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

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Solid State

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 ____ % (nearest integer)

Answer: 59

Let the fraction of metal present as

M^{2 +}

x

, so the fraction as

M^{3 +}

(0.83 - x)

. Balancing the positive charge against one

O^{2 -}

gives

2 x + 3 (0.83 - x) = 2

, which simplifies to

x = 0.49

. The share in the +2 state is then

\frac{0.49}{0.83} \times 100 \approx 59

. The percentage of metal ions in the +2 oxidation state is 59 percent.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer