Equilibrium vapor pressure versus

The vapor pressure of water, which is 24 mm Hg at 25°C, becomes 92 mm Hg at 50°C and 1 atm (760 mm Hg) at 100°C. The data for water are plotted at the top of Figure 9.2. As you can see, the graph of vapor pressure versus temperature is not a straight line, as it would be if pressure were plotted versus temperature for an ideal gas. Instead, the slope increases steadily as temperature rises, reflecting the fact that more molecules vaporize at higher temperatures. At 100°C, the concentration of H20 molecules in the vapor in equilibrium with liquid is 25 times as great as at 25°C. 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

Figure 9.4 Left Adsorption isotherm for benzene (CeLL) adsorbing to graphitized thermal blacks at 20° C. The insert shows the adsorption isotherm for low coverages in more detail. Dotted lines indicate mono- or multilayer coverages at multiples of 4.12 //mol/m2. The equilibrium vapor pressure of benzene at 20°C is Po = 10.2 kPa. Right Differential heat of adsorption versus adsorbed amount. The dashed line corresponds to the heat of condensation of bulk benzene. Redrawn after Ref. [369].

Figure 9.9 Left BET adsorption isotherms plotted as total number of moles adsorbed, n, divided by the number of moles in a complete monolayer, ri7non, versus the partial pressure, P, divided by the equilibrium vapor pressure, Po. Isotherms were calculated for different values of the parameter C. Right Adsorption isotherms of water on a sample of alumina (Baikowski CR 1) and silica (Aerosil 200) at 20°C (P0 = 2.7 kPa, redrawn from Ref. [379]). The BET curves were plotted using Eq. (9.37) with C = 28 (alumina) and C = 11 (silica). To convert from n/nmo to thickness, the factors 0.194 nm and 0.104 nm were used, which correspond to n-mon = 6.5 and 3.6 water molecules per nm2, respectively.

Figure 9.10 Adsorbed amount of water on a silicon oxide surfaces versus relative vapor pressure at 20°C. The continuous line was calculated with the theory of Polanyi and assuming van der Waals forces only (Eq. 9.57). Experimental results as measured on Aerosil 200 were adapted from Ref. [379] (see also Fig. 9.9). The deviation at high pressure is partially due to the porosity of the adsorbent. The equilibrium vapor pressure is P0 = 3.17 kPa.

Ruff and Bergdahl (1919) and Fischer et al. (1932) recorded the change in the mass of the cell at increasing temperature and at constant inert gas pressure. They observed that the dependence of mass of the cell on time or temperature did not show a sharp break at the equilibrium vapor pressure. The results were not substantially improved by plotting the derivative of mass with respect to time (i.e. the rate of mass loss). Fischer et al. (1932) used the variant of recording the changes of mass at a stepwise decreasing pressure and constant temperature. Flowever, even in this variant, a sharp break of the rate of mass loss versus pressure was not observed. 

It is important to note that the equilibrium vapor pressure is the maximum vapor pressure of a liquid at a given temperature and that it is constant at a constant temperature. From the foregoing discnssion we expect the vapor pressure of a liquid to increase with temperatnre. Plots of vapor pressure versus temperature for three different liquids in Figure 11.35 confirm this expectation. 

Since the van der Waals forces are the same as those that produce liquefaction, adsorption does not occur at temperatures that are much above the critical temperature of the gaseous adsorbate. Also, if the pressure of the gas has values near the equilibrium vapor pressure of the liquid adsorbate, then a more extensive adsorption multilayer adsorption— occurs. A plot of the amount of material adsorbed versus p/p°, where p° is the vapor pressure of the liquid, is shown in Fig. 18.17. Near p/p° = 1 more and more of the gas is adsorbed this large increase in adsorption is a preliminary to outright liquefaction of the gas, which occurs at p° in the absence of the solid. 

Figure 5.17 shows a predicted pressure versus excess water composition plot for the ethane+propane+water system at 274 K. At 0.0 mol fraction ethane (propane+ water) sll form at approximately 2 bar, and at 1.0 mol fraction ethane (ethane + water) si form at approximately 5 bar. At the intermediate composition of 0.78 mole fraction ethane, a quadruple point (Aq-sI-sII-V) exists in which both incipient hydrate structures are in equilibrium with vapor and aqueous phase. This point will be referred to as the structural transition composition the composition at which the incipient hydrate formation structure changes from sll to si at a given temperature. 

As an example, Fig. 2.15 shows a plot of AG versus the drop radius for water at different supersaturations. Supersaturation is the actual vapor pressure P divided by the vapor pressure Po of a vapor, which is in equilibrium with a liquid having a planar surface. 

The representation of the amount adsorbed versus equilibrium absolute pressure (P) or relative pressure (P/P°) gives the adsorption isotherm. If the temperature is below the critical temperature of the gas, P° is the liquid vapor pressure at the adsorption temperature. 

First, the effects of gas and liquid flows, co-current versus countercurrent operation, pressure and temperature were checked. As expected, based on the influence of these parameters on the vapor pressure or the vapor-liquid equilibrium (VLE), the fraction of water stripped by the nitrogen increases with increasing gas flows, decreasing liquid flows, lower pressures and higher temperatures. Countercurrent operation is more efficient than co-current operation, because the liquid phase at the inlet was already enriched with the compound which was to be separated. 

Note that Fig. 3.14.3 is also representable as a vapor pressure diagram of P /P versus xi. This is so because when equilibrium prevails /x + RT na =... 

Mathias and Klotz (1994) have shown that utilizing multiproperty fitting (that is, simultaneously fitting the parameters of the a function to data such as the enthalpy of vaporization and heat capacity in addition to vapor pressure) greatly improves the overall performance of an EOS. This should be remembered when saturation pressure versus temperature information is not sufficiently accurate for good parameter estimation and when the EOS is intended for calculation of other properties, such as excess enthalpies, along with phase equilibrium. 

By plotting T versus xA and T versus yA, the lower and upper curves, respectively, of Fig. 1-6 are typical of those obtained when component A is more volatile than B. Component A is said to be more volatile than component B, if for all T in the closed interval TA vapor pressure of A is greater than the vapor pressure of B, that is, PA> PB. The horizontal lines such as CE that join equilibrium pairs (x, y), computed at a given T and P by use of Eqs. (1-5) and (l-6) are commonly called tie lines. 

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. 

Thus, at fixed temperature the occurrence of either a maximum or a minimum in the equilibrium pressure versus mole fraction curve at a given composition indicates that both the vapor and liquid are of this composition (this is indicated in Fig. 10.2-lvapor-liquid mixture is called an azeotrope or an azeotropic mixture and is of special interest (and annoyance) in distillation processes, as will be discussed later. 

Equation 13 l-22b suggests that the logarithm of the equilibrium constant should be a linear function of the reciprocal of the absolute temperature if the heat of reaction is independent of temperature and, presumably, an almost linear function of l/T even if Arxnff° is a function of temperature. (Compare this behavior with that of the vapor pressure of a pure substance in Sec. 7.7, especially Eq. 7.7-6.) Consequently, it is common practice to plot the logarithm of the equilibrium constant versus the reciprocal of temperature. Figure 13.-1-2 gives the equilibrium constants for a number of reactions as a function of temperature plotted in this way. (Can you identify those reactions that are endothermic and those that are exothermic )... 

In humidification and dehumidification operations the liquid phase is always a single pure component. Then, the equilibrium partial pressure of the solute in the gas phase is equal to the vapor pressure of the liquid at its temperature. By Dalton s law, the equilibrium partial pressure of the solute may be converted to the equilibrium mole fraction yA. in the gas phase once the total pressure is specified. Since the vapor pressure of any liquid depends only upon the temperature, for a given temperature and total pressure the equilibrium composition of the gas phase is fixed. Because the liquid is a single pure component, xA. is always unity. Equilibrium data are often presented as plots of yA. versus temperature at a given total pressure, as shown for the system air-water at 1 bar in Figure 8.1. 

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