MIT2_500s09_hw02

# MIT2_500s09_hw02 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 2.500 Desalination and Water Purification Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.500 Desalination and Water Puriﬁcation Homework Set #2 Due 19 March 2009 Problem 1: Two ways to compute Π We have seen that the osmotic pressure, Π , may be determined by considering the partial molar Gibbs energy of a solvent, i , as a function of pressure and composition at constant temperature, G i (p,x i ,T) . To further investigate this, consider a pure solvent at a pressure p I and a solution having mole fraction of solvent x i II at a pressure p II . At osmotic equilibrium, p II p I = Π , the partial molar Gibbs energies are equal, G i (p I ,x i I ,T) = G i (p II ,x i II ,T) . Calculate Π in two ways. First, assume a two step process going from (i) pure solvent at p I to pure solvent at p II , followed by (ii) change in composition from x i I = 1to x i II at ﬁxed pressure p II . Second, assume a two step process having (i) a change in composition from x i I = 1to x i II at ﬁxed pressure p I , followed by (ii) a change in pressure from p I to p II at ﬁxed composition, x i II . Bear in mind that V i ∂G i /∂p . How do these two results diﬀer? What do you conclude about the physical properties in- volved? Problem 2: Constant volume model for density of salt water To estimate the density of salt water (aqueous NaCl), we could try assuming that the volume of solution remains ﬁxed when salt is added to water, so that salt water containing 1 kg of H 2 O would have a the same volume as 1 kg of pure water. Calculate the density of salt water as a function of molality on this basis can compare it to
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## This note was uploaded on 02/27/2012 for the course MECHANICAL 2.500 taught by Professor Miriambalaban during the Spring '09 term at MIT.

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MIT2_500s09_hw02 - MIT OpenCourseWare http:/ocw.mit.edu...

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