Question

Balance each redox reaction occurring in basic solution. (a) \(\mathrm{NO}_{2}{ }^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{AlO}_{2}{ }^{-}(a q)\) (b) \(\mathrm{Al}(s)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)\)

Short answer

The balanced equations in basic solution are (a) \(7\mathrm{NO}_{2}{ }^{-} + 3\mathrm{Al} + 14\mathrm{OH}^{-} \rightarrow 7\mathrm{NH}_{3} + 3\mathrm{AlO}_{2}{ }^{-} + 7\mathrm{H}_{2}\mathrm{O}\) and (b) \(\mathrm{Al} + \mathrm{MnO}_{4}^{-} + 4\mathrm{OH}^{-} \rightarrow \mathrm{Al}(\(\mathrm{OH})_{4}^{-}\) + \mathrm{MnO}_{2} + 2\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

- Assign Oxidation Numbers

First, determine the oxidation states of the atoms in both the reactants and products. For equation (a), \(\mathrm{NO}_{2}{ }^{-}\) has a nitrogen with an oxidation state of +3, aluminum \(\mathrm{Al}\) is at 0, ammonia \(\mathrm{NH}_{3}\) has nitrogen at -3, and in \(\mathrm{AlO}_{2}{ }^{-}\), Al is at +3. In equation (b), \(\mathrm{Al}\) is 0, \(\mathrm{MnO}_{4}^{-}\) has Mn at +7, \(\mathrm{MnO}_{2}\) is Mn at +4, and in \(\mathrm{Al}(\mathrm{OH})_{4}^{-}\), Al is at +3.

- Separate into Half-Reactions

Break down the equations into two half-reactions: one for oxidation and one for reduction. For (a), the two half-reactions are: \(\mathrm{NO}_{2}{ }^{-} \rightarrow \mathrm{NH}_{3}\) and \(\mathrm{Al} \rightarrow \mathrm{AlO}_{2}{ }^{-}\). For (b), the half-reactions are: \(\mathrm{Al} \rightarrow \mathrm{Al}(\(\mathrm{OH})_{4}^{-}\)\) and \(\mathrm{MnO}_{4}^{-} \rightarrow \mathrm{MnO}_{2}\).

- Balance Elements Other Than O and H

For each half-reaction, balance all elements except oxygen and hydrogen. In (a), both half-reactions are already balanced. In (b), \(\mathrm{Al}\) is balanced, while for the reduction reaction, \(\mathrm{MnO}_{4}^{-}\) to \(\mathrm{MnO}_{2}\), no additional balancing is required.

- Balance Oxygen by Adding H2O

Balance oxygen by adding \(\mathrm{H}_{2}\mathrm{O}\) molecules. For (a), add 2 \(\mathrm{H}_{2}\mathrm{O}\) to the product side of the reduction half-reaction. For (b), add 2 \(\mathrm{H}_{2}\mathrm{O}\) to the product side of the reduction half-reaction.

- Balance Hydrogen by Adding OH-

Balance hydrogen by adding \(\mathrm{OH}^{-}\). For (a), add 4 \(\mathrm{OH}^{-}\) to the reactant side of the reduction half-reaction. For (b), add 4 \(\mathrm{OH}^{-}\) to the reactant side to balance the 4 H from the 2 \(\mathrm{H}_{2}\mathrm{O}\) on the product side.

- Balance Charge by Adding Electrons

Balance the charge of each half-reaction by adding electrons. For (a), add 3 e- to the oxidation and 7 e- to the reduction half-reaction. For (b), the oxidation half-reaction is already balanced, add 3e- to the reduction half-reaction.

- Make Electron Transfer Equal

Ensure the number of electrons gained and lost is the same in both half-reactions by finding the least common multiple and scaling the half-reactions appropriately. For (a), multiply the oxidation half-reaction by 7 and the reduction half-reaction by 3 to have 21 electrons in both. For (b), no scaling is needed as 3 electrons are transferred in the reduction half-reaction, and no electrons are transferred in the oxidation half-reaction.

- Combine and Simplify the Half-Reactions

Combine the half-reactions back into one equation and simplify. For (a), combine the scaled half-reactions and cancel out common species to get the final balanced reaction: \(7\mathrm{NO}_{2}{ }^{-} + 3\mathrm{Al} + 14\mathrm{OH}^{-} \rightarrow 7\mathrm{NH}_{3} + 3\mathrm{AlO}_{2}{ }^{-} + 7\mathrm{H}_{2}\mathrm{O}\). For (b), combine the half-reactions to get: \(\mathrm{Al} + 4\mathrm{OH}^{-} + \mathrm{MnO}_{4}^{-} \rightarrow \mathrm{Al}(\(\mathrm{OH})_{4}^{-}\) + \mathrm{MnO}_{2}\), then add 2 \(\mathrm{H}_{2}\mathrm{O}\) to products to balance.

Key concepts

Oxidation Numbers

Understanding oxidation numbers is crucial in the study of redox (reduction-oxidation) reactions, as they help identify how electrons are transferred in a chemical reaction. An oxidation number is a positive or negative number assigned to an atom based on a set of rules. These rules include assigning 0 to a pure element, the charge of an ion to its monatomic form, and specific common oxidation states to elements like oxygen and hydrogen (-2 and +1, respectively, in most cases).

For instance, in the reaction \(\mathrm{NO}_{2}^{-}\) becomes \(\mathrm{NH}_{3}\), the nitrogen's oxidation number changes from +3 to -3. Identifying these numbers allows for the next steps in balancing a redox reaction, where identifying the electrons lost and gained by each atom or ion is essential. Remember, electrons are lost from the atom with an increased oxidation state (oxidation), and gained by the atom with a decreased oxidation state (reduction).

Half-Reaction Method

The half-reaction method is a systematic approach for balancing redox reactions, especially useful in complex reactions occurring in basic or acidic solutions. It involves dividing the overall reaction into two separate half-reactions - one for oxidation and one for reduction - then balancing each individually before recombining them.

Each half-reaction is balanced for mass and charge. Balancing mass involves ensuring that the same number of each type of atom appears on both sides of the reaction. Charge is balanced by adding electrons. In the example provided, the \(\mathrm{NO}_{2}^{-} \rightarrow \mathrm{NH}_{3}\) half-reaction is the reduction process, and \(\mathrm{Al} \rightarrow \mathrm{AlO}_{2}^{-}\) is the oxidation process. Here, balancing involves steps like adding water molecules to balance oxygen atoms and hydroxide ions (\(\mathrm{OH}^{-}\)) to balance hydrogen in a basic solution.

Basic Solution Chemistry

When balancing redox reactions in basic solutions, it is important to remember that the presence of \(\mathrm{OH}^{-}\) ions affects how you balance hydrogen and oxygen atoms. After separating the reaction into half-reactions, you first balance all elements except for oxygen and hydrogen. Then, add water molecules (\(\mathrm{H}_{2}\mathrm{O}\)) to balance the oxygen atoms. Finally, balance hydrogens by adding hydroxide ions to the side deficient in hydrogen.

For instance, in the reaction given, balancing in a basic solution involves adding \(\mathrm{OH}^{-}\) ions to counteract the \(\mathrm{H}_{2}\mathrm{O}\) added for oxygen balance. This maintains the necessary conditions for a reaction within a basic environment.

Electron Transfer

Electron transfer is the essence of redox reactions, where electrons are moved from one species to another. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. In balancing redox reactions, it is mandatory to ensure that the electrons lost are equal to the electrons gained. This principle maintains the conservation of charge.

For example, in the given solution, we balance electrons by adding them directly to the half-reactions. The number of electrons added must equal the difference in oxidation numbers from the reactants to products. In complex cases, half-reactions are often multiplied by appropriate factors to equalize the number of electrons transferred, facilitating the combination of the half-reactions into a balanced overall reaction.

Chemical Reaction Balancing

The final step of balancing a redox reaction is recombining the half-reactions into a single balanced equation. This must account for all atoms and charges. After balancing for mass with atoms and charge with electrons in the half-reactions, it is crucial to make the electron transfer equal. If necessary, multiply the half-reactions by factors to achieve this. Once the electrons are balanced, you can add the half-reactions together.

In our examples, for reaction (a), the oxidation half-reaction is multiplied by 7 and the reduction by 3 to ensure 21 electrons are transferred in each. This way, when combined, the electron numbers cancel out, and you can simplify to arrive at the final balanced equation. The meticulous step-by-step approach ensures accuracy in often complex chemical reaction balancing.