CHAPTER

4
Acid Base Titration
 Syllabus
Topics to be Covered
1. ∙ Standard solutions.
2. ∙ Types of titration curves, concentration changes during
titration,
3. calculation of pH of strong and weak acids and bases,
titration of strong acid-strong base, weak acid-strong base
4. ∙ Feasibility of titration.
5 Acid-base indicators, indicator choice,
6. ∙ indicator error, common types of acid- base indicators.
7. ∙ Application of acid-base titration.
•.
 Acids and Bases:
• Arrhenius: 1887, In water acid dissociates into hydrogen ion and
anions, and bases dissociate into hydroxide ion and cations.
Acid: HX H+ + X- (HCl, HClO4, HNO3)
Base: BOH
• Bronsted theory: 1923, OH -
+ B +
(NaOH, KOH, BaOH)
• Acid: proton donor. NH4+ (cationic), HCl (neutral), HSO4- (anionic)
• Bases: proton acceptor, Proton deficient species.
• HOAc + H 2O H3O+ + OAc-
Acid 1 Base 2 Acid 2 Base 1
• Many solvents (S) (like water) can act as proton donor and proton acceptor.
HB + S HS+ + B (S may be; H2O, MeOH, EtOH, CH3COOH, H2SO4 etc.)
• If an acid give up a proton, the resulting species is termed as conjugate base
of the acid. Similarly, every base when it accept a proton forms an acid
called as conjugate acid of the base.
• The extent of overall reaction depends on the tendency of an acid to donate
proton and a base to accept proton;
Lewis theory: 1923,
• Acid: Electron pair acceptor
• Bases: Electron pair donor

• Amphiprotic species: Species having both acidic and basic

characteristics (for e.g. dihydrogen phosphate ion, H2PO4-).
• Amphoteric/Amphiprotic solvents: ,, ,, ,,
(H2O, MeOH, EtOH, Acetic acid)
• Amphiprotic solvents undergo self ionization or auto
protolysis:
- 2H2O H3O+ + OH-
- 2EtOH EtOH2+ + OEt-
- 2HCOOH HCOOH 2+ + HCOO-
- 2NH3 NH4+ + NH2-
Strength of acids and bases:
• not only the intrinsic property of acid or base chosen.
• depends on the tendency of solvent to accept proton (basicity) or donate proton
(acidity).
e.g. perchloric acid and hydrochloric acids are strong acids in water, but if acetic
acid is chosen as the solvent HClO4 is more strong than HCl (by about 5000times).
• If HB is stronger acid than HS+(protonated solvent), it will transfer its proton to the
solvent,
• i.e. the equilibrium HB + S HS+ + B will shift right,
(i) If HB is slightly strong: just to the right,
(ii) If HB is very strong: almost to ward right (completely dissociated).
The leveling effect and leveling solvents:
• That is if basicity of solvent is high all acids are leveled (completely dissociated) and
if acidity of solvent is high all bases are leveled (completely dissociated).
NH3 + H2O NH4+ + OH-.
• Basic anhydrides like CaO are leveled in water: O2- + H2O 2OH-.
• Similarly, sulphates are leveled in anhydrous sulphuric acid: SO42- + H2SO4 2HSO4-
• Differentiating Solvents: Solvent in which different acids or bases has various
degree of dissociation.
For e.g. in acetic acid solvent: HCl, H2SO4 & HNO3 are differentiated
• Leveling Solvents: Solvent in which all acids/bases are completely dissociated and
thus possess same strength.
For e.g. in water as the solvent : HCl, H2SO4 & HNO3 are leveled, all are completely
dissociated.
• In reaction of leveled acids and base (neutralization reaction of strong acid and
strong base), one of solvent molecule acts as acid and the another as the base, and
neutralization reaction will be reverse of self dissociation or autoprotolysis reaction
of the solvent molecule.
‡ If water is solvent: H3O+ + OH- 2H2O
‡ If liquid ammonia is solvent: NH4+ + NH2- 2NH3
‡ If Glacial acetic acid is solvent: CH3COOH 2+ + CH3COO- 2HCOOH
‡ If Sulphuric acid is solvent: H3SO4+ + HSO4- 2H2SO4
‡ If Ethyl alcohol is solvent: EtOH2+ + OEt- 2EtOH
• If the acid or the base is not leveled, i.e. hydrolysis reaction will occur, for weak
acid, it is similar to dissociation of its conjugate base in the solvent,
- -
Titration Curves:
• Acid base titration curve is a plot of pH or pOH vs
volume of the titrant.
• It is useful
(a) in judging feasibility of titration and
(b) selection of the indicator.
Types of titration curves
• titration of strong acid and strong base
• titration of strong acids and weak bases
• titration of weak acid and strong base
Strong Acid -Strong Base titration: HCl vs NaOH
• H3O+ has two sources,. (i). Acid, (ii). Water (self dissociation.)

• Similar for OH-, (i). The Base (ii). Dissociation of water.

• Strong acid and base both are completely dissociated, thus low

concentration of H3O+ and OH-, from the water can be neglected.

• pH at various point is calculated directly, from the excess moles of acid or

the base.

• But at the equivalent point ????, pH is calculated from Kw (dissociation

constant of water), which is 10-14 at 250C.

• The acid base reaction can be written as,

H3O+ + OH- 2H2O,
with equilibrium constant K = 1/Kw = 1 × 1014
 Q. 50mL 0.100M HCl is treated with 0.100M NaOH, calculate the pH at the
start of titration and after the addition of 10.0, 50.0, and 60.0 mL of titrant
and plot the titration curve.
(b) Addition of 10Ml NaOH:
(a) Initial pH: • 10 mL NaOH contains 1 mmole NaOH, so reacts
• Since HCl is strong acid is with 1 mmole HCl. (The reaction is complete
completely dissociated, since, K = 1/Kw = 1 × 1014)
• [H3O+] = 0.1M, • [H3O+] = 4.00 mmole/60.0mL = 6.67 × 10-2M,
• pH = 1.00 • pH = 1.18 +

(c) At eq. Point: Addition of 50Ml NaOH:

• The reaction is complete, K = 1 × 1014
• Strong acid and bases are not
hydrolyzed. (d) Addition of 60Ml NaOH:
• The only source of H3O+ is • Extra 10 ml of NaOH i.e. 1 mmole
dissociation of water. NaOH is added. +

• [H3O+] = [OH-] = 10-7M, • [ OH-] = 1mmole/110mL

• pH = 7 + = 9.1 × 10-3M
• pOH = 2.04
• pH = 14.00 – 2.04 = 11.96
 • In the similar fashion the pH at different other missing points are calculated.
And a curve is plotted, which is shown in figure.

The summary features of the curves are:

• pH increases rapidly only around the equivalent point (addition of 0.10mL
base pH increases by about 6units, from about 4 to 10 )
• The large range easily span the range of all indicators (any indicator will
change colour with one or two drops at eq. pt.)
• Curve will be inverted if NaOH is to be titrated.
 Effect of concentration of reagent
and analyte:
In the case of strong acid base
titration,
• The magnitude of ΔpH at the
equivalent point depends on the acid base
concentration of analyte and titrant.
• decreasing the concentration of
analyte and titrant decreases the
ΔpH and so the indicator range.
Titration of weak acid and bases:
Weak acid and strong base:
• For weak acid and base, pH is calculated from the
concentration of solute (acid/base) and its dissociation
constant.
• After adding titrant pH of the buffer is calculated from
Henderson-Hasselbalch’s equation (depends on analytical
concentration of conjugate base and concentration of weak
acid)
• At equivalent point pH is calculated from Kb of conjugate base
of the weak acid.
• After eq. point pOH is calculated from excess moles of titrant
and is converted to pH.
• Q. 50mL of a 0.100M solution of weak acid HB (HB + OH- = B- + H2O)Ka
= 1X10-5 is titrated with 0.10M NaOH, Calculate pH before addition
and addition of 10, 50 & 60 mL of titrant.
(a) Initial pH: weak acid/partially dissociated,
• HB + H2O H3O+ + B- and, [H3O+] = [B-] and [HB] ≈ 0.1

gives, [H3O+] =1.0×10-3, pH = 3.00

(b) Addition of 10Ml NaOH:
• 10 mL 0.1M NaOH contains 1mmole NaOH
• from HB + H2O H3O+ + B-
[HB]= 4.00/60.0, [H3O+] ≈ ? [B-]= 1.0/60.0
• Hendersons equation

[H3O+] = 4X10-5M,
pH = 4.40
(c) At eq. Point:
• conjugate base of the acid get hydrolysed
B- + H2O HB + OH-,
[B-] = 5.00/100 – [OH-] ≈ 0.05M.
• [OH-] ≈ [HB ] ≈ small, (For weak base Kb = 10-9 )

• source of H3O+ is dissociation of water,

• [H3O+] = KW /[OH-] =
• pH = 8.85
(d) Addition of 60Ml NaOH:
• Extra mmole of NaOH = 10mL × 0.1 M = 1mmole.
• [ OH-] = 1mmole/110mL = 9.1 × 10-3M
• [H3O+] = KW /[OH-] =
• pH = 11.96
In the similar fashion the pH at different other missing points are calculated. And a curve is
plotted, which is shown in figure.

Features of the titration curve:

• For few drops of base: pH increases.
• After few drops: pH is almost constant.
(Buffered Zone)
• When acid is half is neutralized,
[HB] = [B-] so, pH = pKa
• At the eq. pt. pH Increases rapidly
• The vertical portion predicts the nature of suitable
indicator.
• Effect of concentration of reagent and analyte (weak acid vs strong base):
• Smaller the value of Ka, higher will be the pH at equivalent point
• Smaller will be the Ka, smaller will be the ΔpH at equivalent point.
• ΔpH at equivalent point is the measurement of reaction constant K

Analyte Titrant Error ΔpH

If amount increased keeping Increases the vol Small relative decrease
volume same. of titrant error in Vtitrant s
Keeping amount same if Same volume increase
Vol. is decreased s
▪ condition
Same increasing the amount (moles/concn) Increasing conc
titrated in the same of Large relative
initial increase
n volume decreases ΔpH, (more volume of titrant is
required).
titrant, Decreases error s
▪ but if same amount of HA is titrated with less volume ΔpH is increased.
the vol of titrant

• Closure the equivalence point pH is to 4 or 10, the smaller will be the value of ΔpH / ΔV. When pH at the
equivalent point falls below 4 or above 10, the magnitude of ΔpH / ΔV will not be very large. It is
doubtful that the titration will be considered feasible.
• In case if acid is too weak to be titrated, its conjugate base could be much strong, and could be titrated
with another strong acid. In such situation back titration will give the good analytical result.
(eg. HA, Ka =10-9 cannot be titrated with strong base, where is its salt A- , Kb = 10-5 can be titrated
feasibly with strong acid)
 • Acid base indicators: Are weak organic acids or bases whose conjugate pair
possess different colour (i.e. dissociated and un dissociated forms).

{Acid type indicator}: HIn + H2O In- + H3O

Acid colour Base colour

• {Base type indicator}: In + H 2O InH+ + OH-

Base colour Acid colour
Determination of the indicator range:
• If we consider the acid type indicator,
{Acid type indicator}: HIn + H2O In- + H3O
Acid colour Base colour

• Sensitivity of vision: [HIn]/[In-] > 10 (acid colour)

[HIn]/[In-] < 1/10 (base colour)

• [The indicator range for: methyl orange is 3.1-4.4, bromothymol blue

is 6.0-7.6 and phenolphthalein is 8.0-9.6]
Titration error/ Indicator error:
• pH of indicator colour change differs from the pH at the equivalent point of
the titration causes determinate error.
– minimized by the proper selection of the indicator
– blank correction/ indicator blank.
• If slope of the curve is not greater at the eq. pt, usual for very weak acid bases
in this case, the colour change of indicator is not sharp. Lack of ability to
discriminate slight change or intermediate colour of the indicator causes
indeterminate error. The uncertainty has the range ± 0.5 to ±1 pH,
– uncertainty can be reduced by the use of non aqueous solvents.
– Mixture of two indicators or an indicator and a dye can also be used. For example
modified methyl orange [methyl orange + dye xylene cyanole FF] is used for carbonate
titration. The dye absorbs some of wavelength of light that are transmitted by both
coloured forms thus cutting down on the overlapping of the two colours; at
intermediate pH methyl orange will have gray colour (complementary to the dye).
• Indicator choice/ Selection of proper indicator:
– In strong acid vs strong base titration, the choice can include all three kinds of
indicators.
– In weak acid vs strong base titration, : Phenolphthalein is the suitable indicator. (If acid
is very weak pKa =9, no indicator is available to detect the equivalent point with high
precision i.e. indicator will show the colour change only after addition of excess base.)
– In strong acid and the weak base titration :methyl orange is the best indicator.
Feasibility of acid base titration: (practical feasibility)
• Completion of reaction at the equivalent point
• Reaction should have large eq. constant.
– For strong acid strong base titration K = 1014, ΔpH at the equivalent
point is 5-6 for the volume of titrant ΔV = 0.1mL.
• Fast
• No side reaction
Q. How large the value of K to be for the titration to be feasible?
• It is difficult to give the univocal answer but,
• K can be calculated for 99.90% and 99.99% conversion of
analyte to product at equivalent point. i.e. required for the
desired feasibility.
• -pH should change by 1-2 units for visual indicator on addition
of 1 drop of base.
• We will go through an example: to illustrate the calculation of
Ka for weak acid and K for the reaction to be feasible.
• Q. 50mL of 0.10M HA is titrated with
0.1.M strong base
(a) Calculate minimum value of K, so that
when 49.95 mL titrant is added , the
reaction is essentially complete and pH
changes by two units for the addition of
two drops (0.1mL) of base.
(b) (b) Repaat calculation for ΔpH = 1unit.
(a) pH beyond the eq. point,
• Excess vol of base = 0.05mL

Condition near the eq. point:

If ΔpH = 1.00 then,

For feasibility of titration, K ≥ 2×109

Conclusion:
Depending on the condition the minimum
value of reaction constant K will be different.
Common acid base indicator:
Phenolphthalein
• It is diprotic acid.
• The structure is shown in
the figure.
• It is colerless, on loosing
two H+ gives red colour.
• The indicator range is 8.0-
9.6.
Methyl orange
• It is a weak base.
• The structure is shown in the
figure.
• It is yellow, on accepting H+ gives
pink colour.
• The indicator range is 3.1-4.4
A important and potential source of error in acid base titration (kept under application of A B titration)
CARBONATE ERROR:
a) NaOH contains the small amount of Sodium carbonate as the impurity.
b) NaOH solution readily absorbs CO2 from the atmosphere.
CO2 + 2OH- CO32- + H2O
• Carbonate ion combines with hydrogen ion in two steps
CO32- +H3O+ HCO3- + H2O (phenolphthalein)
HCO3- + H3O+ H2CO3 + H2O (methyl orange)
• Indicator: Phenolphthalein ⇒ Color change occurs in first step ⇒ gives error
– This error has high possibility in the titration of weak acid.
• Methylorange ⇒ Color change occurs in second step ⇒ No error
Methods to minimize carbonate error:
• Use of Ba(OH)2 as titrating reagent:
– The absorbed CO2 forms BaCO3 ppt. with Ba(OH)2
– Ba2+ + 2OH-+ CO2 BaCO32- (s) + H2O
– Limitation is: Ba(OH)2 has limited solubility in water. Solution with concentration > 0.05N cannot be
prepared.
• Preparation of Carbonate free NaOH:
– Concentrated (~ 50%) NaOH solution is prepared.
– Na2CO3 is insoluble in this solution. The precipitate is filtered.
– The solution is diluted and stored in a bottle capped with a tube containing solid sodalime or
Ascarite.
Application of acid base titration:
• Determination of substances that are either acidic or basic and otherwise if can be converted to
acid or base by chemical reaction.

– Dermination of Nitrogen: (amines, amides, nitriles, cyanates, isocyanates, nitro, notroso azo), protein
content in food
• Kjeldahl (1883) NH4+ + OH- NH3(g) + H2O
– Sulfur : Burning to SO2 or SO3, Finally completed to SO3 by oxidizing with H2O2 and converted into H2SO4 and
is titrated by base.
– Boron: Nickel bomb ⇒Boric acid. Boric acid is too weak to be titrated, addition of mannitol forms strong
acid can be titrated with strong base.
– Carbonate mixture: Carbonate ion is titrated in two steps:
CO32- +H3O+ HCO3- + H2O (phenolphthalein)
HCO3- + H3O+ H2CO3 + H2O (methyl orange)
The amount of Na2CO3 impurity in NaOH can be determined by this method.
– Organic functional group:
• Carboxylic acid (RCOOH, pKa about 4-6), and Sulphonic acids (RSO3H),
• Alcohol can be titrated, by addition of excess acetic anhydride
(CH3CO)2O + ROH CH3COOR + CH3COOH
• The excess anhydride is hydrolysed to acetic acid
(CH3CO)2O + H2O 2CH3COOH
• Aliphatic amines, CH3NH2 (pKb abve 5)are directly titrated.
• Aromatic amines like anline pKa =10, are too weak to be titrated in aqueous solution.
• Esters are determinby hydrolyzing with excess base, the excess base is titrated with acid.
- -
• Solvent system:
• Amphiprotic solvent: water,
– Neutral: methyl alcohol, ethyl alcohol, can behave as acid as well base
similar to the water.
– Acidic: acidic acid, formic acid, sulphuric acid
– Basic: liquid ammonia, ethylene diamine
• Aprotic/inert: Neither acidic nor basic, benzene,
carbontetrachloride, chloroform, possess low autoprotolysis
constant.
• Basic (not showing acidic properties: showing the strong affinity
only for the proton, but not exhibiting any acidic properties,
ether, pyridine,some of the ketones