Single Choice

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$$0.200\ m$$
B$$0.192\ m$$
Correct Answer
C$$0.100\ m$$
D$$1.200\ m$$

Solution

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

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

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