Partial pressures The independent pressures

Partial pressures the independent pressures exerted by different gases in a mixture. (5.5)... 

A molecule colliding with the pore wall is reflected in a specular manner so that the direction of the molecule leaving the surface has no correlation with that of the incident molecule. This leads to a Fickian mechanism, known as Knudsen diffusion, in which the flux is proportional to the gradient of concentration of partial pressure. The Knudsen diffusivity is independent of pressure and varies only weaMy with temperature ... 

In order to define completely the solubility of a gas in a liquid, it generally is necessary to state the temperature, the equilibrium partial pressure of the solute gas in the gas phase, and the concentration of the solute gas in the liquid phase. Stric tly speaking, the total pressure on the system also should be stated, but for low total pressures, less than about 507 kPa (5 atm), the solubihty for a particular partial pressure of solute gas normally will be relatively independent of the total pressure of the system. 

For quite a number of gases, Henry s law holds very well when the partial pressure of the solute is less than about 100 kPa (I atm). For partial pressures of the solute gas greater than 100 kPa, H seldom is independent of the partial pressure of the solute gas, and a given value of H can be used over only a narrow range of partial pressures. There is a strongly nonlinear variation of Heniy s-law constants with temperature as discussed by Schulze and Prausnitz [2nd. Eng. Chem. Fun-dam., 20,175 (1981)]. Consultation of this reference is recommended before considering temperature extrapolations of Henry s-law data. 

Plasticization Gas solubility in the membrane is one of the factors governing its permeation, but the other factor, diffusivity, is not always independent of solubility. If the solubility of a gas in a polymer is too high, plasticization and swelhng result, and the critical structure that controls diffusion selectivity is disrupted. These effects are particularly troublesome with condensable gases, and are most often noticed when the partial pressure of CO9 or H9S is high. H9 and He do not show this effect This problem is well known, but its manifestation is not always immediate. 

Steam distillation. When two immmiscible liquids distil, the sum of their (independent) partial pressures is equal to the atmospheric pressure. Hence in steam distillation, the distillate has the composition... 

This remarkably simple relationship is depicted in Figure 14. It was apparent from his results that the volume fraction of the solvent determined the probability of interaction with the solute in much the same way that the partial pressure of a gas determines the probability of collision. It also indicated that the influence of each stationary phase component was independent and unaffected by presence of the other. 

Ellerbee [127, 128] provides an excellent summary of steam distillation basics. The theory of direct steam distillation evolves around the partial pressures of the immiscible organics/petroleum/petroleum component and the presence of direct open steam in the system. The system may consist of the organic immiscible plus steam (vapor and/or liquid). Each hquid exerts its otvn vapor pressure independent of the other. Thus, the total pressure of the system is the sum of the individual vapor pressures of the two liquids (assuming the liquids do not dissolve in each other). An important use of this approach is to separate a volatile organic from non-organic impurities. 

The pressure behavior shown in Figure 4-3 is readily explained in terms of the kinetic theory of gases. There is so much space between the molecules that each behaves independently, contributing its share to the total pressure through its occasional collisions with the container walls. The water molecules in the third bulb are seldom close to each other or to molecules provided by the air. Consequently, they contribute to the pressure exactly the same amount they do in the second bulb—the pressure they would exert if the air were not present. The 0.0011 mole of water vapor contributes 20 mm of pressure whether the air is there or not. The 0.0050 mole of air contributes 93 mm of pressure whether the water vapor is there or not. Together, the two partial pressures, 20 mm and 93 mm, determine the measured total pressure. 

The plot of the rate of disappearance of CO per volume of liquid in the serum bottles versus partial pressure of CO in the gas phase based on (3.14.4.14) could give the constant slope value of KLa/H. Henry s constant is independent of the acetate concentration but it is only dependent on temperature. The overall volumetric mass transfer coefficient can be calculated based on the above assumption. The data for various acetate concentrations and different parameters were plotted to calculate the mass transfer coefficient. 

It is noteworthy that even a separate treatment of the initial data on branched reactions (1) and (2) (hydrogenation of crotonaldehyde to butyr-aldehyde and to crotyl alcohol) results in practically the same values of the adsorption coefficient of crotonaldehyde (17 and 19 atm-1)- This indicates that the adsorbed form of crotonaldehyde is the same in both reactions. From the kinetic viewpoint it means that the ratio of the initial rates of both branched reactions of crotonaldehyde is constant, as follows from Eq. (31) simplified for the initial rate, and that the selectivity of the formation of butyraldehyde and crotyl alcohol is therefore independent of the initial partial pressure of crotonaldehyde. This may be the consequence of a very similar chemical nature of both reaction branches. 

It is almost independent of the presence of indifferent gases in the vapour-space (Law of Partial Pressures). 

If the gas consists of a mixture of two or more simple gases e.fj.y carbon dioxide and oxygen), which dissolve in a liquid, we can assume as a first approximation that the amount of each dissolved will be independent of the presence of the other gases, and will be proportional to its partial pressure in the gas mixture standing in equilibrium over the solution (J. Dalton, 1807). 

Equation (7) is true for volatile as well as involatile solutes, provided n denotes the number of mols of solute in the liquid phase, andp is the -partial pressure of the vapour of the solvent, the latter being independent of the presence of other gases in the vapour space. The sole remaining problem is therefore the determination of the partial pressure of the solute, or, what will lead to this, the total pressure in the vapour space. The partial pressure of the solvent is, from Raoult s law ... 

Dalton s law is based on the assumption of ideal gases so that each behaves independently and exerts the same partial pressure as it would il alone in the container. The Lewis and Randall rule assumes that the fugacitv of the gases is independent so that the gas has the same fugacity coefficient as it would have at the same total pressure when other gases were not present. 

The set of partial pressures given by Eq. (1) must satisfy equilibria among themselves and with the condensed phase. Of the several possible choices of independent equilibria, the following set is a convenient one ... 

However, more recent work has shown that the reaction of thioglycollic acid (HSCH2COOH) with methylcobalamin to give the methyl thioether requires oxygen and shows an induction period [which can be reduced by increasing the pH, the thiol concentration, or the partial pressure of O2, and eliminated by the addition of the Co(II) complex], followed by a steady-state reaction [ whose rate increases with pH, the concentration of the CH3C0 and Co(II) complexes and the partial pressure of O2, but is independent of thiol concentration]. Neither the induction period nor the steady-state... 

Gaseous solutions are easy to prepare and easy to describe. The atoms or molecules of a gas move about freely. When additional gases are added to a gaseous solvent, each component behaves independently of the others. Unless a chemical reaction occurs, the ideal gas equation and Dalton s law of partial pressures describe the behavior of gaseous solutions at and below atmospheric pressure (see Chapter 5). 

Vapor pressure provides a simple illustration of why adding a pure liquid or solid does not change equilibrium concentrations. Recall from Chapter H that any liquid establishes a dynamic equilibrium with its vapor, and the partial pressure of the vapor at equilibrium is the vapor pressure. The vapor pressure is independent of the amount of liquid present. Figure 16-8 illustrates that the vapor pressure of water above a small puddle is the same as the vapor pressure above a large pond at the same temperature. More molecules escape from the larger surface of the pond, but more molecules are captured, too. The balance between captures and escapes is the same for both puddle and pond. 

We now want to estimate the CO coverage when the catalyst is located in a plug-flow reactor with a partial pressure of Pqq = 0-01 bar at T= 1000 K. The desorption energy is estimated to be 147 kj mol and the pre-exponential factor is set to the usual 10 s , while the sticking coefScient is estimated to be 0.2 and independent of temperature. For simplicity we assume that each Ni atom can adsorb a CO molecule. 

At mercury and graphite electrodes the kinetics of reactions (15.21) and (15.22) can be studied separately (in different regions of potential). It follows from the experimental data (Fig. 15.6) that in acidic solutions the slope b 0.12 V. The reaction rate is proportional to the oxygen partial pressure (its solution concentration). At a given current density the electrode potential is independent of solution pH because of the shift of equilibrium potential, the electrode s polarization decreases by 0.06 V when the pH is raised by a unit. These data indicate that the rate-determining step is addition of the first electron to the oxygen molecule ... 

Temperature and composition of the gas phase cannot be controlled independently the partial pressures are determined by the temperature and the physical properties of the reaction mixture, and thus they vary with time. 

The increase in the deposition rate rj (Fig. 63d) corresponds to the increase in the ion flux (Fig. 63c) the fraction of arriving ions per deposited atom, / ,, is constant at about 0.25. Such observations have also been reported by Heintze and Zedlitz [236], who furthermore suggested that the deposition rate may well be controlled by tbe ion flux. The kinetic ion energy per deposited atom, max, is also constant and amounts to about 5 eV. As was shown in Section 1.6.2.3, the material quality as reflected in the refractive index 2 eV (Fig. 63e) and the microstructure parameter R (Fig. 63f) is good 2 cv is around 4.25, and R is low (<0.1). The depletion of the silane stays constant at a value of 4.0 0.4 seem in this frequency range. The partial pressures of silane, hydrogen, disilane (1.3 x 10 - mbar), and trisilane (2 x 10 mbar) in the plasma are also independent of frequency. Similar... 

Consequently, for high concentration of adsorption particles (which is directly linked either with their high partial pressure in gaseous phase or with high value of their adsorption heat) all kinetic curves ait) whose shape (as it will be showed below) is notably dependent on concentration of adsorption particles Nt tend (at long times) to a specific value of (Tp dependent on the nature and history of adsorbent and independent on the value of Nt-... 

The expression for K involving the concentrations of the species involved is found to be independent of volume. This implies that any change of pressure is not going to change the final state of equilibrium. The same result can be obtained by taking into consideration the alternative expression involving the partial pressures. If the pressure on the system is increased to n times its original value then all the partial pressures will be increased in the same proportion. This obviously implies that the equilibrium is independent of the pressure. The effect of some other factors on this reaction may now be considered. One such factor can be the addition of substances. For example, on addition of more A2, the partial pressure of A2 in the reactor would increase momentarily from pAl to some value, p A/. It has already been seen that... 

Both of the above chemical studies point towards the increased importance of the burning process at 285°C in determining the initial rate of heat production. The role of water as yet remains undefined other than at the higher temperature of 285°C it appears to have the opposite effect on the bitumen sample compared to the process at 225°C i.e., it appears that water vapor encourages pathways by which the various components of bitumen react with oxygen. Preliminary calculations of the total heats evolved during the wet oxidation of bitumen sands indicate that they are independent of the partial pressure of oxygen in the system at... 

If ta, and hence partial pressures of the reagents, then the order of the reaction, as is evident from comparison of... 

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