The titration of 0.100 M acetic acid with 0.100 M NaOH is described in the text. What is the pH of the solution when 35.0 mL of the base has been added to 100.0 mL of 0.100 M acetic acid?

Interpretation:

The value of pH has to be calculated when 100 mL,CH3COOH(0.100 mol⋅L−1) is titrated with 35 mL, NaOH(0.100 mol⋅L−1).

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base. There are four types of acid-base titrations.

(1) Strong acid-Strong base, in this type of titration a strong acid is titrated against a strong base for example, HCl is titrated against NaOH.

(2) Strong acid-Weak base, in this type of titration a strong acid is titrated against a weak base for example, HCl is titrated against NH4OH.

(3) Weak acid-Strong base, in this type of titration a weak acid is titrated against a strong base for example, CH3COOH is titrated against NaOH.

(4) Weak acid-Weak base, in this type of titration a weak acid is titrated against a weak base for example, CH3COOH is titrated against NH4OH.

For weak acid-strong base titration the pH value can be calculated at various points before and after equivalence point. The equilibrium established during the titration of CH3COOH with NaOH. The equilibrium can be represented as,

  CH3COOH(aq)+NaOH(aq)⇌H2O(l)+CH3COONa(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using the Ka and its relation with H3O+ ion concentration.

Ka=[H3O+](eq)[A−](eq)[HA](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of NaOH is done there will be formation of buffer solution CH3COOH/CH3COO−. The pH calculation for buffer solution is done by using Henderson-Hesselbalch equation.

pH=pKa+log[conjugate base][acid] (2)

At the midpoint of the titration, when concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugate base][acid]

Substitute, [conjugate base] for[acid].

pH=pKa+log[conjugate base][conjugate base]=pKa+log(1)=pKa+0=pKa

Therefore, pH value at midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point all the acid will be neutralized, and there will be only OH− ion and CH3COO−. The OH− will be produced due to the hydrolysis of acetate ion at equivalence point. The hydrolysis equilibrium is represented as,

CH3COO−(aq)+H2O(l)⇌OH−(aq)+CH3COOH(aq)

By using the value of Kb for the acetate ion, concentration of  OH− can be calculated.  Thus the value of pH is greater than 7 at equivalence point for the weak acid- strong base titrations.

The relation between Ka and Kb for weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

(4) The pH calculation after the equivalence point.

After the equivalence point there will be excess of OH− ion in the solution and there will be very less amount of CH3COO− ion. The amount of CH3COO− produce can be neglected with respect to excess amount of OH−. Concentration of OH− after equivalence point will be calculated by using the expression,

concentration=number of molestotal volume of solution (4)

The pH calculation before equivalence point is done by using Henderson-Hasselbalch equation.

Given:

Refer to table 16.2 in the textbook for the value of Ka.

The value of Ka for acetic acid is 1.8×10−5.

The value of Kw for water is 1.0×10−14.

The pKa value is calculated as follows;

pKa=−log(Ka)

Substitute, 1.8×10−5 for Ka.

pKa=−log(1.8×10−5)=4.74

Therefore, pKa values is 4.74.

The initial concentration of CH3COOH is 0.100 mol⋅L−1.

The initial concentration of NaOH is 0.100 mol⋅L−1.

The volume of CH3COOH is 100 mL.

Conversion of 100 mL into L.

(100 mL)(1 L1000 mL)=0.1 L

The volume of NaOH added 35 mL.

Conversion of 35 mL into L.

(35 mL)(1 L1000 mL)=0.035 L

The total volume after the reaction is calculated as,

total volume=volume of CH3COOH(L) + volume of NaOH(L)

total volume = 0.1(L)+0.035(L)=0.135 L

Therefore, total volume after reaction is 0.135 L.

The calculation of moles is done by using the expression,

Number of moles=concentration(mol⋅L−1)⋅volume(L)

The ICE table (1) for the reaction between NaOH and CH3COOH is given below,

EquationCH3COOH(aq)+NaOH(aq)⇌H2O(l)+CH3COONa(aq)Initial(mol)0.01000.00350Change(mol)−0