Question

0.5 M glucose solution is iso-osmotic with which of the following solutions?
(A)- 0.10 M NaCl
(B)- 0.05 M NaCl
(C)- 0.25 M NaCl
(D)- 1 M NaCl

Answer 1

Hint: An isotonic solution is said to be the one that has the same osmolarity or solute concentration. If two solutions are separated by a semipermeable membrane or SPM, water will flow in equal parts out of each solution and into the other.

Complete Solution :
We see that there are many phenomena for example, raw mangoes shrivel when it is pickled in brine or when the blood cells collapse when it is suspended in saline water, etc.
- We come to find that all of these substances are bound by membranes. These membranes may be of animal or vegetable origin and or can be synthetic such as cellophane.
These membranes may appear to be continuous sheets but they contain a network of sub microscopic holes or pores.
Solutions molecules may pass through these holes present but the passage of quite bigger molecules like solute is restricted.
- Thus, such membranes having this kind of properties are said to be semipermeable membranes (SPM).
We assume that only solvent molecules are able to pass through these membranes.
If this membrane is placed between the solvent and solution then the solvent molecules will flow via these membranes from pure solvent into the solution.
Therefore, this process resulting in the flow of the solvent is called osmosis. The flow will continue until the equilibrium state is attained.

Also, the flow of the solvent from its side to solution side across a SPM can be restricted if some extra pressure is applied on the solution side and the pressure that just stops the flow of solvent is known as the osmotic pressure of solution.
- Osmotic pressure is the colligative property as it is found to depend on the number of solute molecules but not on their identity. For dilute solutions, it has been found experimentally proven that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T given by the following equation:
$\Pi = CRT$
Where $\Pi $ is the osmotic pressure.

For the isotonic
We should determine whether the solute dissociates or not when it dissolves. A general rule is that ionic compounds will dissociate while covalently bonded compounds will not dissociate. Multiply the molarity of the solution by the number of ions formed(or i the dissociation constant) in the solution when a single formula unit of the compound dissociates to find the osmolarity. NaCl would form two on is sodium ion and another is chloride ion. A 1-molar solution of NaCl would be a 2-osmolar solution.
Therefore,
$\begin{gathered}
  {\Pi _{glucose}} = {\Pi _{salt}} \\
  {i_1}{C_1}RT = {i_2}{C_2}RT \\
  1 \times 0.05 = 2 \times {C_2} \\
  {C_2} = \frac{{0.05}}{2} = 0.025M \\
\end{gathered} $
So, the correct answer is “Option C”.

Note: One should remember that the dissociation constant i is also taken in consideration. Multiply the molarity of the solution by the number of ions formed (or i the dissociation constant) in the solution when a single formula unit of the compound dissociates to find the osmolarity. NaCl would form two on is sodium ion and another is chloride ion.