JEE Advanced 2024 Paper 2 Q02 Chemistry Physical Chemistry Mole Concept & Stoichiometry Medium

JEE Advanced 2024 Paper 2 · Q02 · Mole Concept & Stoichiometry

In a metal deficient oxide sample, $M_XY_2O_4$ (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 $M^{2+}$ ions present in M is $\frac{1}{3}$, the value of X is _____.

  1. A. 0.25
  2. B. 0.33
  3. C. 0.67
  4. D. 0.75
Reveal answer + step-by-step solution

Correct answer:D

Solution

Charge balance for $M_xY_2O_4$ with $Y^{3+}$ and $O^{2-}$: total positive charge from M and Y must equal $4 \times 2 = 8$. So $\text{(charge from M)} + 2 \times 3 = 8 \Rightarrow$ charge from M $= 2$. With one-third of M as $M^{2+}$ and two-thirds as $M^{3+}$: $\frac{x}{3}(2) + \frac{2x}{3}(3) = 2 \Rightarrow \frac{2x}{3} + 2x = 2 \Rightarrow \frac{8x}{3} = 2 \Rightarrow x = 0.75$.

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