Because of recent advances in recovery technology, the supply of natural gas, which is mostly methane, has increased significantly. If 1 mole of methane is consumed in a fuel cell powering an automobile, estimate the maximum amount of work that can be produced by the electric motor. The data in the table below may be helpful. $\begin{array} { l l l l } \text { Species } &\Delta^{H_{\mathrm{f}}^{\circ}} & S^{\circ} &\Delta^{G_{\mathrm{f}}^{\circ}}\\mathrm { CH } _ { 4 } ( g ) & - 75 \mathrm {~kJ} \mathrm {~mol} ^ { - 1 } & 186 \mathrm {~J} \mathrm {~mol} ^ { - 1 } \mathrm {~K} ^ { - 1 } & - 51 \mathrm {~kJ} \mathrm {~mol} ^ { - 1 } \ \mathrm { O } _ { 2 } ( g ) & 0 & 205 & 0 \ \mathrm { H } _ { 2 } \mathrm { O } ( g ) & - 242 & 189 & - 229 \ \mathrm { CO } _ { 2 } ( g ) & - 394 & 214 & - 394 \end{array}$

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The Answer of Because of recent advances in recovery technology, the supply of natural gas, which is mostly methane, has increased significantly. If 1 mole of methane is consumed in a fuel cell powering an automobile, estimate the maximum amount of work that can be produced by the electric motor. The data in the table below may be helpful. $\begin{array} { l l l l } \text { Species } &\Delta^{H_{\mathrm{f}}^{\circ}} & S^{\circ} &\Delta^{G_{\mathrm{f}}^{\circ}}\\mathrm { CH } _ { 4 } ( g ) & - 75 \mathrm {~kJ} \mathrm {~mol} ^ { - 1 } & 186 \mathrm {~J} \mathrm {~mol} ^ { - 1 } \mathrm {~K} ^ { - 1 } & - 51 \mathrm {~kJ} \mathrm {~mol} ^ { - 1 } \ \mathrm { O } _ { 2 } ( g ) & 0 & 205 & 0 \ \mathrm { H } _ { 2 } \mathrm { O } ( g ) & - 242 & 189 & - 229 \ \mathrm { CO } _ { 2 } ( g ) & - 394 & 214 & - 394 \end{array}$

Because of Recent Advances in Recovery Technology, the Supply of Natural