Question #44220

Consider the acid-catalyzed esterification of octadecanoic acid with octan-1-ol to form octyl octadecanoate and water. At $298\text{ K}$, the standard enthalpy and entropy of the reaction producing liquid water are $\Delta H^\circ_{rxn} = -12.0\text{ kJ mol}^{-1}$ and $\Delta S^\circ_{rxn} = -10.0\text{ J K}^{-1}\text{ mol}^{-1}$, respectively.

The standard enthalpy of vaporization of water is $\Delta H^\circ_{vap} = 42.0\text{ kJ mol}^{-1}$ and its standard entropy of vaporization is $\Delta S^\circ_{vap} = 110.0\text{ J K}^{-1}\text{ mol}^{-1}$.

The reaction is carried out at $400\text{ K}$ in a continuous flow reactor. Due to the high boiling points of the organic species, they remain entirely in the liquid phase, but water is formed exclusively in the vapor phase. Assuming all standard enthalpies and entropies are independent of temperature, what is the value of $\ln K$ for this specific equilibrium at $400\text{ K}$?

($R$ is the universal gas constant in $\text{J K}^{-1}\text{ mol}^{-1}$)