In a fuel cell, methanol if used as fuel and oxygen gas is used as an oxidiser. The reaction is
`CH_(3)OH(l) +(3)/(2)O_(2)(g)rarrCO_(2)(g)+2H_(2)O(l)`
Calculated standard Gibbs free enegry change for the reaction that can be converted into electrical work. If standard enthalpy of combustion for methanol is `-702 kJ mol^(-1)`, calculate the efficiency of conversion of Gibbs energy into useful work.
`Delta_(f)G^(Theta)` for `CO_(2),H_(2)O, CH_(3)OH,O_(2)` is `-394.00, -237.00,-166.00`and `0 kJ mol^(-1)` respectively.

Explanation

To solve the problem, we need to calculate the standard Gibbs free energy change (ΔG°) for the given reaction and then determine the efficiency of the conversion of Gibbs energy into useful work. Here are the steps to arrive at the solution:

### Step 1: Write the Balanced Reaction
The balanced reaction for the combustion of methanol 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: Identify the Standard Gibbs Free Energy Values
We are given the standard Gibbs free energy of formation (ΔG°f) for the substances involved:
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