PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 382

11.6 Calculation of pH

11.6.1 Definition of pH.

The quantity pH is defined by the relation

pH =−logaH+, (11.83)

whereaH+is the activity of hydrogen ions. For practical calculations it is convenient to rewrite
the equation to

pH =−log

(

cH+

cst

γH+

)

. (11.84)

The activity coefficient of hydrogen ions is calculated from the Debye-H ̈uckel relation (11.43)
at low concentrations. At higher concentrations it is replaced with the mean activity coefficient
γ±.

11.6.2 pH of water

The pH of pure water is calculated from the relation

pH =−

1

2

logKw, (11.85)

whereKwis the ionic product of water, see11.5.2.

Example

Calculate the pH of pure water at the standard pressure and at temperatures of 0◦C, 25◦C

and 100◦C. The ionic product of water at 25◦C is 1.00× 10 −^14 , its values at the other two

temperatures are the results of the Example in Section11.5.2.