Vapor pressure temperature relations, 7, Table

Comprehensive tables of vapor-pressure data of common liquids, such as water, common refrigerants, and others, may be found in Refs. [2,3]. For most liquids, the vapor-pressure data are obtained at a few discrete temperatures, and it might frequently be necessary to interpolate between or extrapolate beyond these measurement points. At a constant pressure, the Clausius-Clapeyron equation relates the slope of the vapor pressure-temperature curve to the latent heat of vaporization through the relation... 

The water-vapor transmission rate (WVTR) is another descriptor of barrier polymers. Strictly, it is not a permeabihty coefficient. The dimensions are quantity times thickness in the numerator and area times a time interval in the denominator. These dimensions do not have a pressure dimension in the denominator as does the permeabihty. Common commercial units for WVTR are (gmil)/(100 in. d). Table 2 contains conversion factors for several common units for WVTR. This text uses the preferred nmol/(m-s). The WVTR describes the rate that water molecules move through a film when one side has a humid environment and the other side is dry. The WVTR is a strong function of temperature because both the water content of the air and the permeabihty are direcdy related to temperature. Eor the WVTR to be useful, the water-vapor pressure difference for the value must be reported. Both these facts are recognized by specifying the relative humidity and temperature for the WVTR value. This enables the user to calculate the water-vapor pressure difference. Eor example, the common conditions are 90% relative humidity (rh) at 37.8°C, which means the pressure difference is 5.89 kPa (44 mm Hg). 

The vapor pressure of a liquid depends on how readily the molecules in the liquid can escape from the forces that hold them together. More energy to overcome these attractions is available at higher temperatures than at low, and so we can expect the vapor pressure of a liquid to rise with increasing temperature. Table 8.3 shows the temperature dependence of the vapor pressure of water and Fig. 8.3 shows how the vapor pressures of several liquids rise as the temperature increases. We can use the thermodynamic relations introduced in Chapter 7 to find an expression for the temperature dependence of vapor pressure and trace it to the role of intermolecular forces. 

To understand vapor pressure, let s consider an empty jar that is partially filled with water and then covered with a lid. We will assume the space above the water in the jar contains only air when we screw on the jar s lid. After the lid is place on the jar, water molecules leave the liquid and enter the air above the liquid s surface. This process is known as vaporization. As time goes by, more water molecules fill the air space above the liquid, but at the same time, some gaseous water molecules condense back into the liquid state. Eventually, a point is reached where the amount of water vapor above the liquid remains constant. At this point, the rates of vaporization and condensation are equal, and equilibrium is reached. The partial pressure exerted by the water at this point is known as the equilibrium vapor pressure or just vapor pressure. Vapor pressure is directly related to the temperature, that is, the higher the temperature, the higher the vapor pressure. Table 9.4 gives... 

Incomplete tables of the physical constants and efficacies of a large number of compounds have been prepared (Table I). However, investigations show that much more information is needed to give a complete understanding of soil fumigation. We need tables showing vapor pressure, aqueous solubility, solvency in or solubility of nemic waxes, and efficacy, for temperatures of 20 , 25 , 30 , 35 , and 40 C. Furthermore, efficacy should be expressed in relation to moisture content of soil and stage of nematode. 

The metalorganic precursor compounds that have been most commonly used to grow thin films of semiconductors and related materials are listed below in Table I, along with the currently available vapor pressure data. These precursors are typically pyrophoric liquids or high-vapor-pressure solids. The simple metal alkyls (methyl and ethyl derivatives) are the most often employed for the growth of III-V compound semiconductors since they have reasonably high vapor pressures and can be readily delivered using a H2 carrier gas and precursor source temperatures conveniently near room temperature. 

Compute the temperature rise for the operating NPSH. An NPSH of 18.8 ft is equivalent to a pressure of 18.8(0.433)(0.995) = 7.78 psia at 220°F, where the factor 0.433 converts feet of water to pounds per square inch. At 220°F, the vapor pressure of the water is 17.19 psia, from the steam tables. Thus the total vapor pressure the water can develop before flashing occurs equals NPSH pressure + vapor pressure at operating temperature = 7.78 + 17.19 = 24.97 psia. Enter the steam tables at this pressure and read the corresponding temperature as 240°F. The allowable temperature rise of the water is then 240 — 220 = 20°F. Using the safe-flow relation of step 2, the minimum safe flow is 62.9 gal/min (0.00397 m3/s). 

You have been assigned to simulate a flash evaporator that separates a liquid feed stream containing benzene and toluene at temperature Tf ( C) into liquid and vapor product streams m equilibrium at temperature T( C) and pressure P mm Hg). The compositions of the product streams are related by Raoulfs law (Equation 6.4-1), and the component vapor pressures are expressed by the Antoine equation (Table B.4). 

Evaluating the equilibrium relations requires us to first compute the vapor pressures and activity coefficients. Note that these thermodynamic properties are computed using the temperature and composition at the interface. Expressions for the activity coefficients are given in Table D.2. Substituting the numerical values of into those equations gives the following results ... 

The Kelvin equation can be combined with the relative humidity, RH, if water is involved as the fluid relative humidity indicates how moist the air is. The amount of water vapor in the air at any given time is usually less than that required to saturate the air. The relative humidity is the percentage of saturation humidity, generally calculated in relation to the saturated vapor density. Relative humidity may be defined as the ratio of the water vapor density (mass per unit volume) to the saturation water vapor density, usually expressed in percent. Relative humidity is also approximately equal (exactly equal when water is assumed as an ideal gas) to the ratio of the actual water vapor pressure to the saturation water vapor pressure, RH = PJP°. The P° values corresponding to each temperature are given in tables which can be found in handbooks. If RH is measured in an experiment, then Pv can be calculated by using the saturation water vapor pressure tables and can be inserted into the Kelvin equation. 

If the air has to be cooled in order to cause condensation, it is obvious that the air could have contained more water vapor at the original temperature. The maximum pressure of water vapor which could exist at this original temperature may be found by again referring to the table. The relation between this maximum pressure and the actual pressure as shown by the dew point is spoken of as the relative humidity of the air. To illustrate the air on a certain day was at a temperature of 25° and it was found necessary to cool it to 16° before the dew point was reached. By reference to the table, on page 542, it appears that the vapor pressure at 16° is 13.5 mm. and at 25° is 23.6 mm. Thus the actual vapor pressure was 13.5 mm., the maximum vapor pressure which could have existed at 25° was 23.6 mm. and the relative humidity on that day was 13.5/23.6 =. 57 + or 57 per cent. 

Referring to the table of vapor pressures of water on page 542, (6) record the vapor pressure for the dew point which you have found and for the temperature of the air. (7) What relation has the first value to the pressure of the water vapor actually existing in the air (8) What is the maximum pressure of water vapor possible in the air at the existing tern-... 

Clark, Nabavian, and Bromley (11) measured a heat of dilution of concentrated (7%) sea water and heat capacities of normal and concentrated sea water at room temperature. From these data and vapor-pressure data of Arons and Kientzler (I), with the aid of thermodynamic relations they calculated heats of concentration and boiling point elevations. Both of these properties are presented in graphs and tables over a temperature range of 77° to 302° F. and for salt concentrations up to 9%. Integral heat of concentration increases with the temperature up to about 180° F. substantially independent of concentration and then decreases. The maximum value for 7% salts is only about 1.0 B.t.u. per pound of original sea water and hence is negligible for most practical purposes. 

The last term is only used for calculating the vapor pressure of compounds that are solids and would be neglected with compounds that are liquids at ambient temperature. Vapor pressures calculated at 25°C for some compounds listed in Table 2.2 are compiled in Table 2.4. The calculated values are well within the range of the recommended experimental values. It should be emphasized that this relation was developed for relatively nonpolar compounds and is not suited to more polar compounds such as phenols. Other procedures for predicting vapor pressure have been oulined. In addition, procedures are available for calculating boiling points from molecular properties. 

You have seen that molecules tend to escape the liquid state and form a vapor. The vapor pressure is the equilibrium partial pressure of this vapor over the liquid it increases with temperature. The boiling point is the temperature at which the vapor pressure equals the pressure applied to the liquid. Both vapor pressure and boiling point are important properties of a liquid. Values of the vapor pressure for some liquids at 20°C are listed in Table 11.2 (column 3). Two additional properties given in Table 11.2 are surface tension and viscosity. All of these properties, as you will see in the next section, depend on intermolecular forces, which are related to molecular structure. 

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