Ionic Product of water

Science > Chemistry > Physical Chemistry > Ionic Equilibria > Ionic Product of water

In this article, we shall study concepts of the ionic product of water, pH and pOH of a solution and their importance.

Ion Equilibrium in Water:

Water has electrical conductivity, hence it must undergo dissociation. “Dissociation of pure water to a very little extent into H⁺ and OH^– ions by itself is called as self ionisation of water. Water is a very weak electrolyte. In water, an equilibrium between ions and unionised water molecule exists as,

H₂O     ⇌        H⁺  +    OH^–

H⁺  +  H₂O    ⇌ H₃O⁺

The net reaction is

H2O  +  H₂O    ⇌   H₃O⁺ +    OH^–

H₃O⁺ is called the hydronium ion

Applying law of mass action to above equilibrium, we have

Now water is a very weak electrolyte. It dissociates in a very small amount. Hence practically the concentration of unionised water is almost the same as starting concentration. Hence [H₂O] = constant. Similarly Practically [H₃O⁺] = [H⁺]. Therefore the equation (1) becomes.

This relation is known as the ionic product of water.

The product of the molar concentration of H+ and OH- ions pure water or an aqueous solution at constant temperature is constant which is called the ionic product of water.

At 298 K, for pure water [H⁺] = [OH^–] = 1 x 10^-7 mole dm^-3

Thus K_w = [H⁺] [OH^–] = (1 x 10^-7) x (1 x 10^-7) = 1 x 10^-14

Thus at 298 K ionic product of water is 1 x 10^-14

• When small amount of acid is added to water, the concentration of H⁺ ions increases and that of OH^– ions decrease. i.e. [H⁺] > [OH^–] i.e. [H⁺]    > 1 x 10^-7
• When an alkali is added to water then OH^– ion concentration becomes higher than that of H⁺ ions. i.e. [OH^–] > [H⁺] i.e. [OH^–]. > 1 x 10^-7
• In neutral solution. H⁺ and OH^– ion concentration are equal. i.e. [H⁺] = [OH^–] = 1 x 10^-7 mole dm^-3
• Thus concept of ionic products of water helps us in classifying aqueous solutions as acidic, basic and neutral.

pH and pOH of a solution:

pH of a solution:

The negative logarithm to the base 10 of molar concentration of H⁺ ions in a solution is called as pH of a solution.

Mathematically, pH = – log₁₀[H⁺]

For pure water or a neutral solution.at 298  K.

[H⁺] = 1 x 10^-7 moles/dm3

∴ pH = – log₁₀(1 x 10^-7)  = – (-7) log₁₀10 = + 7 (1) = 7

pOH of a Solution:

The negative logarithm to the base 10 of molar concentration of OH^– ions in a solution is called as pOH of a solution.

Mathematically, pOH = – log₁₀[OH^–]

For pure water or a neutral solution.at 298  K.

[OH^–] = 1 x 10^-7 moles/dm3

∴ pOH = – log₁₀(1 x 10^-7)  = – (-7) log₁₀10 = + 7 (1) = 7

Relation Between pH  and pOH:

Ionic product of water is given by K_w = [H⁺] [OH^–]

For pure water or an aqueous solution, Kw = 1 x 10^-14   at 298   K

∴  [H⁺] [OH^–]  = 1 x 10^-14

Taking logs of both sides of the equation to the base 10

log₁₀[H⁺] + log₁₀[OH^–] = log₁₀(1 x 10^-14)

∴ log₁₀[H⁺] + log₁₀[OH^–] = -14 log₁₀10

∴ log₁₀[H⁺] + log₁₀[OH^–] = -14(1) = -14

Multiplying both sides of the equation by -1

∴  – log₁₀[H⁺] – log₁₀[OH^–] =  14

But  pH = – log₁₀[H⁺] and  pOH = – log₁₀[OH^–]

∴ pH  + pOH  = 14

Thus the sum of pH and  pOH for pure water or any aqueous solution is equal to 14.

pH Scale or Sorensen’s Scale:

Scientist Sorensen in 1909 introduced a convenient scale to express hydrogen ion  (H⁺) concentration to decide acidic, alkaline or neutral nature of the solution , is known as pH scale. The negative logarithm to the base 10 of the molar concentration of H⁺ ions in a solution is called as pH of a solution. The pH scale expresses all degrees of acidity or alkalinity of a dilute aqueous solution.

As the concentration of acid decreases the pH value increases from 0 to7.while as the concentration of base decreases the pH value decreases from 14 to7. For pure water or aqueous neutral solution, pH = 7.

It is to be noted that pH scale is used for a dilute aqueous solution only i.e. their molarity is less than 1 M.

Two acids monobasic and diabasic have the same pH. Does this mean that the molar concentration of the two acids is identical?

A monobasic acid dissociates as
HA ⇌ H⁺ + A^–
Thus 1 mole of monobasic acid gives 1 mole of H+ ions.
A dibasic acid dissociates as
H₂A ⇌ 2H⁺ + A^–
Thus 1 mole of dibasic acid gives 2 moles of H⁺ ions.

Hence if the pH of the two solutions is equal, the molar concentration of monobasic acid will be twice the molar concentration of dibasic acid.

Science > Chemistry > Physical Chemistry > Ionic Equilibria > Ionic Product of water