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What is the equilibrium constant K(c) fo...

What is the equilibrium constant `K_(c)` for the following reaction at `400K`?
`2NOCI(g) hArr 2NO(g) +CI_(2)(g)`
`DeltaH^(Theta) = 77.2 kJ mol^(-1)` and `DeltaS^(Theta) = 122 J K^(-1) mol^(-1) at 400K`.

Text Solution

Verified by Experts

`DeltaG^(@) = DeltaH^(@) - TDeltaS^(@)`
`DeltaH^(@) = 77200 J mol^(-1)`
`DeltaS^(@) = 122 JK^(-1)mol^(-1), T = 400 K`
`DeltaG^(@) = 77200 - 400 xx 122`
` = 77200 - 48800`
` = 28400J mol^(-1)`
Now, `DeltaG^(@) = -RT In K`
= -2.303 RT log K
`28400 = -2.303 xx 8.314 xx 400 log K`
or `log K = -(28400)/(2.303 xx 8.314 xx 400) = -3.708`
or `log K = -bar(4).292`
K = Antilog(`bar(4)`.292) = `1.96 xx 10^(-4)`.
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