Ionic Product of Water

Pure water is a weak electrolyte and it undergo self ionization or auto-protolysis. In this process water molecules splits into  hydrogen ion (H+) and hydroxide ion (OH-).

As we know hydrogen ion is very reactive and it reacts further with water molecules to form hydronium ion(H₃O⁺)

Applying law of mass action at equilibrium, the value of dissociation constant, K comes to

         K = [H⁺] [OH^-]/[H₂O]

        or   [H⁺][OH^-] = K[H₂O]

Since dissociation takes place to a very small extent, the concentration of undissociated water molecules, [H₂0], may be regarded as constant. Thus, the product #[H₂0] gives another constant which is designated as K_w. So,

[H⁺][OH^-] = K_w

The constant, K_w, is termed as ionic product of water.

Refer to the following video for ionic product of water

It is only because of the self ionization of water that it can act as both acid as well as base.

Any substance which increases the concentration of H⁺ ion would make water acidic.

Similarly, any substance which increases the concentration of OH- ion, would make water basic.

But in pure water, the hydrogen ion (hydroxonium ion) concentration is always equal to the hydroxide ion concentration. For every hydrogen ion formed, there is a hydroxide ion formed as well.

The product of concentrations of H⁺ and OH^- ions in water at a particular temperature is known as ionic product of water. The value of K_w increases with the increase of temperature, i.e., the concentration of H⁺ and OH^- ions increases with increase in temperature.

The value of K_w at 25°C is 1 x 10^-14. Since pure water is neutral in nature, H⁺ ion concentration must be equal to OH^- ion concentration.

[H⁺] = [OH˜] = x

or    [H⁺][OH^-]=x²= 1 x 10^-14

or    x = 1 x 10^-7 M

or    [H⁺] = [OH^-] = 1 × 10^-7 mol litre^-1

This shows that at 25°C, in 1 litre only 10^-7 mole of water is in ionic form out of a total of approximately 55.5 moles.

When an acid or a base is added to water, the ionic concentration product, [H⁺][OH^-], remains constant, i.e., equal to K_w but concentrations of H⁺ and OH^- ions do not remain equal. The addition of acid increases the hydrogen ion concen­tration while that of hydroxyl ion concentration decreases, i.e.,

[H⁺] > [OH^-]; (Acidic solution)

Similarly, when a base is added, the OH^- ion concentration increases while H⁺ ion concentration decreases,i.e.,

[OH^-] > [H⁺]; (Alkaline or basic solution)

In neutral solution,      

[H⁺] = [OH^-] = 1 x 10^-7 M

In acidic solution,

[H⁺] > [OH^-]

or   [H⁺] > 1 x 10^-7 M

and    [OH^-] < 1 x 10^-7 M

In alkaline solution,      

[OH^-] > [H⁺]

 or   [OH^-] > 1 × 10^-7 M

and [H⁺] < 1 x 10^-7 M

Thus, if the hydrogen ion concentration is more than 1 x 10^-7 M, the solution will be acidic in nature and if less than 1 x 10^-7 M, the solution will be alkaline.

We shall have the following table if OH^- ion concentration is taken into account.

It is, thus, concluded that every aqueous solution, whether acidic, neutral or alkaline contains both H⁺ and OH^- ions. The product of their concentrations is always constant, equal to 1 × 10^-14 at 25°C. If one increases, the other decrease accordingly so that the product remains 1×10-14 at 25^o C.

If [H⁺] = 10^-2 M,

then [OH^-] = 10^-12 M;

the product, [H⁺][OH^-] = 10^-2 × 10^-12 = 10^-14; the solution is acidic.

If [H⁺] = 10^-10 M,

then [OH^-] = 10^-4 M; the product, [H⁺][OH^-] = 10^-10 × 10^-4 = 10^-14; the solution is alkaline.

You can also refer to following links

• IIT JEE Syllabus of Chemistry 

•  Reference books of Physical Chemistry for IIT JEE

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