Gases quantitative kinetic molecular

We now have enough information to turn our qualitative ideas about a gas into a quantitative model that can be used to make numerical predictions. The kinetic model ( kinetic molecular theory, KMT) of a gas is based on four assumptions (Fig. 4.23) ... 

Beginning with these assumptions, it s possible not only to understand the behavior of gases but also to derive quantitatively the ideal gas law (though we ll not do so here). For example, let s look at how the individual gas laws follow from the five postulates of kinetic-molecular theory ... 

Gas-phase epr studies have proved useful in the qualitative way described above, and they have been used also in quantitative kinetic studies. Low pressure discharge flow methods are eminently suitable, and the microwave cavity can be incorporated in the flow tube. Krongelb and Strandberg used the method to measure the rate of recombination of atomic oxygen. The spectrometer was calibrated using molecular oxygen that this procedure is valid was shown later by Westenberg and de Haas , who checked the calibration for both O and N by titration with NOj and NO (see Section 5). 

We have just seen how each of the gas laws conceptually follows from kinetic molecular theory. We can also derive the ideal gas law from the postulates of kinetic molecular theory. In other words, the kinetic molecular theory is a quantitative model that implies PV = nRT. Let s now explore this derivation. 

Kinetic molecular theory is a quantitative model for gases. The theory has three main assumptions (1) the gas partieles are negligibly small, (2) the average kinetic energy of a gas particle is proportional to the temperature in kelvins, and (3) the collision of one gas particle with another is completely elastic (the particles do not stick together). The gas laws all follow from the kinetic molecular theory. 

For a quantitative description of the behavior of gases, we will employ some simple gas laws and a more general expression called the ideal gas equation. These laws will be explained by the kinetic-molecular theory of gases. The topics covered in this chapter extend the discussion of reaction stoichiometry from the previous two chapters and lay some groundwork for use in the following chapter on thermochemistry. The relationships between gases and the other states of matter— liquids and solids—are discussed in Chapter 12. 

The science of reaction kinetics between molecular species in a homogeneous gas phase was one of the earliest helds to be developed, and a quantitative calculation of tire rates of chemical reactions was considerably advatrced by the development of the collision theoty of gases. According to this approach the rate at which the classic reaction... 

In Section 4.4, we used a molecular model of a gas to explain qualitatively why the pressure of a gas rises as the temperature is increased as a gas is heated, its molecules move faster and strike the walls of their container more often. The kinetic model of a gas allows us to derive the quantitative relation between pressure and the speeds of the molecules. 

The rather wide variation in barrier parameters derived from different methods is illustrated in Table 1. The neutron frequencies for liquid propane are used for these barrier comparisons since they are more reliable and, indeed, identical to the gas-phase results within the estimated uncertainty. The same molecular parameters used in the microwave study22,23 are used in each calculation, so that uncertainties in kinetic coupling effects do not affect the relative barrier values. It can be seen (not unexpectedly) that the barrier terms obtained by different methods using identical frequencies differ by as much as 30 percent. It should be noted that, as pointed out by Weiss and Leroi,21 the assumption of a harmonic potential in the Lide and Mann method causes an inherent decrease in the derived V3 terms ( 10 percent) compared with methods retaining the sinusoidal potential. These errors are quite similar for different molecules, however, so that comparisons between barrier results for different molecules by this method can be informative.21 It must obviously be concluded that barrier parameters obtained for multitop molecules on the basis of one or two observed frequencies have limited quantitative significance, except in relative terms, and that one must carefully scrutinize the method of calculation in evaluating such results. 

Since the universal gas constant, R, can be determined from independent (macroscopic) experiments, the observation of the motion of individual (microscopic) dispersed particles revealed the possibility of a novel independent determination of Avogadro s number, NA - R/k. Such measurements, carried out by J. Perrin et al with gamboge suspensions, yielded NA = 5.6 - 9.4 xlO23 mol 1. Further studies with oil droplets dispersed in gases, carried out by Fletscher, yielded a value of NA = 6.03 0.12 x 1023 mol 1 which is close to the precise value. As mentioned above, these experiments allowed one to directly observe the thermal motion of particles and to determine its quantitative characteristics, and thus disproved Ostwald s previous statement on the impossibility of experimentally verifying the molecular kinetic hypothesis. 

Although the infrared measurement of methane production leads to qualitative agreement with the direct mass determination, quantitative agreement is not good. This is most probably a result of axial dispersion in the gas product stream which results in a loss of kinetic information, difficulties in precisely regulating the product stream flow rate which would lead to cumulative errors, and the formation of small amounts of higher molecular weight hydrocarbons. 

The principal advantage of the time correlation function method is that it provides a new set of microscopic functions for a fluid, the time correlation functions, which can be studied directly by experimental observations of the fluidt or by computer-simulated molecular dynamics. The time correlation functions depend even more sensitively on the microscopic properties of the fluid molecules than the transport coefficients, which are expressed as time integrals of the correlation functions. Thus, a further test of kinetic theory has been found it must not only lead to expressions for the transport coefficients for dilute and dense gases that are in agreement with experiment, but also describe the dependence of the time correlation functions on both time and the density of the gas. One of the principal successes of kinetic theory is that it provides a quantitatively correct description of the short- and long-time... 

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