Question #44781

A hydrogen concentration cell is constructed at $298\text{ K}$: $\ce{Pt, H_2 (1 bar) | HA (aq, 0.03 M) || HA (aq, 0.03 M) | Pt, H_2 (1 bar)}$ $\ce{HA}$ is a weak monobasic acid. Initially, the EMF of the cell is zero. An equal volume of pure benzene is added to the anode compartment. The mixture is vigorously shaken and allowed to reach equilibrium. The weak acid $\ce{HA}$ partitions into the benzene layer and undergoes partial dimerization. Given: Partition coefficient, $K_p = \frac{[\ce{HA}]_{\text{benzene}}}{[\ce{HA}]_{\text{aq}}} = 1$ Dimerization constant in benzene, $K_d = \frac{[(\ce{HA})_2]_{\text{benzene}}}{[\ce{HA}]_{\text{benzene}}^2} = 50\text{ M}^{-1}$ Assume that benzene and water are completely immiscible, the volume of each phase remains constant, and the degree of dissociation of $\ce{HA}$ in water is negligible for mass balance calculations. Calculate the new EMF of the cell at $298\text{ K}$. (Given: $\frac{2.303 RT}{F} = 0.06\text{ V}$, $\log 3 = 0.48$, $\log 2 = 0.30$)