Question

What is the mass of urea required for making 2.5kgof 0.25 moles aqueous solution?
(A) 37g
(B) 25g
(C) 125g
(D) 27.5g

Answer 1

Molality (m) is defined as the number of moles of the solute per kilograms of solvent. A commonly used unit for molality is mol/Kg. A solution of concentration 1 mol/Kg is also denoted as 1 molal. For example, 1.00 mol/Kg solution of KCl means that 1 mole (74.5 g) of potassium chloride in 1kilogram of water.

Complete step by step solution:
Given molality of aqueous solution = 0.25 molal
This means 0.25 molal aqueous solution of urea, expressed as 0.25 moles of urea dissolved in 1000 g of water.
Mass of water = 1000 g
moles of urea = 0.25 moles
Molar of mass urea ( $CO{{(N{{H}_{2}})}_{2}}$ ) = 60 g/mol
Mass of urea = molar mass of urea X moles of urea
= 60 g/mol X 0.25 = 15 g
Hence, mass of 0.25 moles of urea = 15 g
Mass of solution = 1000 g + 15 g = 1015 g
So, 1015 grams of solution containing urea = 15 g
Mass of required solution = 2.5 Kg = 2500 grams
Therefore, 2500 g of aqueous solution required mass of urea = $\dfrac{15g}{1015g}X2500$
= 36.95 g( approximately 37 g)
Hence, the mass of urea required for making 2.5kgof 0.25 moles aqueous solution = 37 g

The correct answer is option A.

Note: Each method of expressing the concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction, and molality are independent of temperature. Whereas molarity is a function of temperature. Because molarity expressed in volume which depends on temperature and molality expressed in mass does not depend on temperature.