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

To determine whether the reaction \( \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \) at 300 K is spontaneous and exothermic, we will follow these steps:

### Step 1: Calculate the Standard Gibbs Free Energy Change (\( \Delta G^\circ \))

The standard Gibbs free energy change for a reaction can be calculated using the formula:

\[
\Delta G^\circ = \Delta G^\circ_{\text{products}} - \Delta G^\circ_{\text{reactants}}
...