Question

An aqueous solution of sucrose, ${C_{12}}{H_{22}}{O_{11}}$, containing 34.2g/L has an osmotic pressure of 2.38 atmosphere at $17^\circ C$, for an aqueous solution of glucose, ${C_6}{H_{12}}{O_6}$, to be isotonic with this solution, it would have:
A. 34.2 g/L of glucose
B. 17.1 g/L of glucose
C. 18.0 g/L of glucose
D. 36.0 g/L of glucose

Answer 1

Hint: The osmotic pressure is the minimum pressure applied on the solution when it passes through the semipermeable membrane. The osmotic pressure is given as $\pi = CRT$. Osmotic pressure is equal to multiplication of molar concentration, universal gas constant and temperature.

Complete step by step answer:
Given
Strength of the sucrose solution is 34.2g/L.
The osmotic pressure is 2.38.
The osmotic pressure is defined as the minimum pressure applied to the solution so that it can pass through semi permeable membrane. The osmotic pressure is a colligative property which is dependent on the concentration of solute particles present in the solution.
The formula to calculate the osmotic pressure is shown below.
$\pi = CRT$
Where
$\pi $ is the osmotic pressure
C is the molar concentration
R is the universal gas constant
T is the temperature
For isotonic solution,
${\pi _1} = {\pi _2}$
${C_1}RT = {C_2}RT$
The molar mass of sucrose is 342 g/mol.
The molar mass of glucose is 180 g/mol
The molar concentration is given as strength divided by the molar mass.
Substitute the value in the equation.
$ \Rightarrow \dfrac{{34.2}}{{342}} = \dfrac{M}{{180}}$
$ \Rightarrow M = 18g/L$
Thus the strength of the glucose solution is 18 g/L.
Therefore, the correct option is C.

Note:
Don’t forget that the solution is isotonic in nature which means that they have the same osmolarity or solute concentration. When both the solutions are separated by semipermeable membranes then the flow of the solution will be equal.