of theparticipants will use the application to compare differentexperimental conditions (73%). In addition, an importantnumber of user point out that the main applicability will be thetitration of polyfunctional acids or bases (67%). Finally, 27% and20% of users selected the titration of strong acids or bases, as the

Table 3. Comparative Survey Results Concerning Student’s Satisfaction with AChemTitri

Respondents (N = 50) Selecting a Given Satisfaction Ranking by Topic, %

Questionnaire Usability TopicsVery

Unsatisfied Unsatisfied Neutral Satisfied Very Satisfied Not Applicable

Q1. Application setup and configuration 0 0 0 14.3 57.1 28.6Q2. Tutorials tools 0 0 0 20.2 78.0 1.8Q3. The way to work with the application (user-friendly and self-explanatory) 0 0 0 21.4 71.5 7.1Q4. Calculations and application performance 0 0 0 21.4 71.4 7.2Q5. Quality of figures (titration curves) 0 0 7.1 14.3 71.5 7.1



H


most useful function. This percentage could be explained by thesmall representation of high school students in this survey.Finally, in the last part of the survey, participants were asked

how likely they were to recommend the application to otherstudents or professors. The results show that 81% of theparticipants will definitely recommend the application and 19%will probably recommend the application to other peers.

■ CONCLUSIONSA new computer application, to construct acid−base titrationcurves, has been designed to assist students from the last coursesof high school education and undergraduate students, in thestudies of acid−base titration. The application, namedAChemTitri, has been written under theMATLAB environment,and combines graphical with numerical calculations, to ensure abetter understanding of titration concepts. Moreover, with thisapplication, students will be able to practice basic titrationconcepts, such as titration of strong acid/base with a strong base/acid, as well as the titration of more complex systems such asweak and polyfunctional acids/bases. Besides the titration curves,concentration diagrams are also shown, in the case ofpolyfunctional acids and bases. With these diagrams, studentswill evaluate the evolution of the different chemical speciesinvolved in the acid−base equilibrium. To check the capability ofthe proposed computer application, a survey was performedamong different type of users (professor, undergraduate and highschool students, and other professionals) resulting in over 80% ofthe participants recommending the use of this application.Should the reader be interested in testing and using theapplication or the code presented in this work, please contact theauthors by e-mail to get files.

■ ASSOCIATED CONTENT*S Supporting Information

We present four video tutorials about how to use AChemTitri.The first video tutorial shows how to titrate a strong acid, in thesecond one how to titrate a weak acid, the third one is dedicatedto polyfunctional acids, and finally, the last video explains how touse the advance studies options. This material is available via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors

*E-mail: [email protected].*E-mail: [email protected].*E-mail: [email protected].*E-mail: [email protected]

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTSAuthors thank the Extremadura Government, European SocialFunds, and Ministerio de Economia y Competitividad forfinancial support (Grant GR10075 and EDU2012-34140). Jin SuJeong thanks Contratos Puente para Becarios Predoctorales(Universidad de Extremadura).

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