In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_{3} \mathrm{OH}(l)+3 / 2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(l)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation…

Question

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is
$\mathrm{CH}_{3} \mathrm{OH}(l)+3 / 2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(l)$
At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_{3} \mathrm{OH}(l), \mathrm{H}_{2} \mathrm{O}(l)$ and and $\mathrm{CO}_{2}(g)$ are $-166.2-237.2$ and
$-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If standard enthalpy of combustion of methonal is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, find the efficiency (in %) of the fuel cell :

Aicharya · Accepted Answer

$\mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) ightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
$\Delta G_{\mathrm{r}}=\left[\Delta G_{\mathrm{f}}\left(\mathrm{CO}_{2}, gight)+2 \Delta G_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}, \ellight)ight]-$
$\quad\left[\Delta G_{\mathrm{f}}\left(\mathrm{CH}_{3} \mathrm{OH}, \ellight)+\frac{3}{2} \Delta G_{\mathrm{f}}\left(\mathrm{O}_{2}, gight)ight.$
$=-394.4+2(-237.2)-(-166.2)-0$
$=-394.4-474.4+166.2=-702.6 \mathrm{~kJ}$
$\%$ efficiency $=\frac{702.6}{726} \times 100=97 \%$

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is…

Solution