Question

Membrane Separation II Reverse Osmosis (a) Derive van't Hoff's equation (osmotic pressure π-CRT). (b) A feed solution containing 5g NaCl/L (ρ-1001kg/m3) is purified using a reverse osmosis system. Water permeability constant (Aw) and a solute (NaCI) permeability constant (As) are 5 x 10 kg/m2s atm, and 4 x 10-7m/s, respectively. AP 30 atm. Assume that the fraction recovered of the solvent water is 0.15. The flow rate q2 of the permeate water solution is 50 L/min. Calculate ci and c2 in kg NaCl/m3 and the membrane area in m2. Calculate R. (c) Using the same conditions and permeability constants as in Example 13.10-1, calculate the fluxes, solute rejection R, and product concentration c2 for pressures of 17.20, 27.20, and 37.20 atm. Plot the fluxes, R, and c2 versus pressure. (d) Repeat Example 13.10-1 but use a concentration polarization β=1.5. β is defined as the ratio of the salt concentration at the membrane surface to the salt concentration in the bulk stream C1. *when there is significant concentration polarization, the osmotic pressure difference the solute flux (Ns) and the solution rejection (R) can be written as follow. Please show any steps and calculations that helped you arrive at your answers!

Answer 1

1. Vant Hoff's osmotic pressure formula was mainly implemented in the multi-phase equilibrium. It is based on the equilibrium of liquid and gas phases and can be derived by the integration of the equations for both phases.
2. He found that the solute particles in a dil solution possessed kinetic energy and moved randomly in the solutions similar to the behavior as that of a gas molecule.
3. On colliding with a semipermeable membrane, the solute molecules exert osmotic pressure equal to the pressure which the solute molecules would exert if they were gas molecules at the same temperature and volume as that of the solution.
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