Question

An aqueous solution of urea containing 18g urea in 1500 cm${}^3$ of the solution has a density equal to 1.052. If the molecular weight of urea is 60, the molality of the solution is:

• A. $0.200m$
• B. $0.192m$
• C. $0.100m$
• D. $1.200m$

Answer 1

The correct option is B $0.192m$

Density is the ratio of mass to volume.
Density is 1.052 g/ml.
1500 ml of solution corresponds to $1.052g/ml\times 1500ml=1578g$
Molar mass of urea is 60 g/mol. Number of moles of urea is the ratio of mass to molar mass. It is $\frac{18g}{60g/mol}=0.3mol$

Molality of solution is the ratio of the number of moles of urea to the mass of solvent in kg.
Mass of water $=1578g-18g=1560g=1.560kg$ (as 1 kg = 1000 g)
Molality $=\frac{0.3}{1.560}=0.192m$