Question

the mass of urea required in making 5Kg of 5 molal aqueous solution is'

Answer 1

Molality is defined as number of moles of solute present in 1 kg of solvent.

In the question, we are required to prepare a 5 molal solution of urea.

⇒ Molality = 5 moles of urea/ Kg of solution

Molar mass of urea = 60 g

From the question,

Mass of solution = 5 Kg = 5000 g   [Note that mass of solution and solvent are different quantities]

Mass of solvent and solute both are unknown and we are required to find the mass of solute as per the question.

Let mass of solute be x g

Mass of solvent = (5000 - x) g = (5000 -x)/1000 Kg

Number of moles of solute = x/60 moles

Molality = Number of moles of solute/Mass of solvent in Kg

        ⇒ 5 =1000 (x/60) / (5000 - x)

         ⇒0.3= x/(5000-x)

         ⇒1500 - 0.3x = x

       ⇒ x = 1500/1.3 = 1153.84 g ≅ 1.154 Kg

CHECK:

Mass of solute = 1154 g

Moles of solute = 1154/60 = 19.23

Mass of solvent = 5000 - 1154 = 3046 g = 3.846 kg

Molality = Moles of solute/ mass of solvent = 19.23/3.846 = 5