Question #44453

The Finkelstein reaction of 1-chlorobutane ($\ce{R-Cl}$) with $\ce{NaI}$ typically proceeds to completion in acetone due to the precipitation of $\ce{NaCl}$. However, when performed in anhydrous ethanol at $298\text{ K}$, $\ce{NaCl}$ exhibits partial solubility, establishing a thermodynamic equilibrium.

For the homogeneous exchange reaction: $\ce{R-Cl_{(sol)} + I^-_{(sol)} \rightleftharpoons R-I_{(sol)} + Cl^-_{(sol)}}$ The second-order rate constants are $k_{f} = 4.0 \times 10^{-4}\text{ M}^{-1}\text{s}^{-1}$ and $k_{b} = 1.0 \times 10^{-2}\text{ M}^{-1}\text{s}^{-1}$.

The pure solubilities of $\ce{NaI}$ and $\ce{NaCl}$ in anhydrous ethanol at $298\text{ K}$ are $5.0 \times 10^{-2}\text{ M}$ and $1.0 \times 10^{-3}\text{ M}$, respectively.

If 1-chlorobutane is reacted with a large excess of solid $\ce{NaI}$ in ethanol such that both solid $\ce{NaI}$ and solid $\ce{NaCl}$ are present at equilibrium, what is the equilibrium ratio of $[\ce{R-I}]$ to $[\ce{R-Cl}]$ in the solution?