Mixtures kinetic molecular theory

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

The corrections made by van der Waals to the kinetic molecular theory make physical sense, which makes us confident that we understand the fundamentals of gas behavior at the particle level. This is significant because so much important chemistry takes place in the gas phase. In fact, the mixture of gases called the atmosphere is vital to our existence. In the next section we consider some of the important reactions that occur in the atmosphere. 

Most substances can exist in three states depending on the temperature and pressure. A few substances, such as water, exist in all three states under ordinary conditions. States of a substance are referred to as phases when they coexist as physically distinct parts of a mixture. Ice water is a heterogeneous mixture with two phases, solid ice and liquid water. When energy is added or removed from a system, one phase can change into another. As you read this section, use what you know about the kinetic-molecular theory to help explain the phase changes summarized in Figure 13-22. 

As well as pure gases, we can apply the kinetic molecular theory to mixtures of gases. In a mixture of gases, each gas contributes to the pressure in the same proportion as it contributes to the number of molecules of the gas. This makes sense, given the kinetic molecular theory, because molecules have no volume, no interactive forces other than collisions, and kinetic energy is conserved when they collide. Thus, each gas in a mixture essentially behaves as if it were in its container alone. The... 

The kinetic molecular theory states that the average kinetic energy of the gas particles increases as the temperature increases. Kinetic energy is proportional to (velocity)2. Therefore, as the temperature increases the gas particle velocity increases and the rate of mixing increases as well. Dalton s law states that the total pressure of a mixture of gases is the sum of the partial pressures of the component gases. 

According to the kinetic molecular theory, each of the components in a gas mixture acts independently of the others. For example, the nitrogen molecules in air exert a certain pressure—78% of the total pressure—that is independent of fhe... 

The various gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would describe the behaviour of all gases. Gases and mixtures of gases behave in a similar way over a wide variety of physical conditions because (to a good approximation) they all consist of molecules or atoms which are widely spaced a gas is mainly empty space. The ideal gas equation can be derived from kinetic molecular theory. The gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables (pressure, volume and absolute temperature) held constant. 

You can understand Dalton s law in terms of the kinetic-molecular theory. Each of the rapidly moving particles of gases in a mixture has an equal chance to collide with the container walls. Therefore, each gas exerts a pressure independent of that exerted hy the other gases present. The total pressure is the result of the total number of collisions per unit of wall area in a given time. 

Draw a depiction, as described by kinetic molecular theory, of a gas sample containing equal molar amounts of argon and xenon. Use red dots to represent argon atoms and blue dots to represent xenon atoms. Give each atom a tail to represent its velocity relative to the others in the mixture. 

In chemical kinetics the concept of the order of a reaction forms the basis of a kinematics which constitutes a frame for most of the molecular theories of chemical reactions. The fundamental magnitudes of this kinematics are the concentrations and the specific rate constants. In simple cases only the time enters as an independent variable, whereas in a diffusion process both time and space are involved. Diffusion processes are generally described in terms of diffusion coefficients, volume concentrations and thermodynamic potential or activity factors. Partial volume factors and friction coefficients associated with the components of the diffusing mixture are also essential in the description. A feature of the macro-dynamical theory is that it covers any region of concentration. Especially simple equations are connected with the differential diffusion process (diffusion with small concentration differences), for which the different coefficients or factors mentioned above are practically constant. 

Dobmskin [57] proposed a model for the adsorption equilibria of multicomponent vapor mixtures based on the concept of TVFM and an adsorbed phase model in which the adsorbate-adsorbent interactions predominate over the lateral interaction between adsorbed molecules. The proportions of the component in the adsorbed phase are determined by a statistical distribution based on Frenkel s [70] mechanism and kinetic gas theory [71,72]. In Dobruskin s study, the equilibrium is viewed as a dynamic process in which the average molecular residence time T is the reciprocal of the rate constant for desorption, k. For adsorption of a binary mixture in an elementary volume dW, the ratio of the average times between two components is... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

In this text we are concerned exclusively with laminar flows that is, we do not discuss turbulent flow. However, we are concerned with the complexities of multicomponent molecular transport of mass, momentum, and energy by diffusive processes, especially in gas mixtures. Accordingly we introduce the kinetic-theory formalism required to determine mixture viscosity and thermal conductivity, as well as multicomponent ordinary and thermal diffusion coefficients. Perhaps it should be noted in passing that certain laminar, strained, flames are developed and studied specifically because of the insight they offer for understanding turbulent flame environments. 

If we are dealing with mutual diffusion of gases which are close in molecular weight (e.g., carbon monoxide and air), it may be shown that the temperature of the flame pellet will prove to be equal to the theoretical combustion temperature of the mixture. This equality depends on the existence in the kinetic theory of gases of a simple relation between the diffusion coefficient (on which the supply of reagents and heat release rate depend) and the thermal conductivity (on which the heat evacuation depends). 

Consider the problem of steady-state one-dimensional diffusion in a mixture of ideal gases. At constant T and P, the total molar density, c = P/RT is constant. Also, the Maxwell-Stefan diffusion coefficients D m reduce to binary molecular diffusion Dim, which can be estimated from the kinetic theory of gases. Since Dim is composition independent for ideal gas systems, Eq. (6.61) becomes... 

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