For the vapour-phase hydration of ethylene to ethanol [ mathrm{C}_{2} mathrm{H}_{4}+mathrm{H}_{2} mathrm{O} ightarrow mathrm{C}_{2} mathrm{H}_{5} mathrm{OH}

For the vapour-phase hydration of ethylene to ethanol

\[ \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \]

The equilibrium constants were measured at temperature \(420 \mathrm{~K}\) and \(600 \mathrm{~K}\). They are \(6.8 \times 10^{-2}\) and \(1.9 \times 10^{-3}\) respectively. The specific heat \((\mathrm{J} / \mathrm{mol}-\mathrm{K})\) data are

Develop general expressions for the equilibrium constant and standard free energy change as function of temperature.

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Components Ethylene Water Ethanol Cp (J/mol-K) 11.886 +120.12 x 10-37-36.649 10-672 30.4759.652 x 10-37+ 1.189 10-672 29.358 166.9 x 10 37-50.09 x 10 672