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Kohlrausch Law

What is the e...

Question

What is the equilibrium constant $K_{c}$ for the following reaction at $400 K$
$2 N O C l (g) ⇌ 2 N O (g) + {C l}_{2} (g)$
$Δ H^{o} = 77.2 k J, Δ S^{o} = 122 J K^{- 1}$ at $400 K$ .

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Solution

According to Gibbs-Helmholtz equation
$Δ G^{o} = Δ H^{o} - T Δ S^{o} = 77.2 - 400 \times 122 \times 10^{- 3}$
$= 28.4 k J = 28.4 \times 10^{3} J$
we know that $Δ G^{o} = - 2.303 R T log K_{c}$
$∴ log K_{c} = \frac{- Δ G^{o}}{2.303 R T} = \frac{28.4 \times 10^{3}}{2.303 \times 8.314 \times 400} = - 3.7081$
$K_{c} = a n t i log (- 3.7081) = 1.958 \times 10^{- 4}$

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