# Ostwald Dilution Law, Limitations and Verification

## Ostwald Dilution Law

According to Arrhenius electrolytic dissociation theory, ions and unionized electrolytic molecules are in dynamic equilibrium. Ostwald applied the law of mass action to this equilibrium as follows

Let a weak electrolyte AB in aqueous solution has the degree of dissociation 伪 , then-

Hence, from the law of mass action, we get the equilibrium constant(called dissociation constant)-

So, we can say that the degree of dissociation of a weak electrolyte is inversely proportional to the square root of molar concentration or directly proportional to the volume.

This equation is called Ostwald dilution law. Lower the K value, lower the 伪 value i.e. weaker the electrolyte.

## Experimental Verification of Ostwald's Law

The Ostwald's Dilution law can be verified if the values of the degree of dissociation (伪), at different dilutions are known and the values are placed in the equation K = C伪^{2}/(1 − 伪) and thus values of K at different dilutions are calculated. If these values come out to be nearly constant, the law is correct.

The degree of dissociation (伪), is determined by conductance measurements since the degree of ionisation (伪), of a weak electrolyte at a particular dilution is related as-

伪 = 位_{V}/位_{∞}

Where 位_{V} is the equivalent conductance at V- dilution. It can be calculated by conductance measurements and 位_{∞} can be caculated by Kohlrausch's law-

位_{V} = 位_{+} + 位_{−}

Where, 位_{∞} is the equivalent conductance at infinite dilution, 位_{+} is equivalent conductance of cation at infinite dilution and 位_{−} is equivalent conductance of anion at infinite dilution.

## Limitation of Ostwald's Law

Ostwald's Dilution law holds good only for weak electrolytes and fails completely when appliedto strong electrolytes (i.e. HCl, KOH, KCl, etc.).For strong electrolytes, which are highly ionised in solution, the value of the dissociation constant K, far from remaining constant, rapidly falls with dilution.

## Factors that explain the failure of Ostwald's law in case of strong electrolytes

1. The law is based on Arrhenius theory which assumes that only a fraction of the electrolyte is dissociated at ordinary dilutions and complete dissociation occurs only at infinite dilution. However, this is true for weak electrolytes. Strong electrolytes are almost completely ionised at all dilutions and 位_{V}/位_{∞} does not give the accurate value of degree of dissociation (伪).

2. The Ostwald's law is derived on the assumption that the Law of Mass Action holds for theionic equilibria as well. But when the concentration of ions is very high, the presence of charges affects the equilibrium. Thus the Law of Mass Action in its simple form can not be applied.

3. The ions obtained by dissociation may get hydrated and may affect the concentration terms. Better results are obtained by using activities instead of concentrations.

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