Subject: Chemistry — Solid State
Question: 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 M2+ ions
present in $M$ is $\frac{1}{3}$, the value of $X$ is
\_\_\_\_\_\_\_\_\_\_\_.
\(a\) 0.25 (b) 0.33 (c) 0.67 (d) 0.75
Answer: 0.75
Solution: $MxY_{2}O_{4}$
$$M^{+ 2} = \frac{X}{3},M^{+ 3} = \frac{2X}{3}$$
$$\frac{2X}{3} + 3\left( \frac{2X}{3} \right) + 2( + 3) + 4( - 2) = 0$$
$$\frac{2X}{3} + 2X + 6 - 8 = 0$$
$$\frac{8X}{3} = 2$$
$$X = \frac{6}{8} = \frac{3}{4} = 0.75$$