Principles of Titration and errorsPrinciples of Titration and errors

By Dr. A. AmsavelBy Dr. A. Amsavel

IntroductionIntroduction

Volumetric analysis Volumetric analysis Simple and easy Simple and easy Fast and can be done on siteFast and can be done on site Less expensive Less expensive Estimation of content or Assay Estimation of content or Assay Precise and accurate Precise and accurate

Depends on method and specificityDepends on method and specificity

Requirements of a Titration ReactionRequirements of a Titration Reaction

Reaction must complete by 99.9 % Reaction must complete by 99.9 % so that < 0.1 % (or 1 ppt) remains unreactedso that < 0.1 % (or 1 ppt) remains unreacted

Rxn must be rapidRxn must be rapidTitration needs to be performed in a Titration needs to be performed in a reasonable time periodreasonable time period

The stoichiometry must be well defined, and The stoichiometry must be well defined, and knownknownIt can be predicted from equilibrium constantsIt can be predicted from equilibrium constantsA method must be available to determine the A method must be available to determine the equivalence pointequivalence point

Types of TitrationTypes of Titration

1) Precipitation1) Precipitation

– – A(aq) + B(aq) = AB(s)A(aq) + B(aq) = AB(s)

2) Acid-Base rxn2) Acid-Base rxn

– – H+ + OH¯ = H2O (strong acids or bases)H+ + OH¯ = H2O (strong acids or bases)

– – HA + OH¯ = H2O + A¯ (weak acids)HA + OH¯ = H2O + A¯ (weak acids)

– – A¯ + H+ = H2O + HA (weak bases)A¯ + H+ = H2O + HA (weak bases)

3) Complexation rxn3) Complexation rxn

– – Zn2+ + 4NH3 = Zn(NH3)42+Zn2+ + 4NH3 = Zn(NH3)42+

4) Redox rxn (oxidation-reduction)4) Redox rxn (oxidation-reduction)

– – Fe2+ + Ce4+ = Fe3+ + Ce3+Fe2+ + Ce4+ = Fe3+ + Ce3+

StandardsStandards• • Measurements are made with reference to standardsMeasurements are made with reference to standards

– – The accuracy of a result is only as good as the quality The accuracy of a result is only as good as the quality and accuracy of the standards usedand accuracy of the standards used

– – A standard is a reference material whose purity and A standard is a reference material whose purity and composition are well known and well definedcomposition are well known and well defined

• • Primary StandardsPrimary Standards

– – Used as titrants or used to standardize titrantsUsed as titrants or used to standardize titrants

– – RequirementsRequirements• • Usually solid to make it easier to weighUsually solid to make it easier to weigh

• • Easy to obtain, purify and store, and easy to dryEasy to obtain, purify and store, and easy to dry

• • Inert in the atmosphereInert in the atmosphere

• • High formula weight so that it can be weighed with high precisionHigh formula weight so that it can be weighed with high precision

Endpoint DetectionEndpoint DetectionIt is critical, to know the completion of reaction / It is critical, to know the completion of reaction /

determinationdetermination

1) 1) Visual indicators:Visual indicators:• • Observe a colour change or precipitation at the endpoint.Observe a colour change or precipitation at the endpoint.

– – Rxn progress checked by addition of external or self indicator Rxn progress checked by addition of external or self indicator

2) 2) Photometry:Photometry:

• • Use an instrument to follow the colour change or Use an instrument to follow the colour change or precipitationprecipitation

3) 3) Electrochemistry:Electrochemistry:• • Potentiometry - measure voltage change ( pH electrode)Potentiometry - measure voltage change ( pH electrode)

• • Amperometry - measure change in current between electrodes inAmperometry - measure change in current between electrodes in

solutionsolution

• • Conductance – measure conductivity changes of solution Conductance – measure conductivity changes of solution

Later two used for coloured, turbid, end point accurateLater two used for coloured, turbid, end point accurate

Acid-base titrationAcid-base titration

Neutralization titrationNeutralization titration Neutralization IndicatorsNeutralization Indicators Indicators & mixed indicatorsIndicators & mixed indicators Neutralization curveNeutralization curve Non-aqueous titrationNon-aqueous titration

Acids & BasesAcids & BasesAcids:Acids:

Arrhenius acid:Arrhenius acid: Any substance that, when Any substance that, when dissolved in water, increases the dissolved in water, increases the concentration of hydronium ion (Hconcentration of hydronium ion (H33OO++))

Bronsted-Lowry acid:Bronsted-Lowry acid: A proton donor A proton donorconjugate baseconjugate base

Lewis acid:Lewis acid: An electron acceptor An electron acceptor

Bases:Bases: Arrhenius base:Arrhenius base: Any substance that, when Any substance that, when

dissolved in water, increases the dissolved in water, increases the concentration of hydroxide ion (OHconcentration of hydroxide ion (OH--))

Bronsted-Lowery base:Bronsted-Lowery base: A proton acceptor A proton acceptorconjugate acidconjugate acid

Lewis acid:Lewis acid: An electron donor An electron donor

Brønsted-Lowry Theory of Acids & BasesThe conjugate acid of a base is the base plus the attached proton and the conjugate base of an acid is the acid minus the proton

p. 507

p. 506

Lewis Theory of Acids & Bases

pH calculationpH calculationQ1: Calculate the pH of a solution if [H+] = 2.7 x 10-4 M

pH = -log[H+] pH = -log(2.7 x 10-4) = 3.57

Q2: Find the hydrogen ion concentration of a solution if its pH is 11.62.

[H+] = 10-pH [H+] = 10-11.62 = 2.4 x 10-12M

Q3: Find the pOH and the pH of a solution if its hydroxide ion concentration is 7.9 x 10-5M

pOH = -log[OH-] pOH = -log(7.9 x 10-5) = 4.10

pH + pOH = 14 pH = 14 - 4.10 pH = 9.9

A solution with a pH of 1 has [HA solution with a pH of 1 has [H++] of 0.1 mol/L or 10] of 0.1 mol/L or 10-1-1

A solution with a pH of 3 has [HA solution with a pH of 3 has [H++] of 0.001 mol/L or 10] of 0.001 mol/L or 10-3-3

pH of solutionspH of solutions

Stomach juice: pH = 1.0 – 3.0 Human blood: pH = 7.3 – 7.5

Lemon juice: pH = 2.2 – 2.4 Seawater: pH = 7.8 – 8.3

Vinegar: pH = 2.4 – 3.4 Ammonia: pH = 10.5 – 11.5

Carbonated drinks: pH = 2.0 – 4.0 0.1M Na2CO3: pH = 11.7

Orange juice: pH = 3.0 – 4.0 1.0M NaOH: pH = 14.0

ENDPOINT = POINT OF NEUTRALIZATION = ENDPOINT = POINT OF NEUTRALIZATION = EQUIVALENCE POINTEQUIVALENCE POINT

MOLES OF ACID = MOLES OF BASEMOLES OF ACID = MOLES OF BASE

KKaa and and KKbb

The equilibrium constant for a BrThe equilibrium constant for a Brønsted acid is ønsted acid is represented by represented by KKaa, and base is represented by , and base is represented by KKbb..

CH3COOH(aq) + H2O(l) H3O+(aq) + CH3COO–(aq)

[H3O+][CH3COO–]Ka = ––––––––––––––––– [CH3COOH]

[NH4+][OH–]

Kb = ––––––––––––– [NH3]

NH3(aq) + H2O(l) NH4+(aq) + OH–(aq)

Notice that H2O is not included in either

equilibrium expression.

pH of 1M AcoH =2.4

Titration curve: Titration curve: HCl Vs NaOH solutionHCl Vs NaOH solution

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Series1 Series2

NaOH 1 M Sol 0.1M sol

Vol ml pH pH

0.0 0.0 1.0

50.0 0.5 1.5

75.0 0.8 1.8

90.0 1.3 2.3

98.0 2.0 3.0

99.0 2.3 3.3

99.5 2.6 3.6

99.8 3.0 4.0

99.9 3.3 4.3

100.0 7.0 7.0

100.1 10.7 9.7100.2 11.0 10.0

100.5 11.4 10.4

101.0 11.7 10.7

102.0 12.0 11.0

110.0 12.7 11.7

150.0 13.3 12.3

Titration curveTitration curve

NaOH 1 M Sol 0.1M sol

Vol ml pH pH

98.0 2.0 3.0

99.0 2.3 3.3

99.5 2.6 3.6

99.8 3.0 4.0

99.9 3.3 4.3

100.0 7.0 7.0

100.1 10.7 9.7

100.2 11.0 10.0

100.5 11.4 10.4

101.0 11.7 10.7

102.0 12.0 11.0

Titration Curve: Strong Acid with Strong BaseTitration Curve: Strong Acid with Strong Base

Bromphenol blue, bromthymol blue, and

phenolphthalein all change color at very

nearly 20.0 mL

At about what volume would we see a color

change if we used methyl violet as the indicator?

At the equivalence point in an acid–base titration, the acid and base have been brought together in precise stoichiometric proportions.(Endpoint)

Titration Curve: Weak Acid with Strong BaseTitration Curve: Weak Acid with Strong Base

The equivalence-point pH is NOT 7.00 here.

Why not??

Bromphenol blue was ok for the strong acid/strong

base titration, but it changes color far too early

to be useful here.

Acid–Base IndicatorsAcid–Base Indicators

An acid–base An acid–base indicatorindicator is a weak acid or is a weak acid or base.base.

The acid form (HA) of the indicator has one The acid form (HA) of the indicator has one color, the conjugate base (Acolor, the conjugate base (A––) has a different ) has a different color. One of the “colors” may be colorless.color. One of the “colors” may be colorless.

In an acidic solution, [HIn an acidic solution, [H33OO++] is high. Because ] is high. Because HH33OO++ is a common ion, it suppresses the is a common ion, it suppresses the ionization of the indicator acid, and we see ionization of the indicator acid, and we see the color of HA.the color of HA.

In a basic solution, [OHIn a basic solution, [OH––] is high, and it reacts ] is high, and it reacts with HA, forming the color of Awith HA, forming the color of A––..

Function of IndicatorsFunction of IndicatorsExample: phenolphthaleinExample: phenolphthalein

Near pH 8, Indicator dissociates and gives red base Near pH 8, Indicator dissociates and gives red base Human eye can detect it as a pink tinge at that pH Human eye can detect it as a pink tinge at that pH

Indicators must be carefully chosen so that their Indicators must be carefully chosen so that their colour changes take place at the pH values expected colour changes take place at the pH values expected for an aqueous solution of the salt produced in the for an aqueous solution of the salt produced in the titration.titration.

Basis of Indicator selectionBasis of Indicator selection

Indicator colour change, from acid to alkali

pKind pH

range example of titration use

Methyl orange, (red ==> yellow) 3.7 3.1-4.4 weak base - strong acid titration e.g. ammonia titrated with hydrochloric acid

Bromophenol blue, (yellow ==> blue)

4.0 2.8-4.6 weak base - strong acid titration

Methyl red, (red ==> yellow) 5.1 4.2-6.3 weak base - strong acid titration

Bromothymol blue, (yellow ==> blue) 7.0 6.0-7.6

strong acid - strong base titration e.g. hydrochloric acid <=> sodium hydroxide titration

Phenol red, (yellow ==> red) 7.9 6.8-8.4 strong acid - strong base titration e.g. hydrochloric acid <=> sodium hydroxide titration

Thymol blue (base form), (yellow ==> blue)

8.9 8.0-9.6 weak/strong acid - strong base titration

Phenolphthalein, (colourless ==> pinky-red) 9.3

8.3-10.0

weak acid - strong base titration e.g. ethanoic acid titrated with sodium hydroxide

Colours of indicator at different pHColours of indicator at different pH

Indicators: Color changes against pH Indicators: Color changes against pH

Non-Aqueous TitrationNon-Aqueous Titration

Theory is same as acid-Base titrationTheory is same as acid-Base titration Reaction carry out in non-aqueous mediumReaction carry out in non-aqueous medium Applied whereApplied where

Material which are not soluble in waterMaterial which are not soluble in water Week acid and bases are titratedWeek acid and bases are titrated Poor end point in water medium Poor end point in water medium

Principle based on Principle based on Brønsted-Lowry Theory

Brønsted-Lowry Theory The conjugate acid of a base is the base plus the attached proton and the conjugate base of an acid is the acid minus the proton

p. 507

Solvents used in NATSolvents used in NAT

Solvents used can be classified as four types:Solvents used can be classified as four types: Aprotic solvents:Aprotic solvents: Chemically neutral Chemically neutral

Eg. Toluene, carbon tetrachlorideEg. Toluene, carbon tetrachloride

Protogenic solvents:Protogenic solvents: Acidic nature readily donate Acidic nature readily donate protons, protons,

Eg. Anhyd. HF, H2SO4Eg. Anhyd. HF, H2SO4

Amphiprotic solvent:Amphiprotic solvent: Which are sly ionize and donate Which are sly ionize and donate and accept protons, and accept protons,

Eg Alcohols, weak organic acids. Eg Alcohols, weak organic acids. Acetic acid makes weak acid into storing base Acetic acid makes weak acid into storing base

Protophilc solvents:Protophilc solvents: Posses high affinity for protons. Posses high affinity for protons. Eg. Liq ammonia, Amine, KetonesEg. Liq ammonia, Amine, Ketones Increases the acidic strength Increases the acidic strength

Selection of SolventsSelection of Solvents for NATfor NAT

Acetic acid used for titration of weak bases, Acetic acid used for titration of weak bases, Nitrogen containing compounds Nitrogen containing compounds

Acetonitrile / with ACOH: Metal ethanoates Acetonitrile / with ACOH: Metal ethanoates

Alcohols (IPA, nBA) : Soaps and salts of Alcohols (IPA, nBA) : Soaps and salts of organic acids, organic acids,

DMF: Benzoic acid, amides etcDMF: Benzoic acid, amides etc

Titrants for NATTitrants for NAT

Perchloric acid in acetic acidPerchloric acid in acetic acid Amines, amine salts, amino acids, salts of Amines, amine salts, amino acids, salts of

acidsacids

Potassium Methoxide in Toluene-MethanolPotassium Methoxide in Toluene-Methanol Quan ammonium hydroxide in Acetonitrile- Quan ammonium hydroxide in Acetonitrile-

pyridine pyridine Acids, enols, imides & sulphonamidesAcids, enols, imides & sulphonamides

Indicators for NATIndicators for NAT

Principle is similar to acid base titrationPrinciple is similar to acid base titration

Indicators:Indicators: Crystal violet, Methyl red, Thymol blue, & Crystal violet, Methyl red, Thymol blue, &

1-Naphthaol benzein1-Naphthaol benzein

CalculationCalculationo Normality: Eq.wt/1000ml or meq/mLNormality: Eq.wt/1000ml or meq/mLo Morality: Mole/1000mlMorality: Mole/1000mlo V1 N1 = V2N2V1 N1 = V2N2o N1 = V2N2/V1N1 = V2N2/V1

Normality = Wt of sample x 1000 / Eq. Wt x V Normality = Wt of sample x 1000 / Eq. Wt x V

Wt of sample (mg) = V x N x Eq. wtWt of sample (mg) = V x N x Eq. wt

Assay = Qty estimated in sample x 100/ wt of sampleAssay = Qty estimated in sample x 100/ wt of sample

Assay = V x N x Eq. wt x 100/ wt of sample x 1000Assay = V x N x Eq. wt x 100/ wt of sample x 1000

1 ml of 1N HCl = 0.04g of NaOH (40/1000)1 ml of 1N HCl = 0.04g of NaOH (40/1000) 1 ml of 0.1N HCl = 0.004g of NaOH1 ml of 0.1N HCl = 0.004g of NaOH

Titration ErrorTitration Error

Error in methods:Error in methods:

The endpoint method may not show a change The endpoint method may not show a change exactly at the equivalence point due to the exactly at the equivalence point due to the reactions involvedreactions involved

Titration Error = Vol at endpoint - Vol at Titration Error = Vol at endpoint - Vol at equivalence pointequivalence point

• • Negative error & Positive error means endpoint is Negative error & Positive error means endpoint is early - before equiv point or late after equiv pointearly - before equiv point or late after equiv point

Errors in Volume and weight: Errors in Volume and weight: 10 ml titre volume = 100 %10 ml titre volume = 100 %

If difference is 0.1ml error is 1%; 0.2ml = 2% If difference is 0.1ml error is 1%; 0.2ml = 2% 5ml titre volume = 100 %5ml titre volume = 100 %

0.1ml = 2% error0.1ml = 2% error Optimum level is about 25mlOptimum level is about 25ml 25 ml titre volume = 100 %25 ml titre volume = 100 %

0.1ml = 0.4% error0.1ml = 0.4% error

Volumetric apparatusVolumetric apparatus

USP:USP: Burette selection:Burette selection:

NLT 30% nominal volume (15ml in 50ml burette)NLT 30% nominal volume (15ml in 50ml burette) Micro burette for < 10ml Micro burette for < 10ml

Limit of error: Limit of error: Volumetric flask: 25ml, 50ml, 100ml is 0.03, 0.05& Volumetric flask: 25ml, 50ml, 100ml is 0.03, 0.05&

0.08ml0.08ml Pipets:5, 10, 25 ml is 0.01, 0.02 &0.03mlPipets:5, 10, 25 ml is 0.01, 0.02 &0.03ml Burets:10, 25, 50ml is 0.02, 0.1&0.1mlBurets:10, 25, 50ml is 0.02, 0.1&0.1ml

Tips: out flow NMT 500uL per secondTips: out flow NMT 500uL per second

Operational & personal errorOperational & personal error

List several of the variables involved in correctly using a List several of the variables involved in correctly using a 10mL volumetric pipette.10mL volumetric pipette.

drain time; drain time; possible beads on the inner surface possible beads on the inner surface temperature; temperature; bringing meniscus to the proper level;bringing meniscus to the proper level; angle of drain; angle of drain; touching off last drop; touching off last drop; rinsing of the pipet with the solution used; rinsing of the pipet with the solution used; Pipet calibration; etc.Pipet calibration; etc.

Error in weighing can occur.Error in weighing can occur.

• • Misreading of the balance,Misreading of the balance,• • Balance not level,Balance not level,• • Not cleaning the surface of the balance first,Not cleaning the surface of the balance first,• • Touching the weighed object with moist hands,Touching the weighed object with moist hands,• • Leaving the balance doors open during weighing,Leaving the balance doors open during weighing,• • Using a miscalibrated balance,Using a miscalibrated balance,• • Not cooling the sample down to near room temperature,Not cooling the sample down to near room temperature,• • Not removing a static charge from the sample,Not removing a static charge from the sample,• • Excess vibration or air currents from people or nearby Excess vibration or air currents from people or nearby

equipment, andequipment, and• • Prolonged time sample left on pan adds/loses moisture.Prolonged time sample left on pan adds/loses moisture.

Possible contaminationPossible contamination

An analyst couldAn analyst could contaminate a sample during weighing by placing a contaminate a sample during weighing by placing a

contaminated spatulacontaminated spatula placing the sample on or into a contaminated holder placing the sample on or into a contaminated holder

during weighing, during weighing, dropping some lint/hair/skin or sneeze into the sample dropping some lint/hair/skin or sneeze into the sample

while weighing, while weighing, opening up a bottle of chemicals near the sample being opening up a bottle of chemicals near the sample being

weighed. weighed. When performing trace analysis, it is possible for just a When performing trace analysis, it is possible for just a

microgram even massive fingerprint!microgram even massive fingerprint!

Units of measurementUnits of measurementName Defining Units

Molarity (e.g. 0.1200 M)

moles of solute/liter (solutions), or millimoles/milliliter (solutions)

Percent (e.g. 23.45 %)

(grams of substance/grams of sample) x 100%, or centigrams/gram (seldom used)

Parts per million (e.g 2.34 ppm, 2.34 mg/L)

milligrams/liter (solutions), or micrograms/milliliter (solutions) milligrams/kilogram (solids), or micrograms/gram (solids)

Parts per billion (e.g. 0.45 ppb, 0.45 ug/L)

micrograms/liter (solutions), or nanograms/gram (solids)

Oxidation- reduction titrationOxidation- reduction titration

Oxidation-reduction reactionOxidation-reduction reaction Reduction potential is calculated byReduction potential is calculated by

Nernst equation Nernst equation • E1= E’ + 0.591/n log (ox)/(red)E1= E’ + 0.591/n log (ox)/(red)• E=(E1+E2)/2E=(E1+E2)/2

Equivalence point by redox potential Vs Equivalence point by redox potential Vs Volume Volume

Indicator selection Indicator selection

Precipitation titrationPrecipitation titration

Reagents used id based on Solubility Reagents used id based on Solubility products of precipitateproducts of precipitate

Titration curve: Titration curve: -log Conc. Of ion Vs Volume-log Conc. Of ion Vs Volume

Concentration of ions Concentration of ions Eg. Ksol(Agcl) = Ag + Cl Eg. Ksol(Agcl) = Ag + Cl

Indicator:Indicator: Formation of coloured compound (ppt/complex)Formation of coloured compound (ppt/complex) Adsorption indicatorsAdsorption indicators

Complexation titrationComplexation titration

M + EDTA M(EDTA) M + EDTA M(EDTA) Complex formation depend on Stability Complex formation depend on Stability

constant, pH, constant, pH, titration curve pM Vs, Vol of EDTAtitration curve pM Vs, Vol of EDTA Indicators (Metal / metal ion indicators):Indicators (Metal / metal ion indicators):

M-ln + EDTA M(EDTA) + InM-ln + EDTA M(EDTA) + In

Types of Complexation titration Types of Complexation titration

Back titrationBack titration MaskingMasking Selective de-maskingSelective de-masking Separation by ppt and solvent extractionSeparation by ppt and solvent extraction

Application, almost metals, Application, almost metals,

An Equation for Buffer An Equation for Buffer SolutionsSolutions

In certain applications, there is a need to repeat the In certain applications, there is a need to repeat the calculations of the pH of buffer solutions many times. calculations of the pH of buffer solutions many times. This can be done with a single, simple equation, but This can be done with a single, simple equation, but there are some limitations.there are some limitations.

The The Henderson–Hasselbalch equationHenderson–Hasselbalch equation::

• To use this equation, the ratio [conjugate base]/[weak acid] must have a value between 0.10–10 and both concentrations must exceed Ka by a factor of 100 or more.

[conjugate base]pH = pKa + log –––––––––––––– [weak acid]

The Common Ion EffectThe Common Ion Effect Consider a solution of acetic acid.Consider a solution of acetic acid. If we add acetate ion as a second solute (i.e., sodium If we add acetate ion as a second solute (i.e., sodium

acetate), the pH of the solution acetate), the pH of the solution increasesincreases::

LeChâtelier’s principle: What happens to [H3O+] when the

equilibrium shifts to the left?