chapter5 - Chapter 5 Fugacity of a Pure Component This...

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Chapter 5 Fugacity of a Pure Component This chapter introduces a new concept called fugacity, which is the basis for establishing equi- librium criteria between di f erent phases of a pure substance. After showing how to calculate this quantity for gases, liquids, and solids, the variation of temperature with pressure (or vice versa) during phase transformation of pure substances will be discussed. 5.1 MOLAR GIBBS ENERGY OF A PURE IDEAL GAS For a pure substance, molar Gibbs energy is given in di f erential form as d e G = e VdP e SdT (5.1-1) The ideal gas equation of state relates the molar volume to pressure as e V IG = RT P (5.1-2) Substitution of Eq. (5.1-2) into Eq. (5.1-1) leads to d e G = RT P dP e = RT d ln P e (5.1-3) At constant temperature, Eq. (5.1-3) reduces to d e G = RT d ln P at constant T (5.1-4) Integration of Eq. (5.1-4) at constant temperature from the standard state pressure, P o ,to the state of interest at which the pressure is P gives ln μ P P o = e G ( T,P ) e G ( o ) RT (5.1-5) 5.2 DEFINITION OF FUGACITY AND FUGACITY COEFFICIENT Equation (5.1-5) is valid only for pure, ideal gases. In order to generalize it, in 1901 Gilbert Newton Lewis 1 introduced a function f i ,ca l ledthe fugacity of pure component i ,as ln f i ( ) P ¸ = e G i ( ) e G i ( ) RT = e H i ( ) e H i ( ) RT e S i ( ) e S i ( ) R (5.2-1) 1 Professor of physical chemistry and the dean of the College of Chemistry at University of California, Berkeley. 89
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subject to the following constraint f i /P 1 as P 0( ideal gas state ) (5.2-2) which applies to solid, liquid and gas. Note that the term [ e G i ( T,P ) e G IG i ( )] in Eq. (5.2-1) can be interpreted as the departure function for Gibbs energy. Di f erentiation of Eq. (5.2-1) at constant temperature leads to d e G i = RTd ln f i at constant T (5.2-3) The fugacity coe cient of pure component i , φ i ,isde f ned as the ratio of the fugacity to the pressure, i.e., φ i = f i P (5.2-4) It is a measure of the deviation of the system from ideal gas behavior, i.e., φ i =1 for an ideal gas. Note that both fugacity and fugacity coe cient are intensive properties of the system and are a function of any two other intensive properties, such as, temperature and pressure, for a single-phase pure material. Combination of Eqs. (5.1-5) and (5.2-1) leads to an alternative expression for the fugacity of pure component in the form e G i ( )= e G i ( o ) RT ln P o + RT ln f i ( ) (5.2-5) or, e G i ( λ i ( T )+ RT ln f i ( ) (5.2-6) where λ i ( T ) is the molar Gibbs energy of pure component i at unit fugacity, and de f ned by λ i ( T e G i ( o ) RT ln P o (5.2-7) When two phases of a pure substance are in equilibrium, we have T α = T β P α = P β e G α i = e G β i (5.2-8) Letting T α = T β = T and P α = P β = P , equality of molar Gibbs energies leads to λ i ( T RT ln f α i ( λ i ( T RT ln f β i ( ) f α i ( f β i ( ) (5.2-9) indicating that fugacities of a pure component must be equal to each other under the conditions of equilibrium.
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This note was uploaded on 04/06/2010 for the course CHE 327 taught by Professor Ozbelge during the Fall '10 term at Middle East Technical University.

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chapter5 - Chapter 5 Fugacity of a Pure Component This...

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