- StudyBlue
- Michigan
- University of Michigan - Ann Arbor
- Chemical Engineering
- Chemical Engineering 330
- Kotov
- Lecture 1

Anonymous

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CHE 330 Thermodynamics February 22 Instructors: Prof. Nicholas A. Kotov, kotov@umich.edu Bean Getsoian, getsoian@umich.edu Raghu Kainkaryam, raghu@umich.edu Chapter 6/8: Thermodynamics of Multicomponent Mixtures What happens when the pure fluids are mixed? U = (T, P. N1,?NL) ?Vmix = V(T, P, x) ? x1V1(T, P) ? x2V2(T, P) U = (T, P, x1,?xL-1) ?Hmix = H(T, P, x) ? x1H1(T, P) ? x2H2(T, P) Equation of State for mixtures Thermodynamics of Sulfuric Acid and Water Solutions Substantial Emission of Heat + - Dipole-dipole interactions, hydrogen bonding, etc Partial Molar Properties N?=?(N1, N2, ?.NL) at T and P constant N is the total number of moles in the system 2N?=2?(N1, N2, ?.NL) 2N?=?(2N1, 2N2, ?.2NL) 2?(N1, N2, ?.NL) =?(2N1, 2N2, ?2NL) ?(T, P,N1, N2, ?.NL) = ?(T, P, 2N1, 2N2, ?2NL) Dependence of ? on the number of moles N?=N1?1(N2/N1, ?.NL/N1) L ? = ?xi ?(N?)/?Ni |T, P, N, j?i i=1 Molar properties are pretty simple functions of the molar derivatives ?i = ?i(T, P, x) = ?(N?)/?Ni |T, P, N, j?i L ? = ?xi?i(T, P, x) i=1 Partial molar properties Representation of the effects of Mixing ?i(T, P, x) ?i(T, P) These could be very different properties Molar volume Hydrogen alone Hydrogen and platinum L V = ?NiVi(T, P) i L H = ?NiHi(T, P) i ?Vmix(T, P, N1, N2,?) = V(T, P, N1, N2, ?) - L ?NiVi(T, P) i ?Hmix(T, P, N1, N2,?) = H(T, P, N1, N2, ?) - L ?NiHi(T, P) i L ? = ?xi?i(T, P, x) i=1 Molar thermodynamic property for other parameters U = ? xiUi Same for V, H, S, G, A A = U ? TS G = H - TS ?i = ?i(T, P, x) = ?(N?)/?Ni |T, P, N, j?i L ? = ?xi?i(T, P, x) i=1 L H = ?xiHi(T, P) i L CP = ?xiCp I (T, P) i Derivative Quantities Same can be said about other derivatives obtained in the equations (?Gi/?T)P, N = -Si How does the differentials of G, A, H, U?etc depend on the number of moles in the mixture? Chemical Potential Partial molar Gibbs free energy is called chemical potential ? = (?G/?Ni)T, P, N j?I = Gi Chemical potential is in all expressions for partial molar quantities ? = (?G/?Ni)T, P, N j?I = (?H/?Ni)S, P, N j?I = (?U/?Ni)S, V, N j?I = (?A/?Ni)T, V, N j?I Example of change in chemical potential is hydrogen in platinum

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