Ionization of Water

Pure water being a weak electrolyte under goes self ionization to a small extent as follows:

The equilibrium constant for this reaction is:

The concentration of unionized water is taken as constant because the degree on ionization of water is very small. So we can write this equation as:

where K_w is a constant and is known as the ionic product of water whose value is 1.008 x 10^-14 mol² L^-2 at 298 K. In pure water the concentration of H₃O⁺ and OH^- are equal and so we can write,

[H₃O⁺] = [OH^-]

If, K_w = [H₃O⁺] [OH^-] = 1.008 x 10^-14 mol² L^-2 then,

[H₃O⁺] [OH^-] = 1.008 x 10^-14

[H₃O⁺]² = 1.008 x 10^-14

 

 

Thus in pure water [H₃O⁺] = [OH^-] = 1.0 x 10^-7 mol L^-1 at 298 K

Effect of temperature on K

 

The value of Kw varies with the change in temperature. The values of [H₃O⁺] and [OH^-] are always equal to each other at all temperatures but the values of K_w are different at different temperatures. The value of K_w increases with the rise in temperature. This is because increase in temperature will shift the equilibrium in the forward direction producing large concentrations of [H₃O⁺] and [OH^-] ions (Le Chatelier's principle).

Hence, K_w increases with rise in temperature.

In acidic solution

When an acidic solution of HCl is added to a pure neutral solution of water, the concentration of [H₃O⁺] becomes larger than 1.0 x 10^-7 mol L^-1. The dissociation equilibrium of water shifts in the reverse direction (Le Chatelier's principle). The excess [OH^-] ions combine with hydronium ions to form undissociated water molecules so that the value of K_w remains constant in the solution. The concentration of [OH^-] ions will then be equal to

The concentration of [H₃O⁺] is more than the concentration of the [OH^-] ions in acidic solution.

When a few drops of a base like NaOH is added to pure water, the concentration of [OH^-] increases and that of hydrogen ions decreases. The concentration of [H₃O⁺] can be calculated as:

Thus in basic solution the concentration of [OH^-] will be greater than of [H₃O⁺].

It can be concluded that the hydronium and hydroxyl ions are always present in solution whether they are acidic or basic. However their concentrations differ.

Problem

6. Calculate the hydronium and hydroxyl ion concentrations in (i) 0.01 M HCl (ii) 0.001 M NaOH solution at 298 K.

Solution

(i) HCl completely ionizes as:

The concentration of hydronium ions is equal to that of hydrochloric acid,

[H₃O⁺] = [HCl]

[HCl] = 0.01M = 1 x 10^-2 mol L^-1

The ionic product of water is K_w = [H₃O⁺] [OH^-]

Thus [H₃O⁺] = 1 x 10^-2 mol L^-1 and [OH^-] = 1 x 10^-12 mol L^-1

(ii) NaOH ionizes completely as:

NaOH_(aq) Na⁺_(aq) + OH^-_(aq)

The concentration of [OH^-] is equal to that of NaOH i.e.,

[NaOH] = [OH^-]

[NaOH] = 0.001 M = 1 x 10^-3 mol L^-1

[OH^-] = 1 x 10^-3 mol L^-1

K_w = [H₃O⁺] [OH^-]

Thus, [OH^-] = 1 x 10^-3 mol L^-1and [H₃O⁺] = 1 x 10^-11 mol L^-1.