A metal oxide has the formula M_ 0.98 O. The metal M exists as M^ 2+ and M^ 3+ ions. What fraction of the metal exists as M^ 3+ ?

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EEJ MAIN Chemistry QUESTION #7517

Question 1

A metal oxide has the formula M$_{0.98}$O. The metal M exists as M$^{2+}$ and M$^{3+}$ ions. What fraction of the metal exists as M$^{3+}$?

Correct Answer Explanation

Let $x$ = fraction of M as M$^{3+}$, $(0.98 - x)$ = fraction as M$^{2+}$.

Charge balance (O$^{2-}$ contributes $-2$): $2(0.98-x) + 3x = 2$

$1.96 - 2x + 3x = 2$

$x = 0.04$

Fraction of M as M$^{3+}$ $= \dfrac{0.04}{0.98} \times 100 \approx \mathbf{4.08\%}$