Question

The osmotic pressure of a millimolar solution of urea at $27^\circ C$ is:
A. 2.49 bar
B. 5 bar
C. 3.4 bar
D. 1.25 bar

Answer 1

Van’t Hoff law of osmotic pressure states that the osmotic pressure of a solution is directly proportional to the absolute temperature and with the molar concentration of the solute. To solve this question the van’t Hoff law of osmotic pressure should be known. To find out the answer put the values in the question to find out the osmotic pressure.
Formula used:
$\pi = CRT$

Complete step by step answer:
The formula of osmotic pressure is,

$$\pi \,\infty RT \\\ \pi = CRT \\\$$

Where C is the molar concentration of the solute in the solution, R is the universal gas constant, T is the absolute temperature. $\pi$ is the osmotic pressure.
$\pi = \dfrac{w}{{M\, \times V}}RT$
Where w is the weight of the solute, M is the molecular weight of the solute, V is the volume of solution.
Now the concentration is given millimolar. That is 0.1 molar. The molecular mass of urea is,
$(14 \times 2) + (4 \times 1) + (16) + (12)$
=28+4+16+12
=60
Therefore, put these values in the equation of osmotic pressure and find out the value of osmotic pressure as follows,

$$\pi \,\infty RT \\\ \pi = CRT \\\ \pi = 0.1 \times 0.082 \times 300 \\\ \pi = 2.46\,atm \\\$$

So, the osmotic pressure is, 2.46 atm. Now 1 atm= 1.013 bar so the value of osmotic pressure in the bar is, 2.49 bar.

So, the correct option is A.

Note:

Osmotic pressure is the minimum amount of pressure required to stop the flow of solvent through a semipermeable membrane. This osmotic pressure is a colligative property. That means the value of osmotic pressure depends upon the number of solute particles present in the solution only.