Question

A solution ‘X’ is prepared by dissolving three moles of glucose in one litre of water and a solution ‘Y’ is prepared by dissolving 1.5 moles of sodium chloride in one litre of water. Will osmotic pressure of ‘X’ be higher, lower or equal to that of ‘Y’? Give a reason for your answer.

Answer 1

Hint: To solve this question, we can use the formula of osmotic pressure to find out which solution has the higher osmotic pressure. The formula is \[\pi =iCRT\], where ‘i’ is the Van’t Hoff factor which is the dissociation of the electrolyte in a solution and pi is the osmotic pressure.

Complete answer:
 We know that osmotic pressure is the minimum pressure that is required to apply to a solution for stopping the inward flow of the pure solvent across the semipermeable membrane.
We know the formula of osmotic pressure which is-
     \[\pi =iCRT\]
Where, $\pi $ is the osmotic pressure, ‘i’ is the Van’t Hoff factor, C is the concentration of the solution, R is the universal gas constant and T is the temperature.
Now we can use the above formula and find out the osmotic pressure of the solutions and compare if they are equal or not.
For X, the solution is prepared by dissolving 3 moles of glucose in 1 litre of water.
As we know, the molarity of a solution of the fraction of number of moles of solute per litre of the solvent.
Therefore, we can write that concentration of the solution in molarity will be $\dfrac{3}{1}M=3M$.
Now, as we know that glucose is a non-electrolyte and it will not dissociate in a solution. Therefore, the Van’t Hoff factor will be 1 for the glucose solution.
Therefore, osmotic pressure of X will be \[\pi =3RT\].
Now for the solution Y, 1.5moles of NaCl is dissolved in 1 litre of water.
Therefore, the concentration will be $\dfrac{1.5}{1}M=1.5M$.
As we know, sodium chloride is a strong electrolyte and it dissociates into $N{{a}^{+}}\text{ and C}{{\text{l}}^{-}}$ ions on dissolution. Therefore, Van’t Hoff factor for NaCl is 2.
So, we can write that the osmotic pressure of Y will be $\pi =2\times 1.5RT = 3 RT$.
As we can see from the above discussion that the osmotic pressure of both the solutions are equal.
Therefore, the correct answer is osmotic pressure of X is equal to osmotic pressure of Y.

Note: For the above solutions, both of them have equal osmotic pressures across the semipermeable membrane. Such a solution is called isotonic solution. In an isotonic solution, there is free movement of water across the membrane without changing the concentration of any of the solutes.