The correct expression for Ostwald’s dilution law for a solution of weak electrolyte is

# The correct expression for Ostwald’s dilution law for a solution of weak electrolyte is

1. A

${K}_{a}=\frac{{\alpha }^{2}}{\left(1-\alpha \right)V}$

2. B

${K}_{a}={\alpha }^{2}.V$

3. C

${K}_{a}=\frac{{\alpha }^{2}}{1-V}$

4. D

${K}_{a}=\frac{{\alpha }^{2}}{C\left(1-\alpha \right)}$

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### Solution:

Ostwald's law of dilution relates with the dissociation constant of a weak electrolyte to the degree of dissociation and the concentration of the weak electrolyte.

Consider the following reaction,

$C{H}_{3}COOH⇌C{H}_{3}CO{O}^{-}+{H}^{+}$

${K}_{a}=\frac{\left[C{H}_{3}CO{O}^{-}\right]\left[{H}^{+}\right]}{\left[C{H}_{3}COOH\right]}$

${K}_{a}=\frac{\alpha C.\alpha C}{\left(1-\alpha \right)C}$

${K}_{a}=\frac{{\alpha }^{2}}{\left(1-\alpha \right)V}$, Where $C=\frac{1}{V}$

Hence, the correct answer is option (A)${K}_{a}=\frac{{\alpha }^{2}}{\left(1-\alpha \right)V}$.

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