Chapter 7 Equilibrium relationships and equilibrium stage operation
1 Chapter 7 Equilibrium relationships and equilibrium stage operation
1.Phase Rule F=C-Φ+2 F=number of degrees of freedom,or variance C=number of components Φ=number of phases 2-only temperature and pressure may affect the equilibrium state. e.g:In systems of two components,C=2;Φ=2； therefore,F=2-2+2=2
2 1. Phase Rule •F = C – Φ + 2 F = number of degrees of freedom, or variance C= number of components Φ= number of phases 2 —— only temperature and pressure may affect the equilibrium state. e.g.: In systems of two components, C=2；Φ=2； therefore, F = 2 - 2 + 2 = 2
.For binary distillation,F=2,there are four variables of interests:pressure, temperature,and the mole fractions of component A in liquid and vapor phases. If the pressure is fixed,only one variable, e.g.,liquid phase mole fraction,can be changed independently,and temperature and vapor-phase mole fraction follow
3 •For binary distillation, F=2, there are four variables of interests: pressure, temperature, and the mole fractions of component A in liquid and vapor phases. If the pressure is fixed,only one variable, e.g., liquid phase mole fraction, can be changed independently, and temperature and vapor-phase mole fraction follow
2.Equilibrium of Gas and Liquid and equilibrium stage 0 0 ●● Vapor 0 a要 中 0 白 Heater Liquid
2. Equilibrium of Gas and Liquid and equilibrium stage 4 Heater 加热 Vapor Liquid
P=PA+PB yA+yB=1 0 Vapor 8 0 0 0 位 0 百色 XA+XB=1 Heater Liquid
5 Heater 加热 Vapor Liquid P=pA+pB yA+yB=1 xA+xB=1
Equilibrium State: No further changes in composition,temperature, or pressure occur. The chemical potential of the vapor and liquid phases are equal. The apparatus is performing as if it were an “equilibrium.”or“theoretical,.”or“ideal'”stage and the vapor and liquid compositions are the equilibrium compositions
6 Equilibrium State: No further changes in composition, temperature, or pressure occur. The chemical potential of the vapor and liquid phases are equal. The apparatus is performing as if it were an “equilibrium,” or“theoretical,” or “ideal” stage and the vapor and liquid compositions are the equilibrium compositions
3.Thermodynamic relationships 1)Equilibrium ratio or equilibrium constant or K value). K= XA Where KA=Equilibrium ratio yA=mole fraction of component A in vapor XA=mole fraction of component A in liquid
7 3. Thermodynamic relationships 1)Equilibrium ratio ( or equilibrium constant or K value). B A AB A A A K K x y K = = Where KA=Equilibrium ratio yA=mole fraction of component A in vapor xA= mole fraction of component A in liquid
The more volatile components in a mixture will have the higher values of KA, whereas less volatile components will have lower values of KA. 2)Relative volatility(相对挥发度)-key separation factor in distillation. KA (b) Where a=relative volatility(A relative to B)
8 • The more volatile（易挥发） components in a mixture will have the higher values of KA, whereas less volatile components will have lower values of KA. • 2)Relative volatility（相对挥发度）----key separation factor in distillation. Where relative volatility(A relative t oB) K K A B B A A B = = (b)
。3)Ideal system Ideal systems of vapor and liquid mixtures obey Dalton's and Raoult's law. Dalton's law relates the concentration of a component present in an ideal gas or vapor mixture to its partial pressure. PA=PYA (a) Where P=total pressure,force/length2 pA=partial pressure of component A,force/length2 yA=mol fraction of component A,dimensionless(无因次) 9
9 • 3)Ideal system • Ideal systems of vapor and liquid mixtures obey Dalton’s and Raoult’s law. • Dalton’s law relates the concentration of a component present in an ideal gas or vapor mixture to its partial pressure. Where P=total pressure,force/length2 pA=partial pressure of component A,force/length2 yA=mol fraction of component A,dimensionless(无因次) A A A A y P p p = Py (a)
。Raoult'slaw PA=PAXA (b) Pn=Paxn pa(1-xa) 0 Where pA=partial pressure of component A, force/length2 xA=molar fraction of component A, dimensionless(无因次) 10
10 • Raoult’s law Where pA=partial pressure of component A, force/length2 xA=molar fraction of component A, dimensionless(无因次) (1 ) 0 0 0 B B B B A A A A p p x p x p p x = = − = (b)