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Question 3: Calculations of fluxes and solute rejection for reverse osmosis of salty water A reverse osmosis module is being used to desalinate water containing NaCl. The concentration of the NaCl in the feed solution is c₁ = 28.8834 kg NaCl/m³ (P₁ = 1017.2 kg/m³) and that in the product solution is c₂= 0.58264 kg/m³ (P2 = 997.4 kg/ m³). The solvent permeability constant is Aw 2.5 x 10-4 kg solvent/m² s atm and the solute permeability constant is A, = 2 x 10-7 m/s. The unit is to be operated at a temperature of 25 °C and the hydrostatic pressure difference between the feed and the product sides is AP = 60 atm. If the product solution is assumed so dilute that Cw2 is the same as the density of water at 25 °C (i.e. 997 kg/m³), = (a) Calculate the solvent flux (N) (b) Calculate the solute flux (N,) and (c) Calculate the solute rejection, R, to 4 decimal places Take the molecular weight of NaCl as 58.45 kg/kmol. Table of osmotic pressures of various aqueous solutions is shown below. TABLE 13.9-1. Osmotic Pressure of Various Aqueous Solutions at 25°C (PI, S3, SS) Sodium Chloride Solutions Sea Salt Solutions Sucrose Solutions Osmotic Osmotic Solute Density Pressure Wt. % Pressure Mol. Frac. (kg/m³) (atm) Salts (atm) × 10³ 997.0 0 0 0 0 997.4 0.47 1.00 7.10 1.798 1001.1 4.56 3.45* 25.02 5.375 1017.2 22.55 7.50 58.43 1036.2 45.80 10.00 82.12 1072.3 96.2 g mol NaC! kg H₂O 0 0.01 0.10 0.50 1.00 2.00 • Value for standard seawater. 10.69 17.70 Osmotic Pressure (atm) 0 2.48 7.48 15.31 26.33