Question

Consider the fuel cell that accomplishes the overall reaction

$\mathbf{CO}\left(\mathbf{g}\right)\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{O}}_{\mathbf{2}}\left(\mathbf{g}\right)\to {\mathbf{CO}}_{\mathbf{2}}\left(\mathbf{g}\right)$

Calculate the maximum electrical work that could be obtained from the conversion of 1.00 mol of CO(g) to ${\mathbf{CO}}_{\mathbf{2}}\left(\mathbf{g}\right)$ in such a fuel cell operated with 100% efficiency at 25°C and with the pressure of each gas equal to 1 atm.

Short answer

The maximum electrical work obtained per mole of carbon dioxide produced in the fuel cell is 394.36 kJ/ mol.

Step-by-step solution

The fuel cell reaction

The given fuel cell reaction is shown below:

$\mathrm{CO}\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right)$

The standard free energy change of carbon dioxide $\left({\mathrm{CO}}_2\right)$is.

${\mathrm{\Delta G}}_{\mathrm{f}}^{\mathrm{o}}=-394.36{\mathrm{kJmol}}^{-1}$

Calculate the electrical work generated per mole of carbon dioxide produced in the fuel cell

The efficiency of the fuel cell = 100%

=1.00

Standard free energy change of carbon dioxide $\left({\mathrm{CO}}_2\right)$is,

${\mathrm{\Delta G}}_{\mathrm{f}}^{\mathrm{o}}=-394.36{\mathrm{kJmol}}^{-1}$

Now calculate the maximum amount of electrical work generated per mole of carbon dioxide $\left({\mathrm{CO}}_2\right)$produced.

$$\begin{gathered} \begin{array}{l}-{\mathrm{W}}_{\max }{=-\mathrm{\epsilon \Delta G}}_{\mathrm{f}}^{\mathrm{o}}\\ =\left(-1.00\right)\left(-394.36{\mathrm{kJmol}}^{-1}\right)\end{array} \\ -{\mathrm{W}}_{\max }=394.36{\mathrm{kJmol}}^{-1} \end{gathered}$$

Hence, the maximum amount of electrical work generated per mole of carbon dioxide$\left({\mathrm{CO}}_2\right)$produced in the fuel cell is 394.36 kJ/ mol.