Question

The osmotic pressure of a solution is given by the relation:
A. \[p\text{ }=\text{ }RT/c\]
B. \[p\text{ }=\text{ }cT/R\]
C. \[p\text{ }=\text{ }Rc/T\]
D. \[p/c\text{ }=\text{ }RT\]

Answer 1

Hint: Osmotic pressure is the quantitative measure of the force with which the osmosis process occurs. Osmotic pressure or force with which osmosis takes place will increase with the increase in the concentration of solute molecules in the one solution as compared to other.

Complete Step by Step Answer:
Let us take two solutions in one beaker separated through a semipermeable membrane, one solution containing fewer solute particles (less concentrated or dilute) and the other containing a large number of solute particles (more concentrated).
It is very interesting to know that a semi-permeable membrane only allows the passage of solvent molecules from the solution but not solute outside or inside of cell. Now the solvent of the solution which is less concentrated move towards the solution which is highly concentrated through a semi-permeable membrane. And this process is known as osmosis or forward osmosis and this process is spontaneous.
As solvent molecules move toward the highly concentrated solution thus we fit the piston (and also on other side) on the highly concentrated solution and push it until osmosis stops. Thus, the pressure we apply to stop the osmosis process that will be equal to the force with which solvent molecules move towards a concentrated solution. This pressure which we applied is known as osmotic pressure.
Osmotic pressure is directly proportional to the force with which osmosis occurs which in turn is directly proportional to the difference between the concentration of one solution and with other. Indirectly osmotic pressure depends on the concentration of solute molecules in one solution as compared to another.
It was first derived by Dutch chemist, Jacobus and given as
\[p\text{ }=\text{ }cRT\] (Von’t Hoff solution equation)
 Where p is osmotic pressure, c is concentration of solute molecules in moles per litre, R is gas constant, T is temperature in Kelvin or absolute temperature.
Or \[p/c\text{ }=\text{ }RT\]
Thus, the correct option is D.

Additional Information: When a solute is added to a solvent (generally water) it gives out a solution. Now if in any solution the number of moles of solute is present in a large amount then the solution is concentrated otherwise dilute or less concentrated. An osmosis process occurs due to the difference in concentration between two solutions. Osmosis is the reason when beans (rajma) swell when left in water for night.

Note: It is important to note that when pressure is applied to the highly concentrated solution, we need to take care not to apply pressure more than required to stop osmosis otherwise reverse osmosis will take place, and solvent molecules from highly concentrated solution move towards a low concentrated solution through a semipermeable membrane.