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`.

Explanation

Given
`T=400K , DeltaH^(@)=77.2kJmol^(-1)=77200 J " mol"^(-1), DeltaS^(@)-122JK^(-1)mol^(-1)`
`DeltaG^(@)=-2.303RT log K_(eq)`
`logK_(eq)=(DeltaG^(@))/(2.303RT)`
`logK_(eq)=((DeltaH^(@)-TDeltaS^(@)))/(2.303RT)`
`logK_(eq)=((77200-400xx122)/(2.303xx8.314xx400))`
`logK_(eq)=-((28400)/(7659))`
`logK_(eq)=-3.7080`
`K_(eq)` = antilog (-3.7080)
`K_(eq) = 1.95xx10^(-4)`