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For the reaction 

2A(g) + B(g) → 2D(g) 

∆Uθ = –10.5 kJ and ∆Sθ = –44.1 JK–1

Calculate ∆Gθ for the reaction, and predict whether the reaction may occur spontaneously.

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For the given reaction, 

2 A(g) + B(g) → 2D(g) 

∆ng = 2 – (3) 

= –1 mole 

Substituting the value of ∆Uθ in the expression of ∆H: 

∆Hθ = ∆Uθ + ∆ngRT 

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

= –10.5 kJ – 2.48 kJ ∆Hθ = –12.98 kJ 

Substituting the values of ∆Hθ and ∆Sθ in the expression of 

∆Gθ : ∆Gθ = ∆Hθ – T∆Sθ 

= –12.98 kJ – (298 K) (–44.1 J K–1

= –12.98 kJ + 13.14 kJ 

∆Gθ = + 0.16 kJ 

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

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