Chemistry, Third edition

ACIDS AND BASES IN AQUEOUS SOLUTION 293

Calculations involving weak acids

(i)Calculate the percentage of HCN molecules ionized in a HCN solution of concentration
0.020 mol dm^3. What is the pH of the solution? (Use the data in Table 16.2.)

(ii)Benzoic acid is a natural bacteriostatic preservative, i.e. it helps prevent the growth of
bacteria. Some fruit contains 0.050% by mass of benzoic acid. Estimate the pH of 1.0 dm^3
of the solution produced from 4.0 kg of the fruit. (HintStart by calculating the concentration
of benzoic acid.)

Exercise 16F

Weak acid equilibria

(i)25.0 cm^3 of 0.10 mol dm^3 HCl requires 25.0 cm^3 of 0.10 mol dm^3 NaOH for
neutralization. Even though only 1.3% of ethanoic acid molecules are ionized at room
temperature, 25.0 cm^3 of 0.10 mol dm^3 CH 3 COOH also requires 25 cm^3 of 0.10 mol dm^3
NaOH for neutralization. Explain this.

(ii)The enthalpy change of neutralization (H—N^ ) is the standard enthalpy change whenone mol of
water is made in the neutralization of an acid by a base. Values are:

Acid–base pair H^ —N/kJ mol^1

HNO 3 –KOH 57.3

HCl–NaOH 57.1

CH 3 COOH–NaOH 55.2

Why are the values for the first two pairs approximately the same? Why is H^ —Nfor the

neutralization of ethanoic acid less negative than the others?

Exercise 16G

BOX 16.1

An expression to calculate the pH of a weak acid

We need the two following relationships to derive equation (16.5):

1.The equilibrium concentration of unionized ethanoic acid will be the difference between CA
and the equilibrium hydronium ion concentration:
[CH 3 COOH(aq)]CA[H 3 O(aq)] (16.6)

2.For every molecule of ethanoic acid that ionizes, one hydronium and one ethanoate ion is
produced. Thus,
[CH 3 COO(aq)][H 3 O(aq)] (16.7)

Using the equilibrium expression

Ka(T)

[CH 3 COO(aq)][H 3 O(aq)]

[CH 3 COOH(aq)]

and substituting the right-hand sides of equations (16.6) and (16.7) gives

Ka(T)

[H 3 O(aq)]^2

CA[H 3 O(aq)]

For acids that are only slightly ionized (5%) we are justified in assuming that CA[H 3 O(aq)]
is approximately equal to CA. We then obtain equation (16.5):

Ka(T)

[H 3 O(aq)]^2

CA