Question

A solution of 0.0470 M HCl is used to titrate 26.0 mL of an ammonia solution of unknown concentration. The equivalence point is reached when 16.0 mL HCl solution have been added. (Assume KW = 1.01 e−14.)
What was the pH at the equivalence point?

Answer 1

The pH at equivalence point is 12.46

At equivalence point, number of moles of acid, n equals number of moles of base, n'

So, n = n'

CV = C'V' where

• C = concentration of acid (HCl) = 0.0470 M,
• V = volume of acid = 16.0 mL,
• C' = concentration of base (ammonia solution) and
• V' = volume of base = 26.0 mL.

Concentration of ammonia solution

Making C' subject of the formula, we have

C' = CV/V'

Substituting the values of the variables into the equation, we have

C' = CV/V'

C' = 0.0470 M × 16.0 mL/26.0 mL

C' = 0.752 MmL/26.0 mL

C' = 0.0289 M

The concentration of acid at equivalence point

We know that the ion-product of water Kw is

Kw = [H⁺][OH⁻] =  where

• [H⁺] = concentration of HCl at equivalence point,
• [OH⁻] = C' = concentration of ammonia solution = 0.0289 M and
• Kw = 1.01 × 10⁻¹⁴

Making [H⁺] subject of the formula, we have

[H⁺} = Kw/[OH⁻]

[H⁺] = 1.01 × 10⁻¹⁴/0.0289

[H⁺] = 34.95 × 10⁻¹⁴

[H⁺] = 3.495 × 10⁻¹³

pH at equivalence point

Since pH = -㏒[H⁺]

pH = -㏒[3.495 × 10⁻¹³]

pH = -㏒[3.495] + (-㏒10⁻¹³)

pH = -㏒[3.495] + [-13(-㏒10)]

pH = 13 - 0.5434

pH = 12.4566

pH ≅ 12.46

So, the pH at equivalence point is 12.46

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