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Chapter 17: Problem 75

A fuel cell uses methanol, CH \(_{3} \mathrm{OH},\) as fuel. Assuming complete oxidation of the fuel to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) in acidic aqueous solution, how many electrons are transferred per \(\mathrm{CH}_{3} \mathrm{OH}\) molecule?

Short Answer

Expert verified
The total number of electrons transferred per molecule of methanol (\(CH_{3}OH\)) during the complete oxidation process is 4.

Step by step solution

01

Write the Balanced Chemical Equation for the Complete Oxidation of Methanol

The complete oxidation of methanol (\(CH_{3}OH\)) in an acidic aqueous solution can be represented as follows:\n\n\(CH_{3}OH + H_{2}O -> CO_{2} + 4H^{+} + 4e^{-}\)\n\nWhich shows that for each molecule of methanol, 4 electrons are released.
02

Determine Oxidation Numbers

We calculate the oxidation number of carbon in \(CH_{3}OH\) and \(CO_{2}\). In \(CH_{3}OH\), carbon has an oxidation number of -2 while in \(CO_{2}\), carbon has an oxidation number of +4. The difference in oxidation state corresponds to the number of electrons transferred.
03

Calculate Electron Transfer

The change in oxidation state from -2 to +4 shows a change of 6. However, looking back at the balanced equation, we see that the transfer from each \(CH_{3}OH\) molecule is actually 4 electrons. This implies that our balanced equation accommodates for other molecular mechanisms, making the effective transfer from methanol 4 electrons.

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