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Gibbs Free Energy & Spontaneity

In a fuel cel...

Question

In a fuel cell, methanol is used as fuel and oxygen gas is used as an oxidiser. The reaction is:
${C H}_{3} O H (l) + \frac{3}{2} O_{2} (g) ⟶ \frac{1}{2} C O_{2} (g) + 2 H_{2} O (l)$
Calculate standard Gibbs free energy change for the reaction that can be converted into electrical work. If the standard enthalpy of combustion for methanol is $- 726 k J {m o l}^{- 1}$ , calculate the efficiency of conversion of Gibbs energy into useful work.

$Δ G_{f}^{o}$ for ${C O}_{2}, H_{2} O, {C H}_{3} O H, O_{2}$ are $- 394.36; - 237.13; - 166.27$ and zero respectively.

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Solution

The reaction for combustion of methanol is:
${C H}_{3} O H (l) + \frac{3}{2} O_{2} (g) ⟶ \frac{1}{2} C O_{2} (g) + 2 H_{2} O (l)$

$Δ G_{r e a c t i o n}^{o} = [Δ G_{f}^{o} C O_{2} (g) + 2 Δ G_{f}^{o} H_{2} O (l)] - [Δ G_{f}^{o} {C H}_{3} O H (l) + \frac{3}{2} Δ G_{f}^{o} O_{2} (g)]$

$[- 394.36 + 2 (- 237.13)] - [- 166.27 + 0]$

$= - 702.35 k J {m o l}^{- 1}$

The efficiency of conversion of Gibbs free energy into useful work

$= \frac{Δ G_{r e a c t i o n}^{o} \times 100}{Δ H_{r e a c t i o n}^{o}} = \frac{- 702.35 \times 100}{- 726} = 96.7$

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Q. If a fuel cell, methanol is used as fuel and oxygen gas is used as an oxidiser. The reaction is

C H_{3} O H_{(l)} + \frac{3}{2} O_{2} (g) \to C O_{2} (g) + 2 H_{2} O (g)

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standard Gibb’s energies of formation for

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The reaction is:

C H_{3} O H (l) + \frac{3}{2} O_{2} (g) \to C O_{2} (g) + 2 H_{2} O (l)

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, standard Gibb's energies of formation for

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