Question

The density of $3M$ sodium thiosulphate is $1.25g/ml$. Identify the correct statements among the following.

• A. $\%$ by weight of sodium thiosulphate is $37.92$
• B. The mole fraction of sodium thisoulphate is $0.065$
• C. The molarity of $N{a}^{+}$ is $2.53$ and $S_2{O}_3^{2-}$ is $1.25$
• D. Both $\left(A\right)$ and $\left(B\right)$

Answer 1

The correct option is D Both $\left(A\right)$ and $\left(B\right)$

The molecular weight of sodium thiosulphate pentahydrate = $248$.
$1000$ ml of $3$ M solution contains $248\times 3$ g thiosulphate.
$1$ ml of $3$ M solution contains $\frac{248\times 3}{1000}$ g or $0.744$ g thiosulphate.
Amount of water per ml of aqueous thiosulphate solution
$=1.25-0.744=0.506$ g .
Mole fraction of thiosulphate = (mole of thiosulphate)/(total number of moles)

$=\frac{\left(0.744/248\right)}{\left(0.744/248\right)+\left(0.506/18\right)}$
$=\frac{0.003}{(0.003+0.02811)}$
$=0.0964$ .
Molarity of sodium & thiosulphate ions:
One molecule of thiosulphate gives $2$ atoms of sodium ;
One mole of thiosulphate gives $2$ moles of sodium ;
$1000$ ml of $3$M thiosulphate will give $2\times 3$ gram-atoms or $6$ gram-atoms of sodium and $3$ moles of thiosulphate ions.
Hence, option (D) is correct option