The mole fraction of a solute in 2.5m aqueous solution is           

Molality $=2.5\text{ m}$

Mole fraction of solute ,${\text{X}}_{\text{A}}=?$

GMW of water,${\text{GMW}}_{\text{B}}=\text{18 g}$

The relation between molality and mole fraction is given below.

        $\text{m}=\frac{{\text{X}}_{\text{A}}\times 1000}{\left(1-{\text{X}}_{\text{A}}\right){\text{GMW}}_{\text{B}}}$

         $2.5=\frac{{\text{X}}_{\text{A}}}{1-{\text{X}}_{\text{A}}}\times \frac{1000}{18}$

$\Rightarrow \frac{{\text{X}}_{\text{A}}}{1-{\text{X}}_{\text{A}}}=\frac{2.5\times 18}{1000}=\frac{45}{1000}$

$\Rightarrow {\text{X}}_{\text{A}}=0.0\text{45}\left(\text{1}-{\text{X}}_{\text{A}}\right)$

$\Rightarrow {\text{X}}_{\text{A}}=0.0\text{45}-0.0{\text{45 X}}_{\text{A}}$

$\Rightarrow \text{1}.0{\text{45 X}}_{\text{A}}=0.0\text{45}$

$\therefore {\text{X}}_{\text{A}}=\frac{0.045}{1.045}=0.043$