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Question

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.

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Solution

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 = ΔHθTΔSθ

= –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.


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