Question

Balance each redox reaction occurring in basic aqueous solution. $$\begin{array}{l}{\text { a. } \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)} \\ {\text { b. } \mathrm{Al}(s)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)} \\\ {\text { c. } \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{Cl}^{-}(a q)+\mathrm{ClO}^{-}(a q)}\end{array}$$

Short answer

After balancing each equation using the half-reaction method, the balanced reactions in basic solution are: a) \(3H_2O_2(aq) + 2ClO_2(aq) \longrightarrow 2ClO_2^-(aq) + O_2(g) + 2H_2O(l)\), b) \(4Al(s) + 3MnO_4^-(aq) + 8OH^-(aq) \longrightarrow 3MnO_2(s) + 4Al(OH)_4^-(aq) + 2H_2O(l)\), c) \(3Cl_2(g) + 6OH^-(aq) \longrightarrow 5Cl^-(aq) + ClO^-(aq) + 3H_2O(l)\).

Step-by-step solution

Separate the Reaction into Two Half-Reactions

For each equation, we need to separate the redox reaction into two half-reactions: one for oxidation and one for reduction.

Balance the Atoms in Each Half-Reaction

Balance all atoms except for hydrogen and oxygen. Then balance oxygen by adding water molecules and balance hydrogen by adding hydroxide ions on the same side.

Balance the Charges in Each Half-Reaction

Balance the charges by adding electrons. In basic solution, for every H+ that needs to be added, add an OH- to both sides of the reaction.

Equalize the Number of Electrons in Both Half-Reactions

Multiply the half-reactions by appropriate coefficients so that the number of electrons gained and lost in each half-reaction will be equal when they are added.

Combine the Half-Reactions

Add the two half-reactions together, canceling out terms that appear on both sides to get the final balanced equation.

Verify the Balance of Atoms and Charges

Check that all atoms and the charge are balanced in the final equation to ensure the law of conservation of mass and charge is satisfied.

Key concepts

Half-Reaction Method

The half-reaction method is a systematic approach for balancing redox (oxidation-reduction) reactions, particularly useful in basic aqueous solutions. This method divides the overall chemical reaction into two separate half-reactions: one for the oxidation process and one for the reduction process.

In oxidation, an element loses electrons, which is represented by an increase in its oxidation state. Conversely, during reduction, an element gains electrons, resulting in a decrease in its oxidation state. By splitting the reaction, it becomes easier to balance the chemicals involved in each half-reaction.

Steps in the Half-Reaction Method

• Identify and write down the oxidation and reduction half-reactions separately.
• Balance all atoms in each half-reaction, except for oxygen and hydrogen.
• Balance oxygen atoms by adding H₂O molecules and hydrogen atoms by adding OH^- ions to the appropriate side of the equation.
• Balance the charges by adding electrons (e^-) to either the reactants or products side, as needed.
• Equalize the number of electrons lost in the oxidation half-reaction with the number gained in the reduction half-reaction by multiplying the half-reactions by appropriate coefficients.
• Combine the two half-reactions and cancel out common terms to obtain the balanced overall reaction.
• Verify that the number of atoms and the charge are balanced in the final equation.

Oxidation-Reduction Reactions

Oxidation-reduction, or redox, reactions are chemical processes where electrons are transferred between substances. These reactions involve a change in the oxidation states of elements—during oxidation, the oxidation state increases, and during reduction, it decreases.

Redox reactions are essential in various biological processes, industrial applications, and energy storage systems like batteries. Understanding these reactions is critical for many fields of science, such as chemistry, biochemistry, and environmental science.

Identifying Redox Reactions

Paying attention to substance changes can help identify redox reactions:

• An element's oxidation state increases or decreases.
• Electrons are explicitly mentioned in the reaction.
• The reaction involves transfer of oxygen, hydrogen, or electrons between substances.

In complex scenarios, the half-reaction method is a valuable tool to differentiate and balance the processes of oxidation and reduction.

Chemical Equations Balancing

Balancing chemical equations is the process of ensuring that the number of atoms for each element, as well as the total charge, is the same on both sides of the equation. This practice honors the law of conservation of mass and charge. When dealing with redox reactions, balancing becomes more intricate due to the electron transfer that occurs.

The aim is not only to balance the atoms but also to make sure that the electrons lost in oxidation equal the electrons gained in reduction. In basic solutions, hydroxide ions (OH^-) are used to balance hydrogen atoms, while in acidic solutions, hydrogen ions (H⁺) are used.

Critical Points for Balancing

• Ensure all elements except oxygen and hydrogen are balanced first.
• Use water (H₂O) to balance oxygen atoms.
• Use hydroxide ions (OH^-) to balance hydrogen atoms in basic solutions.
• Add electrons (e^-) to balance the overall charge.
• Combine balanced half-reactions and cancel repeating entities.

Balanced reactions are vital for accurately predicting the quantities of reactants needed and products formed in chemical processes.

Stoichiometry

Stoichiometry is the aspect of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. It's based on the balanced chemical equation and allows for calculations of how much of a substance is needed or produced.

In redox reactions, stoichiometry involves meticulous accounting not just for the amount of each substance but also for the electrons transferred. This ensures that the equivalence in consumption and production is maintained, and all mass and charge are conserved.

Stoichiometric Calculations

Steps in stoichiometric calculations include:

• Starting with a balanced chemical equation.
• Using molar ratios from the balanced equation to convert between moles of different substances.
• Accounting for the limiting reagent, which determines the maximum amount of product formed.
• Calculating theoretical yields and possibly comparing them with actual yields to determine efficiency.

Successful stoichiometric calculations require a solid understanding of the mole concept, molar masses, and Avogadro's number.