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)toCO_(2)(g)`
`DeltaG^(@)("For reaction")=G_(CO_(2))^(@)-G_(CO)^(@)-((1)/(2))G_(O_(2))^(@)`
`=-394.4-(-137.2)-0`
`=257.2kJ" "mol^(-1)`
`DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)`
`-257.2=DeltaH^(@)-298xx(-0.094)`
or `DeltaH^(@)=-285.2kJ`
or `DeltaG^(@)` is -ve, hence the process is spontaneous, and `DeltaH^(@)` is also -ve, hence the process is also exothermic.