ate the balanced half-equation for the reduction of dichromate ions to chromium(III) ions.

The balanced half-equation for the reduction of dichromate ions (Cr2O7^2-) to chromium(III) ions (Cr^3+) in acidic solution is:

Cr2O7^2- + 14H^+ + 6e^- → 2Cr^3+ + 7H2O

Here's the step-by-step process:

1. Write the unbalanced equation for the reaction: Cr2O7^2- → Cr^3+

2. Balance the chromium atoms: Cr2O7^2- → 2Cr^3+

3. Balance the oxygen atoms by adding water molecules to the side that needs oxygen: Cr2O7^2- → 2Cr^3+ + 7H2O

4. Balance the hydrogen atoms by adding H^+ ions to the side that needs hydrogen: Cr2O7^2- + 14H^+ → 2Cr^3+ + 7H2O

5. Balance the charge by adding electrons (e^-) to the side that is more positive: Cr2O7^2- + 14H^+ + 6e^- → 2Cr^3+ + 7H2O

This equation is balanced in terms of both mass (atoms of each element) and charge.