In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_{\mathbf{2}} \mathbf{O}_{\mathbf{4}}$ ($\mathbf{M}$ and $\mathbf{Y}$ are metals), $\mathbf{M}$ is present in both +2 and +3 oxidation states and $\mathbf{Y}$ is in +3 oxidation state. If the fraction of $\mathbf{M}^{2+}$ ions present in $\mathbf{M}$ is $\frac{1}{3}$, the value of $\mathbf{X}$ is ____.

JEE Advanced · 2024 · 26 May 2024 · Paper 2 · Solid State

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

Y

is in +3 oxidation state. If the fraction of

M^{2 +}

ions present in

M

\frac{1}{3}

, the value of

X

is ____.

(A)0.25
(B)0.33
(C)0.67
(D)0.75✓ Correct

Answer: (D)

Solution

The average oxidation state of M is calculated as:

Average O.S. = \frac{1}{3} \times 2 + \frac{2}{3} \times 3 = \frac{8}{3}

For the compound

M_{x} Y_{2} O_{4}

, applying charge balance:

\frac{8}{3} \times x + 3 \times 2 + 4 (- 2) = 0

\frac{8}{3} \times x = 2

x = \frac{3}{4} = 0.75

JEE Advanced · 2024 · 26 May 2024 · Paper 2 · Single correct option

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