For dilute aqueous solutions in which the density of the solution is roughly equal to that of the pure solvent, the molarity of the solution is equal to its molality. Show that this statement is correct for a 0.010 M aqueous urea [ (NH2) 2CO] solution.

Given: Molarity = 0.01 M

Let the volume of the solution = 1 L

Hence, moles = 0.01 moles (Molarity*Volume)

Molar mass of urea = 60 g/mol

So, mass of urea = moles x molar mass = 0.01 moles x 60 g/mol = 0.6 g = 0.0006 kg,

Given: Density of solvent = Density of solution = 1 Kg/liter (Water).

So,

The mass of solution = vol x density = 1 L x 1 kg/L = 1 kg

Also,

Mass of solution = Mass of solute + Mass of solvent

1 kg = 0.0006 kg + mass of solvent

Mass of solvent = 1-0.0006 = 0.9994 kg

Molality is the moles of solute present in 1 kg of the solvent. So,

Molaity = (0.01/0.9994) ≈ 0.01 m

Molarity = Molality

Hence proved.