Vapor liquid equilibrium constant relative volatility

If the temperature dependence of the vapor pressure of both componoits is the same, a Avill be independent of temperature. In other words, relative volatility is constant if the vapor pressiure lines are parallel in a In P versus 1/T plot. This is true for many components over a limited temperature range, particularly when the components are chemically similar. Distillation columns are frequently designed assuming constant relative volatility because it greatly simplifies the vapor—liquid equilibrium calculations. Relative volatilities usually decrease somewhat widi increasing temperature in most systems. 

The forward reaction is first order in the mole fraction of A, and the backward reaction is proportional to the mole fractions of B and C. The equilibrium eonstant K q is set to 0.2 as a result of an imbalance in reaction stoichiometry. Note also that this is an endothermic reaction as one would expect from a decomposition reaction (cracking). For phase equilibrium, constant relative volatility is assumed and the tray temperature can be computed from the tray liquid composition using the Antoine vapor pressiue equations. 

Most batch distillations/separations are assumed to follow the constant relative volatility vapor-liquid equilibrium curve of... 

The digital simulation of a distillation column is fairly straightforward. The main complication is the large number of ODEs and algebraic equations that must be solved. We will illustrate the procedure first with the simplified binary distillation column for which we developed the equations in Chap. 3 (Sec. 3.11). Equimolal overflow, constant relative volatility, and theoretical plates have been assumed. There are two ODEs per tray (a total continuity equation and a light component continuity equation) and two algebraic equations per tray (a vapor-liquid phase equilibrium relationship and a liquid-hydraulic relationship). 

The compositions of vapor and liquid phases of two components at equilibrium sometimes can be related by a constant relative volatility which is defined as... 

The vapor-liquid equilibrium (VLE) is assume to be described by a constant relative volatility between components A and B of a= 1.5. On each tray in the column, the compositions (mole fraction A) of the liquid x and vapor v are related as follows ... 

Assuming constant relative volatilities ay of the components, the vapor-liquid equilibrium is given by ... 

Further, an ideal vapor liquid equilibrium is assumed with constant relative volatilities according to... 

Example A 50mol% mixture of heptane and octane is placed in a batch and heated. Plot the composition of the remaining liquid as a function of the fraction of the initial charge which remains. At the pressure in the still, the vapor-liquid equilibrium can be reasonably represented by a constant relative volatility of a = 1.7 (for a discussion on when this might arise, see pl05). 

The other assumption in the model relates to the vapor-liquid equilibrium coef-hcients, or /<-values. The /f-values at a given pressure are assumed to be a function of temperature only, and not of composition. It is further assumed that the temperature dependence of the A -values for the different components is similar, that is, the ratio of the /f-values of any pair of components is independent of temperature. Thus, the relative volatilities, defined as the ratios of A -values of any two components, are assumed constant throughout the column. 

This assumption is more restrictive than the assumption of constant relative volatilities, or relative X-values, that is used in the Fenske and Underwood methods. The payback for this assumption is the ability to generalize the model to different degrees of column complexity. The success of the method is dependent on proper evaluation of effective /C-values or other model parameters that would represent actual behavior of the column section. The equilibrium coefficient is commonly lumped with the vapor and liquid molar flows in the column to define the stripping factor. 

One method of removing a volatile contaminant from a liquid—for example, water— is by gas stripping, in which air or some other gas is bubbled through the liquid so that vapor-liquid equilibrium is achieved. If the contaminent is relatively volatile (as a result of a high value of its Henry s constant, vapor pressure, or activity coefficient), it will appear in the exiting air, and therefore its concentration in the remaining liquid is reduced. An example of this is given in the next illustration. 

Binary Vapor-Liquid Equilibrium Curves Based on Constant Relative Volatility... 

Then calculate tray by tray from xr up Nr trays (using component balances and constant relative volatility vapor-liquid equilibrium relationships) to obtain the vapor composition on the top tray yvr- Compare this value with that obtained from a component balance around the reactor, Eq. (5.43). 

Intuitively, all vapor liquid equilibrium models obey this relationship in positive composition space, but in order to be sure that it is useful, and valid, to analyze negative compositions, the Gibbs Duhem relationship should be maintained for negative composition too. Since 7/= I for the ideal and constant relative volatility cases, this condition is always valid for the entire composition spectrum, since the derivative of a constant is zero. Fortunately, it can be shown that all other models where y, is a function of composition (NRTL, Wilson, and so on) obey this rule, except in areas of discontinuity. Therefore, it is safe and thermodynamically sound, to analyze and interpret these negative compositions as they still obey fundamental thermodynamic rules. 

The chemical equilibrium constant is assumed to be constant, K = 5, and k is taken as independent of temperature. The vapor-liquid equilibrium is described by means of constant relative volatilities with a c 1> bc 1> and a c + asc-... 

D5. We have a column that has a 6-foot section of packing. The column can be operated as a stripper with liquid feed, as an enricher with a vapor feed or at total reflux. We are separating methanol from isopropanol at 101.3 kPa. The equilibrium can be represented by a constant relative volatility, a = 2.26. 

Reported experimental findings were muddled. But the solvent properties with the most significant effects upon the relative volatility of the azeotrope were those with extreme values of dielectric constant (Ref. 3, Table 10.3 and Chapter 12.5.4)and dipole moment (Ref. 2, Appendix C5, Chapter Cl). This finding engenders the proposition that the tramp contaminant, water, could have a substantial effect on the vapor-liquid equilibrium of binary azeotropes because of its extraordinarily high value of dielectric constant (80) and relatively high value of dipole moment (1.84D). 

After heat recovery, via HXl and HX2, the reactor effluent is fed into a distillation column. The two reactants, A B, are light key (LK) and intermediate boiler (IK), respectively, while the product, X, is the heavy component (HK). The Antoine constants of the vapor pressure equation are chosen such that the relative volatilities of the components are ttA = 4, ttB = 2, and Oc=l for this equal molar overflow system (Table 1). Only one distillation column is sufficient to separate the product (C) from the unreacted reactants (A B). Ideal vapor-liquid equilibrium is assumed. Physical property data and kinetic data are given in Table 1. 

The relative volatility % of the light key relative to the heavy key is an average value, assumed constant on all the stages. Its value is determined independently from vapor-liquid equilibrium data or correlations. The temperature at which the relative volatility is calculated must be assumed. It is some average column temperature that could be verified by applying Equation 12.17 to check if B = "Lbi. (See Section 12.1.4). 

H-H ) - molar enthalpy departure frm the ideal gas state AHmix molar liquid heat of solution k - liquid thermal conductivity K - vapor-liquid equilibrium ratio P - absolute pressure Pref reference pressure R - gas constant T - absolute temperature - liquid molar volume - liquid partial molar volume X - mole fraction in liquid phase y - mole fraction in vapor phase relative volatility Y - liquid activity coefficient liquid viscosity... 

Using Equation 7-12, a curve can be established that shows the relationship between the liquid composition and the equilibrium vapor composition at a constant relative volatility. Figure 7-1 shows curves at a values of 1.4, 2.0, and 4.0, which represent separations of increasing ease. The equilibrium relationships between vapor and liquid compositions for some nonideal binary systems are shown in Figure 7-2. Curve I is a methanol/water system, and Curve II is a water/acetic acid system. Note that these curves no longer are symmetrical like those in Figure 7-1. 

Constant relative volatility is used to describe vapor/liquid equilibrium. 

In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid. Hence, the vapor composition xp is related to the hquid composition xb by an equiUbrium relation of the form xp = fixs)- The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperature and pressure. For a system following the ideal behavior given by Raoult s law, the equilibrium relationship between the vapor composition y (or xp) and liquid composition x (or xb) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility a), and is given by ... 

In the next three chapters we will explore various aspects of the ideal quaternary chemical system introduced in Chapter 1. This system has four components two reactants and two products. The effects of a number of kinetic, vapor-liquid equilibrium, and design parameters on steady-state design are explored in Chapter 2. Detailed economic comparisons of reactive distillation with conventional multiunit processes over a range of chemical equilibrium constants and relative volatilities are covered in Chapter 3. An economic comparison of neat versus excess-reactant reactive distillation designs is discussed in Chapter 4. 

Ideal vapor-liquid equilibrium is assumed, in which constant relative volatilities are used. The tray temperature is computed from the bubblepoint temperature calculation provided with the Antoine vapor pressure coefficients (Table 17.1). That is. 

Another issue is that the effect of pressure on the design is not explored here because we are assuming constant relative volatility systems. The column pressure is fixed at 8 bar in this work. Pressure is very important in reactive distillation because of the effect of temperature on both vapor-liquid equilibrium and reaction kinetics. For exothermic reactions, the optimum column pressure is affected by the competing effects of temperature on the specific reaction rates and the chemical equilibrium constant. 

When temperature is constant and at equilibrium for a homogeneous mixture (such as azeotrope), the composition of the liquid is identical with the composition of the vapor, thus xj = y, and the relative volatility is equal to 1.0. 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

The partition or distribution coefficient between a gas and a liquid is constant at a given temperature and pressure. The relative volatility is used in defining the equilibrium between a volatile liquid mixture and the atmosphere. The partition coefficient expresses the relative volatility of a species A distributed between a vapor phase (Al) and a liquid phase (A2). Henry s law applies to the distribution of dilute solutions of chemicals in a gas, liquid, or solid at a specific ambient condition. Equilibrium is defined by... 

Assuming that the relative volatilities of the components are constant and that the vapor and liquid phases on the column stages are at equilibrium, we... 

If phase equilibrium is assumed between liquid and vapor, the right-hand side of Eq. (13-126) may be evaluated from the area under a curve of / y — x) versus x between the limits Xj and Xf. If the mixture is a binary system for which the relative volatility a can be approximated as a constant over the range considered, then the VLE relationship... 

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