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.

Answer

`Delta G^(@)` is negative; `Delta H` is negative

Explanation

Following reaction takes places `CO(g) + (1)/(2) O_(2) rarr CO_(2) (g)`
We know, `Delta G^(0) = Delta G_(("Product"))^(@) - Delta G_(("Reactant"))^(@) = -394.4 - [- 137.2 + 0] = - 257.2 kJ mol^(-1)`
Since `Delta G^(@)` is negative so the reaction is feasible i.e., spontaneous, Again `Delta G^(@) = Delta H^(@) - T Delta S^(@) - 257.2 = Delta H^(@) - 300 (-0.094) rArr Delta H^(@) = - 285.4 kJ mol^(-1)`
since the value of `Delta H` is negative so the reaction is exothermic.