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)`

Answer

`:. K_(C) = 1.958 xx 10^(-4)`

Explanation

`Delta H^(0) = 77.2 mol^(-1) , Delta S^(0) = 122 JK^(-1) mol^(-1)`
`T = 400 k, Delta G^(0) = Delta H^(0) - T Delta S^(0)`,
`Delta G^(0) = 77200 - 400 xx 122 = 28400 J`
Also, we have `-Delta G^(0) = 2.303 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)`