Question

For the reaction 

2A_(g) + B_(g) → 2D_(g) 

∆U^θ = –10.5 kJ and ∆S^θ = –44.1 JK^–1 . 

Calculate ∆G^θ for the reaction, and predict whether the reaction may occur spontaneously.

Answer 1

For the given reaction, 

2 A_(g) + B_(g) → 2D_(g) 

∆ng = 2 – (3) 

= –1 mole 

Substituting the value of ∆U^θ in the expression of ∆H: 

∆H^θ = ∆U^θ + ∆ngRT 

= (–10.5 kJ) – (–1) (8.314 × 10–3 kJ K^–1 mol^–1 ) (298 K) 

= –10.5 kJ – 2.48 kJ ∆H^θ = –12.98 kJ 

Substituting the values of ∆H^θ and ∆S^θ in the expression of 

∆G^θ : ∆G^θ = ∆H^θ – T∆S^θ 

= –12.98 kJ – (298 K) (–44.1 J K^–1 ) 

= –12.98 kJ + 13.14 kJ 

∆G^θ = + 0.16 kJ 

Since ∆Gθ for the reaction is positive, the reaction will not occur spontaneously.