Question

What will be the emf of the given cell?
$Pt|H_2\left(P_1\right)|H^{+}\left(aq\right).|H_2\left(P_2\right)|Pt$

• A. $\frac{RT}{F}ln\frac{P_2}{P_1}$
• B. $\frac{RT}{2F}ln\frac{P_1}{P_2}$
• C. $\frac{RT}{F}ln\frac{P_2}{P_1}$
• D. None of these

Answer 1

The correct option is B $\frac{RT}{2F}ln\frac{P_1}{P_2}$

Anode: $H_2\left(P_1\right)\to 2H^{+}+2e^{-}$
Cathode: $\underset{–}{2H^{+}+2e^{-}\to H_2\left(P_2\right)}$
$\underset{–}{H_2\left(P_1\right)\to H_2\left(P_2\right)}$
$E_{\text{cell}}=E_{\text{cell}}^{\circ }-\frac{RT}{nF}ln\frac{P_2}{P_1}$
$E_{\text{cell}}^{\circ }=0$
n = 2
$E_{\text{cell}}=\frac{RT}{2F}ln\frac{P_1}{P_2}$