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Gibb's Helmholtz equation

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Question

$For the reaction, X_{2} O_{4 (l)} ⟶ 2 {XO}_{2 (g)}$
$Δ U = 2.1 kcal, Δ S = 20 {calK}^{- 1} at 300 K$
$Hence, Δ G is$

Moderate

Solution

$Δ H = Δ U + Δ n_{g} R T$
$Given, Δ U = 2.1 kcal, Δ n_{g} = 2$
$R = 2 \times 10^{- 3} kcal, T = 300 K$
$∴ Δ H = 2.1 + 2 \times 2 \times 10^{- 3} \times 300 = 3.3 kcal$
$Again, Δ G = Δ H - T Δ S$
$Given, Δ S = 20 \times 10^{- 3} {kcalK}^{- 1}$
$On putting the value of Δ H in the equation, we get$
$Δ G = 3.3 - 300 \times 20 \times 10^{- 3}$
$= 3.3 - 6 \times 10^{3} \times 10^{- 3} = - 2.7 kcal$

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