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Boyle's Law

4.215 g of a ...

Question

$4.215$ g of a metallic carbonate was heated and the $C O_{2}$ evolved was found to measure $1336$ mL at 27 $^{o} C$ and $700$ mm pressure. The equivalent mass of metal is (as the nearest integer)

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Solution

For $C O_{2}$ gas $P V = (\frac{w}{m}) R T$
$\frac{700}{760} \times \frac{1336}{1000} = \frac{w}{44} \times 0.0821 \times 300$
$∴ w_{C O_{2}} = 2.20 g$
Suppose metal carbonate is $M_{2} {(C O_{3})}_{n}$ and let atomic mass of metal be a, then
$M_{2} {(C O_{3})}_{n} \to M_{2} O_{n} + n C O_{2}$
$∵ (2 a + 60 n) g M_{2} {(C O_{3})}_{n} = 44 n g C O_{2}$
$∴ 4.215 g M_{2} {(C O_{3})}_{n} = \frac{44 n \times 4.215}{2 a + 60 n} g C O_{2}$
$∴ \frac{44 n \times 4.215}{2 a + 60 n} = 2.20 ∴ \frac{a}{n} = 12.15$
Also, equivalent mass of metal $=$ a/n $=$ 12.15
So, nearest integer is 12.

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