Relative volatility defined

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 equilibrium ratios of two components in the system may be compared at the same conditions by means of the relative volatility, defined as... 

The relative volatility defined by (1-7) is the ratio of vapor pressures and, thus, depends only on temperature... 

The selectivity is a function of concentration, pressure and temperature since the individual permeabilities depend on concentration, pressure, and temperature. However, tends to be less dependent on these factors than the individual permeabilities. Note that q b is analogous to the relative volatility defined in Chapter 2. Since we prefer to operate gas permeation as a one-stage system, q b... 

The relative volatility, defined as the ratio of distribution coefficients,... 

For an equiUbrium-based separation, a convenient measure of the intrinsic selectivity of the adsorbent is provided by the separation factor which is defined by analogy with the relative volatility as... 

Separation by distillation is dependent on the fact that when a Hquid is partially vaporized the vapor and Hquid compositions differ. The vapor phase becomes enriched ia the more volatile components and depleted ia the less volatile components with respect to its equiUbrium Hquid phase. By segregating the phases and repeating the partial vaporization, it is often possible to achieve the desired degree of separation. One measure of the degree of enrichment or the ease of separation is the relative volatiHty defined as ... 

To calculate a distillation, the relative volatility a is needed, it is defined as... 

A term of great importance is relative volatility. Relative volatility is a measure of the differences in volatility between two components, and hence their boiling points. It indicates how easy or difficult a particular separation will be. The relative volatility of component i with, respect to component j is defined by the following relationship ... 

More oftea than the assumption of eonstant K-values, the assumption of eonstant relative volatilities is applied. The relative volatility of two components i and j is defined as the ratio of their K-values ... 

By taking the ratio of the distribution coefficients for the two Components i and j, the separation factor can be defined, which is analogous to relative volatility in distillation ... 

The relative volatility, a, is a constant that under equilibrium conditions can be used to express the distribution of a volatile compound between a gas phase made of A and water vapor and a water phase containing A. This constant is for a component A defined as follows ... 

The principle of azeotropic and of extraction distillation lies in the addition of a new substance to the mixture so as to increase the relative volatility of the two key components, and thus make separation relatively easy. Benedict and Rup,in(43) have defined these two processes as follows. In azeotropic distillation the substance added forms an azeotrope with one or more of the components in the mixture, and as a result is present on most of the plates of the column in appreciable concentrations. With extractive distillation the substance added... 

Another measure of the preference of an ion exchanger for one other ionic species is the separation factor a. This is defined in a similar way to relative volatility in vapour-liquid binary systems, and is independent of the valencies of the ions. 

Relative volatility. The relative volatility of component i to component j is defined ... 

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... 

In other words, the equation defines an improvement factor, which consists of the ratio of relative volatility with salt present (calculated using liquid composition on a salt-free basis for direct comparison purposes) to relative volatility at the same liquid composition but without salt present. It relates the logarithm of this improvement factor in a direct proportionality with N3, the mole fraction of salt present in the liquid on a ternary basis. Jaques and Furter (17) tested the equation with data taken at several constant liquid compositions in four alcohol-water-inorganic salt systems, and observed good agreement. 

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... 

Consider two very similar components, propylene [1] and propane [3], with close boiling points. The ideal relative volatility is now defined as... 

The relative volatility, or selectivity factor, for each component in the presence of carbon dioxide is also given in Table I. Relative volatility is defined as the ratio of K-value for component i to K-value for limonene. The K-value for component i is defined as mole fraction i in the vapor (extract) phase to mole fraction i in the liquid (raffinate) phase. 

Separation factor Defined according to Eq. (5) in analogy with relative volatility provides a quantitative... 

As discussed in the previous section, the work of Mayur et al. (1970) and Christensen and Jorgensen (1987) on the optimal recycle policy was restricted to binary mixtures. The benefits of recycling were measured in terms of a reduction in batch time although increase in productivity could be a possible alternative. Luyben (1988) considered this productivity measure (as defined as "capacity" which includes both batch time and a constant charging and cleaning time) in a simulation of multicomponent batch distillation with recycle. Luyben (1988), however, showed the effect of different parameters (no of plates, relative volatilities, etc.) on the productivity and did not actually consider the effect of off-cuts recycle on the productivity. 

The simple K-value model is completed by defining a set of relative volatilities ... 

By convention, relative volatility is defined as the Jf-value ratio of the more-volatile to the less-volatile component, and therefore, relative volatility is always greater or equal to unity,... 

Relative volatility, a, which describes the equilibrium relationship between vapor and liquid compositions, is defined as... 

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. 

The relative volatilities are defined by Eq. (13-33), R m is the minimum reflux ratio, and q describes the thermal condition of the feed (1 for a saturated liquid feed and 0 for a saturated vapor feed). The Zfj values are available from the given feed composition. The 0 is the common root for the top section equations and the bottom section... 

The relative volatilities 0 are defined by Eq. (13-33), is the minimum-reflux ratio L +i/D) ia, and q describes the thermal condition of the feed (e.g., 1.0 for a bubble-point feed and 0.0 for a saturated-vapor feed). The values are available from the given feed composition. The 0 is the common root for the top-section equations and the bottom-section equations developed by Underwood for a column at minimum reflux with separate zones of constant composition in each section. The common root value must fall between ahk and aik, where hk and Ik stand for heavy key and light key respectively. The key components are the ones that the designer wants to separate. In the butane-pentane splitter problem used in Example 1, the light key is n-C4 and the heavy key is i-Cs. 

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