Question

Equal volumes of M/20 urea solution and M/20 glucose solution are mixed. The mixture will have osmotic pressure :
(A) equal to either of the solution
(B) less than either of the solution
(C) higher than either of the solution
(D) zero

Answer 1

Hint: Osmotic pressure is one of the colligative properties. We know that colligative properties depend on the quantity of solute particles and not the type of solute. Calculate osmotic pressure of either of the solutions and then calculate the osmotic pressure of the resultant solution and then make your observations and conclusions.

Complete step-by-step answer:
Colligative properties are the properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.
The number ratio can be related to the various units for concentration of a solution, for example, molarity, molality, normality etc.

The colligative properties are:
Relative lowering of vapor pressure
Elevation of boiling point
Depression of freezing point
Osmotic pressure

Osmotic pressure is the minimum pressure to be applied to a solution in order to prevent the inward flow of its pure solvent across a semipermeable membrane. The formula for calculating osmotic pressure is :
\[\text{ }\!\!\pi\!\!\text{ = C}\text{.R}\text{.T}\]
where,
C is the concentration of solute in the solution
R is the universal gas constant
T is the temperature at which osmotic pressure is calculated

We will now calculate osmotic pressure of the two solutions individually and then the osmotic pressure of the total solution.
Concentration of urea (${{C}_{1}}$) = 1/20
Concentration of glucose (${{C}_{2}}$) = 1/20
Concentration of glucose and urea solutions combined (${{\text{C}}_{final}}$) = $\dfrac{\dfrac{1}{20}+\dfrac{1}{20}}{2}$ = 1/20
Temperature = T Kelvin
Osmotic pressure of urea solution (${{\text{ }\!\!\pi\!\!\text{ }}_{1}}$) = $\dfrac{1}{20}.\text{R}\text{.T}$
Osmotic pressure of glucose solution (${{\text{ }\!\!\pi\!\!\text{ }}_{2}}$) = $\dfrac{1}{20}.\text{R}\text{.T}$
Osmotic pressure of the final solution (${{\text{ }\!\!\pi\!\!\text{ }}_{final}}$) = $\dfrac{1}{20}.\text{R}\text{.T}$
The osmotic pressure of the mixture of two solutions given above is equal to either of the solutions.
\
Therefore, the correct answer is option (A).

Note: Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as per its mass. The value of the Van't Hoff factor is greater than 1 for dissociation of ionic compounds. The factor is used when the solute undergoes dissociation or association in the solvent.