1 / 13

Fugacity of Non-Ideal Mixtures (SVNA 11.6 and 11.7)

Fugacity of Non-Ideal Mixtures (SVNA 11.6 and 11.7). In our attempt to describe the Gibbs energy of real gas and liquid mixtures, we examine two “sources” of non-ideal behaviour: Pure component non-ideality concept of fugacity Non-ideality in mixtures partial molar properties

prosper
Download Presentation

Fugacity of Non-Ideal Mixtures (SVNA 11.6 and 11.7)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Fugacity of Non-Ideal Mixtures (SVNA 11.6 and 11.7) • In our attempt to describe the Gibbs energy of real gas and liquid mixtures, we examine two “sources” of non-ideal behaviour: • Pure component non-ideality • concept of fugacity • Non-ideality in mixtures • partial molar properties • mixture fugacity and residual properties • We will begin our treatment of non-ideality in mixtures by considering gas behaviour. • Start with the perfect gas mixture model derived earlier. • Modify this expression for cases where pure component non-ideality is observed. • Further modify this expression for cases in which non-ideal mixing effects occur. Lecture 11

  2. Perfect Gas Mixtures • We examined perfect gas mixtures in a previous lecture. The assumptions made in developing an expression for the chemical potential of species i in a perfect gas mixture were: • all molecules have negligible volume • interactions between molecules of any type are negligible. • Based on this model, the chemical potential of any component in a perfect gas mixture is: • where the reference state, Giig(T,P) is the pure component Gibbs energy at the given P,T. • We can choose a more convenient reference pressure that is standard for all fluids, that is P=unit pressure (1 bar,1 psi,etc) • In this case the pure component Gibbs energy becomes: Lecture 11

  3. Perfect Gas Mixtures • Substituting for our new reference state yields: • (11.29) • which is the chemical potential of component i in a perfect gas mixture at T,P. • The total Gibbs energy of the perfect gas mixture is provided by the summability relation: • (11.11) • (11.30) Lecture 11

  4. Ideal Mixtures of Real Gases • One source of mixture non-ideality resides within the pure components. Consider an ideal solution that is composed of real gases. • In this case, we acknowledge that molecules have finite volume and interact, but assume these interactions are equivalent between components • The appropriate model is that of an ideal solution: • where Gi(T,P) is the Gibbs energy of the real pure gas: • (11.31) • Our ideal solution model applied to real gases is therefore: Lecture 11

  5. Non-Ideal Mixtures of Real Gases • In cases where molecular interactions differ between the components (polar/non-polar mixtures) the ideal solution model does not apply • Our knowledge of pure component fugacity is of little use in predicting the mixture properties • We require experimental data or correlations pertaining to the specific mixture of interest • To cope with highly non-ideal gas mixtures, we define a solution fugacity: • (11.47) • where fi is the fugacity of species i in solution, which replaces the product yiP in the perfect gas model, and yifi of the ideal solution model. Lecture 11

  6. Non-Ideal Mixtures of Real Gases • To describe non-ideal gas mixtures, we define the solution fugacity: • and the fugacity coefficient for species i in solution: • (11.52) • In terms of the solution fugacity coefficient: • Notation: • fi, i - fugacity and fugacity coefficient for pure species i • fi, i - fugacity and fugacity coefficient for species i in solution Lecture 11

  7. Calculating iv from Compressibility Data • Consider a two-component vapour of known composition at a given pressure and temperature • If we wish to know the chemical potential of each component, we must calculate their respective fugacity coefficients • In the laboratory, we could prepare mixtures of various composition and perform PVT experiments on each. • For each mixture, the compressibility (Z) of the gas can be measured from zero pressure to the given pressure. • For each mixture, an overall fugacity coefficient can be derived at the given P,T: • How do we use this overall fugacity coefficient to derive the fugacity coefficients of each component in the mixture? Lecture 11

  8. Calculating iv from Compressibility Data • It can be shown that mixture fugacity coefficients are partial molar properties of the residual Gibbs energy, and hence partial molar properties of the overall fugacity coefficient: • In terms of our measured compressiblity: Lecture 11

  9. Calculating iv from the Virial EOS • We have used the virial equation of state to calculate the fugacity and fugacity coefficient of pure, non-polar gases at moderate pressures. • Under these conditions, it represents non-ideal PVT behaviour of pure gases quite accurately • The virial equation can be generalized to describe the calculation of mixture properties. • The truncated virial equation is the simplest alternative: • where B is a function of temperature and composition according to: • (11.61) • Bij characterizes binary interactions between i and j; Bij=Bji Lecture 11

  10. Calculating iv from the Virial EOS • Pure component coefficients (B11≡ B1, B22≡ B2,etc) are calculated as previously and cross coefficients are found from: • (11.69b) • where, • and • (11.70-73] • Bo and B1 for the binary pairs are calculated using the standard equations 3.65 and 3.66 at Tr=T/Tcij. Lecture 11

  11. Calculating iv from the Virial EOS • We now have an equation of state that represents non-ideal PVT behaviour of mixtures: • or • We are equipped to calculate mixture fugacity coefficients from equation 11.60 Lecture 11

  12. Calculating iv from the Virial EOS • The result of differentiation is: • (11.64) • with the auxilliary functions defined as: • In the binary case, we have • (11.63a) • (11.63b) Lecture 11

  13. 6. Calculating iv from the Virial EOS • Method for calculating mixture fugacity coefficients: • 1. For each component in the mixture, look up: • Tc, Pc, Vc, Zc,  • 2. For each component, calculate the virial coefficient, B • 3. For each pair of components, calculate: • Tcij, Pcij, Vcij, Zcij, ij • and • using Tcij, Pcij for Bo,B1 • 4. Calculate ik, ij and the fugacity coefficients from: Lecture 11

More Related