(a) Define the following terms:
(i) Molarity (ii) Molal elevation constant $(k_{b})$
(b) A solution containing $15 g$ urea (molar mass $= 60 g {m o l}^{- 1}$ ) per litre of solution in water has the same osmotic pressure (isotonic) as a solution of glucose (molar mass $= 190 g {m o l}^{- 1}$ ) in water. Calculate the mass of glucose present in one litre of its solution.

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Solution

(a)
(i) Molarity of a solution is defined as the number of moles of solute present in one litre of the solvent.
(ii) Molal elevation constant $(K_{b})$ is defined as the elevation in boiling point of a solution when one mole of a non volatile solute is dissolved in one kilogram of a volatile solvent.

(b) Osmotic pressure $π = C R T$
when n is the number of moles of solute present in volume V of solvent

It is given that the solution of urea is isotonic with the solution of glucose, thus
$\frac{n_{G l u c o s e}}{V} R T = \frac{n_{U r e a}}{V} R T$
=Glucose = $\frac{15}{60} \times 180 = 45 g$
Hence, the mass of glucose present in one litre of its solution = 45g

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