Pressure and Rate of Evaporation Total

VAPOR PRESSURE AND RATE OF EVAPORATION (TOTAL) (continued) 

Phase Tem- pera- ture Total rate of evaporation, g/cm sec Vapor pressure, atm Vapor pressure equation Source Year Remarks 

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Kinetic-molecular theory provides an explanation on a molecular level for this equilibrium. Evaporation from the liquid occurs as fast moving molecules on the surface escape from the liquid. In turn, molecules in the gas phase strike the liquid and condense, As the concentration (pressure) of gas molecules builds up in the gas phase, the rate of condensation increases. Eventually, a pressure is reached where the rate of condensation and rate of evaporation just balance, and equilibrium is achieved. The equilibrium pressure is denoted by p and is known as the vapor pressure. The magnitude ofp depends upon the substance, composition of the liquid, and any two of our thermodynamic variables such as temperature and total pressure. The criteria for equilibrium that we will now derive provide the thermodynamic relationships that will help... 

When the temperature of the liquid is such that the equilibrium vapor pressure of the sample equals the total pressure, the rate of evaporation increases dramatically, and bubbles form in the liquid. This is referred to as the boiling process, and the temperature associated with it is the boiling point of the liquid. Since the boiling... 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

Langmuir2 has used the reciprocal of the rate of evaporation as a measure of the resistance to evaporation, and considers the total resistance as the sum of the several partial resistances due to the water itself (a nearly negligible resistance), the film, and the vapour above. That of the water itself was taken as the reciprocal of the theoretical rate of evaporation, calculated from the vapour pressure as in Chap. I, 6. 

Some factors that influence the rate of evaporation of a solvent include temperature, flow of air over sample, vapor pressure of the solvent, latent heat, specific heat, and molecular weight (53). Galstaun (55) in 1950 reported a thorough study of the evaporation of some hydrocarbon solvents and developed equations for evaporation rates as related to several factors including temperature drop of liquid as it evaporates. Sletmoe (56) developed equations for the evaporation of neat solvent blends. The total rate of evaporation was proposed to be equal to the sum of the rates for the individual solvent components ... 

Example 16.1. The open beaker of Fig. 16.3 is filled with liquid benzene to 0.5 cm of the top. A gentle 25°C breeze blows across the mouth of the beaker so that the benzene vapor is carried away by convection after it diffuses through the 0.5-cm air layer in the beaker. The total pressure P is 101.3 kPa (1 atm), the vapor pressure, P of benzene at 25 C is 13.3 kPa and its diffusivity in air at 25°C multiplied by the total gas concentration is 3.5 X 10 gmole/cm sec. Calculate the initial rate of evaporation of benzene. 

Maintaining water quality is a major environmental priority and it has been demonstrated that evaporation from water can be a significant process in the dynamics determining levels of contaminants. When dealing with compounds that are completely miscible with water, the rate of evaporation can be defined by the same relation used with pure compounds. Partial pressures derived from Raoult s law would be used and the total rate of evaporation would be the sum of the losses of the individual constituents. This approach cannot be used with slightly soluble compounds since their solution behavior is quite different. Two models will be introduced to define the evaporation of the latter and illustrate how their properties influence the process. 

If 6 is the fraction of the total catalyst surface covered by adsorbed molecules at any instant, then the fraction of bare catalyst surface available for adsorption is (1 — 6). According to kinetic theory, since the rate at which molecules strike a unit area of a surface is proportional to the pressure of the gas, the rate of condensation of molecules should be determined both by the partial pressure and the fraction of bare catalyst surface or i(l — 6)p, where ki is a proportionality constant. If 2 is the rate at which molecules evaporate from a unit surface when the surface is fully covered, then for a fraction 0 of a fully covered surface, the rate of evaporation will be k2d. For adsorption equilibrium, these rates must be equal. Therefore,... 

However, it does not appear to be necessary to make the mean free path as large as the distance between the condenser and the evaporating surface to obtain molecular distillation conditions. Bronsted and Hevesy (Ref. 1) obtained separations of mercury isotopes that corresponded closely to molecular distillation rates imder conditions where the condenser was separated from the evaporating mercury surface by a distance approximately 100 times the mean free path. Taylor (Ref. 7) distilling petroleum fractions found the rate of evaporation to be independent of the total pressure over a range corresponding to mean... 

The area occupied by menisci decreases faster than the total area of the body as it shrinks, and the rate of evaporation might be expected to decrease correspondingly. However, lateral diffusion within a boundary layer allows the vapor pressure to equilibrate, so that evaporation continues at a constant rate per unit area of surfaee even when the surface is partially dry. After Suzuki and Maeda [14],... 

The insulation material was wrapped onto the calorimeter in a continuous spiral. The aluminum foil was interrupted after each revolution because the conduction around the spiral would contribute significantly to the total heat transport. After the samples were wrapped on the 4-in.-diameter test and guard chambers, they were inserted into the vacuum chamber and evacuated. The inside chambers were heated electrically to about 100°C during evacuation to help drive off residual moisture in the insulation material. Each sample was heated and evacuated for about 3 days. The guard and test chambers were then filled with cryogenic fluid, either liquid N2 or H2, and the rate of evaporation of liquid was measured with a wet test meter and timer. The rate of evaporation was measured for a period of several days, until equilibrium was attained. Conditions of equilibrium were sometimes disturbed by changing barometric pressure and, therefore, we had to wait additional lengths of time to be completely certain of our results. 

Volatilization. The susceptibility of a herbicide to loss through volatilization has received much attention, due in part to the realization that herbicides in the vapor phase may be transported large distances from the point of application. Volatilization losses can be as high as 80—90% of the total applied herbicide within several days of application. The processes that control the amount of herbicide volatilized are the evaporation of the herbicide from the solution or soHd phase into the air, and dispersal and dilution of the resulting vapor into the atmosphere (250). These processes are influenced by many factors including herbicide application rate, wind velocity, temperature, soil moisture content, and the compound s sorption to soil organic and mineral surfaces. Properties of the herbicide that influence volatility include vapor pressure, water solubility, and chemical stmcture (251). 

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