Question

Which statement is incorrect about osmotic pressure (π), volume (V) and temperature (T)?
A. \[\pi ~\propto 1/V,\text{ }if\text{ }T\text{ }is\text{ }constant\]
B. \[\pi ~\propto T,\text{ }if\text{ }V\text{ }is\text{ }constant\]
C. \[\pi ~\propto V,\text{ }if\text{ }T\text{ }is\text{ }constant\]
D. \[\pi V\text{ }is\text{ }constant,\text{ }if\text{ }T\text{ }is\text{ }constant\]

Answer 1

Hint: If in any solution 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. Concentration is defined as the moles of solute in per litre volume of solution such as\[C\text{ }=\text{ }n/V\], where n is the number of moles of solute and V is volume of solution.

Complete Step by Step Answer:
When a solute is added to a solvent (generally water) it gives out a solution.
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 inside or outside of the cell. Now the solvent of the solution which is less concentrated moves towards the solution which is highly concentrated through a semipermeable membrane. And this process is known as osmosis or forward osmosis and this is a spontaneous process.

As solvent molecules move toward the highly concentrated solution thus we fit the piston on the highly concentrated solution (also on the other side) and push it until osmosis stops. Thus, the pressure we apply to stop the osmosis process is 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 coccus which in turn is directly proportional to the difference between the concentration of one solution and with another. 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
\[\pi \text{ }=\text{ }CRT\]
π 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.
Where C is equal to number of moles of solute per litre volume \[\left( n/V \right)\]such as
\[\pi \text{ }=\text{ }n/V\left( RT \right)\]
\[\pi \text{ }=\text{ }1/V,\text{ }if\text{ }T\text{ }is\text{ }constant\]
Thus, the correct option is A.

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. Osmosis is the reason due to which beans (rajma) swell when left for night in the water.