Question

A promising technology based on a redox reaction is the direct methanol fuel cell. Instead of hydrogen, it uses liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), as a fuel. The unbalanced reaction is \(\mathrm{CH}_{3} \mathrm{OH}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\). (a) Assign oxidation states to each atom in the reaction. (b) Determine what is being oxidized and what is being reduced. (c) Write and balance the separate half-reactions. (Hint: Methanol reacts to form carbon dioxide, and oxygen reacts to form water.) (d) Balance the overall reaction if it occurs in acidic solution. (e) Methanol fuel cells must be designed to allow \(\mathrm{H}^{+}\)to pass from one electrode to the other. Do they start at the electrode with the methanol or at the electrode with the oxygen? How do you know?

Short answer

Carbon in \(\mathrm{CH}_{3}\mathrm{OH}\) is oxidized and oxygen in \(\mathrm{O}_{2}\) is reduced. The balanced half-reactions in acidic solution are \(\mathrm{CH}_{3}\mathrm{OH} + \mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{CO}_{2} + 6 \mathrm{H}^{+} + 6 \mathrm{e}^{-}\) for oxidation and \(\frac{3}{2} \mathrm{O}_{2} + 6 \mathrm{H}^{+} + 6 \mathrm{e}^{-} \longrightarrow 3 \mathrm{H}_{2}\mathrm{O}\) for reduction. \(\mathrm{H}^{+}\) ions start at the electrode with methanol.

Step-by-step solution

Assign Oxidation States

To assign oxidation states, remember that the sum of oxidation states for a compound must equal the charge of the compound, which is 0 for neutral molecules. Oxygen is typically assigned an oxidation state of -2 in compounds (except in peroxides or when bonded to fluorine). Hydrogen is usually +1 when bonded to nonmetals, and -1 when bonded with metals. Carbon's oxidation state is determined by balancing the overall charge of the molecule. Start by assigning the oxidation states to all elements in the reactants and products: For \(\mathrm{CH}_{3}\mathrm{OH}\), C is -2, each H is +1, and O is -2. For \(\mathrm{O}_{2}\), each O is 0 (oxygen molecule). For \(\mathrm{CO}_{2}\), C is +4, each O is -2. For \(\mathrm{H}_{2}\mathrm{O}\), each H is +1, and O is -2.

Identify Oxidation and Reduction

Elements that increase in oxidation state are oxidized, and elements that decrease in oxidation state are reduced. Comparing the assigned oxidation states: Carbon in methanol (from -2 to +4) is oxidized; Oxygen in \(\mathrm{O}_{2}\) (from 0 to -2) is reduced.

Write Half-Reactions

Write the half-reactions by considering oxidation and reduction separately. Oxidation half-reaction: \(\mathrm{CH}_{3}\mathrm{OH} \longrightarrow \mathrm{CO}_{2}\); Reduction half-reaction: \(\mathrm{O}_{2} \longrightarrow \mathrm{H}_{2}\mathrm{O}\). Now balance the elements other than O and H, then balance O by adding \(\mathrm{H}_{2}\mathrm{O}\), and H by adding \(\mathrm{H}^{+}\), finally balance charge by adding electrons, \(\mathrm{e}^{-}\).

Balance Overall Reaction in Acidic Solution

Combine the half-reactions by making the number of electrons equal in both half-reactions. Multiply the oxidation and reduction half-reactions by appropriate coefficients to balance the electrons. Then sum the half-reactions to get the balanced overall reaction, ensuring that the number of atoms and charges on both sides are equal.

Determine Electrode for \(\mathrm{H}^{+}\) Transfer

Since \(\mathrm{H}^{+}\) ions are produced at the anode where oxidation occurs, and are consumed at the cathode where reduction occurs, \(\mathrm{H}^{+}\) ions start at the electrode with methanol (where \(\mathrm{H}^{+}\) ions are produced) and move to the electrode with oxygen (where they are consumed).

Key concepts

Redox Reactions

Redox reactions are a fundamental type of chemical reaction involving the transfer of electrons from one substance to another. These reactions consist of two components: oxidation, where one species loses electrons, and reduction, where another gains electrons. In a direct methanol fuel cell, methanol (CH₃OH) reacts with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O). During the process, methanol is oxidized to CO₂, losing electrons, and oxygen is reduced to water, gaining those electrons.

To grasp these concepts better, remember that in redox reactions, look for atoms that change their environment in a way that affects electrons. In methanol fuel cells, carbon's environment changes significantly from methanol to carbon dioxide, indicating an oxidation reaction has occurred. Similarly, oxygen's environment changes in reduction when forming water from molecular oxygen.

Oxidation States

Understanding oxidation states is crucial for analyzing redox reactions. Oxidation state, also known as oxidation number, is a conceptual charge assigned to an atom in a molecule or ion based on certain rules. It indicates the degree of oxidation or reduction of an atom. For example, in the provided exercise, carbon in methanol has an oxidation state of -2 but in carbon dioxide, it's +4.

Here's a simple tip: elements in their elemental form have an oxidation state of 0. Oxygen usually has an oxidation state of -2 (except in peroxides and when bonded to fluorine), and hydrogen is typically +1 when bonded to nonmetals. Assigning these helps identify which atoms undergo change in redox reactions.

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry, ensuring that the same number of each type of atom appears on both sides of the equation, in accordance with the Law of Conservation of Mass. In the context of methanol fuel cells, the initial unbalanced equation is CH₃OH + O₂ → CO₂ + H₂O. The process of balancing involves adjusting coefficients (the numbers before molecules) without altering the subscripts that indicate the number of atoms in each molecule.

For instance, after identifying the reactants and products, determine the number of each type of atom on both sides and systematically add coefficients to balance the atoms step by step. Remember, balance less common atoms first and leave oxygen and hydrogen for last, as they are often found in multiple compounds.

Half-Reaction Method

The half-reaction method is an effective way to balance complex redox reactions. It breaks down the overall reaction into two separate halves—one for oxidation and one for reduction. Each half-reaction is balanced on its own for both atoms and charge. After balancing, the two half-reactions are combined to form the balanced overall redox reaction.

To put it into practice, first write down the half-reactions for the species being oxidized and reduced. Next, balance all atoms other than oxygen and hydrogen, balance oxygen atoms by adding H₂O, hydrogen atoms by adding H⁺ ions, and finally, balance the charge by adding electrons, e^-. To complete the process, ensure the electrons cancel out by multiplying each half-reaction by the appropriate coefficients.

Acidic Solution Reactions

Reactions in acidic solutions are important considerations when balancing redox reactions. In an acidic medium, the presence of excess H⁺ ions must be factored into the balancing process, particularly when dealing with half-reactions. In the direct methanol fuel cell's redox reaction, once half-reactions are written, they are balanced for hydrogen by adding H⁺ ions as required.

When balancing reactions in an acidic solution, after equilibrating the number of atoms and the charge, verify that the number of H⁺ ions aligns with the acidic environment conditions. Understanding the movement of protons (H⁺ ions) in fuel cells is vital as they're an integral part of the cells' electrochemistry and relate to the cell's design.