For a weak electrolyte such as acetic acid, the relation among conductance (λ), equilibrium constant (K) and concentration (C) can be expressed as: (λ^° is the conductance at infinite dilution)

Concept:

• For weak acid acetic acid, the dissociation is weak 
• \(CH_{3}COOH\rightleftharpoons CH_{{3}}COO^{-}\, +\, H^{+} \)
• If C is the initial concentration of acetic acid and \(\alpha \) is the degree of dissociation, the equilibrium constant for the reaction can be expressed as;
• \(K\, =\, \frac{C\alpha ^{2}}{1-\alpha } \)
• \(\alpha \) can be expressed as \(\alpha =\frac{\lambda }{\lambda ^{0}} \)
• Where, \(\lambda\) and \(\lambda^{0} \) are the conductances at concentration C and zero.
• Putting the values of  \(\alpha \) in equilibrium constant we get,
• \(K=\frac{C\lambda ^{2}}{\lambda ^{0}\left ( \lambda ^{0}-\lambda \right )}\)

Explanation:

• We know,  \(K=\frac{C\lambda ^{2}}{\lambda ^{0}\left ( \lambda ^{0}-\lambda \right )} \)
• Rearranging this we can write
• \(\frac{C}{K\lambda ^{0}}=\frac{\lambda ^{0}-\lambda }{\lambda ^{2}} \)
• Multiplying \(\frac{\lambda }{\lambda ^{0}}\) on both sides we get
• \(\frac{C\lambda }{K\lambda ^{0^{2}}}=\frac{\lambda ^{0}-\lambda }{\lambda\, \lambda ^{0}}=\frac{1}{\lambda }-\frac{1}{\lambda ^{0}} \)
• Further rearranging this we can get 
• \(\frac{1}{\lambda}=\frac{1}{\lambda^\circ}+\frac{C\lambda}{K\lambda^{\circ^2}} \)

Conclusion: -

For a weak electrolyte such as acetic acid, the relation among conductance (λ), equilibrium constant (K) and concentration (C) can be expressed as  \(\frac{1}{\lambda}=\frac{1}{\lambda^\circ}+\frac{C\lambda}{K\lambda^{\circ^2}} \)