Answer:
c. Six electrons are consumed
Step-by-step explanation:
The first step is to ensure that the chromium atoms are balanced by adjusting the coefficients if needed. Do so by giving the Cr3+ ion a coefficient of 2.
Cr2O2−7 ⟶ 2Cr3+ (aq)
Next, balance the oxygen atoms by adding H2O molecules. The half-reaction has seven O atoms on the left and none on the right, so add 7H2O (l) to the right side.
Cr2O2−7 ⟶ 2Cr3+ (aq) + 7H2O (l)
Next, balance the hydrogen atoms by adding H+ ions. The half-reaction has 14 H atoms on the right side and none on the left, so add 14H+(aq) to the left side.
Cr2O2−7 + 14H+ (aq) ⟶ 2Cr3+ (aq) + 7H2O (l)
At this point, the charge can be balanced by adding electrons (e−). To do so, find the total charge on each side of the reaction. The left side has a total charge of (−2) + 14 × (+1) = 12+. The right side has a total charge of 2 × (+3) = 6+. Adding 6e− to the left side brings the charge down to 6+ to match the right side.
Cr2O2−7 + 14H+ (aq) +6e− ⟶ 2Cr3+ (aq) + 7H2O (l)
This gives us the answer to the question, which is that six electrons are consumed, since they are on the left side of the equation. Note that it does not make a difference whether the reaction is assumed to be in an acidic or a basic solution. The extra step taken for a basic solution is to add the same number of OH− ions to both sides of the reaction, which does not affect the number of electrons needed to balance the charges.