Vapor-liquid equilibria relative volatility

The separation power in a distillation column comes from the thermodynamic vapor-liquid equilibrium relative volatility, the number of theoretical stages achieved by the column, and the... 

For equilibrium-stage calculations involving the separation of two or more components, separability factors are defined by forming ratios of equilibrium ratios. For the vapor-liquid case, relative volatility is defined by (1-7) as an = KilKj. For the liquid-liquid case, the relative selectivity is defined by (1-8) as Pii = KoJKoj-... 

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

Example 2.7. To show what form the energy equation takes for a two-phase system, consider the CSTR process shown in Fig. 2.6. Both a liquid product stream f and a vapor product stream F (volumetric flow) are withdrawn from the vessel. The pressure in the reactor is P. Vapor and liquid volumes are and V. The density and temperature of the vapor phase are and L. The mole fraction of A in the vapor is y. If the phases are in thermal equilibrium, the vapor and liquid temperatures are equal (T = T ). If the phases are in phase equilihrium, the liquid and vapor compositions are related by Raoult s law, a relative volatility relationship or some other vapor-liquid equilibrium relationship (see Sec. 2.2.6). The enthalpy of the vapor phase H (Btu/lb or cal/g) is a function of composition y, temperature T , and pressure P. Neglecting kinetic-energy and potential-energy terms and the work term,... 

The effect of salts on the vapor-liquid equilibrium of solvent mixtures has been of considerable interest in recent years. Introduction of a salt into a binary solvent mixture results in a change in the relative volatility of the solvents. This effect can be used to an advantage where the separation of the solvents is of interest. Furter and co-workers have demonstrated the potential importance of salts as separating agents in extractive distillation (J, 2, 3). 

The use of a dissolved salt in place of a liquid component as the separating agent in extractive distillation has strong advantages in certain systems with respect to both increased separation efficiency and reduced energy requirements. A principal reason why such a technique has not undergone more intensive development or seen more than specialized industrial use is that the solution thermodynamics of salt effect in vapor-liquid equilibrium are complex, and are still not well understood. However, even small amounts of certain salts present in the liquid phase of certain systems can exert profound effects on equilibrium vapor composition, hence on relative volatility, and on azeotropic behavior. Also extractive and azeotropic distillation is not the only important application for the effects of salts on vapor-liquid equilibrium while used as examples, other potential applications of equal importance exist as well. 

The establishment of the method of prediction has been attempted by the reverse calculation of the preferential solvation number from measured values, using Equations 4 and 7 which are based on the assumption that the salt effect in the vapor-liquid equilibrium is caused by the preferential solvation formed between a volatile component and a salt. The observed values were selected from Ciparis s data book (4), Hashitani s data (5-8), and the author s data (9-15). S was calculated by Equation 7 when the relative volatility as in the vapor-liquid equilibrium with salt is increased with respect to the relative volatility a in the vapor-liquid equilibrium with salt, but by Equation 4 when as is decreased. The results are shown in Figures 5-12. From these figures, it will be seen that the following three relations exist ... 

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

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... 

Assuming the relative volatility of a benzene-toluene mixture is 2.90, the vapor-liquid equilibrium compositions can be calculated as shown in Table 5.1. The resultant curve is plotted in Fig. 5.1a. 

Using this value of relative volatility, the following vapor-liquid equilibrium compositions can be calculated ... 

Determine the relevant vapor-pressure data. Design calculations involving vapor-liquid equilibrium (VLE), such as distillation, absorption, or stripping, are usually based on vapor-liquid equilibrium ratios, or K values. For the tth species, K, is defined as K, = y, /x, where y, is the mole fraction of that species in the vapor phase and x, is its mole fraction in the liquid phase. Sometimes the design calculations are based on relative volatility c/u], which equals K,/Kj, the subscripts i and j referring to two different species. In general, K values depend on temperature and pressure and the compositions of both phases. 

Isobaric vapor-liquid equilibrium data at atmospheric pressure are reported for the four systems of the present investigation in Tables I-VI. Salt concentrations are reported as mole fraction salt in the solution, while mixed-solvent compositions are given on a salt-free basis. A single fixed-liquid composition was used for potassium iodide and sodium acetate potassium acetate used three—all chosen from the region of ethanol-water composition where relative volatility is highest. In the... 

Vapor-liquid equilibrium calculations can sometimes be simplified through the use of a quantity called the relative volatility, which may be defined m terms of the tollowing depiction of vapor and liquid phases in equilibrium ... 

Plot the vapor-liquid equilibrium curve from data available at the column operating pressure. In terms of relative volatility... 

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). 

Eew multicomponent systems exist for which completely generalized equilibrium data are available. The most widely available data are those for vapor-liquid systems, and these are frequently referred to as vapor-liquid equilibrium distribution coefficients or K value. The K values vary with temperature and pressure, and a selectivity that is equal to the ratio of the K values is used. Eor vapor-liquid systems, this is referred to as the relative volatility and is expressed for a binary system as... 

According to the rules proposed by Seader and Westerberg (1977), the components in the feed are arranged by decreasing volatility and two sets of parameters are checked the relative volatilities of adjacent pairs and the molar percentages of the components in the feed. The relative volatility, (x,y, of component i with respect to component j is used as an indicator of how readily they could be separated and is defined as the ratio of their vapor-liquid equilibrium coefficients ... 

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. 

The vapor-liquid equilibrium coefficients are expressed in terms of the relative volatility, oc, and a reference A -valuc at the top and bottom stages ... 

For vapor-liquid equilibrium, the ideal separation factor is termed the relative volatility and is written as the ratio of the vapor pressure of each component ... 

In vapor-liquid equilibrium the relative volatility ttij is defined to be the ratio of the separation or K factor for species i to that for species j, that is,... 

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). 

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