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 AΔrG=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)=33.305−75.312=−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 ΔrS373−ΔrS323=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 ΔrH373−ΔrH323=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=ΔrH323−TΔrS323 ΔrG323=42739.35−323(115) ΔrG323=5594.35J=5.59kJ/mole
Hence, the Gibbs free energy change for the reaction is 5.59kJ/mol.