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

Explanation

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