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unsw ceic3001 lecture w2 advance thermo

# unsw ceic3001 lecture w2 advance thermo - SCHOOL OF...

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1 SCHOOL OF CHEMICAL ENGINEERING CEIC3001 Advanced Thermodynamics and Separation NON-IDEALITY IN THE GAS PHASE (Text: Smith et al., Chapter 11) CONTENTS Gibbs Energy. ............................................................................................................................. 2 Fugacity and Fugacity Coefficient: Pure Gas . ........................................................................... 2 Fugacity and Fugacity Coefficient: Pure Saturated Vapour/Liquid. .......................................... 5 Fugacity and Fugacity Coefficient: Pure Unsaturated Liquid. ................................................... 5 Fugacity and Fugacity Coefficient: Species i in a Mixture of Gases. ........................................ 6 HIGHLIGHTS - We define the fugacity f which is analogous to pressure. - For an ideal gas, fugacity is equal to pressure. - For a real gas, the deviation from ideal gas behaviour is measured by the residual Gibbs energy G R or the fugacity coefficient (ratio of fugacity to pressure). - When a pure liquid and its vapour are in equilibrium (saturated condition), their fugacity coefficients are equal. - The fugacity coefficient of a gas can be calculated from the compressibility factor Z (for a pure gas) or its partial molar value i Z (for a component in a gas mixture), provided the equation of state of the gas is available.

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2 Gibbs Energy The Gibbs energy is defined by G H TS in a closed system (no material movement across system boundaries) of constant composition, it can be shown (see text Section 6.1) that the Gibbs energy change associated with a change in T and P is given by dT nS dP nV nG d ) ( ) ( ) ( (1) From Eq. 1, a reversible phase change at constant T and P involves no change in Gibbs energy, i.e. phases at equilibrium with each other have the same G value. Eq. 1 is an example of a total differential equation in which the dependent variable ( nG ) is expressed as a function of 2 independent variables ( T and P ) the terms ( nV ) and ( nS ) in Eq. 1 can also be expressed in terms of the independent variables T , P through the use of an equation of state, e.g. ideal gas equation, so that Eq. 1 is of the form dT P T g dP P T f nG d ) , ( ) , ( ) ( in order to calculate the Gibbs energy change in going from state 1 to state 2, Eq. 1 is integrated by using any selected path on the T, P diagram. Of course we will always select the most convenient path to simplify our calculations (e.g. constant P followed by constant T ). Fugacity and Fugacity Coefficient: Pure Gas for 1 mole of a pure ideal gas, application of Eq. 1 to 1 mole of gas ( n = 1) leads to the fundamental property relation for the Gibbs energy dT S dP V dG ig i ig i ig i (2) at constant T this equation simplifies to dP V dG ig i ig i and from the ideal gas equation of state ) constant ( T dP P RT dG ig i (3) integration of Eq. 3 from a reference pressure P ref to P at constant T leads to the following equation   ref ref ig i ig i P RT P RT T P G G ln ln , P RT T G i ig i ln ) ( (4) where Γ i ( T ) is the constant of integration and is a function of T only for a real gas we write an analogous equation to Eq. 4 in which P is replaced by the fugacity ( f i ) of pure species i
3 i i i f RT T G ln ) ( (5) where f i

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unsw ceic3001 lecture w2 advance thermo - SCHOOL OF...

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