Vapor mixture

Equation (12), applicable at low or moderate pressures, is used in this monograph for typical vapor mixtures. However, when the vapor phase contains a strongly dimerizing component such as carboxylic acid. Equation (7) is not applicable and... 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

This chapter presents a general method for estimating nonidealities in a vapor mixture containing any number of components this method is based on the virial equation of state for ordinary substances and on the chemical theory for strongly associating species such as carboxylic acids. The method is limited to moderate pressures, as commonly encountered in typical chemical engineering equipment, and should only be used for conditions remote from the critical of the mixture. 

The fugacity coefficient is a function of temperature, total pressure, and composition of the vapor phase it can be calculated from volumetric data for the vapor mixture. For a mixture containing m components, such data are often expressed in the form of an equation of state explicit in the pressure... 

If the vapor mixture contains only ideal gases, the integrals in Equations (3) and (6) are zero, z is unity for all compositions, and ()i equals 1 for each component i. At low pressures, typically less than 1 bar, it is frequently a good assumption to set ( ) = 1, but even at moderately low pressures, say in the vicinity of 1 to 10 bars, (f) is often significantly different from unity, especially if i is a polar component. 

Equation (10b) is used in this work whenever the vapor mixture does not contain one or more carboxylic acids. 

A component in a vapor mixture exhibits nonideal behavior as a result of molecular interactions only when these interactions are very wea)c or very infrequent is ideal behavior approached. The fugacity coefficient (fi is a measure of nonideality and a departure of < ) from unity is a measure of the extent to which a molecule i interacts with its neighbors. The fugacity coefficient depends on pressure, temperature, and vapor composition this dependence, in the moderate pressure region covered by the truncated virial equation, is usually as follows ... 

The enthalpy of a vapor mixture is obtained first, from zero-pressure heat capacities of the pure components and second, from corrections for the effects of mixing and pressure. 

For an ideal vapor mixture of m components, there is no enthalpy of mixing. The enthalpy of such a mixture is then... 

For a real vapor mixture, there is a deviation from the ideal enthalpy that can be calculated from an equation of state. The enthalpy of the real vapor is given by... 

For an associating vapor mixture, where strong dimerization occurs (i.e., either > 4.5 or > 4.5), the molar enthalpy,... 

For such associating vapor mixtures, the "chemical" theory is used, as discussed in Chapter 3. The derivation of Ah... 

As mentioned in Section IX-2A, binary systems are more complicated since the composition of the nuclei differ from that of the bulk. In the case of sulfuric acid and water vapor mixtures only some 10 ° molecules of sulfuric acid are needed for water oplet nucleation that may occur at less than 100% relative humidity [38]. A rather different effect is that of passivation of water nuclei by long-chain alcohols [66] (which would inhibit condensation note Section IV-6). A recent theoretical treatment by Bar-Ziv and Safran [67] of the effect of surface active monolayers, such as alcohols, on surface nucleation of ice shows the link between the inhibition of subcooling (enhanced nucleation) and the strength of the interaction between the monolayer and water. 

Butane lighters contain about 5% n butane and 95% isobutane in a sealed con tamer The pressure pro duced by the two com pounds (about 3 atm) is enough to keep them in the liquid state until opening a small valve emits a fine stream of the vaporized mixture across a spark which ignites it... 

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

Isopropyl alcohol can be oxidized by reaction of an a,P-unsaturated aldehyde or ketone at high temperature over metal oxide catalysts (28). In one Shell process for the manufacture of aHyl alcohol, a vapor mixture of isopropyl alcohol and acrolein, which contains two to three moles of alcohol per mole of aldehyde, is passed over a bed of uncalcined magnesium oxide [1309-48-4] and zinc oxide [1314-13-2] at 400°C. The process yields about 77% aHyl alcohol based on acrolein. 

Flow Sheet Generation for Separating Gas—Vapor Mixtures... 

Flash Point. As a liquid is heated, its vapor pressure and, consequendy, its evaporation rate increase. Although a hquid does not really bum, its vapor mixed with atmospheric oxygen does. The minimum temperature at which there is sufficient vapor generated to allow ignition of the air—vapor mixture near the surface of the hquid is called the dash point. Although evaporation occurs below the dash point, there is insufficient vapor generated to form an igrhtable mixture below that point. 

In Figure 2 the lines, volume, m /kg dry air, indicate humid volume, which includes the volume of 1.0 kg of dry gas plus the volume of vapor it carries. Enthalpy at saturation data are accurate only at the saturation temperature and humidity however, for air—water vapor mixtures, the diagonal wet bulb temperature lines are approximately the same as constant-enthalpy adiabatic cooling lines. The latter are based on the relationship ... 

Cg = humid heat for humidity H in units of kj / (kg-K) and = latent heat of vaporization at / in kj /kg. The slope of the constant-enthalpy adiabatic cooling line is —C j which is the relationship between temperature and humidity of gas passing through a totally adiabatic direct-heat dryer. The humid heat of a gas—vapor mixture per unit weight of dry gas includes the specific heat of the vapor... 

Esters of medium volatility are capable of removing the water formed by distillation. Examples are propyl, butyl, and amyl formates, ethyl, propyl, butyl, and amyl acetates, and the methyl and ethyl esters of propionic, butyric, and valeric acids. In some cases, ternary azeotropic mixtures of alcohol, ester, and water are formed. This group is capable of further subdivision with ethyl acetate, all of the ester is removed as a vapor mixture with alcohol and part of the water, while the balance of the water accumulates in the system. With butyl acetate, on the other hand, all of the water formed is removed overhead with part of the ester and alcohol, and the balance of the ester accumulates as a high boiler in the system. 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

For nonpolar, nonhydrocarbon vapor mixtures at high pressures, the method of Dean and Stiel [Eq- (2-102)] discussed earlier can be used. The accuracy of the method is excellent and dependent on the pure component viscosity values used as input parameters. 

Although developed for pure materials, this correlation can be extended to gas or vapor mixtures. Basic to this extension is the mixing rule for second virial coefficients and its temperature derivative ... 

Carbon Dioxide—Water-Vapor Mixtures When these gases are present together, the total radiation due to both is somewhat less than the sum of the separately calculated effects, because each gas is somewhat opaque to radiation from the other in the wavelength regions 2.7 and 15 [Lm. 

Thermodynamic and Mass-Transfer Considerations Multi-component vapor mixture includes several different cases all the components may be hquids at the lowest temperature reached in the condensing side, or there may be components which dissolve substantially in the condensate even though their boiling points are below the exit temperature, or one or more components may be both noncondensable and nearly insoluble. 

Psychrometry is concerned with determination of the properties of gas-vapor mixtures. The air-water vapor system is by far the system most commonly encountered. 

FIG. 12-4 Humidity chart for air-water vapor mixtures. To convert British thermal units per pound to joules per Idlo-gram, multiply by 2326 to convert British thermal units per pound dry air-degree Fahrenheit to joules per Idlogram-kelvin, multiply hy 4186.8 and to convert cubic feet per pound to cubic meters per kilogram, multiply by 0.0624. 

From air-water vapor-mixture tables, the enthalpy hi of the ambient air at 78 F wet-bulb temperature is 41.58 Btu/lb. 

FIG. 12-36 Psychrometric chart properties of air and water-vapor mixtures from 20 to 120 C, Catrier Corp. )... 

For air-water-vapor mixtures, it so happens that h /k = C, approximately, although there is no theoretical reason for this. Hence, since the ratio — H )/(f , — t) equals h /k /X, which represents the slope of the wet-bulb-temperature lines, it is also equal to C, /X, the slope of the adiabatic-saturation lines as shown previously. 

A rate balance between evaporation and heat transfer when radiation occurs may be modified by means of the psychrometric ratio for air-water vapor mixtures to give ... 

In distillation operations, separation results from differences in vapor-and liquid-phase compositions arising from the partial vaporization of a hquid mixture or the partial condensation of a vapor mixture. The vapor phase becomes enriched in the more volatile components while the hquid phase is depleted of those same components. In many situations, however, the change in composition between the vapor and liquid phases in equihbrium becomes small (so-called pinched condition ), and a large number of successive partial vaporizations and partial condensations is required to achieve the desired separation. Alternatively, the vapor and liquid phases may have identical compositions, because of the formation of an azeotrope, and no separation by simple distillation is possible. 

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