Wt. of solute (urea) dissolved= 3.0 gm
Wt. of the solvent (water) = 250 gm
Mol. wt. of the solute = 60
Calculation of molality
3.0 gm of the solute \(= \frac{3.0}{60}\) moles = 0.05 moles
Thus 250 gm of the solvent contain = 0.05 moles of solute
\(\therefore\) 1000 gm of the solvent contain \( = \frac{0.5 \times 1000}{250} = 0.2\ \text{moles}\)
Hence molality of the solution = 0.2 m
In short,
Molality = No. of moles of solute / 1000 g of solvent
\(\therefore \) Molality = \(\frac{3/60}{250} \times 1000 = \) 0.2 m
Calculation of mole fraction
3.0 gm of solute = 3/60 moles = 0.05 moles
250 gm of water \(= \frac{250}{18}\) moles = 13.94 moles
\(\therefore \) Mole fraction of the solute \(= \frac{0.05 }{0.05 + 13.94} = \frac{0.05}{13.99} = \) 0.00357
