Question

Mole fraction of $A$ in $H_{2}O$ is $0.2$. The molality of $A$ in $H_{2}O$ is:

• A. $13.8$
• B. $15.5$
• C. $14.5$
• D. $16.8$

Answer 1

The correct option is A $13.8$

Assume $1000$ g (or $1000$ mL ) of water.
It contains $\frac{1000}{18}=55.55$ mol of water.
Let the number of moles of $A$ be $x$.
The mole fraction is $0.2$.
$0.2=\frac{x}{55.55+x}$
$55.55+x=5x$
$55.55=4x$
$x=13.88$ mol.
The molality of the solution is $m=\frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}=\frac{13.88g/mol}{1kg}=13.88m$.