GATE 2021 CH – Question 19
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
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Correct answer: (D) $P_1-\pi_1=P_2-\pi_2$
Explanation
The solvent driving force across an ideal semipermeable membrane is the hydraulic-pressure difference minus the osmotic-pressure difference: $J_v=L_p[(P_1-P_2)-(\pi_1-\pi_2)]$.
At equilibrium the solvent chemical potentials are equal and the net flux is zero. Thus $P_1-P_2=\pi_1-\pi_2$, or $\mathbf{P_1-\pi_1=P_2-\pi_2}$. Equal hydraulic or osmotic pressures alone are not the general criterion. **Answer: D.**