Question

In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are $P_1$ and $\pi_1$, respectively. The corresponding values are $P_2$ and $\pi_2$ at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is:

• A. $\pi_1 = \pi_2$
• B. $P_1 = P_2$
• C. $P_1 + \pi_1 = P_2 + \pi_2$
• D. $P_1 - \pi_1 = P_2 - \pi_2$

Hint:

In membrane systems, net driving pressure is always hydraulic pressure minus osmotic pressure. Set feed and permeate driving pressures equal for equilibrium.

Answer 1

The Correct Option is D

The condition for equilibrium across a semipermeable membrane is that the net driving force must be zero.

Step 1: Osmotic pressure opposes water flow.
Water moves from low solute concentration to high solute concentration due to osmotic pressure. Hydraulic pressure opposes this flow.

Step 2: Write the force balance.
Net driving pressure at feed side: \[ P_1 - \pi_1 \] Net driving pressure at permeate side: \[ P_2 - \pi_2 \] For equilibrium: \[ P_1 - \pi_1 = P_2 - \pi_2. \] This means there is no net solvent flow through the membrane.