Question

Two solutions, each of 100mL having 4g glucose and 10g sucrose respectively. Amount of urea should be added to one of them in order to make them isotonic.
A) 0.4218g urea in glucose solution
B) 0.4218g urea in sucrose solution
C) 0.2268g urea in glucose solution
D) 0.2268g urea in sucrose solution.

Answer 1

the answer to this question is based on the concepts of colligative properties of the compounds which is based on the osmotic pressure which is given by the formula $\pi =\dfrac{nRT}{V}$ at volume being same.

Complete step – by – step solution:
From the lower classes of chemistry, we have studied the basic concepts of colligative properties of solutions.
Now, let us know what is the meaning of osmotic pressure and how it can be calculated.
- Osmotic pressure is nothing but the minimum pressure required for the solution to prevent the inward flow of its pure solvent across a semipermeable membrane.
- Here, the formula to measure the osmotic pressure is given by,
$\pi =\dfrac{nRT}{V}$
where n is the total number of moles of solute.
R is the gas constant.
V Is the volume of solution
and T is the temperature in K
Now, the above question is based on an isotonic solution.
Isotonic solutions are those solutions which have the same osmotic pressure.
Therefore for solution 1 :
Number of moles of glucose = mass of sucrose/molecular mass [since mol. mass of sucrose = 180 g/mol]
Number of moles of glucose$=\dfrac{4}{180}=0.0222moles$
For solution 2:
Number of moles of sucrose= mass of sucrose/ mol. wt.
Thus,
Number of moles of sucrose = $\dfrac{10}{342}=0.0292moles$
Here, R, T and V for both the solutions are the same.
For the isotonic solutions, we need to make the number of moles of solute of both solutions equal. Therefore, urea has to be added to the first solution.
Now, let ‘x’ moles are added to first solution then the number of moles of solute become x+0.0222 moles
Therefore, for isotonic solution to be made, we have
0.0292 = x+0.0222
Thus, x = 0.0070 moles of urea.
Now, total amount of urea added will be = g
The answer near to this value approximately is option A)

Therefore, the correct answer is option A)

Note: Osmotic pressure is also given by the formula$\pi =icRT$ in terms of the Van't hoff index ‘i’. and ‘c’ is the molar concentration of solute and this formula applies only when the concentration of solute is low.