60 g of urea is dissolved in 90 g of water. Then, the mole fraction of solute is         

GMW of urea ${\text{W}}_1=\text{6}0\text{ g}{\text{.mol}}^{-1}$

Weight of water ${\text{w}}_2=\text{9}0\text{ g}$

GMW of water ${\text{W}}_2=\text{18 g}{\text{.mol}}^{-1}$

No.of moles of urea $\text{=}{\text{n}}_{\text{1}}$

${\text{n}}_1=\frac{w_1}{{\text{W}}_{\text{1}}}=\frac{60\text{g}}{60gmo{l}^{-1}}=1\text{mol}$

No.of moles of water$\text{=}{\text{n}}_2$

 $\Rightarrow {\text{n}}_2=\frac{w_2}{{\text{W}}_2}=\frac{90\text{g}}{18\text{g}{\text{.mol}}^{-1}}=5\text{mol}$

The mole fraction of urea (solute) is, 

             ${\chi }_{urea}=\frac{n_{urea}}{n_{urea}+n_{water}}$

Now, we will get,

  ${\chi }_{urea}=\frac{n_1}{n_1+n_2}=\frac{1}{1+5}=\frac{1}{6}$