PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 387

whereKis the dissociation constant of the acid.
If the dissociation degree is low,α < 0 .1 in order, relation (11.91) can be simplified to

pH =−

1

2

log

(

K′c γ^2 ±

(cst)^2

)

. (11.93)

Example

Calculate the pH of a dichloroacetic acid solution in water of the concentrationc= 0. 01 mol dm−^3

at a temperature of 298.15 K and the standard pressure. Under the given conditions the disso-

ciation constant of the acid isK= 0.0514. Assume that all the activity coefficients are unity.

Compare the result with the value calculated from the simplified relation (11.93).

Solution

We calculateK′and the degree of dissociation from relation (11.92)

K′ =

0. 0514 × 1 × 1

12

= 0. 0514 ,

α =

− 0 .0514 +

√

0. 05142 + 4× 0. 0514 × 0. 01

2 × 0. 01

= 0. 857

and the pH value from (11.91)

pH=−

1

2

log (0. 0541 × 0 .01)−

1

2

log (1− 0 .857) = 2. 06.

If we used the simplified relation (11.93), we would obtain

pH=−

1

2

log (0. 0514 × 0 .01) = 1. 63.

This value is considerably different from the correct result pH = 2.06. It is so because the

condition allowing for applying formula (11.93), i.e. a low degree of dissociation, is not fulfilled.

Equations (11.91) and (11.93) apply on condition that the effect of water dissociation on
the pH can be neglected, which is usually so. However, we have to consider water dissociation
if by calculation we obtain pH>6. This happens in two limiting cases: