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Question:

Consider the following reversible reaction, A(g) + B(g)⇌AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J mol⁻¹). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔG° (in J mol⁻¹) for the reaction at 300 K is _______. [Given ln(2) = 0.7, RT = 2500 J mol⁻¹ at 300 K and G is the Gibbs energy].

Solution:

A(g) + B(g)⇌AB(g)
(Ea)b − (Ea)f = 2RT
Af/Ab = 4
ΔGo = −RTlnKeq
Kf = Afe^−(Ea)f/RT
Kb = Abe^−(Ea)b/RT
Keq = Kf/Kb = (Af/Ab) × e^−(Ea)f/RT × e^(Ea)b/RT = 4 × e^((Ea)b−(Ea)f)/RT
Keq = 4 × e^2
ΔGo = −RT × ln(4 × e^2)
ΔGo = −RT(ln4 + 2lne)
ΔGo = −RT(2 × 0.7 + 2)
ΔGo = −RT(1.40 + 2)
ΔGo = −RT(3.40)
ΔGo = −2500 × 3.40
ΔGo = −8500 J