A batch reactor is used to synthesize ethyl acetate via esterification:
CH3COOH(l)+C2H5OH(l)⟷CH3COOC2H5(l)+H2O(l)ΔHrxn=−2.2kJ mol−1
At 298 K the equilibrium constant based on activities is K=4.0. The reaction is catalyzed by a strong acid, and its specific rate constant obeys the Arrhenius expression k=Ae−Ea/RT with an activation energy Ea=55kJ mol−1.
One metric for productivity is moles of ethyl acetate produced per unit batch time. Engineers may vary the operating temperature between 298 K and 360 K, but cooling water capacity limits the reactor to a maximum temperature rise of 10 K above the set point.
(a) Explain qualitatively how increasing the set-point temperature affects (i) the equilibrium conversion of the reactants and (ii) the forward rate constant for the reaction. Support each explanation with appropriate thermodynamic or kinetic reasoning.
(b) Assume ideal-solution behavior and equal initial concentrations of acetic acid and ethanol. Calculate the percent conversion to ethyl acetate at equilibrium for set-point temperatures of 298 K and 360 K.
(c) The batch time is dominated by the time required to reach 95 \% of equilibrium conversion at the operating temperature. Using the Arrhenius information provided, outline a method to estimate how the required batch time would change between the two temperatures. No numerical integration is necessary, but your reasoning must be explicit.
(d) Considering both equilibrium and kinetic effects, as well as the 10 K temperature-rise constraint, recommend an operating temperature that maximizes overall productivity. Defend your recommendation with an integrated argument.