Final answer:
The balanced half-reaction in basic solution for the conversion of (Cr₂O₇²- → Cr³+) is (Cr₂O₇²- + 14OH⁻ → 2Cr³+ + 6H₂O + 6e⁻).
Step-by-step explanation:
The balanced half-reaction in basic solution for the conversion of (Cr₂O₇²- → Cr³+) is option d: (Cr₂O₇²- + 14OH⁻ → 2Cr³+ + 6H₂O + 6e⁻).
To balance the half-reaction, the charges on both sides of the equation need to be equal. In this case, the left side of the equation has a charge of 2- from the dichromate ion, while the right side has a charge of 6+ from the two chromium ions. By adding 6 OH⁻ ions (hydroxide ions) to the left side, the charges are balanced and the reaction is correctly balanced in basic solution.
Therefore, option d is the correct balanced half-reaction in basic solution for the conversion of (Cr₂O₇²- → Cr³+).