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 (to the nearest integer) is $2x$. Find $x$.

Answer 1

For $CO{}_2$ gas, $PV=\left(\frac{w}{m}\right)RT$
$\frac{700}{760}\times \frac{1336}{1000}=\frac{w}{44}\times 0.0821\times 300$
$\therefore w_{C{O}_2}=2.20g$
Suppose metal carbonate is $M_2{\left(C{O}_3\right)}_n$ and let atomic mass of metal be a, then
$M_2{\left(C{O}_3\right)}_n\to M_2{O}_n+nC{O}_2$

$\because$ 1 mole of metal carbonate corresponds to $n$ moles of $C{O}_2$
$(2a+60n)g{M}_2{\left(C{O}_3\right)}_n=44ngC{O}_2$
$\therefore 4.215g{M}_2{\left(C{O}_3\right)}_n=\frac{44n\times 4.215}{2a+60n}gC{O}_2$

$\therefore \frac{44n\times 4.215}{2a+60n}=2.20$

$\therefore \frac{a}{n}=12.15$
Also, equivalent mass of metal $=\frac{a}{n}$ $=$ $12.15$ .
So, nearest integer is $12$.

Hence, $x$ is 6.