Question #44758

An electrochemical concentration cell is set up at 298 K:

$\ce{Pt(s) | Mn^{2+}(aq, 0.1 M), MnO4^{-}(aq, 0.01 M), H^{+}(aq, pH_a) || MnO4^{-}(aq, 0.1 M), Mn^{2+}(aq, 0.01 M), H^{+}(aq, pH_c) | Pt(s)}$

In the cathodic half-cell, the $\ce{H+}$ concentration is maintained by a $0.1\text{ M}$ solution of a weak monoprotic acid $\ce{HA}$ ($K_a = 10^{-5}$). In the anodic half-cell, the $\ce{H+}$ concentration is governed by a buffer of $\ce{HA}$ and $\ce{A-}$. Initially ($t=0$), the anodic compartment contains $0.1\text{ M HA}$ and $0\text{ M A-}$. A zero-order reaction continuously converts $\ce{HA}$ into $\ce{A-}$ in the anodic compartment at a constant rate of $1.0 \times 10^{-3}\text{ M s}^{-1}$ (assume no volume change).

Calculate the instantaneous rate of change of the cell potential, $\frac{dE_{\text{cell}}}{dt}$ (in $\text{mV s}^{-1}$), at $t = 50\text{ s}$.

(Given: $\frac{2.303 RT}{F} = 0.059\text{ V}$)