Question #43991

The acid-catalyzed Fischer esterification of acetic acid (\ce{CH3COOH}) with ethanol at 298 K has an equilibrium constant $K_c = 4.0$. A student attempts to synthesize ethyl trifluoroacetate by reacting 1.0 mol of trifluoroacetic acid (\ce{CF3COOH}) with 1.0 mol of ethanol in a 1.0 L flask at 298 K. The student erroneously assumes that the strong electron-withdrawing \ce{-CF3} group, which increases the acid's $K_a$ by a factor of $\approx 10^4$, will proportionally increase the esterification equilibrium constant, predicting a near quantitative yield. In reality, while the \ce{-CF3} group increases the electrophilicity of the carbonyl carbon, it also severely destabilizes the positively charged tetrahedral intermediate via inductive effects. Thermodynamically, the \ce{-CF3} group stabilizes the carboxylic acid more than the ester (due to differential resonance demands of the \ce{-OH} vs \ce{-OEt} groups), making the standard free energy of esterification for \ce{CF3COOH} less favorable by $\Delta(\Delta G^\circ) = RT \ln(16)$ compared to acetic acid. Assuming ideal behavior, calculate the actual equilibrium concentration of ethyl trifluoroacetate.