Question

Which of the following aqueous solutions produces the same osmotic pressure? This question has multiple correct options
(A) $0.1M$ $NaCl$solution
(B) $0.1M$glucose solution
(C) $0.6g$ urea in $100ml$ solution
(D) $1.0g$ of a non-electrolyte solute (X) in $50ml$ solution (Molar mass of X = 200)

Answer 1

Hint: The minimum pressure which is required to be applied to the solution to prevent the inward flow of the solvent across a semipermeable membrane is known as osmotic pressure. This process is known as osmosis.

Formula Used: The formula used to calculate the osmotic pressure of a solution is:
$\pi = icRT$; where $i$ = van’t hoff index
$c$ = Concentration of solute, $R$ = Gas constant, $T$ = Temperature (Kelvin), $\pi $= Osmotic pressure.

Complete Step by Step Answer:
For two solutions to be isotonic, they should have the same osmotic pressure. So, we will calculate the osmotic pressure of each of the solutions given in the options, and the two solutions that will have the same osmotic pressure will be our answer.
(A) $0.1M$ $NaCl$solution
As $NaCl$ dissociates and gives 2 ions, so $i=2$
Thus, osmotic pressure will be
$\pi =2\times 0.1\times R\times T$
$\pi =0.2RT$

(B) $0.1M$glucose solution
As glucose does not dissociates, that is, it does not give any ions, so $i=1$
Thus, osmotic pressure will be
$\pi =1\times 0.1\times R\times T$
$\pi =0.1RT$

(C) $0.6g$ urea in $100ml$ solution
Urea does not dissociate, so $i=1$
Also, the concentration is calculated as
$c=\frac{0.6\times 1000}{60\times 100}$
$c=0.1$
Thus, osmotic pressure will be
$\pi =1\times 0.1\times R\times T$
$\pi =0.1RT$

(D) $1.0g$ of a non-electrolyte solute (X) in $50ml$ solution (Molar mass of X = 200)
As a non-electrolyte does not dissociate, so $i=1$
Also, the concentration is calculated as
$c=\frac{1.0\times 1000}{200\times 50}$
$c=0.1$
Thus, osmotic pressure will be
$\pi =1\times 0.1\times R\times T$
$\pi =0.1RT$
Hence, 0.1M glucose solution, 0.6g urea in 100ml solution, and 1.0g of a non-electrolyte solute (X) in 50 ml solution are isotonic solutions.
Correct Options: (B), (C) and (D).

Note: The process of osmosis is important for the human body. In the human body, osmosis occurs in the small and large intestines. It plays an important role in the gastro-intestinal system and kidneys. It helps in getting all the essential nutrients from our food and also removes the waste products from the blood.