Question

Which of the following condition is correct for reverse osmosis?
\[ [C = \text{Concentration of solution in mol L}^{-1}, \; T = \text{Temperature in Kelvin scale}, \; n = \text{number of moles of solute}] \]

• A. \(P_{\text{ext}} = CRT\)
• B. \(P_{\text{ext}} \gt CRT\)
• C. \(P_{\text{ext}} \lt CRT\)
• D. \(P_{\text{ext}} \gt nRT\)

Hint:

Reverse osmosis occurs only when the applied external pressure exceeds the osmotic pressure of the solution.

Answer 1

The Correct Option is B

Step 1: Define osmotic pressure.
Osmotic pressure ($\pi$) is the pressure required to stop the flow of solvent through a semipermeable membrane from the pure solvent side to the solution side. It is given by: \[ \pi = CRT \] where $C$ = molar concentration, $R$ = gas constant, $T$ = absolute temperature.
Step 2: Explain normal osmosis.
In normal osmosis, solvent flows from low concentration (pure solvent) to high concentration (solution) through a semipermeable membrane. The applied pressure that just stops this flow is the osmotic pressure $\pi = CRT$.
Step 3: Define reverse osmosis.
Reverse osmosis is the process in which solvent flows from the solution side to the pure solvent side - the REVERSE of normal osmosis. This is achieved by applying an external pressure GREATER than the osmotic pressure.
Step 4: Write the condition for reverse osmosis.
For reverse osmosis to occur: \[ P_{ext} > \pi = CRT \] The externally applied pressure must exceed the osmotic pressure of the solution.
Step 5: Physical interpretation.
When $P_{ext} > CRT$, the applied pressure overcomes the natural tendency of solvent to flow into the solution, forcing solvent to move in the reverse direction - from solution to pure solvent. This principle is used in water purification plants.
Step 6: State the answer.
The condition for reverse osmosis is that the external pressure must exceed the osmotic pressure, i.e., $P_{ext} > CRT$.
\[ \boxed{P_{ext} > CRT \text{ (option 2)}} \]