What are the numbers of protons ( H ^+ ) and electrons ( e ^- ), respectively, required for the reduction of [ Cr ₂ O ₇]²⁻ to Cr ³⁺ under an aqueous acidic condition?

Step-by-step solution

The balanced half-reaction for the reduction of dichromate ion in an acidic medium is written as follows: [ Cr ₂ O ₇]²⁻ Cr ³⁺ Balancing the chromium atoms: [ Cr ₂ O ₇]²⁻ 2 Cr ³⁺ Balancing the oxygen atoms by adding water molecules: [ Cr ₂ O ₇]²⁻ 2 Cr ³⁺ + 7 H ₂ O Balancing the hydrogen atoms by adding protons ( H ^+ ): [ Cr ₂ O ₇]²⁻ + 14 H ^+ 2 Cr ³⁺ + 7 H ₂ O Balancing the charge by adding electrons ( e ^- ): [ Cr ₂ O ₇]²⁻ + 14 H ^+ + 6 e ^- 2 Cr ³⁺ + 7 H ₂ O Thus, 14 protons and 6 electrons are required. Answer: