Question

An X molal solution of a compound in benzene has mole fraction of solute equal to $0.2$.The value of X is:-

• A. $14$
• B. $3.2$
• C. $1.4$
• D. $2$

Answer 1

The correct option is B $3.2$

Given:

Mole fraction of solute$=0.2$

Molality of benzene$=x$

Molar mass of Benzene$=78g/mol$

Let $n_1$ be moles of solvent and $n_2$ be moles of solute

Now,

Mole fraction of solvent$=1-0.2=0.8$

Mole fraction of solute$=\frac{n_2}{n_1+n_2}=0.2$ …..($i$)

Mole fraction of solvent$=\frac{n_1}{n_1+n_2}=0.8$ …..($ii$)

Dividing ($i$) and ($ii$),

$\frac{n_2}{n_1}=\frac{0.2}{0.8}$ ….($iii$)

Since we are dealing in terms of molality we are taking the mass of solvent as $1000g$

Solvent moles $=\frac{1000}{78}=12.8moles$

From ($iii$),

$n_2=3.2moles$

$\Rightarrow$$3.2$ moles of solute is present in $1$ Kg,

Hence Molality $=3.2$

Hence correct option is B .