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

The given reaction is,
`CO(g) + (1//2) O_(2)(g) rarr CO_(2)(g)`
`DeltaG^(Theta) ("for reaction") =G^(Theta) underset(CO_(2)).-G^(Theta)underset(CO).-(1//2) G^(Theta)underset(O_(2))`
`=- 394.4 - (-137.2)-0`
`=- 257.2 kJ mol^(-1)`
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)`
`-257.2 DeltaH^(Theta) - 298 xx (0.094)`
or `DeltaH^(Theta) =- 288.2 kJ`
`DeltaG^(Theta)` is `-ve`, hence the process is spontaneous, and `DeltaH^(Theta)` is also -ve, hence the process is also exothermic.