Ionic Equilibrium : Common ion Effect

Common ion effect

Let AB be the weak electrolyte. Considering its dissociation,

AB ⇌ A+ + B– and applying law of mass action we have  \[K=\frac{[{{A}^{+}}][{{B}^{-}}]}{[AB]}

The equilibrium constant, K, has a definite value at any given temperature. If now another electrolyte furnishing the A+ or B– ions be added to the above solution, it will increase the concentration of either A+ ions or B– ions (whichever has been added) and in order that K may remain constant, the concentration of AB must increase, i.e., the equilibrium will shift to the left hand side.

In other words, the degree of dissociation of an electrolyte (Weak) is supressed by the addition of another electrolyte (strong) containing a common ion this is termed as common ion effect. Acetic acid is a weak electrolyte and its ionisation is suppressed in presence of a strong acid ( ion as common ion) or a strong salt like sodium acetate (acetate ion is a common ion). Similarly, the addition of NH4Cl or NaOH to NH4OH solution will suppress the dissociation of NH4OH due to common ion either NH4+ or OH–.

\[C{{H}_{3}}COOH\rightleftharpoons C{{H}_{3}}CO{{O}^{-}}+{{H}^{+}}

\[C{{H}_{3}}COONa\to {{\underset{Common\,\,ion}{\mathop{C{{H}_{3}}COO}}\,}^{-}}+N{{a}^{+}}

\[N{{H}_{4}}OH\rightleftharpoons NH_{4}^{+}+O{{H}^{-}}

\[N{{H}_{4}}Cl\to \underset{Common\,\,ion}{\mathop{NH_{4}^{+}}}\,+C{{l}^{-}}                           

As a result of common ion effect, the concentration of the ion not in common in two electrolytes, is decreased. The use of this phenomenon is made in qualitative analysis to adjust concentration of S2– ions in second group and  ion concentration in third group of analysis.

Isohydric solutions

If the concentration of the common ions in the solution of two electrolyes, for example H+ ion concentration in HCl and HNO3 or OH– ion concentration in Ca(OH)2 and Ba(OH)2 is same, then on mixing them there is no change in the degree of dissociation of either of the electrolytes. Such solutions are called isohydric solutions.

Consider two isohydric solutions of acids HA1 and HA2. Let V1 and V2 be their dilutions and α1 and α2 be their degree of dissociation at the respective dilution.

Applying Ostwald’s dilution law on the two acids,

\[{{K}_{1}}=\frac{\alpha _{1}^{2}}{(1-{{\alpha }_{1}}){{V}_{1}}}    (For acid )             …..(i)

\[{{K}_{2}}=\frac{\alpha _{2}^{2}}{(1-{{\alpha }_{2}}){{V}_{2}}}    (For acid )             …..(ii)

When the two solutions are mixed, then total volume on mixing = V1 + V2

Concentration of hydrogen ion on mixing  \[=\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{{{V}_{1}}+{{V}_{2}}}

Applying Ostwald’s law to the acid HA1 in the mixture, we get

\[{{K}_{1}}=\frac{({{\alpha }_{1}}+{{\alpha }_{2}}){{\alpha }_{1}}}{({{V}_{1}}+{{V}_{2}})(1-{{\alpha }_{1}})}        ….(iii)

Dividing equation (iii) by (i), we get

\[1=\frac{({{\alpha }_{1}}+{{\alpha }_{2}}){{V}_{1}}}{({{V}_{1}}+{{V}_{2}}){{\alpha }_{1}}}=\frac{{{\alpha }_{2}}{{V}_{1}}}{{{\alpha }_{1}}{{V}_{2}}}

\[\frac{{{\alpha }_{1}}}{{{V}_{1}}}=\frac{{{\alpha }_{2}}}{{{V}_{2}}}                             …..(iv)

Above equation is useful for calculating the relative dilution of two acids at which they would be isohydric.