Question

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`.

Answer 1

According to Gibbs-Helmholtz equation,
`DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)=77.2-400xx122xx10^(-3)`
`=28.4kJ=28.4xx10^(3)J`
We know that, `DeltaG^(@)=-2.303RT" log "K_(C)`
`thereforelogK_(C)=(-DeltaG^(@))/(2.303RT)=-(28.4xx10^(3))/(2.303xx8.314xx400)=-3.7081`
`K_(C)=antilog(-3.7081)=1.958xx10^(-4)`