In a metal deficient oxide sample, M X Y 2 O 4 (M and Y are metals), M is present in both +2 and +3 oxidation states and…
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In a metal deficient oxide sample, MXY2O4(M and Y are metals), M is present in both +2 and +3 oxidation states and Y is in +3 oxidation state. If the fraction of M2+ ions present in M is \(\frac{1}{3}\), the value of X is _______.
[JEE Advanced 2024, Paper-2]
✓ Correct answer: d)
0.75
Explanation
Formula: MₓY₂O₄.
M exists as M²⁺ and M³⁺, Y is +3.
Fraction of M²⁺ = 1/3.
Total M per formula = x.
M²⁺ ions = (1/3)x → charge = 2·(1/3)x = (2/3)x.
M³⁺ ions = (2/3)x → charge = 3·(2/3)x = 2x.
Y³⁺ ions = 2 → charge = 2·3 = 6.
O²⁻ ions = 4 → charge = 4·(−2) = −8.
Charge neutrality: (2/3)x + 2x + 6 − 8 = 0
⇒ (8/3)x − 2 = 0 ⇒ (8/3)x = 2 ⇒ x = 6/8 = 0.75.
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