Question

What weight of $CaC{O}_3$ must be decomposed to produce a sufficient quantity of carbon dioxide to convert $21.2\text{g}$ of $N{a}_{2}C{O}_3$ completely into $NaHC{O}_3$. (Molar mass of $Na=23\text{g/mol},Ca=40\text{g/mol}$):
$CaC{O}_3\to CaO+C{O}_2$ $N{a}_{2}C{O}_3+C{O}_2+H_{2}O\to 2NaHC{O}_3$

• A. $100\text{g}$
• B. $20\text{g}$
• C. $120\text{g}$
• D. $30\text{g}$

Answer 1

The correct option is B $20\text{g}$

$CaC{O}_3\to CaO+C{O}_2$
$N{a}_{2}C{O}_3+C{O}_2+H_{2}O\to 2NaHC{O}_3$

Mol of $N{a}_{2}C{O}_3=\frac{21.2}{106}=0.2\text{mol}$

1 mol of $N{a}_{2}C{O}_3$ reacts with 1 mol of $C{O}_2$ and
1 mol of $C{O}_2$ is produced from 1 mol of $CaC{O}_3$
i.e. $\text{mol of}N{a}_{2}C{O}_3=\text{mol of}C{O}_2=\text{mol of}CaC{O}_3$

So, 0.2 mol of $N{a}_{2}C{O}_3$ reacts with 0.2 mol of $C{O}_2$ which means 0.2 mol of $C{O}_2$ is produced from 0.2 mol of $CaC{O}_3$.
weight of $CaC{O}_3$ formed = Moles $\times$ Molar mass
hence, weight of $CaC{O}_3=0.2\text{mol}\times 100\text{g/mol}=20\text{g}$