Question #44066

Gaseous bromoethane ($\ce{CH3CH2Br}$) undergoes a heterogeneous Swarts exchange with solid silver fluoride ($\ce{AgF}$) at $298\text{ K}$ in a closed $2.0\text{ L}$ vessel:

$\ce{CH3CH2Br(g) + AgF(s) <=> CH3CH2F(g) + AgBr(s)}$

The reaction occurs entirely on the solid surface. The intrinsic rate laws for the forward and reverse reactions are $r_f = k_f [\ce{CH3CH2Br}][\ce{AgF}]_{eff}$ and $r_b = k_b [\ce{CH3CH2F}][\ce{AgBr}]_{eff}$. The vessel contains a mixed powder bed such that the effective surface site concentrations remain constant at $[\ce{AgF}]_{eff} = 3.0\text{ mol L}^{-1}$ and $[\ce{AgBr}]_{eff} = 1.0\text{ mol L}^{-1}$.

Given the intrinsic rate constants $k_f = 2.0 \times 10^{-2}\text{ L mol}^{-1}\text{ s}^{-1}$ and $k_b = 1.0 \times 10^{-2}\text{ L mol}^{-1}\text{ s}^{-1}$, if $1.4\text{ moles}$ of $\ce{CH3CH2Br(g)}$ are initially introduced into the vessel, determine the true thermodynamic equilibrium constant ($K_c$) and the equilibrium concentration of $\ce{CH3CH2F(g)}$.