Concentration types partial pressures

For gases and vapors, the amount absorbed is highly dependent on the partial pressure of the gas and the solubility of the gas in blood. Let s take the simple case of a gas that is not metabolized and is excreted by exhalation (e.g., an anesthetic gas or a Halon-type fire-extinguishing agent). At any given concentration (or partial pressure) in the atmosphere, the concentration in the blood will reach a steady state in the blood. Accordingly, prolonged exposure does not lead to continual buildup. 

In heterogeneous systems, the rate expressions have to be developed on the basis of (a) a relation between the rate and concentrations of the adsorbed species involved in the rate-determining step and (b) a relation between the latter and the directly observable concentrations or partial pressures in the gas phase. In consequence, to obtain adequate kinetic rate expressions it is necessary to have a knowledge of the reaction mechanism, and an accurate means of relating gas phase and surface concentrations through appropriate adsorption isotherms. The nature and types of adsorption isotherm appropriate to chemisorption processes have been discussed in detail elsewhere [16,17] and will not be discussed further except to note that, in spite of its severe theoretical limitations, the Langmuir isotherm is almost invariably used for kinetic interpretations of surface hydrogenation reactions. The appropriate equations are... 

The amount of adsorbate that can be held depends on the concentration or partial pressure and temperature, on the chemical nature of the fluid, and on the nature, specific surface, method of preparation, and regeneration history of the solid. For single adsorbable components of gases, the relations between amount adsorbed and the partial pressure have been classified into the six types shown in Figure 15.2. Many common systems conform to Type I, for example, some of the curves of Figure 15.3. Adsorption data are not highly reproducible because small contents of impurities and the history of the adsorbent have strong influences on their behavior. 

Obviously, rpEi can be expressed in terms of reaction temperature and concentration or partial pressure of chemicals and so on. Therefore, the PEI rate-law expression can be helpful to analyze the effect of concentrations and temperature on the PEI transformation rate, rpEi, and to study the influence of back-mixing on process environmental performance. At least, the PEI rate-law expression can reveal the factors that control the transformation rate of PEI, so as to provide guidance for the selection of reactor type and operation conditions, and the inner structure of the reactor, which produce desired products while creating minimum undesired potential environmental impact. 

Different concentration types are used for different reaction systems. For gas-phase reactions, volumetric concentration or partial pressures are equally useful and can be related by the thermodynamic equation of state. For instance, for ideal gases (approximation valid for gases at very low pressure)... 

In this section we focus on the three main types of ideal reactors BR, CSTR, and PFR. Laboratory data are usually in the form of concentrations or partial pressures versus batch time (batch reactors), concentrations or partial pressures versus distance from reactor inlet or residence time (PFR), or rates versus residence time (CSTR). Rates can also be calculated from batch and PFR data by differentiating the concentration versus time or distance data, usually by numerical curve fitting first. It follows that a general classification of experimental methods is based on whether the data measure rates directly (differential or direct method) or indirectly (integral of indirect method). Table 7-13 shows the pros and cons of these methods. 

In one type, we are given equilibrium quantities (concentrations or partial pressures) and solve for K. 

The measurement of oxygen concentration or partial pressure is usually effected using Clark type sensors (Figure 3). 

Chemists frequently need to calculate the amounts of reactants and products present at equilibrium in a reaction for which they know the equilibrium constant. The approach in solving problems of this type is similar to the one we used for evaluating equilibrium constants We tabulate initial concentrations or partial pressures, changes in those concentrations or pressures, and final equilibrium concentrations or partial pressures. Usually we end up using the equilibrium-constant expression to derive an equation that must be solved for an unknown quantity, as demonstrated in Sample Exercise 15.11. 

The quantitative description of the course of a chemical reaction with time is a relation between the reaction rate and the parameters influencing the rate, which are usually the temperature, concentrations (or partial pressures for gas reactions), and type and concentration of the catalyst in catalytic reactions. For simple reactions of the type ... 

We start by noting that gas permeahon is driven by a concentration or partial pressure difference across the membrane, i.e., it is a process based on diffusion, and not on D Arcy-type bulk flow. For diffusion to take place, the feed partial pressure must be higher than that on the permeate side i.e., we must have... 

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

Expressions of this type can be written for both gas and liquid films in which the absorption coefficients are the gas- and liquid-film coefficients, respectively. The driving force across the gas film is given by the difference between the actual partial pressure of the soluble gas and that at the interface, v/hile the driving force across the liquid film is given by the difference between the concentration of the soluble gas at the interface and that in the main bulk of liquid. 

The experimental determination of the relationship between the electronic concentration and the partial pressure or activity of a component is commonly the best method to determine the type of disorder in a material. 

Figure 7.9 Brouwer diagram for a phase MX in which Schottky defects are the main point defect type (a) initial points on the diagram, (b) variation of defect concentrations in the near-stoichiometric region, (c) extension to show variation of defect concentrations in the high partial pressure region, (d) extension to show variation of defect concentrations in the low partial pressure region, and (e) complete diagram.

The low-pressure region displays the electroneutrality equation approximation [e ] = 2[Vx ]. Electrons predominate so that the material is an n-type semiconductor in this regime. In addition, the conductivity will increase as the partial pressure of the gaseous X2 component decreases. The number of nonmetal vacancies will increase as the partial pressure of the gaseous X2 component decreases, and the phase will display a metal-rich nonstoichiometry opposite to that in the high-pressure domain. Because there is a high concentration of anion vacancies, easy diffusion of anions is to be expected. 

It is necessary to write the electroneutrality equation in terms of just two variables, a defect type and the partial pressure, to obtain a polynomial capable of solution. For example, the equation for the concentration of holes, [h ], is obtained thus Electroneutrality ... 

Defect populations and physical properties such as electronic conductivity can be altered and controlled by manipulation of the surrounding atmosphere. To specify the exact electronic conductivity of such a material, it is necessary to specify its chemical composition, the defect types and populations present, the temperature of the crystal, and the surrounding partial pressures of all the constituents. Brouwer diagrams display the defect concentrations present in a solid as a function of the partial pressure of one of the components. Because the defect populations control such properties as electronic and ionic conductivity, it is generally easy to determine how these vary as the partial pressure varies. 

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