An unknown oxide of manganese is reacted with carbon to form manganese metal and $C O_{2}$ . If $31.6 g$ of the oxide, $M n_{x} O_{y}$ yielded $13.2 g$ of $C O_{2}$ then the simplest formula of the oxide is:
(if atomic mass of $M n = 55 u$ )

M n O

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M n O_{2}

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M n_{2} O_{3}

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M n_{3} O_{4}

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Solution

The correct option is C $M n_{2} O_{3}$
According to the question, the balanced reaction would be:
$M n_{x} O_{y} + \frac{y}{2} C \to \frac{y}{2} C O_{2} + x M n$

Given mass of $C O_{2}$ produced = $13.2 g$
$∴ \frac{y}{2} = \frac{13.2}{44}$
$\Rightarrow y = 0.6$
Since 1 mole of $M n_{x} O_{y}$ produces $\frac{y}{2}$ moles of $C O_{2}$ , thus,
$55 x + 0.6 \times 16 = 31.6$
$\Rightarrow x = 0.4$
$∴ x : y = 2 : 3$

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