Chemistry

Chemistry

Problem

The vapor-phase hydration of ethene to produce ethanol is represented below. C2H4(g)+H2O(g)→C2H5OH(g)\text{C}_2\text{H}_4(g)+\text{H}_2\text{O}(g) \rightarrow \text{C}_2\text{H}_5\text{OH}(g) Standard molar free energies of formation at 298\,K are provided. $ Species  ΔGf∘ (kJ mol−1)C2H4(g)+68.1H2O(g)−228.6C2H5OH(g)−174.8\begin{array}{lcl} \text{Species} & & \;\Delta G_f^{\circ}\,(\text{kJ\,mol}^{-1})\\ \text{C}_2\text{H}_4(g) & & +68.1\\ \text{H}_2\text{O}(g) & & -228.6\\ \text{C}_2\text{H}_5\text{OH}(g) & & -174.8\\ \end{array} $ (a) Determine the standard free-energy change ΔG∘\Delta G^{\circ} for the hydration reaction at 298\,K. (b) Using your result from part (a), calculate the equilibrium constant KK at 298\,K. (c) A sealed vessel at 298\,K initially contains only 1.00\,mol C2H4\text{C}_2\text{H}_4 and 1.00\,mol H2O\text{H}_2\text{O} at a total pressure of 1.00\,atm. No ethanol is present initially. Based on the value of KK you obtained in part (b), estimate whether the conversion of ethene to ethanol under these conditions will be less than 10\%, between 10\% and 90\%, or greater than 90\%. Justify your choice with quantitative reasoning.

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