JEE Chemistry 2023 Question with Solution

Given: The oxide has formula $M_{0.83}O_{1.00}$. Metal $M$ exists as $M^{2+}$ and $M^{3+}$.

Find: The percentage of metal ions in the $+2$ oxidation state.

Let the amount of metal in the $+2$ oxidation state be $x$, and the amount in the $+3$ oxidation state be $0.83 - x$.

From the charge balance equation:

Simplifying the equation:

Thus, the percentage of metal ions in the $+2$ oxidation state is:

Therefore, the percentage of metal ions in the $+2$ oxidation state is $59\%$, so the required numerical answer is 59.

Given: The oxide composition is $M_{0.83}O_{1.00}$.

Find: Percentage of metal present as $M^{2+}$.

The extracted solution states that on solving

we get $x = 0.49$, and then the percentage is reported as $59\%$.

Using the extracted value $x = 0.49$, the percentage of $M^{2+}$ ions is

So, the correct numerical answer is 59.

Note: The second approach text contains an internal inconsistency in the written fraction, but the concluded answer is still reported as $59\%$.