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Derivation of Kp and Kc

For the react...

Question

For the reaction, $A (g) + B (g) \to C (g) + D (g)$ ,
$Δ H^{0}$ and $Δ S^{0}$ are,respectively, $- 29.8 k J$ $m o l^{- 1}$ and $- 0.100 k J$ $K^{- 1}$ mol−1 at 298K.
The equilibrium constant for the reaction at $298 K$ is :

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Solution

Both sides are equal number of moles
So $Δ n = 0$
We know $K_{p} = K_{c} R T^{Δ n}$
$K_{p} = 49 \times (0.821 \times 300)^{0} = 49$

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