Question

The synthesis of ethanol from ethylene and water proceeds using the following reaction. C2H4(g) + H2O(l) C2H5OH(l) ΔGºrxn = -116.6 kJ/mol Determine the Gibbs free energy if the pressure of the vessel is 325 atm at 570 K.

A) -144.0 kJ/mole

B) -89 kJ/mole

C) -27526 kJ/mole

D) none of these

I tried B but it is incorrect

Answer 1

C₂H₄(g) + H₂O (l)C₂H₅OH (l)

where=Gibbs free energy

=Standard state Gibbs free energy=-116.6 kJ/mol=-116600 J/mol

R=Gas constant=8.314 J/molK

T=Temperature in K=570 K

Q=Reaction quotient=[C₂H₅OH]/p_C2H4

Assuming [C₂H₅OH]=1 as it is in liquid state, also pressure of the vessel is due to gas C₂H₄

So

=-116600 J/mol+(8.314 J/mol-K)x570Kln1/325 atm

=-116600 J/mol+8.314 J/mol-Kx570 K(-5.784)

=-116600 J/mol-27410.26 J/mol=-144010.26 J/mol=-144.010 kJ/mol

So option (A) -144.0 kJ/mol is correct answer.