For the reaction
2A(g) + B(g) → 2D(g)
ΔUθ = –10.5 kJ and ΔSθ= –44.1 JK–1.
Calculate ΔGθ for the reaction, and predict whether the reaction may occur spontaneously.
For the given reaction,
2 A(g) + B(g) → 2D(g)
Δng = 2 – (3)
= –1 mole
Substituting the value of ΔUθ in the expression of ΔH:
ΔHθ = ΔUθ + ΔngRT
= (–10.5 kJ) – (–1) (8.314 × 10–3 kJ K–1 mol–1) (298 K)
= –10.5 kJ – 2.48 kJ
ΔHθ = –12.98 kJ
Substituting the values of ΔHθ and ΔSθ in the expression of ΔGθ:
ΔGθ = ΔHθ – TΔSθ
= –12.98 kJ – (298 K) (–44.1 J K–1)
= –12.98 kJ + 13.14 kJ
ΔGθ = + 0.16 kJ
Since ΔGθ for the reaction is positive, the reaction will not occur spontaneously.