Question

Calculate the mole fraction of HCI in the solution of HCI containing $24.8\%$ of HCI by mass.

$[H=1,Cl=35.5]$

Answer 1

As we know that,

$\text{No. of moles}=\frac{\text{given mass}}{\text{mol. mass}}$

Molecular mass of $HCl=36.5g$

Molecular mass of water $\left(H_{2}O\right)=18g$

The solution contains $24.8\%$ of $HCl$ by mass, i.e. $24.8g$ of $HCl$ is present in $100g$ of solution.

Therefore,

Mass of $HCl$ in solution $=24.8g$

$\therefore$ No. of moles of $HCl$ in solution $=\frac{24.8}{36.5}=0.698\text{moles}$

Mass of water in the solution $=100-24.8=75.2g$

$\therefore$ No. of moles of water in the solution $=\frac{75.2}{18}=4.18$

Total no. of moles in the solution $=$ moles of $HCl+$ moles of water $=0.698+4.18=4.878\text{moles}$

As we know that,

$\text{Mole fraction}=\frac{\text{no. of moles}}{\text{total moles}}$

Therefore,

Mole fraction of $HCl$ in the solution $=\frac{0.698}{4.878}=0.14$.

Hence the mole fraction of $HCl$ in the solution will be $0.14$.