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

`DeltaG^(@)` (For the reaction)
`=G_((f))^(@)("products")-G_((f))^(@)("reactants")`
`=G_(f)^(@)(CO_(2))-[G_((f))^(@)(CO)+1/2G_((f))^(@)(O_(2))]`
`=-394.4-[-137.2+0][ :' G_((f))^(@)(O_(2))=0]`
`=-257.2 kJ`
Since `DeltaG^(@)` for reaction is negative, so the reaction is
Spontaneous.
Also, `DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)`
or `-257.2=DeltaH^(@)-(300xx-0.094)`
`:. DeltaH^(@)=-285.4 k J`
`DeltaH^(@)` is negative and thus reaction is exothermic.