For the reaction:
`CO(g) +H_(2)O(g) hArr CO_(2)(g) +H_(2)(g)`
`(Delta_(r)H)_(300K) = 41.2 kJ mol^(-1)`
`(Delta_(r)H)_(1200K) =- 33.0 kJ mol^(-1)`
`(Delta_(r)S)_(300K) = -4.2 xx 10^(-2) kJ mol^(-1)`
`(Delta_(r)S)_(1200K) =- 3.0 xx10^(-2) kJ mol^(-1)`
Predict the direction of spontaneity of the reaction at `300K` and `1200K`. also calculated `log_(10)K_(p)` at `300K` and `1200K`.

Explanation

Using, `Delta_(r)G = Delta_(r)H - T Delta_(r)S`
At `300K: (Delta_(r)G)_(300K) =- 4.12 - 300 xx (-4.2 xx 10^(-2))`
`= - 28.6 kJ mol^(-1)`
At `1200K: (Delta_(r)G)_(1200K) =- 33.0 - 1200 xx (-3.0 xx 10^(-2))`
`=-3 kJ mol^(-1)`
Since `Delta_(r)G` is negative at `300K` and positive at `1200K`, reaction is spontaneous at `300K` and non-spontaneous at `1200K`.
Also, `Delta_(r)G^(Theta) =- RT In K_(eq)`
SInce, `Delta_(r)G^(Theta) ` is not given, assume `(Delta_(r)G^(Theta)) = (Delta_(r)G)_(300K)`
At `300K:-28.6 =- (8.314 xx 10^(-3)) xx 300 In K_(Eq)`
`= 4.98`
`rArr log_(10) (K_(eq))_(300K) [ :' In x = 2.303 log_(10)x]`
and at `1200K: -28.6 =-(8.314 xx 10^(-3)) xx1200 In K_(eq)`
`rArr log_(10) (K_(eq))_(1200K) = 1z.24`