In a fuel cell methanol is oxidised with oxygen as : `CH_(3)OH(l) + 3/2O_(2)(g) to CO_(2)(g) + 2H_(2)O(l)`
Calculate the standard Gibbs energy change for the reaction that can be converted into electrical works. If standard enthalpy of combustion for methanol is `726 kJ mol^(-1)`, calculate the efficiency of conversion of Gibbs energy into useful work. The standard Gibbs energies of formation, `Delta_(f)G^(@)(kJ mol^(-1))` are :
`CO_(2)(g) = -394.4, H_(2)O(l) = -237.2, CH_(3)OH(l) = -166.2`.

Explanation

To solve the problem, we need to calculate the standard Gibbs energy change (ΔG) for the given reaction and then determine the efficiency of converting Gibbs energy into useful work.

**Step 1: Write the reaction and identify the components.**
The reaction given is:
\[ \text{CH}_3\text{OH}(l) + \frac{3}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \]

**Step 2: Use the Gibbs energy of formation values to calculate ΔG.**
The formula for calculating ΔG for the reaction is:
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