Question

Osmotic pressure of 40 % (mass/vol.) the urea solution is $\text{1}\text{.68 atm}$ and that of 3.42 % (mass/vol.) cane sugar is $\text{2}\text{.46 atm}$. When equal volume of the above two solutions are mixed, the osmotic pressure of the resulting solution is:
(A) $\text{1}\text{.64 atm}$
(B) $\text{2}\text{.46 atm}$
(C) $\text{4}\text{.10 atm}$
(D) $\text{2}\text{.05 atm}$

Answer 1

Hint: 40% (mass/vol.) of urea solution means \[\text{100 ml}\] solution contains \[\text{40gm}\] of urea.
- Osmotic pressure is the applied external pressure on the solution which prevents the osmosis or the flow of the solvent into the solution through the semipermeable membrane.
- Osmotic pressure $\text{ }\!\!\pi\!\!\text{ =}\,\text{CRT}$
- Osmotic pressure is a colligative property because it depends upon the number of solute particles but not the nature of the solute particles.
- Van’t hoff factor of sugar, urea, glucose is one (i.e.: i = 1), because these are neither dissociated or associated in the solution.

Complete Solution :
Osmotic pressure of two solutions will be added when equal volumes of two solutions are mixed, and this new osmotic pressure will be the average value of the osmotic pressure of the added solutions.
Hence, osmotic pressure of the resulting solution :
\[\begin{align}
& {{\text{P}}_{\text{avg}}}\,\text{= }\dfrac{{{\text{P}}_{\text{1}}}\,\text{+}\,{{\text{P}}_{\text{2}}}}{\text{2}} \\
& {{\text{P}}_{\text{avg}}}\,\text{= }\dfrac{\text{1}\text{.64 atm}\,\text{+}\,\text{2}\text{.46 atm}}{\text{2}} \\
& {{\text{P}}_{\text{avg}}}\,\text{=}\,\,\text{2}\text{.05 atm} \\
\end{align}\]

Note: On mixing equal volume of two non- reacting solutions the mixture will have approximately the same to the osmotic pressure of the two individual values, because there is no change in molar concentration of both the solutions.
- Osmotic pressure is a colligative property that depends only upon the number of solute particles or ions in the solution. Since osmotic pressure of solution is directly proportional to the concentration of the solution so, on mixing equal volume non-reacting solutions we take the average value of moles in the calculation of osmotic pressure.