Question

At a certain temperature, $1.6\%$ solution of an unknown substance is isotonic with $2.4\%$ solution of urea. If both the solutions have the same solvent and both the solutions have same density $1{\text{ gm/c}}{{\text{m}}^3}$ , what will be the molecular mass of unknown substance in ${\text{gm/mol}}$
(Molecular mass of urea $= 60{\text{ gm/mol}}$ )
(A) 30
(B) 40
(C) 80
(D) 90

Answer 1

Those solutions are said to be isotonic that have the same osmotic pressure. To answer this question, you must recall the formula for osmotic pressure. Osmotic pressure is a colligative property and depends on the concentration of the solution
Formula used: ${{\pi }} = {\text{cRT}}$
Where, $\pi$ represents the osmotic pressure of the solution
$c$ represents the concentration of the solution
And, $T$ represents the temperature.

Complete step by step solution
Osmotic pressure can be termed as the minimum pressure required to be applied to a solution in order to halt the flow of the particles of the solvent. It depends on the concentration of the solute in the solution but not on the properties of the solute. Basically, osmosis is the movement of the molecules of solvent particles from a region of higher concentration to a region of lower concentration through a semi- permeable membrane. Osmosis occurs until an equilibrium is established resulting in equal concentration on both sides of the membrane.
In the question, the two given solutions are said to be isotonic, that is, they have the same osmotic pressure. We can write, ${\pi _1} = {\pi _2}$
At the same temperature conditions, the osmotic pressure depends only on the concentrations of the solutions. So, we can write, ${c_1} = {c_2}$
$\Rightarrow \dfrac{{1.6}}{{\text{M}}} = \dfrac{{2.4}}{{60}}$
$\Rightarrow {\text{M}} = 40{\text{ g/mol}}$
Thus, the correct answer is B.

Note
Colligative properties are those properties which depend only on the number of solute particles in the solution and not on the nature of the solute. Other than osmotic pressure, the other colligative properties are relative lowering of vapour pressure, depression in freezing point and elevation in boiling point.