Question #44711

An advanced electrochemical cell is designed to study the thermodynamics of 'bubble-free' water electrolysis at $298\text{ K}$. Two inert platinum electrodes are immersed in an aqueous buffer solution of $pH = 2.0$.

During steady-state electrolysis, the products exist entirely as dissolved gases before any bubbles can form. The local concentration of dissolved hydrogen at the cathode is maintained at $1.0 \times 10^{-4}\text{ M}$, and dissolved oxygen at the anode is $1.0 \times 10^{-5}\text{ M}$.

The Henry's Law constants for the gases in water at $298\text{ K}$ are $K_H(\ce{H2}) = 1.0 \times 10^{-3}\text{ M bar}^{-1}$ and $K_H(\ce{O2}) = 1.0 \times 10^{-3}\text{ M bar}^{-1}$.

Given the standard electrode potential $E^\circ_{\ce{O2(g)/H2O}} = 1.23\text{ V}$ and $\frac{2.303 RT}{F} = 0.06\text{ V}$.

Calculate the minimum theoretical applied voltage ($V_{min}$) required to sustain this electrolysis.