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Vapor Liquid Equilibria: a Review Maya B Sci. Revs. Chem. Commun.: 2(2), 2012, 158-171 ISSN 2277-2669 VAPOR LIQUID EQUILIBRIA: A REVIEW MAYA B. MANE* and S. N. SHINDE Master Student in Chemical Engineering, Chemical Engineering Department, Bharati Vidyapeeth Deemed University, College of Engineering, PUNE (M.S.) INDIA (Received : 30.05.2012; Revised : 03.06.2012; Accepted : 04.06.2012) ABSTRACT Vapor-liquid equilibrium data may be readily evaluated and extended when they are calculated as activity coefficients. The equations proposed by Van Laar, Margulas, Wilson, NRTL and UNIQUAC, which express the activity coefficients of the components of a mixture as functions of the liquid composition and empirical constants, are capable of fitting most of the available vapor liquid equilibrium data. Equations of state play an important role in chemical engineering design and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. Key words: VLE, Van Laar, Margulas, Wilson, NRTL, UNIQUAC, Equation of States. INTRODUCTION The term “Vapor-Liquid Equilibrium (VLE)” refers to systems in which a single liquid phase is in equilibrium with its vapor, schematic diagram of the vapor-liquid equilibrium is illustrated in Fig. 1. In studies of phase equilibrium, however, the phase containing gradients is not considered. Wherever gradients exist there is a tendency for change with time; hence there is no equilibrium. On the other hand, there can be two or more phases, each of which is homogenous throughout, with no tendency for any change in properties with time, even though the phases are in intimate physical contact with one another. The latter is the condition that we denote by the term “phase equilibrium”. In a condition of phase equilibrium there are some properties that are drastically different between the phases and others that must be identical for all phases to prevent a change in properties within individual phases from occurring1. The thermodynamic equilibrium determines how components in a mixture are distributed between phases. ● liquid ▲vapor Fig. 1: Schematic diagrams illustrating the vapor-liquid equilibrium of binary system1 ________________________________________ Available online at www.sadgurupublications.com *Author for correspondence; E-mail: [email protected], [email protected]; Mo.: +91-7875089217; 91-8805001490 Sci. Revs. Chem. Commun.: 2(2), 2012 159 The system is in the equilibrium state, if only reversible process can occur in it. This verbal formulation makes it possible mathematically to express the condition of equilibrium: Let us consider a closed system on which a constant pressure is acting as the only external force. In an infinitesimal reversible process at constant temperature and pressure, the free enthalpy of this system does not change; hence at equilibrium we have – dT = 0, dP = 0, dG = 0 …(1) where T is the absolute temperature, P the pressure and G the free enthalpy of the system. This formulation of the condition of equilibrium is sufficiently general for all cases with which we shall be concerned2. Vapour liquid equilibrium laws Vapour liquid equilibria are best understood with the help of simple, empirical laws which may, however, only apply within certain limits. Dalton’s law It describes the vapour phase: pi"/pt" = ni"/nt" …(2) where p is the pressure and n the number of moles of substance. The subscript i denotes component i. since ni"/nt" = yi (where yi is the mole fraction of component i in the vapour). This law generally holds low pressure (pt < pcr, where pcr is the critical pressure). At higher pressure, however, it may require modification instead of using pressure p, the equation is written in terms of fugacity f: fi" = yi ft" …(3) Raoult’s law The liquid phase is described by Raoult’s law giving a relation for the partial pressure pi' of component i over a liquid mixture: o pi' = xi pi …(4) o According to Equation (4) the partial pressure pi' depends only on the vapour pressure pi of the pure component i and its liquid mole fraction xi; it is not affected by the nature and concentration of other substances in the mixture. Raoult’s law holds only as the forces of interaction between different types of molecules are equal (ideal mixture). Nonideal liquid phase behavior is described by using the activity coefficient γi which is defined as follows: o pi' = γixi pi …(5) 160 M. B. Mane and S. N. Shinde: Vapor Liquid Equilibria…. Equations (4) and (5) are valid only for mole fractions. The activity coefficient γi is often called as “Raoult’s law correction factor” and is highly concentration dependent. Eq. (4) and (5) apply only at temperatures below the critical temperature (T < Tcr). Henry’s law At higher temperatures, Henry’s law is applied instead of Raoult’s law: pi' = Hijxi …(6) Where Hij is the Henry’s coefficient for substance i in solvent j. Again, a correction must be made for nonideal mixtures by using the activity coefficient γi : pi' = Hijγixi …(7) This relationship is analogous to Raoult’s law, except that the proportionality constant3. Vapour liquid equilibrium in ideal systems (I) Binary systems (a) At constant temperature Let us first consider a system with the two constituents A and B; according to equation (4) P = x po , …(8) A A A P = x po , …(9) B B B The total pressure, according to Dalton’s law, is given by the sum of the partial pressures: p = pA + pB = x po + x po …(10) A A B B As the system is binary, it is possible to substitute (1-xA) for xB; after this modification: P = x ()po − po ) + po …(11) A A B B Equation (11) states that the total pressure over an ideal solution is, at constant temperature, a linear function of composition. According to Dalton’s law we have for the vapour phase: pA = yAp, …(12) pB = yBp = (1 – yA)p, …(13) where yA denotes the mole fraction of constituent A in the vapour phase and similarly for yB. It follows from the relations (8), (9), (12) and (13) that yp = x po , …(14) A A A yp = xpo , …(15) B B B On taking the ratio of these equations we find Sci. Revs. Chem. Commun.: 2(2), 2012 161 y x y (1− x ) po A / A = A A = A = α; …(16) y x x (1− y ) po B B A A B For an ideal solution α is a constant independent of the composition; it is called the relative volatility or enrichment ratio. Equation (16) states that the ratio of the mole fractions of the constituents A and B in the vapour phase divided by the corresponding ratio in the liquid phase is constant. From (11) and (12) it is possible after elimination of xA to obtain a relation expressing the isothermal dependence of the total pressure on the composition of the vapour phase po p = A …(17) α − y (α −1)′ A or po po p = A B …(18) po − y ( po − po )′ A A A B The relation giving the dependence between the mole fraction of constituent A in the liquid phase and its mole fraction in the vapour phase is obtained from equation (18) by a simple rearrangement: αx A yA = …(19) 1+ x (α −1)′ A (b) At constant pressure Practically speaking however knowledge of the isobaric vapour-liquid equilibrium is more important. In this case we have by equation (14) - p = p + p = x po (T ) + (1− x ) po (T ) A B A A A B …(20) We write po (T) to emphasize that the vapour pressures of the pure constituent i dependes on the i temperature, which in this case is not constant. The relation giving the dependence between the compositions of the vapour and liquid phases is given by the equation – x α(T ) A yA = …(21) 1+ x [α(T ) −1] A α(T) = po (T) / po (T ) is generally speaking a function of temperature; however the ratio of the vapour A B pressures of the pure constituents varies but little in a short range of temperatures, so that α can often be considered as constant over the entire range of compositions. (II) Multicomponent systems In a multicomponent system containing an ideal liquid phase and a vapour phase that obeys the ideal gas laws, it is possible to derive relations similar to those for binary systems. 162 M. B. Mane and S. N. Shinde: Vapor Liquid Equilibria…. For an arbitrary constituent I we have p = x po …(22) I I I p x po I I I yI = = K …(23) p x po ∑J =A J J o By division of the numerator and denominator of the right side of (23) by pK we obtain after a simple rearrangement. x α I IK yI = …(24) 1+ x (α −1) + x (α −1) + ...+ x (α −1)′ A IK B BK K−1 K−1,K po po where α = A ,α = A etc. IK po AK po K K Thus in a ternary system- p = x po …(25) A A A p = x po , …(26) B B B p = x po , …(27) C C C p = x po + x po + (1− x − x ) po , …(28) A A B B A B C p x po A A A yA = = …(29) p x po + x po + (1− x − x ) po ' A A B B A B C p x po B B B yB = = …(30) p x po + x po + (1− x − x ) po ' A A B B A B C o By division of numerator and denominator of the right sides of (29) and (30) by pC and by substitution ofα = po / po and α = po / po we obtain – AC A C BC B C x α A AC yA = …(31) 1− x (α −1) + x (α −1) A AC B BC x α B BC yB = …(32) 1− x (α −1) + x (α −1) A AC B BC Strictly speaking, equations (31) and (32) are valid only at constant temperature; they can however be used for the case of constant pressure in many problems, since the ratio of the vapour pressures of the pure constituents is only weakly dependent on temperature, and the ranges of temperature that occur in distillation problems are frequently small2.
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