Show that the reaction
`CO(g) +(1//2)O_(2)(g) rarr CO_(2)(g)`
at `300K` is spontaneous and exothermic, when the standard entropy change is `-0.094 k J mol^(-1) K^(-1)`. The standard Gibbs free energies of formation for `CO_(2)`and `CO` are `-394.4`and `-137.2kJ mol^(-1)`, respectively.

Explanation

`CO(g) +(1)/(2)O_(2) (g) rarr CO_(2)(g)`
`DeltaG^(Theta) = {G^(Theta) (CO_(2)) -[G^(Theta)(CO)+(1)/(2)G^(Theta)(O_(2))]}`
`={-394.4 -[-137.2 +0]}`
`=- 257.2 kJ`
`DeltaS^(Theta) =- 0.094 kJ mol^(-1) K^(-1)`
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)` (Gibbs-Helmholtz equation)
or `-257.2 = DeltaH^(Theta) - 300 xx (-0.094)`
or `DeltaH^(Theta) =- 285.4 kJ`
The reaction is spontaneous because `DeltaG^(Theta)` is negative.
The reaction is exothermic because `DeltaH^(Theta)` is negative.