Pressure, vapor dependence

The vapor pressure is an important property of the material to be thermally vaporized. In a closed container at equiUbrium, the number of atoms returning to the surface is the same as those leaving the surface, and the pressure above the surface is the equiUbrium vapor pressure. Vapor pressures are strongly dependent on the material and the temperature (Fig. 4). 

While the dilated van Laar model gives a reliable representation of constant-pressure activity coefficients for nonpolar systems, the good agreement between calculated and experimental high-pressure phase behavior shown in Fig. 14 is primarily a result of good representation of the partial molar volumes, as discussed in Section IV. The essential part of any thermodynamic description of high-pressure vapor-liquid equilibria must depend,... 

On the meniscus surface the deviation of vapor pressure from the saturation pressure Psat depends on the surface tension a, liquid density p( gas constant R, temperature T, and radii of curvature r. When p( > -Psat(T) < (2[Pg.354]

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

If the reactor has a relief device, the pressure response depends on the relief device characteristics and the properties of the fluid discharged through the relief. This is illustrated by curve A (Figure 8-2) for vapor relief only and by curve B for a two-phase froth (vapor and liquid). The pressure will increase inside the reactor until the relief device activates at the pressure indicated. 

Another volatility situation can occur if ethanol-blended fuel is mixed with hydrocarbon-only fuel in a vehicle fuel tank. This event is called commingling . In effect, the ethanol in the blend increases the vapor pressure of the hydrocarbon-only gasoline. The increase in vapor pressure is dependent on the ratio of the two components and the amount of ethanol in the blend. 

The condensation rate in the condenser L, changes as the pressure in the condenser varies since the condensing temperature depends on pressure. Thus depends on column pressure, overhead vapor composition, and the temperature of the coolant in the condenser. Equation (S.33) assumes ideal gas behavior, which is usually adequate in these low-pressure columns where pressure changes are significant. 

That characteristic of a chemical called vapor pressure determines the quantity of that chemical that can be contained in a specific volume of air at a given temperature and pressure. Vapor pressures of the explosive chemicals of interest are strong functions of temperature. See Chapter 2. In fact, it has been shown [10] that, for the entire temperature range of interest, the vapor pressure of DNT is about 20 times that of TNT, but that the vapor pressures of both show similar temperature dependence. The vapor pressure of each increases by about a factor of 4 for each decade increase in temperature, from about 5°C to about 50°C. 

Vapor pressure is exerted by a solid or liquid in equilibrium with its own vapor. All liquids have vapor pressures. Vapor pressure depends on temperature and is characteristic of each substance. The higher the vapor pressure at ambient temperature, the more volatile the substance. Vapor pressure of water at 20 0 is 17.535 torr. 

At 1 atm pressure, 298 K, and 50% relative humidity, kl()1 = 5.5 X 10 12 cm3 molecule-1 s-1 (see Problem 13). The pressure and water vapor dependences are quite significant. For example, Stockwell (1995) points out that the relative error can be as much as 75% near the earth s surface and 30% at 10 km, leading to underestimates of the rate of formation of H202 and overestimates of the rates of formation of organic peroxides (formed from H02 + R02 see the following) and of 03. 

As we saw in Section 5.1, a single substance can exist in a variety of different phases, or different physical forms. The phases of matter include the solid, liquid, and gaseous forms and the different solid forms, such as the diamond and graphite forms of carbon. In one unique case— helium—there are two liquid forms of the same substance. There are several different forms of ice, which differ in the way the water molecules pack together when high pressures are applied. The conversion of a substance from one phase to another, such as the melting of ice, the vaporization of water, or the conversion of graphite into diamond, is called a phase transition. Phase transitions take place at specific temperatures and pressures that depend on the purity of the substance. Seawater, for instance, freezes at a lower temperature than pure water does. 

The value of E in Equations 1, 2, and 3, as obtained from Equation 3, depends on terms already described and on other factors. The ratio wdJwmo is the pounds of dry air circulating in the distiller per pound of water distilled. Assuming the air is continually saturated, alternately at basin temperature and cover temperature, this ratio depends only on vapor pressures, which depend in turn on the two temperatures. The term (Hab — Hag) may be replaced by Cp(tb — tg), and... 

We have assumed that the molar volume remains constant, which is certainly a reasonable assumption because most liquids are practically incompressible for the pressures considered. For a spherical drop in its vapor, we simply have AGm = 2-yVm/r. The molar Gibbs free energy of the vapor depends on the vapor pressure / o according to... 

Although the atmosphere can be described in terms of a number of vertical layers, up to -100 km it remains well-mixed, with a composition of 78% N2, 21% 02, 0.9% Ar, 0.036% C02, varying amounts of water vapor depending on altitude and temperature, and minute amounts of a number of trace gases (Mcllveen, 1992). Pressure decreases monotonically with increasing altitude, from an average of 1013 millibar (mb) at the earth s surface to 140 mb at 14 km (the average altitude of the tropopause). 

The pressure increase depends on the nature of the pressure source, that is, gas or vapor pressure. Further, the characteristics of the system, that is, if the reactor is closed or open to the atmosphere will determine the consequences. In an open system, the gas or vapor will be released from the reactor, whereas in a closed system, the result of a runaway will be a pressure increase. The resulting pressure can be compared to the set pressure of the pressure relief system (Pset) or to the maximum allowed working pressure (PJ, or also to the test pressure (PM) of the equipment... 

Winkelmann et al. (54) have studied air-water flows in a corrugated heat exchanger. Flow visualization and two-phase pressure drop measurements have been performed. The flow visualizations have shown that the flow pattern is complex and that a wavy or a film flow occurs in most cases (Figure 29). The two-phase pressure drop depends on the total flow rate and vapor quality, and Chisholm-type correlation is proposed. More work is required to characterize the flow structure in compact heat exchangers and to develop predictive methods for the frictional pressure drop and the mean void fraction. 

Pressure is more directly connected to the concept of explosion nevertheless, it is less directly connected to the reactor status, since, for liquid-phase reactors, pressure nonlinearly depends on temperature (trough the vapor pressure relationship) and concentration (through the activity coefficients in liquid phase). Moreover, since pressure measurements are usually less accurate than temperature measurements, they are to be considered in particular for gassy reactions, i.e., when the runaway produces small temperature effects but large amounts of incondensable products in gaseous phase. 

The vapor pressure, Pvp, of a liquid or solid is the pressure of the compound s vapor (gas) in equilibrium with the pure, condensed liquid or solid phase of the compound at a given temperature [5-9]. Vapor pressure, which is temperature dependent, increases with temperature. The vapor pressure of chemicals varies widely according to the degree of intermolecular attractions between like molecules The stronger the intermolecular attraction, the lower the magnitude of the vapor pressure. Vapor pressure and the Henry s law constant should not be confused. Vapor pressure refers to the volatility from the pure substance into the atmosphere the Henry s law constant refers to the volatility of the compound from liquid solution into the air. Vapor pressure is used to estimate the Henry s law constant [equation (2.4)]. 

Redistribution of vapor depends on a balance between the vertical and horizontal pressure gradients (157). The horizontal pressure gradient depends on column diameter, and diminishes rapidly as column diameter increases. This explains the strong effect of diameter in item 4 above. Another important factor cited by Porter and Ali (157) is vortex formation. This can cause downward flows of vapor in the bed. Downward flows were actually measured by Kabakov and Rozen (154) and Porter and Ali (157). 

The temperature dependent vapor pressure of pure elements or compounds is frequently used to define volatility. For the adsorbed state the relevant quantity is the desorption pressure, which depends on the temperature and on the surface coverage. The individual crystal lattices with their characteristic binding properties and thus, their standard entropy of the pure solid phase,... 

Liquids are constantly evaporating at their surface. That is, the molecules at the surface of the liquid can achieve enough kinetic energy to overcome the forces between them and they can move into the gas phase. This process is called vaporization or evaporation. As the molecules of the liquid enter the gas phase, they leave the liquid phase with a certain amount of force. This amount of force is called the vapor pressure. Vapor pressure depends upon the temperature of the liquid. Think about a pot of water that is being heated in preparation for dinner. The water starts out cold and you do not see any steam. As the temperature of the water increases you begin to see more steam. As the temperature of the water molecules increases, the molecules have more kinetic energy, which allows them to leave the liquid phase with more force and pressure. You can then conclude that as the temperature of a liquid increases, the vapor pressure increases as well. This is a direct relationship. 

For ideal systems (adhering to Raoult s law) the relative volatility reduces to the ratio between two components vapor pressures. The dependency on total pressure is eliminated, and there is only a weak residual dependency on temperature. In many systems the relative volatilities can be considered constant, and this provides an easy means of calculating the vapor phase composition given the liquid phase mole fraction ... 

The vapor pressure of a pure substance is dependent only on the nature of the substance and the temperature (Chapter 14). If we add a solute to the substance, its vapor pressure is lowered because the molecules of the substance cannot evaporate from the surface as rapidly as they could in the absence of the solute. The vapor-pressure lowering depends on the concentration of the solute particles, not on their nature. Raoult s law states that the vapor pressure of a component of an ideal solution is equal to the mole fraction of the component times its vapor pressure when it is a pure substance. That is, for component Z ... 

Also, listed in Table 4.4 are pressure-drop ranges for heat exchangers for making preliminary estimates. The pressure drop depends on whether the fluid is a gas or a liquid, or if the fluid is condensing or vaporizing. For gases, the pressure drop depends on the total pressure. Below atmospheric pressure, the pressure drop is critical and should be small because of the cost of vacuum pun s. 

The saturated vapors of /3-diketonates of Group 2 elements" " contain a mixture of [M(dik)2] molecules with different degrees of oligomerization. The ratio between the forms in vapor depends on the metal atom, the type of ligand, the vapor temperature and the total pressure. It seems natural to start by investigating the structure of the monomeric form, having created the necessary conditions for sample evaporation. As shown for Ca(dpm)2 and Ba(dpm)2" when superheating increases, the composition contains only the monomeric form. 

The constant m2 for the particular constituent of the solution is independent of the composition, but depends on the temperature and preS surCf for the relationship between the mole fraction and the vapor pressure is dependent on the total pressure of the system. 

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