Question

The density of 3M solution of $N{a}_2{S}_2{O}_3$ is $1.25$ g mL${}^{-1}$. Calculate, mole fraction of $N{a}_2{S}_2{O}_3$.

• A. $0.065$
• B. $0.165$
• C. $0.015$
• D. $0.265$

Answer 1

The correct option is A $0.065$

Given $N{a}_2{S}_2{O}_3\text{has molarity}=3mol{L}^{-1}$
$\therefore$ Mole of $N{a}_2{S}_2{O}_3=3$
$\therefore$ $\text{Weight of}N{a}_2{S}_2{O}_3=3\times 158=474g$
and V of solution $=$ 1 litre $=1000$ mL
$\therefore \text{Weight of solution}=1000\times 1.25=1250g$
$\therefore \text{Weight of water}=1250-474=776g$
$\text{Mole fraction of}N{a}_2{S}_2{O}_3=\frac{\text{Mole of}N{a}_2{S}_2{O}_3}{\text{Mole of}N{a}_2{S}_2{O}_3+\text{mole of}{H}_{2}O}$
$=\frac{3}{3+\frac{776}{18}}=0.065$