Gases equilibrium expressions containing

The Kp/s for substances containing carbon tabulated by JANAF are in reality Kp, and the condensed phase is simply ignored in evaluating the equilibrium expression. The number of moles of carbon (or any other condensed phase) is not included in the n, since this summation is for the gas phase components contributing to the total pressure. 

The equilibrium constant Kp can be used for gas-phase reactions. It is defined in the same way as Kc except that the equilibrium constant expression contains partial pressures (in atmospheres) instead of molar concentrations. The constants Kp and Kc are related by the equation Kp = Kc(RT)An, where A n = (c + d) — (a + b). 

Experiments show that as long as some liquid water is in the container, the pressure of water vapor at 25°C is 0.03126 atm. The position of this equilibrium is not affected by the amount of liquid water present, and therefore liquid water should not appear in the mass action law. Recall that for a gas or solute, a ratio of pressures or concentrations appears in the law of mass action. This ratio is equal to 1 when the gas or solute is in its reference state (1 atm or 1 M). For a pure liquid appearing in an equilibrium chemical equation, the convention is to take that pure liquid as the reference state, so the liquid water contributes only a factor of 1 to the equilibrium expression and can thus be entirely omitted. We postpone justification of this rule to Section 14.3. 

A liquid is in contact with a well-mixed gas containing substance A to be absorbed. Near the surface of the liquid there is a film of thickness 8 across which A diffuses steadily while being consumed by a first-order homogeneous chemical reaction with a rate constant ky At the gas-liquid interface, the liquid solution is in equilibrium with the gas and its concentration is cAl at the other side of the film, its concentration is virtually zero. Assuming dilute solutions, derive an expression for the ratio of the absorption flux with chemical reaction to the corresponding flux without a chemical reaction. 

An increase in water concentration in the gas phase would shift the equilibrium towards higher OH concentration on the surface, titrating the unsaturated Pd and PdO sites required for the combustion reaction. A similar argument was used in this work to explain the inhibition by CO2. From a detailed kinetics analysis, a complex rate expression was obtained. This expression contains both water and CO2 concentrations in the denominator. Under low CO2 concentrations, the most abundant species is OH, so the rate appears to be of — 1 in water and... 

A gas is in a container which undergoes uniform translational motion in the X direction with velocity e.g., the container is in an airplane. Assuming that the gas is at equilibrium, express the Maxwell distribution with respect to a stationary origin, e.g., the airport. 

It may be worthwhile to summarize our discussion of the kinetic step in gas-solid reactions by stating that on the basis of the analogy with heterogeneous catalysis, the overall reaction process may be broken down into individual steps, namely, adsorption, the formation of a surface complex, and desorption. Each of these steps can be regarded as reversible and assigned both a forward and a reverse rate constant. The resultant overall rate expressions may then be simplified with the aid of the steady state approximation and a knowledge of the overall reaction equilibrium. This then results in characteristic rate expressions containing certain constants and the partial... 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

After the solid sample has been weighed and degassed, a known amount of the adsorbate is admitted to the vessel containing the evacuated sample. When equilibrium has been reached, the amount of gas adsorbed can be calculated from the pressure change. Thus, a correlation between the equilibrium pressure, p, and the amount of gas adsorbed, Wad, can be established. Usually, the pressure is expressed as the relative pressure, where p represents the saturation pressure of the adsorbate at the temperature of measurement. 

This expression for the equilibrium constant is found to contain the term V in the denominator. Since K must remain constant, an increase in V would cause % also to increase. Stated in an another form, the dissociation of AB is favoured by a reduction in the pressure. A pressure increase would bring down V, and to maintain the constant value of K, x must decrease. Thus, a pressure increase would tend to inhibit the dissociation of AB. As in the previous case, it will be of interest in this case also to examine the effects of some other factors on the equilibrium. It is left to the readers as an exercise to establish for this case the following results (i) the effect of the addition of either A or B is to suppress the degree of dissociation of AB (ii) the addition of an inert gas at constant volume does not alter the degree of dissociation of AB and (iii) the addition of an inert gas at constant pressure increases the degree of dissociation of AB. 

The relative volatility, a, is a constant that under equilibrium conditions can be used to express the distribution of a volatile compound between a gas phase made of A and water vapor and a water phase containing A. This constant is for a component A defined as follows ... 

The systems we have in mind here are pure monatomic solids such as metals and inert gas solids which contain only one kind of defect in a single electronic state. We consider only vacancies explicitly, but rather similar expressions hold for systems containing only interstitials. From Eqs. (74a) and (75) we find that at equilibrium... 

As a result of the above two reactions, Eq. (a) and Eq. (b), the external solution containing dissolved gaseous analyte (D) immediately attains an equilibrium with the film of internal electrolyte solution (F) present very close to the gas-permeable membrane (A). Thus, another equilibrium gets established that affords the pH of the internal-surface film to alter according to the following expression ... 

The inhalational anesthetics have distinctly different solubility (affinity) characteristics in blood as well as in other tissues. These solubility differences are usually expressed as coefficients and indicate the number of volumes of a particular agent distributed in one phase, as compared with another, when the partial pressure is at equilibrium (Table 25.3). For example, isoflurane has a blood-to-gas partition coefficient (often referred to as the Ostwald solubility coefficient) of approximately 1.4. Thus, when the partial pressure has reached equilibrium, blood will contain 1.4 times as much isoflurane as an equal volume of alveolar air. The volume of the various anesthetics required to saturate blood is similar to that needed to saturate other body tissues (Table 25.3) that is, the blood-tissue partition coefficient is usually not more than 4 (that of adipose tissue is higher). 

Rate of Heat Transfer. Whatever the source of the heat, the principal method for its dissipation is undoubtedly conduction through the bed to the container walls, and thence, to the boiling liquid bath. Radiation, being proportional to the fourth power of the absolute temperature, is negligible. Some natural convection in the gas above the sample will occur and help to cool the top surface of the bed as well as the sides. The outside of the bed will cool quickly to bath temperature, but the center of the bed will cool much more slowly. This is the well known (9) cooling rate problem, for which mathematical solutions have been developed giving the temperature at various points in the bed. These solutions always involve some sort of exponential approach to thermal equilibrium and the physical constants of the system appear in the following expression ... 

Note that the brackets contain an expression for the total amount of gas added to the system and the second term represents the amount remaining in the gas phase at equilibrium. Since the effect of errors is cumulative in this method, care should be exercised in measuring all pressures. 

The factor introduces into equation (9) an explicit dependence of m on the concentration of species 1 in the gas adjacent to the interface [see equation (B-78)]. Except for this difference, equation (9) contains the same kinds of parameters as does equation (6), since the coefficient a can be analyzed from the viewpoint of transition-state theory. Although a may depend in general on and the pressure and composition of the gas at the interface, a reasonable hypothesis, which enables us to express a in terms of kinetic parameters already introduced and thermodynamic properties of species 1, is that a is independent of the pressure and composition of the gas [a = a(7])]. Under this condition, at constant 7] the last term in equation (9) is proportional to the concentration j and the first term on the right-hand side of equation (9) is independent of. Therefore, by increasing the concentration (or partial pressure) of species 1 in the gas, the surface equilibrium condition for species 1—m = 0—can be reached. If Pi e(T denotes the equilibrium partial pressure of species 1 at temperature 7], then when m = 0, equation (9) reduces to... 

Suppose A is a substance contained in a gas-liquid system in equilibrium at temperature T and pressure P. Two simple expressions—Raoult s law and Henry s law—provide relationships between pA. the partial pressure of A in the gas phase, and x, the mole fraction of A in the liquid phase. 

The gas stream leaving the cyclone contains hot air, the excess ammonia, water evaporated from the nitric acid solution in the reactor and from the collected liquid in the cyclone, and 3% of the ammonium nitrate in the reactor effluent. The stream leaves the separator at 233°C, passes through the air preheater, and enters a partial condenser where some of the water and ammonia and essentially all of the nitrate are condensed. The equilibrium relationship between the compositions of the vapor and liquid streams leaving this unit may be expressed in the form... 

In water solution containing small particles (i.e., suspended solids or turbidity) and non-surface-active solutes, when air is bubbled through it, little or no particles will be removed by any adsorptive bubble separation process. This is because the particles have virtually no natural affinity for air bubbles and hence there is no adhesion when contact is made. This particular phenomena may be explained by the contact angle between a particle and an air bubble. Consider the case of the three-phase fine of contact between a smooth, rigid, solid phase, a liquid phase and a gas phase. The equilibrium contact angle can be expressed in terms of the average surface tensions (i.e., interfacial tensions, dyne/cm) of the liquid-gas solid-liquid (r j ), and solid-gas (r ) interfaces, by the well-known Young s equation ... 

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