Vaporization equilibrium with condensation

Fig. 1.1a) is in equilibrium with vapor containing mole fraction MVC (yx 0.71 in Fig. 1.1a). If this vapor is collected and condensed, one will end up with a mixture in which the MVC mole fraction has been enriched from 0.45 to 0.71.

The saturation vapor pressures of HDO and H2 0 are lower than those of H2 0, both over liquid and solid phases. These differences play an important role in the course of the atmospheric water cycle as they cause fractionation effects at vapor/liquid and vapor/solid phase changes, with the condensed phase in equilibrium with vapor being enriched in heavy isotopes. The fractionation coefficient a is defined as the ratio of D/H or in the condensed phase to the value of... 

Lower irv-x surface phase diagram where data for upper curve containing point a are obtained from F-F of the 7r-A isotherm lower curve containing point b is obtained from G-G of the 7r—A isotherm. At any value of ttV7 condensed film at point a (x = x(c)) is in equilibrium with vapor film at point a (x-x(v)). 

FIGURE 7.2 Systems with more volume than condensed phase will always have a vapor phase in equilibrium with that condensed phase. Although we usually picture liquid in equilibrium with vapor, in many cases solid phases also exist in equilibrium with a vapor phase. 

It must also be realized that this thin surface region is in a very turbulent state. Since the liquid is in equilibrium with its vapor, then, clearly, there is a two-way and balanced traffic of molecules hitting and condensing on the surface from the vapor phase and of molecules evaporating from the surface into the vapor phase. From the gas kinetic theory, the number of moles striking 1 cm of surface per second is... 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

The effect of the partial condenser is indicated in Figure 8-13 and is otherwise represented by the relations for the rectifying and stripping sections as just given. The key point to note is that the product is a vapor that is in equilibrium with the reflux to the column top tray, and hence the partial condenser is actually serving as an external tray for the system and should be considered as the top tray when using the equations for total reflux conditions. This requires just a little care in step-wise ctdculation of the column performance. 

Both liquid and vapor products are withdrawn, with liquid reflux composition being equal to liquid product composition. Note that on an equilibrium diagram the partitd condenser liquid and vapor stream s respective compositions are in equilibrium, but only when combined do they represent the intersection of the operating line with the 45° slope (Figure 8-14). 

For partial condenser replace Dho by DHd in Step 3. A dew point on compositions of yp (vapor) give to or total pressure. Also get liquid composition x (liquid reflux in equilibrium with product vapor yo. Overhead vapor is sum of compositions of yp and xp. A dew point on this vapor (overhead from tray one top)) gives top tray temperature, tj. 

Thus, if a gas mixture exerts 100 psia total pressure and is composed of 20% by volume (mol%) propane and 80% by volume butane, the partial pressures are 20 and 80 psia for propane and butane, respectively. The liquid in equilibrium with this mixture of vapors would have a lower percentage of propane and a higher percentage of butane. If this mixture is used as a refrigerant, the low-boiling component (propane) reaches equilibrium with a higher concentration in the condenser (as liquid) and increases the total pressure in the condenser. This requires more head and more horsepower at the compressor. 

The condensed liquid at the top of the condenser is in equilibrium with the vapor composition entering the condenser, which is also the composition of the vapor leaving the evaporator. 

In connection with the thermodynamic state of water in SAH, it is appropriate to consider one more question, i.e., their ability to accumulate water vapor contained in the atmosphere and in the space of soil pores. It is clear that this possibility is determined by the chemical potential balance of water in the gel and in the gaseous phase. In particular, in the case of saturated water vapor, the equilibrium swelling degree of SAH in contact with vapor should be the same as that of the gel immersed in water. However, even at a relative humidity of 99%, which corresponds to pF 4.13, SAH practically do not swell (w 3-3.5 g g1). In any case, the absorbed water will be unavailable for plants. Therefore, the only real possibility for SAH to absorb water is its preliminary condensation which can be attained through the presence of temperature gradients. 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

One of the most Important thermophysical properties of reactor fuel In reactor safety analysis Is vapor pressure, for which data are needed for temperatures above 3000 K. We have recently completed an analysis of the vapor pressure and vapor composition In equilibrium with the hypostolchiometric uranium dioxide condensed phase (1 ), and we present here a similar analysis for the plutonium/oxygen (Pu/0) system. 

General. The methods we have used to calculate the vapor pressures and vapor compositions at high temperatures are the same as those used previously (1-2) for the U/0 system. The total pressure, p(total), In equilibrium with a Pu02 x condensed phase Is... 

An alternative way to view the oxygen enrichment of the vapor relative to the condensed phase Is to calculate the oxygen-to-plutonium ratio of the gas, R(gas), with Eq. (2). The value of R(gas) exceeds that of the condensed phase with which It Is In equilibrium by a large amount. Like the U/0 system, this oxygen enrichment of the vapor relative to the condensed phase Is Increasing with temperature. One Implication of these results Is that the condensed-phase and vapor-phase compositions will depend upon the extent of vaporization of a sample with overall composition given by 0/Pu = 2 - x. 

Vapor compositions In equilibrium with a PuOj.q condensed phase (top) and a PuOj.go condensed phase (bottom). 

The vapor pressure of a given phase of a substance is the pressure exerted by its vapor when the vapor is in dynamic equilibrium with the condensed phase. 

A vapor pressure is the pressure exerted by a gas in equilibrium with its condensed phase. When this equilibrium has been reached, the gas is saturated with that particular vapor. Notice in Table 5A that at 25 °C the atmosphere is saturated with water vapor when the partial pressure of H2 O is 23.756 torr. At this pressure, the molecular density of H2 O in the gas phase is sufficient to make the rate of condensation equal to the rate of evaporation. Any attempt to add more water molecules to the gas phase results in condensation to hold the partial pressure of H2 O fixed at 23.756 torr. 

Figure 12-11 is a molecular view of how a solute changes this liquid-vapor equilibrium of the solvent. The presence of a solute means that there are fewer solvent molecules at the surface of the solution. As a result, the rate of solvent evaporation from a solution is slower than the rate of evaporation of pure solvent. At equilibrium, the rate of condensation must be correspondingly slower than the rate of condensation for the pure solvent at equilibrium with its vapor. In other words, the vapor pressure drops when a solute is added to a liquid. A solute decreases the concentration of solvent molecules in the gas phase by reducing the rates of both evaporation and condensation. 

Distillation is a suitable technique for the isolation of volatile organic compounds from liquid samples or the soluble portion of solid samples [24,27-30]. The physical basis of separation depends on the distribution of constituents between the liquid mixture and the vapor in equilibrium with that mixture. The more volatile constituents are concentrated in the vapor phase, which is collected after condensation. The effectiveness of the separation is dependent on the physical properties of the... 

When the VOC-laden gas stream contains a mixture of VOCs, then the calculations must be performed using the methods described for single-stage equilibrium calculations in Chapter 4. The temperature at the exit of the condenser must be assumed, together with a condenser pressure. The vapor fraction is then solved by trial and error using the methods described in Chapter 4, and the complete mass balance can be determined on the basis of the assumption of equilibrium. 

The vapor pressure of a liquid in equilibrium with its vapor cannot be treated like an ideal gas that obeys the gas laws the equilibrium (liquid vapor) controls the vapor pressure. As conditions are changed, the system adjusts itself until the system reaches equilibrium again either the liquid which is present evaporates, or the vapor condenses. 

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