Metal deficiency defect is shown by Fe 0.93 O. In the crystal, some Fe²⁺ cations are missing and loss of positive charge is compensated by the presence of Fe³⁺ ions. The percentage of Fe²⁺ ions in the Fe 0.93 O crystals is __________. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

Let the oxide ions fix the total charge, then split the 0.93 iron between +2 and +3.

1. Set up unknowns. For every 1 oxide ion there are 0.93 iron ions in total. Let x of them be Fe²⁺, so 0.93 - x are Fe³⁺.
2. Balance the charge. The crystal is neutral, so the positive charge on the iron must equal the -2 charge on one O²⁻.

   2x + 3(0.93 - x) = 2 ⇒ 2.79 - x = 2 ⇒ x = 0.79

3. Take the fraction. So there are 0.79 Fe²⁺ and 0.14 Fe³⁺ out of 0.93 iron ions. The percentage of Fe²⁺ is 0.79/0.93 × 100 = 84.9%.
4. So. The percentage of Fe²⁺ ions is about 84.9%, which rounds to 85.

The common slip: 79. Dividing by 1 instead of by the 0.93 iron actually present gives 79, not 85.

The idea to keep. In non-stoichiometric oxides, write the total charge balance with one unknown, then take the percentage out of the total metal present, not out of 1.

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