In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ and…
In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ 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 ________.
0.25
0.33
0.67
0.75
Solution
Average oxidation state of $\mathrm{M}=\frac{1}{3} \times 2+\frac{2}{3} \times 3=+\frac{8}{3}$
$\begin{aligned} & \therefore \text { For } \mathrm{M}_{\mathrm{X}} \mathrm{M}_{2} \mathrm{Y}_4 \\ & \frac{8}{3} \times \mathrm{x}+3 \times 2+4(-2)=0 \\ & \frac{8}{3} \times \mathrm{x}=2 \\ & \mathrm{x}=\frac{3}{4}=0.75\end{aligned}$
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