Physical Chemistry Third Edition

182 4 The Thermodynamics of Real Systems 4.5 Multicomponent Systems In an equilibrium open multicomponent system with one gas or ...

4.5 Multicomponent Systems 183 However, the partial derivatives in this equation are not equal to any simple thermody- namic var ...

184 4 The Thermodynamics of Real Systems so that the natural independent variables forAareT,V,n 1 ,n 2 ,...,nc. By inspection μi ...

4.5 Multicomponent Systems 185 Exercise 4.15 a.Show thatμiAi+PVi b.Show thatμiUi+PVi−TSi There are some equations similar to t ...

186 4 The Thermodynamics of Real Systems In a one-component system any partial molar quantity is equal to the corresponding mola ...

4.5 Multicomponent Systems 187 EXAMPLE4.19 Find the expression for the partial molar Helmholtz energy of a one-component ideal g ...

188 4 The Thermodynamics of Real Systems PROBLEMS Section 4.5: Multicomponent Systems 4.41 Following are data on the density of ...

4.6 Euler’s Theorem and the Gibbs–Duhem Relation 189 kwith independent variablesn 1 ,n 2 ,...,nc,Euler’s theoremstates that kf ...

190 4 The Thermodynamics of Real Systems The Gibbs–Duhem Relation From Euler’s theorem, Eq. (4.6-3), we can write an expression ...

4.6 Euler’s Theorem and the Gibbs–Duhem Relation 191 where we have used the relationdP 2 −dP 1 , which follows from our conditi ...

192 4 The Thermodynamics of Real Systems EXAMPLE4.23 At constant temperature and pressure, the volume of a solution made from co ...

4.6 Euler’s Theorem and the Gibbs–Duhem Relation 193 Experimental curve Tangent line Value of V 2 at x 15 0.500 0 0.2 0 0.4 x 1 ...

194 4 The Thermodynamics of Real Systems 0 0.2 2 1.4 2 1.2 2 1.0 2 0.8 2 0.6 2 0.4 Tangent point atx 15 0.500 5 x ́ 1 x 1 2 0.2 ...

4.6 Euler’s Theorem and the Gibbs–Duhem Relation 195 of 350.0 K and a constant pressure of 1.000 bar. a.Find∆Smix. b.Find∆Gmix. ...

196 4 The Thermodynamics of Real Systems whereμiis the chemical potential of componenti, and additional useful formulas were obt ...

4.6 Euler’s Theorem and the Gibbs–Duhem Relation 197 d.Find the final volume of 1.000 mol of liquid water if it is compressed ad ...

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5 Phase Equilibrium PRINCIPAL FACTS AND IDEAS The laws of thermodynamics determine equilibrium between phases. The fundamental ...

200 5 Phase Equilibrium 5.1 The Fundamental Fact of Phase Equilibrium The principal business of this chapter is to establish the ...

5.1 The Fundamental Fact of Phase Equilibrium 201 IfTandPare constant, the fundamental criterion of equilibrium implies thatdGmu ...