Question

Which has the maximum osmotic pressure at temperature $T$?
A. $100{\text{ }}mL$ of $1M$ urea solution
B. $300mL$ of $1M$ glucose solution
C. Mixture of $100{\text{ }}mL$ of $1M$ urea solution and $300mL$ of $1M$ glucose solution
D. All are isotonic

Answer 1

Osmotic pressure is a colligative property which depends on the amount or number of particles present in the system. It is equivalent to the minimum pressure which must be applied to the solution in order to prevent the flow of solvent through the membrane.

Complete step by step answer: The osmotic pressure can be equivalent to the pressure difference between the solution and the pure solvent when both are present across a semipermeable membrane. This pressure difference must be applied on a side to inhibit the flow of molecules from one side to another.
Initially there occurs flow of molecules from the side of pure solvent to solution. But after the equilibrium reaches the flow stops and the pressure becomes equal to osmotic pressure.
The osmotic pressure of a solution is governed by two laws.
-The osmotic pressure is directly proportional to the concentration at constant temperature.
-The osmotic pressure is directly proportional to absolute temperature.
The mathematical equation for osmotic pressure can be written as:
$\pi = cRT$
where, $\pi$ is the osmotic pressure, $c$ is the molar concentration, $R$ is molar gas constant and $T$ is absolute temperature.
Following the equation, as the temperature is constant; the osmotic pressure will depend on the concentration of the solutions. For the given set of options, all the solutions have an equal concentration of $1M$, so the osmotic pressure will be the same for all the solutions.
Thus option D is the correct answer, i.e. all are isotonic.

Note: Osmotic pressure can also be viewed as the pressure which is required to stop the flow of ions from a high concentration side to low concentration side. Several other colligative properties which depend on the number or amount of molecules are lowering of vapour pressure, elevation in boiling point and depression in freezing point.