A sample of a metal oxide has formula $M_{0.83}O_{1.00}$. The metal M can exist in two oxidation sta

Question

A sample of a metal oxide has formula $M_{0.83}O_{1.00}$. The metal M can exist in two oxidation states +2 and +3. In the sample of $M_{0.83}O_{1.00}$, the percentage of metal ions existing in +2 oxidation state is X %. (Nearest integer)

Professor PC Thomas Classes · Answer

Let fraction of $M^{2+}$ be x. $2x + 3(0.83 - x) = 2 \implies 2x + 2.49 - 3x = 2 \implies x = 0.49$. The percentage of $M^{2+}$ out of the total metal ions is $(0.49 / 0.83) 	imes 100 \approx 59\%$.