For a half-cell containing a Pt rod immersed in a solution of $1 \mathrm{M} \mathrm{H} A, \mathrm{O}_2(g)$ is bubbled at $1 \mathrm{~atm}$. The standard reduction potential for water formation is $1.23 \mathrm{~V}$. Given a dissociation constant, $K_a=1 \times 10^{-4}$ for $\mathrm{H} A$, what is $E_{\text {Half-cell }}$ at $298 \mathrm{~K}$ in V ?

• A

  1.289
• B

  1.171
• Correct answer
  C

  1.348
• D

  1.112

Solution

Given, Standard reduction potential for water formation $=1.23 \mathrm{~V}$ Dissociation constant $\left(K_a\right)$ for $\mathrm{H} A=1 \times 10^{-4}$ $E_{\text {half-cell }}$ at $298 \mathrm{~K}=$ ? Number of electrons $=2$ $$ \begin{aligned} & E=E^{\circ}-\frac{0.0592}{2} \log Q\left(K_a\right) \\ & E=1.23-\frac{0.0592}{2} \log \left(1 \times 10^{-4}\right) \\ & E=1.23-\frac{0.0592}{2} \times-4 \\ & E=1.348 \mathrm{~V} \end{aligned} $$

Hence, the correct answer is option: 'C'.