Calculate the equilibrium constant for the reaction given below at `400K`, if `DeltaH^(Theta) = 77.2 kJ mol^(-1)` and `DeltaS^(Theta) = 122 J K^(-1) mol^(-1)`
`PCI_(5)(g) rarr PCI_(3)(g) +CI_(2)(g)`

Explanation

`DeltaH^(Theta) = 77.2 mol^(-1)`
`DeltaS^(Theta) = 122 J K^(-1) mol^(-1)`
`T = 400K`
`:. DeltaG^(Theta) - T DeltaS^(Theta)`
`DeltaG^(Theta) = 77200 - 400 xx122 = 28400 J`
Also, we have `-DeltaG^(Theta) = 2.303 RT log_(10)K_(c)`
where `K_(c)` is equilibrium constant
`:. -28400 = 2.303 xx 8.314 xx 400 log_(10)K_(c)`
`:. K_(c) = 1.958 xx 10^(-4)`