Question

How many grams of ${Na}_2{CO}_3$ should be dissolved in 250 g of water to prepare 0.1 M solution?

Answer 1

As we know that

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

Mass of water $=250g\left(\text{Given}\right)$

$\because$ Density of water $=1gm/mL$

$\therefore$ Volume of water $=250mL=0.25L$

As we know that molality is given as-

$\text{Molarity}=\frac{\text{No. of moles of solute}}{{\text{Volume of solvent}}_{\left(\text{in L}\right)}}$

Given:-

Volume of solvent (water) $=0.25L$

No. of moles of solute $\left({Na}_{2}C{O}_3\right)=n=?$

Molarity of solution $=0.1M$

Therefore,

$n=0.1\times 0.25=0.025\text{mol}$

Molecular weight of ${Na}_{2}C{O}_3=106g$

As we know that,

$\text{No. of moles}=\frac{\text{Weight}}{\text{Mol. wt.}}$

$\therefore$ Weight weight of $0.025$ mole of ${Na}_{2}C{O}_3=106\times 0.025=2.65g$

Hence $2.65g$ of ${Na}_{2}C{O}_3$ required.