We have learnt that when an acidic or a basic substance is dissolved in water, depending

upon its nature, it can either donate (or) accept a proton. In addition to that the pure water itself has a little tendency to dissociate. i.e, one water molecule donates a proton to an another water molecule. This is known as auto ionisation of water and it is represented as below.

Conjugate acid - base pairs

. . + -

2 3acid 1 base 1base 2 acid 2 HO-H+H O H O +OH

In the above ionisation, one water molecule acts as an acid while the another water molecule acts as a base.

The dissociation constant for the above ionisation is given by the following expression

K= [H O ][OH ]

[H O] 3

+ -

2 2 …..(8.3)

The concentration of pure liquid water is one. i.e, [H O] 2

2 = 1

 K =[H O ][OH ]w 3 + - …..(8.4)

Here, Kw represents the ionic product (ionic product constant) of water

It was experimentally found that the concentration of H O3 + in pure water is -7 o1×10 at 25 C .

Since the dissociation of water produces equal number of H O and OH3 + -

, the concentration of OH- is also equal to 1×10 at 25 C

-7 o .

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Therefore, the ionic product of water oat 25 C is

Kw =[H3O]+[OH-]……(8.4)

Kw =(1 10-7)(1 10-7)

= 1 1

× ×

× 0-14.

Like all equilibrium constants, Kw is also a constant at a particular temperature. The dissociation of water is an endothermic reaction. With the increase in temperature, the concentration of H O3

+ and OH - also increases, and hence the

ionic product also increases.

In neutral aqueous solution like NaCl solution, the concentration of H O3

+ is always equal to the concentration of OH

- whereas in case of an aqueous solution of a substance which may behave as an acid (or) a base, the concentration of H O

3

+ will not be equal to [OH-] .

We can understand this by considering the aqueous HCl as an example. In addition to the auto ionisation of water, the following equilibrium due to the dissociation of HCl can also exist.

HCl+H2O H3O +Cl-+ 

In this case, in addition to the auto ionisation of water, HCl molecules also produces H3O

+ ion by donating a proton to water and hence [H O ]>[OH-]3 + . It means that the aqueous

HCl solution is acidic. Similarly, in basic solution such as aqueous NH 3 , NaOH etc…..

[OH–]>[H3O +].

Example 8.1

Calculate the concentration of OH- in a fruit juice which contains 2 10 M, H O-3 3

+× ion. Identify the nature of the solution.

Given that H3O+=2 10 M-3×

K =[H O ][OH ]

[OH ]= K

[H O ] =1 10

2 10 =5 10 M

w 3 +

w

3 +

14

3 12

-

- - -

-∴ × ×

×

2 10-3 12× » ×5 10-

i.e., [H O ]»[OH ], 3

+ -

hence the juice is acidic in nature

K w values at different temperatures

are given in the following below

Temperature ( o C ) Kw

0 1 14 10 15. × −

10 2 95 10 15

. × −

25 1 00 10 14. × −

40 2 71 10 14. × −

50 5 30 10 14. × −

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Evaluate yourself - 5

At a particular temperature, the Kw of a neutral solution was equal to 4 10-14× . Calculate the concentration of [H O ] and [OH ]3

+ - .