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11.4 Estimation of Osmotic Pressure Osmotic pressure is a thermodynamic property and can therefore be obtained by measurement of a variety of properties. The osmotic pressure of solutions can be related to the freezing points or vapor pressures of those solutions. Data on freezing points and vapor pressure is available in data handbooks. For dilute, ideal solutions the van’t Hoff equation provides a means of calculating the osmotic pressure, by: where: c = ionic concentration R = Gas Constant T = temperature in “K x=cRT Even though the van? Hoff equation is frequently not valid for practical problems, it is often useful to tit experimental or calculated data to a linear form, such as: n = UC where a is a constant The relationship s = UC”, where a and n are constants (n > 1 and often -21, is more general and can also be used for engineering design (Wijmans et al., 1984). The general flux equation contains the term AZ, which is the difference in osmotic pressure on the two sides of the membrane based on the concentrations C!, and Cr. Therefore, using the linear form for n from above, and the definition of the intrinsic rejection: R" = CC,- Cp)/Cw results in: Arr = a(C, - Cr, = UPC, To calculate the osmotic pressure from vapor pressure data, the following relationship can be used (Reid, 1966): where: “SOl”EYVLt= R = T = Psolvent = PUsolution = R ~ ~ ~ ~ ~ ~ = ~ R~ T l n partial molar volume of the solvent gas constant solution temperature, “K vapor pressure of pure solvent vapor pressure of solution with concentration CPDF Image | DESALTING AND WATER TREATMENT MEMBRANE
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