Balance the following half-reactions. (a) (acidic) Cr₂O₇^2-(aq) → Cr³⁺(aq)

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Identify the oxidation states of chromium in \( \text{Cr}_2\text{O}_7^{2-} \) and \( \text{Cr}^{3+} \).

Determine the change in oxidation state for chromium and balance the number of chromium atoms on both sides of the equation.

Balance the oxygen atoms by adding water molecules (\( \text{H}_2\text{O} \)) to the side that needs more oxygen.

Balance the hydrogen atoms by adding hydrogen ions (\( \text{H}^+ \)) to the side that needs more hydrogen.

Balance the charge by adding electrons (\( e^- \)) to the more positive side to equalize the charge on both sides.

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Half-Reaction Method

The half-reaction method involves separating a redox reaction into its oxidation and reduction components. Each half-reaction is balanced for mass and charge, allowing for a clearer understanding of electron transfer. This method is particularly useful in acidic or basic solutions, where additional ions like H+ or OH- may be added to achieve balance.

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Method 1 of Radioactive Half-Life

Balancing Redox Reactions in Acidic Medium

When balancing redox reactions in an acidic medium, one must account for hydrogen ions (H+) and water (H2O) to balance the number of atoms and charges. In the case of the given half-reaction, H+ ions are added to balance the oxygen atoms from the Cr2O7^2- ion, while water is used to balance any excess hydrogen atoms.

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Balancing Acidic Redox Reactions

Oxidation States

Oxidation states indicate the degree of oxidation of an atom in a compound, helping to identify which species are oxidized and reduced in a reaction. In the provided half-reaction, chromium changes from an oxidation state of +6 in Cr2O7^2- to +3 in Cr^3+, illustrating the reduction process. Understanding oxidation states is crucial for correctly balancing redox reactions.

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