Complete and balance the following equations, and identify the oxidizing and reducing agents. (Recall that the O atoms in hydrogen peroxide, H₂O₂, have an atypical oxidation state.) (a) NO₂^-(aq) + Cr₂O₇^2-(aq) → Cr³⁺(aq) + NO₃^-(aq) (acidic solution) (b) S(s) + HNO₃(aq) → H₂SO₃(aq) + N₂O(g) (acidic solution) (c) Cr₂O₇^2- (aq) + CH₃OH(aq) → HCOOH(aq) + Cr³⁺(aq) (acidic solution) (d) BrO₃^-(aq) + N₂H₄(g) → Br^-(aq) + N₂(g) (acidic solution)

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Identify the oxidation states of each element in the reactants and products. For example, in \( \text{Cr}_2\text{O}_7^{2-} \), chromium has an oxidation state of +6, and in \( \text{Cr}^{3+} \), it is +3.

Determine which elements are oxidized and which are reduced by comparing the changes in oxidation states. Oxidation involves an increase in oxidation state, while reduction involves a decrease.

Write the half-reactions for the oxidation and reduction processes. For example, the reduction half-reaction involves \( \text{Cr}_2\text{O}_7^{2-} \) being reduced to \( \text{Cr}^{3+} \).

Balance each half-reaction for mass and charge. In acidic solutions, add \( \text{H}^+ \) ions to balance hydrogen and \( \text{H}_2\text{O} \) to balance oxygen.

Combine the balanced half-reactions, ensuring that the electrons lost in the oxidation half-reaction equal the electrons gained in the reduction half-reaction. Identify the oxidizing agent (the species that is reduced) and the reducing agent (the species that is oxidized).

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Oxidation and Reduction

Oxidation and reduction are chemical processes that involve the transfer of electrons between substances. Oxidation refers to the loss of electrons, resulting in an increase in oxidation state, while reduction involves the gain of electrons, leading to a decrease in oxidation state. In redox reactions, one species is oxidized and another is reduced, which is essential for balancing chemical equations.

Balancing Redox Reactions

Balancing redox reactions requires ensuring that both mass and charge are conserved. This often involves separating the reaction into half-reactions for oxidation and reduction, balancing each half for atoms and charge, and then combining them to form the overall balanced equation. In acidic solutions, hydrogen ions (H+) and water (H2O) are commonly used to achieve balance.

Identifying Oxidizing and Reducing Agents

In a redox reaction, the oxidizing agent is the substance that gains electrons and is reduced, while the reducing agent is the substance that loses electrons and is oxidized. Identifying these agents involves analyzing the changes in oxidation states of the elements involved in the reaction. This understanding is crucial for determining the roles of different reactants in the overall chemical process.