Final answer:
Chromium is reduced from +6 to +3, and carbon is oxidized from +3 to +4 in the provided chemical reaction, which takes place in a basic solution.
Step-by-step explanation:
In the given reaction Cr₂O₇²⁻ (aq) + C₂O₄²⁻ (aq) = Cr⁺³(aq) + CO₂ (g), we can identify the elements that are oxidized and reduced by analyzing the changes in their oxidation states. Chromium (Cr) is reduced since its oxidation state decreases from +6 in Cr₂O₇²⁻ to +3 in Cr⁺³(aq). Carbon (C) is oxidized as its oxidation state increases from +3 in C₂O₄²⁻ to +4 in CO₂.
Reduction: Cr₂O₇²⁻ (aq) + 14H+ (aq) + 6e⁻ → 2Cr⁺³ (aq) + 7H₂O (l)
Oxidation: C₂O₄²⁻ (aq) → 2CO₂ (g) + 2e⁻
The overall reaction occurs in a basic solution where the balance of atoms and charge is maintained with the addition of OH⁻ as opposed to H+ ions.