Vaporization equilibrium

Figure 7-1. Incipient equilibrium vapor-phase compositions calculated with subroutine BUDET.

Subroutine MULLER. MULLER iteratively solves the equilibrium relations and computes the equilibrium vapor composition when organic acids are present. These compositions are used by subroutine PHIS2 to calculate fugacity coefficients by the chemical theory. 

FLASH determines the equilibrium vapor and liquid compositions resultinq from either an isothermal or adiabatic equilibrium flash vaporization for a mixture of N components (N 20). The subroutine allows for presence of separate vapor and liquid feed streams for adaption to countercurrent staged processes. 

An interesting consequence of covering a surface with a film is that the rate of evaporation of the substrate is reduced. Most of these studies have been carried out with films spread on aqueous substrates in such cases the activity of the water is practically unaffected because of the low solubility of the film material, and it is only the rate of evaporation and not the equilibrium vapor pressure that is affected. Barnes [273] has reviewed the general subject. 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

Fig. 3. AHoy evaporation from a single rod-fed source under steady-state conditions p° = 10p° AB feed rod, A B molten pool, A qB and vapor and deposit, A B, where p° = the equilibrium vapor pressure of component B B, and p° = the equilibrium vapor pressure of component A A. Part (a) shows...

In a simple single-column process, although the oxygen purity is high, the nitrogen effluent stream is impure. The equilibrium vapor... 

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. 

In this section the terms gas and vapor are used interchangeably. The latter is often used in distillation, in which the gas phase is represented by an equilibrium vapor. 

The equilibrium vapor pressure of a flammable hquid at its closed-cup flash point about equ s its LFL in percent by volume. Thus, the vapor pressure of toluene at its closed-cup flash point (4.4°C or 40°F) of 1.2 percent (1.2 kPa) is close to its LFL of 1.1 percent. The composite LFL of a mixture may be estimated by Le Cnatelier s Rule ... 

TABLE 26-15 Liquids Having Equilibrium Vapor Pressure near the... 

Defining tray efficiency as the difference between the actual and the equilibrium vaporization, the efficiency is ... 

Toxic Volatile Ratio of Equilibrium Vapor Concentration over the Acute Substances Toxic Concentration (in ppm) is greater than 1000... 

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

The equilibrium vapor pressure above a confined liquid depends only on temperature. The fraction of the total pressure exerted by vapor pressure determines the composition of the vapor-air mixture. Thus when the total pressure is reduced, for example at high elevations or in vacuum tmcks, the vapor concentration in air increases. Since flash points are reported at a... 

The vapor pressure (P ) of a pure liquid at a given temperature (T) is the pressure exerted by its vapor in equilibrium with the liquid phase in a closed system. All liquids and solids exhibit unique vapor pressure-temperature curves. For instance, in Figure 2-79, lines BA and AC represent the equilibrium vapor pressure curves of the solid and liquid phases, respectively. 

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

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. 

Consider an experiment in which liquid carbon dioxide is introduced into an otherwise evacuated glass tube, which is then sealed (Figure 9.4, p. 232). At 0°C, the pressure above the liquid is 34 atm, the equilibrium vapor pressure of C02(Z) at that temperature. As the tube is heated, some of the liquid is converted to vapor, and the pressure rises, to 44 atm at 10°C and 56 atm at 20°C. Nothing spectacular happens (unless there happens to be a weak spot in the tube) until 31°C is reached, where the vapor pressure is 73 atm. Suddenly, as the temperature goes above 31°C, the meniscus between the liquid and vapor disappears The tube now contains only one phase. 

Curve AB is a portion of the vapor pressure-temperature curve of liquid water. At any temperature and pressure along this line, liquid water is in equilibrium with water vapor. At point A on the curve, these two phases are in equilibrium at 0°C and about 5 mm Hg (more exactly, 0.01°C and 4.56 mm Hg). At B, corresponding to 100°C, the pressure exerted by the vapor in equilibrium with liquid water is 1 atm this is the normal boiling point of water. The extension of line AB beyond point B gives the equilibrium vapor pressure of the liquid above the normal boiling point. The line ends at 374°C, the critical temperature of water, where the pressure is 218 atm. 

Figure 9-3 shows this schematically. If the partial pressure of the vapor is less than the equilibrium value (as in Figure 9-3A), the rate of evaporation exceeds the rate of condensation until the partial pressure of the vapor equals the equilibrium vapor pressure. If we inject an excess of vapor into the bottle (as in Figure 9-3Q, condensation will proceed faster than evaporation until the excess of vapor has condensed. The equilibrium vapor pressure corresponds to that concentration of water vapor at which condensation and evaporation occur at exactly the same rate (as in Figure 9-3B). At equilibrium, microscopic processes continue but in a balance that yields no macroscopic changes.

Direct or indirect methods may be used to determine moisture in dehydrated foods. Indirect methods must be calibrated in terms of direct methods—the most common of which are the oven, distillation, and Fischer methods. Accuracy of the direct methods is difficult to evaluate except by comparison with a chosen reference method. Several reference methods are reviewed, but none can be given an unqualified recommendation as most practical and suitable for all foods. An indirect measure of moisture is the equilibrium vapor pressure of water, which can be measured easily and accurately. Arguments are presented to show that vapor pressure may be a better index of the stability of dehydrated foods than the moisture content, which has been frequently used for this purpose. 

The pair of Eqs. 12, 13 epitomizes the relation between the equilibrium vapor pressure, composition, and chemical potential of the solvent in a clathrate obeying the present model. These expressions were used in the calculation of the thermodynamic properties of gas hydrates30 and have also been formulated by Barrer and Stuart 4 for a clathrate with a single type of cavity and one occluded component they reduce to the equations of ref. 52. 

The radii av a2 and coordination numbers zv z2 follow from x-ray analysis (cf. Section I.B), and aQ/2 — 1.25 A corresponds to Pauling s van der Waals radius of 1.40 A for a covalently bound oxygen atom.25 The value of eQlk — 166.9°K was chosen to obtain agreement between calculated and experimental values of the equilibrium vapor pressure of argon hydrate at 0°C. 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

The two basic requirements for efficient bromine storage in zinc-bromine batteries, which need to be met in order to ensure low self-discharge and more over a substantial reduction of equilibrium vapor pressure of Br2 of the polybromide phase in association with low solubillity of active bromine in the aqueous phase. As mentioned by Schnittke [4] the use of aromatic /V-substitucnts for battery applications is highly problematic due to their tendency to undergo bromination. Based on Bajpai s... 

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