Question

The density of 3 molal sodium thiosulphate solution is ^​​​​​$1.25g/c{m}^3$. The mole fraction of sodium thiosulphate is

Answer 1

Step 1: Calculating the mass of solution, solvent and solute

Let consider volume of solution $=1000mL$

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

$\text{Mass of solution}=1.25g/c{m}^3\times 1000c{m}^3=1250g$

$Concentration=3molal$

Molecular mass of Sodium thiosulphate$\left(N{a}_2{S}_2{O}_3\right)=2\left(23\right)+2\left(32\right)+3\left(16\right)=158g$

$\text{Mass of sodium thiosulphate}=\text{molality}\times \text{molecular mass}$

$\text{mass of sodium thiosulphate}=3mol\times 158g/mol=474g$

Mass of solution = mass of solute + mass of solvent

Mass of solvent $=1250g-474g=776g$

Step 2: Calculating the mole fraction of sodium thiosulphate

Moles of sodium thiosulphate $=3$
​Moles of solvent(water) $=\frac{Givenmass}{Molarmass}=\frac{776g}{18g/mol}=43.1mol$
Mole fraction of sodium thiosulphate $=\frac{Molesofsodiumthiosulphate}{Molesofsodiumthiosulphate+molesofwater}$

Mole fraction of sodium thiosulphate $=\frac{3}{3+43.1}=0.065$