Question #44098

Consider the esterification of a weak organic acid \ce{RCOOH} with an alcohol \ce{R'OH} in an aqueous buffer solution at $373\text{ K}$: $\ce{RCOOH(aq) + R'OH(aq) <=> RCOOR'(aq) + H2O(l)}$ The true thermodynamic equilibrium constant for this reaction, expressed in terms of the un-ionized acid, is $K_{eq} = 10.0\text{ M}^{-1}$ at $373\text{ K}$. The acid dissociation constant of \ce{RCOOH} at $373\text{ K}$ is $K_a = 4.0 \times 10^{-6}$. The reaction is carried out in a heavily buffered aqueous solution containing a weak base $B$ and its conjugate acid $BH^+$ in a molar ratio of $[B]:[BH^+] = 1:10$. At $373\text{ K}$, the ionic product of water is $K_w = 1.0 \times 10^{-12}$ and the base dissociation constant of $B$ is $K_b = 1.0 \times 10^{-5}$. Initially, the total analytical concentration of the acid species ($[\ce{RCOOH}] + [\ce{RCOO^-}]$) is $1.0\text{ M}$ and the concentration of \ce{R'OH} is $1.0\text{ M}$. Assuming the buffer capacity is large enough to maintain a strictly constant pH, what is the equilibrium concentration of the ester \ce{RCOOR'}?