Chemistry, Third edition

288 16 · ACID–BASE EQUILIBRIA

pH, pOH and pKw

Taking logs on both sides of equation (16.2) gives

logKwlog [H 3 O(aq)]log [OH(aq)]

Multiplying throughout by 1 gives

logKwlog [H 3 O(aq)]log [OH(aq)]

We know that pH log [H 3 O(aq)]. We similarly define pOH and pKwas

pOHlog[OH(aq)] and pKwlogKw

from which we see that

pKwpHpOH

This expression is just another form of equation (16.2), and also applies to all

aqueous solutions. At 25 °C, pKw–log (1.0  10 –14)14, so that

pHpOH 14

Now try Exercises 16D and 16E.

Example 16.2

A 0.020 mol dm^3 solution of sodium hydroxide at 25 °C contains

0.020 mol dm^3 of hydroxide ion. Calculate its pH.

Answer

First, calculate the hydronium ion concentration:

[OH(aq)]0.020 mol dm^3. We know that

[H 3 O(aq)][OH(aq)]1.0 10 ^14 mol^2 dm^3

Rearranging,

[H 3 O(aq)]

1.0 10 ^14



1.0 10 ^14

5.0 10 ^13 mol dm^3

[OH(aq)] 0.020

To calculate the pH:

pHlog [H 3 O(aq)]log (5.0  10 ^13 )12.30

Comment

The pH of strongly basic solutions is above 11, so this is a reasonable answer.

Now try Exercise 16C.

Relationship

between pH and

pOH

The pH of a solution is

5.80 at 25 °C. Calculate its

pOH and [OH(aq)].

Exercise 16D

Calculations involving solutions of alkalis

(i)0.10 g of calcium hydroxide (Ca(OH) 2 ), is dissolved in water and made up to 200 cm^3.

Calculate the pH of the solution at 25 °C. (Calcium hydroxide is a ‘strong base’, i.e. it is

completely dissociated into hydroxide and calcium ions in solution.)

(ii)A solution of sodium hydroxide (also a strong base) has a pH of 11.10. What is the

concentration of (a) hydroxide ion and (b) hydronium ion in the solution? (Take the

temperature to be 25 °C.)

Exercise 16C