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Characteristics of Chemical Equilibrium

For the react...

Question

For the reaction
$2 N O C l (g) ⇌ 2 N O (g) + {C l}_{2} (g)$
calculate the standard equilibrium constant at $298 K$ . Given that the values of $Δ H^{o}$ and $Δ S^{o}$ of the reaction at $298 K$ are $77.2 k J {m o l}^{- 1}$ and $122 J K {m o l}^{- 1}$

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Solution

$Δ H^{o} = 77.2 k J / m o l \times 1000 J / k J = 77200 J / m o l$
Using the relation
$Δ G^{o} = Δ H^{o} - T {Δ S}^{o}$
$Δ G^{o} = 77200 J / m o l - (298 K \times 122 J / m o l / K)$
$Δ G^{o} = 40844 J {m o l}^{- 1}$
Let the equilibrium constant be $K_{c}$ , we know that
$Δ G^{o} = - 2.303 R T log K_{c}^{o}$
or $log K_{c}^{o} = - \frac{Δ G^{o}}{2.303 R T}$
$log K_{c}^{o} = - \frac{40844 J / m o l}{2.303 \times 8.314 J / m o l / K \times 298 K} = - 7.158$
$K_{c}^{o} = 6.95 \times 10^{- 8}$

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