Constant-pressure equilibrium, vapor-liquid

The flash curve of a petroleum cut is defined as the curve that represents the temperature as a function of the volume fraction of vaporised liquid, the residual liquid being in equilibrium with the total vapor, at constant pressure. 

TABLE 13-1 Constant-Pressure Liquid-Vapor Equilibrium Data for Selected Binary Systems... 

It is important to realize that so long as both liquid and vapor are present the pressure exerted by the vapor is independent of the volume of the container. Ifa small amount ofliquid is introduced into a closed container, some of it will vaporize, establishing its equilibrium vapor pressure. The greater the volume of the container, the greater will be the amount ofliquid that vaporizes to establish that pressure. The ratio nIV stays constant, so P = nRTIV does not change. Only if all the liquid vaporizes will the pressure drop below the equilibrium value. 

Source Considerations. Many CVD sources, especially sources for or-ganometallic CVD, such as Ga(CH3)3 and Ga(C2H5)3, are liquids at near room temperatures, and they can be introduced readily into the reactor by bubbling a carrier gas through the liquid. In the absence of mass-transfer limitations, the partial pressure of the reactant in the gas stream leaving the bubbler is equal to the vapor pressure of the liquid source. Thus, liquid-vapor equilibrium calculations become necessary in estimating the inlet concentrations. For the MOCVD of compound-semiconductor alloys, the computations have also been used to establish limits on the control of bubbler temperature to maintain a constant inlet composition and, implicitly, a constant film composition (79). Similar gas-solid equilibrium considerations govern the use of solid sources such as In(CH3)3. 

When we consider a one-component, two-phase system, of constant mass, we find similar relations. Such two-phase systems are those in which a solid-solid, solid-liquid, solid-vapor, or liquid-vapor equilibrium exists. These systems are all univariant. Thus, the temperature is a function of the pressure, or the pressure is a function of the temperature. As a specific example, consider a vapor-liquid equilibrium at some fixed temperature and in a state in which most of the material is in the liquid state and only an insignificant amount in the vapor state. The pressure is fixed, and thus the volume is fixed from a knowledge of an equation of state. If we now add heat to the system under the condition that the temperature (and hence the pressure) is kept constant, the liquid will evaporate but the volume must increase as the number of moles in the vapor phase increases. Similarly, if the volume is increased, heat must be added to the system in order to keep the temperature constant. The change of state that takes place is simply a transfer of matter from one phase to another under conditions of constant temperature and pressure. We also see that only one extensive variable—the entropy, the energy, or the volume—is necessary to define completely the state of the system. 

Calculate dew-point equilibrium for the feed. A vapor is at its dew-point temperature when the first drop of liquid forms upon cooling the vapor at constant pressure and the composition of the vapor remaining is the same as that of the initial vapor mixture. At dew-point conditions, K, = A = Ki Xt, or Xj = Nj /Kj, and Nj /Kj = 1.0, where Yj is the mole fraction of component i in the vapor phase, Xi is the mole fraction of component i in the liquid phase, A is the mole fraction of component i in the original mixture, and Kj is the vapor-liquid equilibrium K value. 

The result just obtained is applicable to any liquid-vapor equilibrium, irrespective of the behavior of the gas phase or the solution if, however, these are assumed to be ideal, equation (34.21) can be greatly simplified. For an ideal gas mixture, the fugacity /<, or partial pressure, of any constituent is proportional to its mole fraction n <, at constant temperature and total pressure ( 5b) it can be readily seen, therefore, that... 

The differentiation in this equation is carried out at constant pressure P. One must distinguish between this derivative and the derivative along the liquid-vapor equilibrium line. The relation between the two quantities is discussed in section 7.6. 

However, if the calculated pressure is greater than 1.013 bar, a lower temperature is guessed and the calculation repeated, whereas if the calculated pressure is too low. a higher temperature is tried. Figure c is a plot of the vapor composition versus the liquid composition at constant pressure (another x-y plot), calculated in this way, and Fig. d gives the equilibrium temperature as a function of both the vapor and liquid compositions on a single plot. 

Note that a bubble-point type calculation on the feedstream composition is used to arrive at a value for K, (or K. Albeit this value, in principle, varies from cell to cell as the composition changes, it nevertheless furnishes a means for determining a value. Whereas in vapor-liquid operations such as absorption, the operating temperature and pressure are used to assign a constant value for the liquid-vapor equilibrium vaporization ratio K for a particular component namely, the key component or components. (And, in general, the equilibrium vaporization ratio is also a function of composition, especially near the critical point of the mixture, and even in absorption, the temperature varies somewhat up and down the column due to enthalpic effects.)... 

For this method, we choose to adopt convention (I). Thus, the equilibriiun constant for the liquid/vapor equilibrium is the same as the saturating vapor pressure of the pure liquid in question P°, which is expressed by ... 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

The simplest method to measure gas solubilities is what we will call the stoichiometric technique. It can be done either at constant pressure or with a constant volume of gas. For the constant pressure technique, a given mass of IL is brought into contact with the gas at a fixed pressure. The liquid is stirred vigorously to enhance mass transfer and to allow approach to equilibrium. The total volume of gas delivered to the system (minus the vapor space) is used to determine the solubility. If the experiments are performed at pressures sufficiently high that the ideal gas law does not apply, then accurate equations of state can be employed to convert the volume of gas into moles. For the constant volume technique, a loiown volume of gas is brought into contact with the stirred ionic liquid sample. Once equilibrium is reached, the pressure is noted, and the solubility is determined as before. The effect of temperature (and thus enthalpies and entropies) can be determined by repetition of the experiment at multiple temperatures. 

Boltzmann, L. 18. 19 Boltzmann constant 337 Boltzmann distribution law 514-23 bubble-pressure curve in vapor + liquid phase equilibrium 406... 

SOLUTION Although the phase diagram in Fig. 8.6 is not to scale, we can find the approximate locations of the points. Point A is at 5 Torr and 70°C so it lies in the vapor region. Increasing the pressure takes the vapor to the liquid-vapor phase boundary, at which point liquid begins to form. At this pressure, liquid and vapor are in equilibrium and the pressure remains constant until all the vapor has condensed. The pressure is increased further to 800 Torr, which takes it to point B, in the liquid region. 

The vaporization of a liquid can be treated as a special case of an equilibrium. How does the vapor pressure of a liquid vary with temperature Hint Devise a version of the van t Hoff equation that applies to vapor pressure by first writing the equilibrium constant K for vaporization. 

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

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