Electrochemical Methods of AnalysisElectrochemical Methods of Analysis

Lecture 14Lecture 14

Associate prof . L.V. VronskaAssociate prof . L.V. VronskaAssociate prof . M.M. MykhalkivAssociate prof . M.M. Mykhalkiv

OutlineOutline

1.1. Classification of electrochemical methods of Classification of electrochemical methods of analysisanalysis

2.2. PotentiometryPotentiometry

3.3. ElectrogravimetryElectrogravimetry

4.4. Conductometry Conductometry

5.5. CoulometryCoulometry

6.6. VoltammetryVoltammetry

1. Classification of electrochemical 1. Classification of electrochemical methods of analysismethods of analysis

Electrochemical methodsElectrochemical methods are based on measurement are based on measurement of electric parameters of the electrochemical of electric parameters of the electrochemical phenomena which arise in an investigated solution.phenomena which arise in an investigated solution.

Electrochemical methods of analysis:Electrochemical methods of analysis: Methods without potential imposing from the Methods without potential imposing from the

outsideoutside ( (potentiometrypotentiometry).). Methods with potential imposing from the outsideMethods with potential imposing from the outside

which are based on measurement different electric which are based on measurement different electric parameter (all another methods)parameter (all another methods)

Methods with potential imposing from the Methods with potential imposing from the outside which are based on measurement of:outside which are based on measurement of: electric conductivity of solutions - electric conductivity of solutions - conductometryconductometry;; quantities of electricians which has passed through a quantities of electricians which has passed through a

solution - solution - coulometrycoulometry;; dependences of current value from the imposed potential dependences of current value from the imposed potential

- - voltammetryvoltammetry;; Time which is necessary for passage of electrochemical Time which is necessary for passage of electrochemical

reaction - reaction - chronoelectric methodschronoelectric methods (chronovolammetry, (chronovolammetry, chronoconductometry);chronoconductometry);

Weights of substance which was allocated owing to Weights of substance which was allocated owing to passage of certain current force through a solution - passage of certain current force through a solution - electrogravimetryelectrogravimetry..

Electrochemical methods on usage Electrochemical methods on usage can be classified on:can be classified on:

Direct methodsDirect methods in in which substance which substance

concentration concentration measure by instrument measure by instrument

readingreading

Electrochemical titration –Electrochemical titration – in in which for indication of equivalence which for indication of equivalence

point use of electrochemical point use of electrochemical measurementsmeasurements

PotentiometryPotentiometry potentiometric titration

ConductometryConductometry conductometric titration

Voltammetry amperometric titration

CoulometryCoulometry coulometric titration

ElectrogravimetryElectrogravimetry -

Electrochemical cellElectrochemical cell is is vessel with vessel with investigated solution in which dipped investigated solution in which dipped

electrode.electrode.

Electrochemical cellElectrochemical cellMethods without Methods without potential imposingpotential imposing

Methods with potential Methods with potential imposingimposing

- galvanic cell - electrolytic cell- conductometric cell

with two different metals connected by a salt bridge or a porous disk between the individual half-cells

decomposes chemical compounds by means of electrical energy, in a process called electrolysis (except for conductometric cell)

2. Potentiometry2. PotentiometryIt is pharmacopeia’s method of analysis

In an ideal case such dependence is In an ideal case such dependence is described by Nernst equationdescribed by Nernst equation

red

ox

a

a

nEE lg

059,00

!!! Direct measurement of potential value is impossible, therefore apply system of electrodes and compare potential of one electrode with potential of the second electrode

Electrochemical measurements are made in an electrochemical cell, consisting of two or more electrodes and associated electronics for controlling and measuring the current and potential.

Indicator electrode is the electrode whose potential is a function of the analyte’s concentration (also known as the working electrode).

Counter electrode is the second electrode in a two-electrode cell that completes the circuit.

Reference electrode is an electrode whose potential remains constant and against which other potentials can be measured.

Electrochemical cell for Electrochemical cell for potentiometrypotentiometry

Classification of electrodesClassification of electrodes

nMeanF

RTEE ln0 xAna

nF

RTEE ln0

Electrodes

I sorts ІІ sorts

Reversible on cation Reversible on anion

The electrode potential is defined by cation activity which is like to the metal

dipped into electrolyte

The electrode potential is defined by anion activity

- Metal electrodes- membrane or ion-selective electrodes- A glass electrode- A hydrogen electrode- quinhydrone electrode

- An covered electrode slightly soluble salt of those cation, from which made electrode (silver-chloride and calomel (SCE) electrode)- Gas electrodes (oxygen, chlorine-chloride, etc.)

Oxidation-reduction electrodes (precious metals)The potential depends from ratio of oxidized and reduced forms of redox-pair

The characteristic of electrodesThe characteristic of electrodesElectrode Nernst Equations Possibilities

Quinhydroneelectrode

рН=0-8.0

The glass

Е0 is depends from asymmetry potential and equilibrium constant

H+(solution) H+(glass)

1.рН=0-12.0-13.02. possible presence

Ox and Red3. possibility

measurement in colloidal solutions

Hydrogen Е = - 0,058рН. inconveniences of application

Silver E=E0(Ag+/Ag)+0,058 lgaAg+ I sorts

Mercury E=E0(Hg2+/Hg)+0,029 lgaHg2+. I sorts

Silver-chloride Ag,AgCl | KClsat.||

E(Ag+/Ag) = E0(Ag+/AgCl) –

ІІ sorts (reference electrodes )

Calomel Hg,Hg2Cl2|KClsat.||

E(Hg22+/Hg2Cl2) =E0(Hg22+/2Hg) + ІІ sorts

(reference electrodes )

]lg[2

058.00 HEEx

pHF

RTEE glass 303,20

ClaF

RTln

22S ClHgKln

F2

RT

Direct potentiometryDirect potentiometry

Direct potentiometry is basedDirect potentiometry is based on direct on direct application of Nernst equationapplication of Nernst equation for calculation for calculation of activity or concentration of substance which of activity or concentration of substance which take part in electrode reaction on take part in electrode reaction on experimentally measured experimentally measured of EMFof EMF or electrode or electrode potentialpotential

Theoretical basis of the quantitative Theoretical basis of the quantitative analysis:analysis:

Potentiometric electrochemical cells are on structed such that one of the half-cells provides a known reference potential, and the potential of the other half-cell indicates the analyte’s concentration.

Ecell = Eind – Eref + Elj

where: where: Eind – potential of indicator electrode

Eref - potential of reference electrode

Elj - liquid junction potential (a potential that develops at the interface between two ionic solutions that differ in composition, because of a difference in the mobilities of the ions)

Mindljref

MM fRT

nFЕЕEECpC lg

303,2

)]([lg

0...

Methods ofMethods of quantitative analysisquantitative analysis:: A method of calibrationA method of calibration chart chart (at constant ionic

strength of solution and constant activity coefficients will be identical, and liquid junction potential will aspire to zero)

The basic equation will be:

рСМ = аЕ + bE

lgCM

If concentration and structure of investigated and standard solutions similar to each other so it is possible to use concentration:

A method of a concentration elementA method of a concentration element

ljXX

stasta ЕfC

fCln

nF

RTE

X

st

C

Cln

nF

RTE

At Е = 0, lnCst/Cx = 0, then Сst = Сх.

To carry out this condition (Е = 0) is possible to reach by dilution of standard solution by background electrolyte solution or addition of more concentrated standard solution.

Method of additivesMethod of additives

ljXX0

X ЕfClnnF

RTEE

ljXX0

staX Еf)СCln(nF

RTEE

X

X

X

XstaX C

CClgk

C

CCln

nF

RTEEE

X

X

C

CClgkE

1k/EX 10

CC

Before addition of standard solution (EMF)

And after addition:

where ΔС - incremental value of concentration

The difference of electrode potentials is equal:

Potentiometric titrationPotentiometric titration

The scheme of equipment for potentiometric titration

Potentiometric titrationPotentiometric titration is based on definition of a is based on definition of a equivalence point by results equivalence point by results of potentiometricof potentiometric measurements.measurements.

Requirements to reactions:Requirements to reactions:- - stoichiometrystoichiometry- - quantitativelyquantitatively- - rapidlyrapidly- Selectively- Selectively- There should be fitted corresponding electrode- There should be fitted corresponding electrode

Types of used reactions:- Acid-base- Precipitation- Complexing- Oxidation-reduction

Titration curves:Titration curves:

- integral curve- integral curve

- differential curve - differential curve

- curves on Gran method- curves on Gran method

- curves of double differentiation- curves of double differentiation

Integral curve Integral curve (the (the acid-base titration)acid-base titration) Differential curve (the Differential curve (the

acid-base titration) acid-base titration)

curves on Gran methodcurves on Gran method

curves of double curves of double differentiationdifferentiation

Features of potentiometric titration:Features of potentiometric titration: Separate titration of acid mixture is probably if acid Separate titration of acid mixture is probably if acid

constants differ more than on 4 order (accuracy to 1 %)constants differ more than on 4 order (accuracy to 1 %) Separate titration of mix of strong and weak acids is Separate titration of mix of strong and weak acids is

probably if acid constants differ more than on 6 order probably if acid constants differ more than on 6 order (accuracy to 0,1 %) (accuracy to 0,1 %)

Separate titration of a mix of oxidizers (reducers) is Separate titration of a mix of oxidizers (reducers) is probably if potentials differ not less than on 0,4 Vprobably if potentials differ not less than on 0,4 V

Separate titration of a mix on precipitation method is Separate titration of a mix on precipitation method is possible, if solubility products of precipitates differ not possible, if solubility products of precipitates differ not less than on 3 orderless than on 3 order

Advantages Advantages of potentiometricof potentiometric titration titration1. High accuracy (accuracy of titration to 0,1 % at 1. High accuracy (accuracy of titration to 0,1 % at

ΔΔЕ=0,01mV)Е=0,01mV)2. High sensitivity2. High sensitivity3. Possibility of definition of several substances3. Possibility of definition of several substances4. Titration possibility in the painted and muddy 4. Titration possibility in the painted and muddy

mediumsmediums5. Possibility of usage of nonaqua mediums5. Possibility of usage of nonaqua mediums6. Possibility of automation of titration processes 6. Possibility of automation of titration processes 7. rapid analysis method 7. rapid analysis method

Lacks: Lacks:

1. A considerable quantity of measurements1. A considerable quantity of measurements

2. Not always fast stabilisation of potential2. Not always fast stabilisation of potential

Usage of potentiometry in the analysis Usage of potentiometry in the analysis of chemical compounds and drugsof chemical compounds and drugs

- The analysis of substances (streptocide, - The analysis of substances (streptocide, ofloxacin, trimethoprimum)ofloxacin, trimethoprimum)

- The analysis of ready medicinal forms (a - The analysis of ready medicinal forms (a tablet of Biseptolum, streptocide, tablet of Biseptolum, streptocide, clotrimazolum etc.)clotrimazolum etc.)

- Definition of рН substances, drugs- Definition of рН substances, drugs

3. Electrogravimetry 3. Electrogravimetry

Electrogravimetric methodElectrogravimetric method of analysis is method of analysis is method of quantitative allocation of defined substance on of quantitative allocation of defined substance on preliminary weighed electrode and an preliminary weighed electrode and an establishment of the contain of substance in establishment of the contain of substance in sample on increase of electrode weightsample on increase of electrode weight

electrodeinitial

electrodefinal

substance mmm

Faraday’s 1st Law of ElectrolysisFaraday’s 1st Law of Electrolysis:: The mass of a substance altered at an electrode The mass of a substance altered at an electrode

during electrolysis is directly proportional to the during electrolysis is directly proportional to the quantity of electricity transferred at that quantity of electricity transferred at that electrode. Quantity of electricity refers to electrode. Quantity of electricity refers to electrical charge, typically measured in electrical charge, typically measured in coulombs, and not to electrical current.coulombs, and not to electrical current.

m = k Q

Q = i t

Faraday’s 2nd Law of Electrolysis

96500

EtI

96500

EQm

mm

For a given quantity of electricity (electric charge), the mass of an elemental material altered at an electrode is directly proportional to the element's equivalent weight. The equivalent weight of a substance is its molar mass divided by an integer that depends on the reaction undergone by the material.

Electrolysis must be with ensuringElectrolysis must be with ensuring 100% 100% current efficiency (CE)(CE)

%.100m

mCE

theor

pract

Scheme of electrolysis of sodium Scheme of electrolysis of sodium chloride meltchloride melt

Requirements to precipitatesRequirements to precipitates

The precipitate should be the certain crystal The precipitate should be the certain crystal form.form.

The precipitate should be practically The precipitate should be practically insoluble.insoluble.

Cleanliness of a precipitate should be Cleanliness of a precipitate should be maintained strictly.maintained strictly.

The precipitate should have the chemical The precipitate should have the chemical formula (structure).formula (structure).

Conditions of electrolysisConditions of electrolysis

The physical:The physical: Pressure,Pressure, Current force, Current force, Resistance of solution, Resistance of solution, Current density (than more density, the Current density (than more density, the

there passes sedimentation faster, but if it there passes sedimentation faster, but if it very big so may be formation of too big or very big so may be formation of too big or small crystals, leaky precipitates). Optimum small crystals, leaky precipitates). Optimum value of current density 0,01-0,1 А/сmvalue of current density 0,01-0,1 А/сm22..

The chemical:The chemical: The sedimentation medium (in the The sedimentation medium (in the

presence of sulphatic acid is optimal)presence of sulphatic acid is optimal) Competitive complexing for “masking" Competitive complexing for “masking"

with formation solutions with low with formation solutions with low concentration (precipitates must be crystal concentration (precipitates must be crystal and clean)and clean)

Scheme for electrogravimetryScheme for electrogravimetry

Usage electrogravimetryUsage electrogravimetry

For separate metal definitions. It is possible For separate metal definitions. It is possible if:if:

- For singly charged cations if difference in - For singly charged cations if difference in potential of allocation is equal potential of allocation is equal 0.40.4 VV

- For two charged cations if difference in - For two charged cations if difference in potential of allocation is equal potential of allocation is equal 0.20.2 V V

Electrical conductanceElectrical conductance is a measure of how is a measure of how easily electricity flows along a certain path easily electricity flows along a certain path through an electrical elementthrough an electrical element

Unit ofUnit of electrical conductivityelectrical conductivity is conductivity of is conductivity of a conductor resistance 1 Ohm. The SI derived a conductor resistance 1 Ohm. The SI derived unit of conductance is the Siemens.unit of conductance is the Siemens.

,R

1W S

lR

4. Conductometry4. Conductometry

Electrical conductivityElectrical conductivity or or specific conductancespecific conductance is a is a measure of a material's ability to conduct an electric measure of a material's ability to conduct an electric currentcurrent.. Conductivity Conductivity (()) is the reciprocal (inverse) of is the reciprocal (inverse) of electrical resistivity, ρ, and has the SI units of siemens electrical resistivity, ρ, and has the SI units of siemens per metre (S·mper metre (S·m-1-1):):

Specific conductanceSpecific conductance corresponds electric corresponds electric conductivity of 1 cmconductivity of 1 cm33 solution which are solution which are placed between placed between electrodes with area 1 electrodes with area 1 cmcm22 which are on which are on distances of 1 cm one distances of 1 cm one from anotherfrom another

= 1/.

Equivalent conductivityEquivalent conductivity is equal electric is equal electric conductivity such volume of a solution which conductivity such volume of a solution which is placed between two parallel electrodes on is placed between two parallel electrodes on distance 1 cm, containing 1 mol of distance 1 cm, containing 1 mol of substances.substances.

C

1000 .

mol

сmS 2

Value of Value of equivalent conductivityequivalent conductivity depends depends on concentration and ions charge, and also on concentration and ions charge, and also speed of their mobility:speed of their mobility:

At infinitely big dilution At infinitely big dilution = 1 and equivalent = 1 and equivalent conductivityconductivity aspires to the greatest value aspires to the greatest value

).(

)(1000

Cx

.

Limiting equivalent conductivityLimiting equivalent conductivity is equal is equal sum of limiting equivalent conductivitiessum of limiting equivalent conductivities of of ions or sum mobilitiesions or sum mobilities of ionsof ions at infinitely big at infinitely big dilutiondilution..

HH++ 349,8349,8 OHOH- - 198,3198,3

NHNH44++ 73,6 1/2SO 73,6 1/2SO44

2-2- 80,0 80,0

AgAg++ 61,9 I 61,9 I-- 78,8 78,8

LiLi++ 38,7 NO 38,7 NO33-- 71,5 71,5

FF-- 55,4 55,4

CC66HH55COOCOO-- 32,4 32,4

Factors which influence on equivalent Factors which influence on equivalent conductivityconductivity of electrolytesof electrolytes::

Nature of solvent (viscosity and inductivity Nature of solvent (viscosity and inductivity of solvent)of solvent)

Nature of electrolyteNature of electrolyte Concentration of electrolyteConcentration of electrolyte

equivalent conductivityequivalent conductivity an electrolyte solution depends an electrolyte solution depends on concentration: than more concentration, the low on concentration: than more concentration, the low conductivity (because of strengthening interionic conductivity (because of strengthening interionic interactions due to cathophoretic and relaxation effects)interactions due to cathophoretic and relaxation effects)

Dependence of Dependence of equivalent conductivityequivalent conductivity strong strong electrolytes which dissociates only on two kinds of ions, electrolytes which dissociates only on two kinds of ions, from concentration is expressed by from concentration is expressed by OnsagerOnsager equation: equation:

where В is the function depending from: a ions charge, where В is the function depending from: a ions charge, dynamic viscosity of solvent, temperature, dielectric dynamic viscosity of solvent, temperature, dielectric permeability of solvent.permeability of solvent.

B

Conductivity Conductivity (()) of solution depends also of solution depends also from its concentrationfrom its concentration..

HClHCl

KOHKOH

CHCH33COOHCOOH

С, С, molmol//LL

Conductivity (Conductivity ()) of solution in the diluted of solution in the diluted solutions of strong and weak electrolits solutions of strong and weak electrolits can be calculated, if concentration of ions can be calculated, if concentration of ions and their equivalent conductivity are and their equivalent conductivity are knownknown

iiC1000

1

Dependence of conductivity from Dependence of conductivity from temperature express the equation:temperature express the equation:

Rise in temperature on 1 °С causes increase Rise in temperature on 1 °С causes increase conductivity of solution on 2-2,5 %. conductivity of solution on 2-2,5 %.

)1( 20 ttt

Scheme of conductometric definitionsScheme of conductometric definitions

Direct conductometryDirect conductometry

Qualitative analysisQualitative analysis is used for definition any is used for definition any ionsions

Quantitative analysisQuantitative analysis is used for definition of is used for definition of electrolytes concentrationelectrolytes concentration

Usage Usage of direct conductometryof direct conductometry:: For definition of individual electrolytes in solutionFor definition of individual electrolytes in solution For definition of electrolytes in mix when impurities For definition of electrolytes in mix when impurities

concentration don’t changeconcentration don’t change For continuous control of manufactures For continuous control of manufactures For control of water treatment process For control of water treatment process For sewage pollution assessmentFor sewage pollution assessment For definition of general content of salts in mineral, ocean and For definition of general content of salts in mineral, ocean and

fluvial waterfluvial water For control of operations filter washing and ion-exchange For control of operations filter washing and ion-exchange

material regenerationmaterial regeneration For definition of cleanliness slightly soluble precipitate or For definition of cleanliness slightly soluble precipitate or

organic drugsorganic drugs For definition of dampness of organic solvent, gases, crystal For definition of dampness of organic solvent, gases, crystal

salts, papersalts, paper For detecting in chromatographyFor detecting in chromatography

Installation for reception of the cleared Installation for reception of the cleared water with conductometric gauge for water with conductometric gauge for

water quality assurancewater quality assurance

conductometric titration

Requirement to reaction: as in classic Requirement to reaction: as in classic titrimetric analysis.titrimetric analysis.

Types of reaction:Types of reaction: Acid-baseAcid-base Precipitation Precipitation ComplexingComplexing

!!! !!! ox-redox-red reaction practical don’t use reaction practical don’t use

conductometric titration curves

Schema for Schema for conductometricconductometric titrationtitration

5. Coulometry5. Coulometry

Coulometric analysis is one of electrochemical Coulometric analysis is one of electrochemical methods and it ismethods and it is absoluteabsolute..

Coulometry is an electrochemical method in which the current required to exhaustively oxidize or reduce the analyte is measured.

It is based on measurement of It is based on measurement of quantity the quantity the electricians, which spent for quantitative electricians, which spent for quantitative realisation of the given electrochemical realisation of the given electrochemical process in the given sampleprocess in the given sample

Current efficiency (CE)(CE) must be must be 100%100%

CoulometryCoulometry

at constant potential at direct current

potentiostatic potentiostatic coulometrycoulometry

amperostatic amperostatic coulometrycoulometry

6. Voltammetry6. Voltammetry

Voltammetry is an electrochemical method in which we measure current as a function of the applied potential.

Mercury electrodes: (a) hanging mercury drop electrode; (b) dropping mercury

electrode; (c) static mercury drop electrode.

hanging mercury drophanging mercury drop electrode is an electrode in which a electrode is an electrode in which a drop of Hg is suspended from a capillary tube.drop of Hg is suspended from a capillary tube.

dropping mercury electrodedropping mercury electrode is an electrode in which successive is an electrode in which successive drops of Hg form at the end of a capillary tube as a result of drops of Hg form at the end of a capillary tube as a result of gravity, with each drop providing a fresh electrode surface.gravity, with each drop providing a fresh electrode surface.

static mercury drop electrodestatic mercury drop electrode is an electrode in which is an electrode in which successive drops of Hg form at the end of a capillary tube as successive drops of Hg form at the end of a capillary tube as the result of a mechanical plunger, with each drop providing the result of a mechanical plunger, with each drop providing a fresh electrode surface.a fresh electrode surface.

Advantages of dropping mercury Advantages of dropping mercury electrode:electrode:

The surface is constantly updated.The surface is constantly updated. Range of used potentials from -2.5 V to +0,2 VRange of used potentials from -2.5 V to +0,2 V The electrode area is small, and currents big, so The electrode area is small, and currents big, so

that potential of a mercury dropping electrode that potential of a mercury dropping electrode differs from the equilibrium potential necessary differs from the equilibrium potential necessary for carrying out of electrochemical reaction. This for carrying out of electrochemical reaction. This phenomenon is called as electrode polarisation, phenomenon is called as electrode polarisation, and from it there was a name and from it there was a name polarographypolarography..

reference electrodesreference electrodes: mercury bottom or : mercury bottom or may be silver-chloride and calomel may be silver-chloride and calomel

21Е - the individual characteristic of substance. It is used for qualitative analysis in polarography.

On halfwave potential influence:On halfwave potential influence:

The nature of defined substance - The nature of defined substance - depolarizer;depolarizer;

The nature of indifferent electrolyte -The nature of indifferent electrolyte -depolarizer;depolarizer;

рНрН of medium; of medium; Presence of ions or molecules which can Presence of ions or molecules which can

form with form with depolarizerdepolarizer complex. complex.

Electrode potential Electrode potential ЕЕ in range of in range of polarographic waves is connected with polarographic waves is connected with halfwave potential halfwave potential ЕЕ1/21/2 and value of the and value of the measured current measured current I I and and IIdd current which is current which is called as the equation of polarographic called as the equation of polarographic waves:waves:

wwhere nhere n - - numbernumber of electronsof electrons::

ZnZn22++ + 2 + 2e e →→ Zn Zn ( (HgHg). ). nn = 2. = 2.

II

Ilg

n

059.0EE

d2/1

or

Methods of quantitative analysisMethods of quantitative analysis

Method of calibrationMethod of calibration chartchart Method of additivesMethod of additives

;C

h

C

h

X

X

h

hCC X

X

Comparison methodComparison method

;C

C

h

h

ст

X

ст

X ст

XстX h

hCC

Theoretically on Ilkovich equation.

I = 607 nD1/2m2/3t1/6 × CСХ = I / (607 nD1/2m2/3t1/6)

Amperometric titrationAmperometric titration Amperometric titration refers to a class of titrations in Amperometric titration refers to a class of titrations in

which the equivalence point is determined through which the equivalence point is determined through measurement of the electric current produced by the measurement of the electric current produced by the titration reaction. It is a form of quantitative analysistitration reaction. It is a form of quantitative analysis

Types of reactions:Types of reactions: PrecipitPrecipitation;ation; ComlexingComlexing;; The oxidation-reductionThe oxidation-reduction

Indicating electrodesIndicating electrodes

The platinum;The platinum; The graphite;The graphite; Other firm electrodes;Other firm electrodes; Mercury dropping electrode.Mercury dropping electrode.

Titration curves Titration curves I

I

I

V

V

V

On a current of defined substance

On a titrant current

on a product current

Application:Application:

amperometry is used for definition cations amperometry is used for definition cations and anions, organic substances.and anions, organic substances.

It is applied to substance mix titration at a It is applied to substance mix titration at a combination of titration conditions.combination of titration conditions.

Titration of the diluted solutions of 10Titration of the diluted solutions of 10 -5-5 mol/L and less.mol/L and less.

Titration of very painted and muddy Titration of very painted and muddy solutions. solutions.

Thanks for your attention!