Phase_Equilibria_2

# Phase_Equilibria_2 - The thermodynamic description of...

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1 The thermodynamic description of mixtures Gibbs energy of a mixture: A AB B Gn n µ =+ In all discussions of mixtures we will be using the concept that at equilibrium the chemical potential of a substance must be the same throughout the sample, regardless of how many phases are present. Suppose that we have liquid and vapor: ) , ( ) , ( P T P T liquid vapor = () l n ( / ) oo vapor T TR T P P µµ , P o is the standard pressure (1 bar) - ideal gas The higher the partial pressure of the gas the higher is the chemical potential. The ideal solution – Raoult’s law Suppose that we have liquid and vapor phases and two components, solvent A and solute B. Then, Solution and its vapor: liquid A vapor A , , = and ) 1 / ln( , A o T vapor A P RT + = (ideal) pure liquid and its vapor, use * to denote values for pure substance: liquid A vapor A , * , * = Subtract : ) / ln( * * , , A A liquid A liquid A P P RT = (ideal vapor) Raoult discovered experimentally the limiting behavior for solutions made up of mostly solvent A, the relation between P the vapor pressure of A over a solution containing A and P * A the vapor pressure of A over pure liquid. Raoult’s law Definition: A solution that obeys Raoult’s law for all concentrations is an ideal solution (the vapor does not have to behave as an ideal gas) A liquid A liquid A x RT ln * , , = ideal solution liquid A , is the chemical potential of the solvent in the liquid solution * , liquid A is the chemical potential of the pure liquid solvent x A is the mole fraction of solvent in the liquid solution A A x P P = * /

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2 Molecular interpretation of Raoult’s law This law can be understood by considering the rates at which molecules leave and return to the liquid. The rate at which A molecules leave the surface is proportional to the number of them at the surface, which in turn is proportional to its mole fraction: rate of vaporization = k x A The rate at which molecules condense is proportional to their concentration in the gas phase, which in turn is proportional to its partial pressure: rate of condensation = k P A At equilibrium: rate of vaporization = rate of condensation k x A = k P A And A A x k k P ' = For the pure liquid x A = 1, so ' * k k P A = and A A x P P = * /
3 Vapor pressure diagrams: Ideal solution model to binary The vapor pressures of the components of an ideal solution of two volatile liquids are related to the composition of the liquid mixture by Raoult’s law * A A A P x P = and * B B B P x P = A B A B B A A A B A TOTAL x P P P P x P x P P P ) ( ) 1 ( * * * * * + = + = + = It is a straight line connecting * A P and * B P (bubble line) If, in addition, the vapor behaves ideally, then the mole fraction of A in the vapor phase, y A , is according to partial pressures in the vapor: TOTAL A A P P y = and TOTAL B B P P y = . The compositions of the liquid and vapor that are in equilibrium are not necessarily the same, and common sense suggests that the vapor should be richer in the more volatile component.

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## This note was uploaded on 04/07/2012 for the course CHEM 340 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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Phase_Equilibria_2 - The thermodynamic description of...

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