Constant-temperature equilibrium vapor-liquid

Source Considerations. Many CVD sources, especially sources for or-ganometallic CVD, such as Ga(CH3)3 and Ga(C2H5)3, are liquids at near room temperatures, and they can be introduced readily into the reactor by bubbling a carrier gas through the liquid. In the absence of mass-transfer limitations, the partial pressure of the reactant in the gas stream leaving the bubbler is equal to the vapor pressure of the liquid source. Thus, liquid-vapor equilibrium calculations become necessary in estimating the inlet concentrations. For the MOCVD of compound-semiconductor alloys, the computations have also been used to establish limits on the control of bubbler temperature to maintain a constant inlet composition and, implicitly, a constant film composition (79). Similar gas-solid equilibrium considerations govern the use of solid sources such as In(CH3)3. 

When we consider a one-component, two-phase system, of constant mass, we find similar relations. Such two-phase systems are those in which a solid-solid, solid-liquid, solid-vapor, or liquid-vapor equilibrium exists. These systems are all univariant. Thus, the temperature is a function of the pressure, or the pressure is a function of the temperature. As a specific example, consider a vapor-liquid equilibrium at some fixed temperature and in a state in which most of the material is in the liquid state and only an insignificant amount in the vapor state. The pressure is fixed, and thus the volume is fixed from a knowledge of an equation of state. If we now add heat to the system under the condition that the temperature (and hence the pressure) is kept constant, the liquid will evaporate but the volume must increase as the number of moles in the vapor phase increases. Similarly, if the volume is increased, heat must be added to the system in order to keep the temperature constant. The change of state that takes place is simply a transfer of matter from one phase to another under conditions of constant temperature and pressure. We also see that only one extensive variable—the entropy, the energy, or the volume—is necessary to define completely the state of the system. 

The result just obtained is applicable to any liquid-vapor equilibrium, irrespective of the behavior of the gas phase or the solution if, however, these are assumed to be ideal, equation (34.21) can be greatly simplified. For an ideal gas mixture, the fugacity /<, or partial pressure, of any constituent is proportional to its mole fraction n <, at constant temperature and total pressure ( 5b) it can be readily seen, therefore, that... 

Let us consider the equilibrium between a drop of radius r and a large volume of surrounding vapor, at constant temperature and pressure in each phase. Let us assume that near the equilibrium small amount of vapor condenses into liquid, causing an increase in drop radius equal to 5r. Changes in pressure and, therefore, in chemical potential due to this process are negligible and thus these two quantities remain essentially constant. At the equilibrium the thermodynamic potential,, reaches its minimum and therefore under these conditions its first variation 5 0, i.e ... 

Figures 3 and 4 are the predicted profiles of vapor and liquid composition along the column with 43 ml of catalyst and a reflux flow rate of 22 g/tnin. It is important to note that both the liquid and vapor concentration profiles for acetone in the column are relatively high and hence it is favorable for the formation of DAA. The equilibrium constants calculated from the equilibrium conversion data [9,10] are given in Figure 5, which indicates that at 54 °C, the Ac conversion at equilibrium conversion is only 4.3 wt %. In order to carry out the aldol condensation of acetone in the CD column, the temperature at the reaction zone of the CD column will be near the boiling point of Ac in order to maintain liquid vapor equilibrium. Our CD experimental results show that a maximum concentration of 55 wt% of DAA concentration was obtained which clearly exceeds the equilibrium conversion. The aldol condensation of Ac to produce DAA is an excellent example to demonstrate that in situ separation in a CD column results in an increased yield for equilibrium limited reactions.

AH estimations of the pore size of a material from its gas adsorption isotherm measurements are based on the well-known Kelvin equation suggested more than 100 years ago. It considers an equilibrium between the vapor phase and the bulk liquid at a constant temperature and relates the relative vapor pressure p/p to the radius r of the convex (plus) or concave (minus) spherical meniscus of the Hquid placed in a capillary ... 

Note that a bubble-point type calculation on the feedstream composition is used to arrive at a value for K, (or K. Albeit this value, in principle, varies from cell to cell as the composition changes, it nevertheless furnishes a means for determining a value. Whereas in vapor-liquid operations such as absorption, the operating temperature and pressure are used to assign a constant value for the liquid-vapor equilibrium vaporization ratio K for a particular component namely, the key component or components. (And, in general, the equilibrium vaporization ratio is also a function of composition, especially near the critical point of the mixture, and even in absorption, the temperature varies somewhat up and down the column due to enthalpic effects.)... 

Vapor concentration depends on several factors such as the size of the dispersion bottle, the temperature of the liquid, and the carrier gas flow rate. It can be expected that the carrier gas at a higher flow rate may not be vapor saturated at the outlet since it is constantly passing through the liquid without sufficient residence time to reach liquid — vapor equilibrium. Increasing the volume above the liquid or decreasing the flow rate of the dilution gas prolongs residence time and increases the saturation level of the generated vapor at the outlet. If equilibrium can be established. 

A piston-cylinder assembly contains a pure mixture of liquid water and steam in equilibrium. A second species that has negligible vapor pressure is mixed into the liquid at a constant temperature and constant pressure. Describe how the system will respond to maintain equilibrium. 

The flash curve of a petroleum cut is defined as the curve that represents the temperature as a function of the volume fraction of vaporised liquid, the residual liquid being in equilibrium with the total vapor, at constant pressure. 

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. 

Once equilibrium between liquid and vapor is reached, the number of molecules per unit volume in the vapor does not change with time. This means that the pressure exerted by the vapor over the liquid remains constant The pressure of vapor in equilibrium with a liquid is called the vapor pressure. This quantity is a characteristic property of a given liquid at a particular temperature. It varies from one liquid to another, depending on the strength of the intermolecular forces. At 25°C, the vapor pressure of water is 24 mm Hg that of ether, in which intermolecular forces are weaker, is 537 mm Hg. 

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

The vapor pressure of ethanol at 25°C is 58.9 Torr. A sample of ethanol vapor at 25°C and 58.9 Torr partial pressure is in equilibrium with a very small amount of liquid ethanol in a 10.0-L container also containing dry air, at a total pressure of 750.0 Torr. The volume of the container is then reduced at constant temperature to 5.0 1,. (a) What is the partial pressure of ethanol in the smaller volume Explain your reasoning. 

The vaporization of a liquid can be treated as a special case of an equilibrium. How does the vapor pressure of a liquid vary with temperature Hint Devise a version of the van t Hoff equation that applies to vapor pressure by first writing the equilibrium constant K for vaporization. 

A rate of reaction usually depends more strongly on temperature than on concentration. Thus, in a first-order (n = 1) reaction, the rate doubles if the concentration is doubled. However, a rate may double if the temperature is raised by only 10 K, in the range, say, from 290 to 300 K. This essentially exponential behavior is analogous to the temperature-dependence of the vapor pressure of a liquid, p, or the equilibrium constant of a reaction, K. In the former case, this is represented approximately by the Clausius-Clapeyron equation,... 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

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. 

A. System NH3 H S-H20. The dissociation of water (re-action 9) and the second dissociation of H2S (reaction 6) are neglected at given temperature and total molalities of NHo and H2S there remain four unknown molalities in the liquid phase (e.g. NH3, NH4+, H2S and HS ), the composition of the vapor phase and the total pressure, which are calculated from 8 equations The dissociation constants of ammonia and hydrogen sulfide (eqs.I and III) together with the phase equilibrium for hydrogen sulfide (eq. XII) are combined resulting in a equilibrium constant K 2... 

At constant total pressure, Equation (8.20) can be differentiated with respect to T to give the temperature dependence of the vapor pressure of a liquid in equilibrium with its vapor in the presence of air at a fixed atmosphere pressure ... 

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