The specific conductance $$(\mathrm{k})$$ of $$0.02(\mathrm{M})$$ aqueous acetic acid solution at $$298 \mathrm{~K}$$ is $$1.65 \times 10^{-4} \mathrm{~S} \mathrm{~cm}^{-1}$$. The degree of dissociation of acetic acid is

$$[\lambda_{\mathrm{O}^{+}}+=349.1 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1} \text { and } \lambda_{{ }^{\circ} \mathrm{CH}_3 \mathrm{COO}^{-}}=40.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}]$$

At STP, the dissociation reaction of water is $$\mathrm{H_2O\rightleftharpoons H^+~(aq.)+OH^-~(aq.)}$$, and the pH of water is 7.0. The change of standard free energy ($$\Delta$$G$$^\circ$$) for the above dissociation process is given by