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Question

Compute ΔrG for the reaction H2O(;,1atm,323K)H2O(g,1atm,323K)
Given that : ΔvapH at 373K=40.639kJmol1,CP(H2O,l)=75.312JK1mol1,CP(H2O,g)=33.305JK1mol1

A
ΔrG=5.59kJmol1
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B
ΔrG=5.59kJmol1
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C
ΔrG=55.9kJmol1
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D
None of these
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Solution

The correct option is A ΔrG=5.59kJmol1
The change in the molar heat capacity at constant pressure for the reaction is as shown.
ΔrCP=Cp(H2O,g)CP(H2O,l)=33.30575.312=42.007J/Kmole
The entropy change at 323 K is as shown.
ΔrS323=ΔHT=40639323=108.95J/Kmole
The relationship between the entropy change and the change in molar heat capacity at constant pressure is as shown.
d(ΔrS)=ΔrCPdTT
ΔrS373ΔrS323=ΔrCPlnT2T1
ΔrS373=108.95(42.007ln373323)
=115J/Kmole
The relationship between the enthalpy change and the change in molar heat capacity at constant pressure is as shown.
d(ΔrH)=ΔrCPdT
ΔrH373ΔrH323=42.007(50)
ΔrH373=42739.35J/mole
The relationship between Gibbs free energy change, the entropy change and the enthalpy change is as shown.
ΔrG323=ΔrH323TΔrS323
ΔrG323=42739.35323(115)
ΔrG323=5594.35J=5.59kJ/mole

Hence, the Gibbs free energy change for the reaction is 5.59kJ/mol.

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