Kinetic-molecular theory phase changes

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. 

COMPETENCY 15.0 APPLY KNOWLEDGE OF THE KINETIC MOLECULAR THEORY TO THE STATES OF MATTER, PHASE CHANGES, AND THE GAS LAWS. 

The kinetic energy of molecules is unaltered during phase changes, but the freedom of molecules to move relative to one another increases dramatically. The following table summarizes the application of kinetic molecular theory to the addition of heat to ice, first changing it to liquid water and then to water vapor. 

We can apply the kinetic-molecular theory quantitatively to phase changes by means of a heating-cooling curve, which shows the changes that occur when heat is added to or removed from a particular sample of matter at a constant rate. As an example, the cooling process is depicted in Figure 12.3 for a 2.50-mol sample of gaseous water in a closed container, with the pressure kept at 1 atm and... 

The answer is yes and we will digress a bit at this point to introduce these concepts as we did earlier in the chapter. The temperature and pressure conditions that govern physico-chemical behavior of liquids are defined in terms of thermodynamics. The Gibbs Phase Rule is a direct outcome of the physical chemistry of changes in the state of matter. The phase rule helps to interpret the physico-chemical behavior of solids, liquids, and gases within the framework of the kinetic-molecular theory of phase equilibria. 

In the condensed phase the AC permanently interacts with its neighbors, therefore a change in the local phase composition (as were demonstrated on Figs. 8.1 and 8.2) affects the activation barrier level (Fig. 8.6). Historically the first model used for surface processes is the analogy of the collision model (CM) [23,48,57]. This model uses the molecular-kinetic gas theory [54]. It will be necessary to count the number of the active collisions between the reagents on the assumption that the molecules represent solid spheres with no interaction potential between them. Then the rate constant can be written down as follows (instead of Eq. (6)) ... 

Simulations—isoergic and isothermal, by molecular dynamics and Monte Carlo—as well as analytic theory have been used to study this process. The diagnostics that have been used include study of mean nearest interparticle distances, kinetic energy distributions, pair distribution functions, angular distribution functions, mean square displacements and diffusion coefficients, velocity autocorrelation functions and their Fourier transforms, caloric curves, and snapshots. From the simulations it seems that some clusters, such as Ar, 3 and Ar, 9, exhibit the double-valued equation of state and bimodal kinetic energy distributions characteristic of the phase change just described, but others do not. Another kind of behavior seems to occur with Arss, which exhibits a heterogeneous equilibrium, with part of the cluster liquid and part solid. 

Thermodynamics is, similarly, well suited for the description of processes which lead to changes of the molecular structure, as just seen for phase changes. A reaction with unfavorable thermodynamics expressed by a positive AG does not occur. However, with a negative AG, a reaction may still fail kinetically, while another mechanism may succeed. A typical example is the preparation of polypropylene. Although the polymerization of propylene is possible thermodynamically, it was not achieved until the work of Ziegler (139) and Natta (140), who discovered the catalyzed mechanism with favorable kinetics. Thus, much effort has been devoted to understand the kinetics of polymerization (118). Early work concentrated on predicting molecular masses and their distribution. In this section the thermodynamics of polymerization is briefly discussed. Most attention is paid to addition (chain) polymerization, but the theory is also applicable to condensation (stepwise) polymerization. The subject is extensively reviewed (141-145). 

In contrast molecular interaction kinetic studies can explain and predict changes that are brought about by modifying the composition of either or both phases and, thus, could be used to optimize separations from basic retention data. Interaction kinetics can also take into account molecular association, either between components or with themselves, and contained in one or both the phases. Nevertheless, to use volume fraction data to predict retention, values for the distribution coefficients of each solute between the pure phases themselves are required. At this time, the interaction kinetic theory is as useless as thermodynamics for predicting specific distribution coefficients and absolute values for retention. Nevertheless, it does provide a rational basis on which to explain the effect of mixed solvents on solute retention. 

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

Several papers in this volume deal with transport in various kinds of liquids others examine critically the fundamental statistical-mechanical theory determining isotope effects for both equilibrium and kinetic processes in condensed as well as gaseous systems. These studies are of interest not only because they serve as a framework for comparing the merits of different isotope separation processes, but they provide powerful tools for using isotope effect data to obtain an understanding of inter-molecular forces in condensed and adsorbed phases and changes in intramolecular forces in isolated molecules. The title of this volume has accordingly been broadened from that of the symposium to reflect the wider scope of its contents. 

In Eq. 12.6-1, the second term is the physical transport of the particles, and in the third term the u, = dCJdt represent the rate of change of property in the phase space of The equation is very similar to the Boltzmann equation of kinetic theory, where then represents the distribution function of molecular velocities, 5-... 

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