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Question: Calculate the mass of urea \(\text{N}{{\text{H}}_{2}}\text{CON}{{\text{H}}_{2}}\) required in making...

Calculate the mass of urea NH2CONH2\text{N}{{\text{H}}_{2}}\text{CON}{{\text{H}}_{2}} required in making 2.5 kg of 0.25 molal aqueous solutions.

Explanation

Solution

Hint: The term molality is the number of moles of solute dissolved in one kilogram of solvent. For example to make a one molal aqueous solution of sodium chloride, we should take one kilogram of water and add one mole of the solute, NaCl to it.

Complete step by step solution:
Molality-It is defined as the number of moles of solute dissolved per kilogram of solvent. It is designated by the symbol m.
Molality is expressed as
m=1000nBWA\text{m=}\dfrac{1000{{\text{n}}_{\text{B}}}}{{{\text{W}}_{\text{A}}}}
where, nB{{\text{n}}_{\text{B}}}is the number of moles of the solute and WA{{\text{W}}_{\text{A}}}is the mass in grams of solvent. The molality of a solution does not change with temperature.
Mass of solution= 2.5kg
Molar Mass of urea= 60g/mol
Mass of urea=No.of moles of urea x Molar Mass
Mass of 0.25 moles of urea=0.25mol x 60g/mol =15g
Also, Mass of solution=1000g+15g=1015g
1015g of aqueous solutions contains urea=15g
2500g of aqueous solution=15×25001015=36.95≈37g15\times\dfrac{2500}{1015}=36.95\approx 37\text{g}
Therefore, the amount of urea required in making 2.5kg of 0.25 molal aqueous solution is 37g

Note: The molal unit is not used nearly as frequently as the molar unit and is used in thermodynamic calculations where temperature independent unit of concentration is needed. The term molality and molarity should not be confused. While expressing the Molality it is represented by a small “m” whereas molarity is represented by an uppercase “M”.