The standard Gibbs free energy change (ΔG∘) is related to the enthalpy change (ΔH∘) and entropy change (ΔS∘) by the equation:
ΔG∘=ΔH∘−TΔS∘.
Substitute the given values:
ΔH∘=77.2×103J,T=400K,ΔS∘=122J/K.
ΔG∘=77.2×103−400×122=28400J.
The relationship between ΔG∘ and the equilibrium constant (K) is:
ΔG∘=−2.303RTlogK.
Substitute ΔG∘=28400J,R=8.314J K,T=400K:
28400=−2.303×8.314×400logK.
Simplify:
logK=2.303×8.314×400−28400.
Calculate:
logK=7668.8−28400=−3.708.
Thus: K=10logK=10−3.708.
The Correct answer is: 37