Question #44760

A galvanic concentration cell at $298\text{ K}$ is constructed as follows:

$\ce{Ag(s) | Ag+(aq, C_1) || Ag+(aq, C_2) | Ag(s)}$

The concentrations $C_1$ and $C_2$ are determined by the following kinetic data:

1. A bimolecular elementary reaction has a pre-exponential factor $A = 6.022 \times 10^9\text{ L mol}^{-1}\text{ s}^{-1}$ and an activation energy $E_a = 0$. The concentration $C_1$ is numerically equal to its rate constant when expressed in units of $\text{cm}^3\text{ molecule}^{-1}\text{ s}^{-1}$.
2. A separate reaction follows $n^{\text{th}}$ order kinetics. Let $k_L$ be its rate constant in units of $(\text{mol L}^{-1})^{1-n}\text{ s}^{-1}$ and $k_C$ be its rate constant in units of $(\text{mol cm}^{-3})^{1-n}\text{ s}^{-1}$. Given the ratio $k_L / k_C = 10^{-6}$, the concentration $C_2$ is numerically equal to $10^{-n}\text{ M}$.

Given $N_A = 6.022 \times 10^{23}\text{ mol}^{-1}$ and $\frac{2.303 RT}{F} = 0.059\text{ V}$ at $298\text{ K}$, calculate the electromotive force ($E_{\text{cell}}$) of the cell.