See the following chemical reaction:
Cr₂ O₇²⁻+XH⁺+6 Fₑ²⁺ → YCr³⁺+6 Fₑ³⁺+Z H₂ O
The sum of X, Y and Z is ___________

Solution

Chemistry ma’am · 4 steps

The 6 Fe already gives you 6 electrons, so balance Cr, then O with water, then H with H⁺.

1. Chromium and electrons. Each Cr goes from +6 in Cr₂O₇²⁻ to +3, gaining 3 electrons. Two Cr atoms gain 6 electrons in total, which matches the 6 lost by 6Fe²⁺ → 6Fe³⁺. Two Cr atoms on the left means Y = 2.
2. Oxygen, then hydrogen. The 7 oxygen atoms of dichromate end up in water, so Z = 7. Seven H₂O contain 14 hydrogen atoms, all supplied by H⁺, so X = 14.

   Cr₂O₇²⁻ + 14H⁺ + 6Fe²⁺ → 2Cr³⁺ + 6Fe³⁺ + 7H₂O

3. Check the charge. Left side: -2 + 14 + 12 = +24. Right side: +6 + 18 = +24. The charges match, so the equation is balanced.
4. So. X + Y + Z = 14 + 2 + 7 = 23.

The common slip: 22. Leaving Y = 1 because the formula has one dichromate ion gives 22. Dichromate holds two Cr atoms, so Y = 2.

The idea to keep. In acidic redox balancing, first match the electrons, then balance O with H₂O, then H with H⁺. Always finish with a charge check.

Answer from the NTA final answer key. Solution by PrepWiser.