Kinetic motion of molecules

The kinetic motion of molecules may cause them to change their spatial distribution through successive random movements. This is the process of diffusion, which is a transport property. Other transport properties include viscosity, electrical conductivity, and thermal conductivity. While diffusion is concerned with the transport of matter, these are associated with the transport of momentum, electrical charge, and heat energy, respectively. Transport is driven in each case by a gradient in the respective property. Thus, the diffusion rate of species A is given by Pick s law. 

In analytical chemistry, NMR is a technique that enables us to study the shape and structure of molecules. In particular, it reveals the different chemical environments of the NMR-active nuclei preseut in a molecule, from which we can ascertain the structure of the molecule. NMR provides informatiou on the spatial orientation of atoms in a molecule. If we already know what types of compounds are present, NMR can provide a means of determining how much of each is in the mixture. It is thus a method for both qualitative and quantitative analysis, particularly of organic compounds. In addition, NMR is used to study chemical equilibria, reaction kinetics, motion of molecules, aud intermolecular interactions. 

Kinetic Molecular Theory of Gases Macroscopic properties like pressure and temperature of a gas can be related to the kinetic motion of molecules. The kinetic molecular theory of gases assumes that the molecules are ideal, the number of molecules is very large, and that their motions are totally random. Both gas diffusion and gas effusion demonstrate random molecular motion and are governed by the same mathematical laws. 

Lastly, molecules in an oriented layer at an interface are in a dynamic condition. Molecules are continuously leaving and entering it. An increase in temperature disrupts orientation by increasing the kinetic motion of molecules. 

A fourth and different approach is that of Martin (1984), who utilized an analogy between particle motion in fluidized beds and kinetic motion of molecules in gases. From the kinetic theory of gases, Martin developed a model to account for thermal energy transport by particle motion across the boundary layer at surfaces. The resulting Nusselt number for convection was obtained as... 

The kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

A gas condenses to a liquid if it is cooled sufficiently. Condensation occurs when the average kinetic energy of motion of molecules falls below the value needed for the molecules to move about independently. Thus, the molecules in a liquid are confined to a specific volume by intermolecular forces of attraction. Although they cannot readily escape, liquid molecules remain free to move about within the liquid phase, hi this behavior, liquid molecules behave like the molecules of a gas. The large-scale consequences of the molecular-level properties are apparent. Like gases, liquids are fluid, so they flow easily from place to place. Unlike gases, however, liquids are compact, so they cannot expand or contract significantly. 

Figure 4-16 Role of kinetics in determining which of the two stable products to form, compared with stability of a ball on uneven ground, (a) Because the activation energy for forming product 1 is smaller, product 1 will form even though it is less stable than product 2. (b) Stability of a ball on uneven ground. The ball is initially in hole R. It would be gravitationally more stable if it goes to either hole PI or P2. The most stable position would be hole P2. However, if the ball was given an initial push (similar to thermal motion of molecules), it is much more likely that it would end up in hole PI.

The molecular interpretation of this result is as follows above the glass temperature T0 the molecular segments are in vigorous motion and change their positions frequently. Hence, the average nuclear spin interaction is reduced to a minimum. This causes a narrow absorption line. As the kinetic motion of the molecules is decreased by cooling, the frequency of position changes is reduced, and... 

The kinetic theory of gases is a simple model that can be used to relate the motion (kinetic energy) of molecules to some thermodynamic properties. The theory makes the following assumptions ... 

Relaxation times T, and T2 depend on the motion of molecules which contain the nuclei (236) and their measurement often leads to the various kinetic parameters for the adsorbed molecules, the knowledge of which is essential for the understanding of the mechanism of many zeolite-mediated processes. The diffusion coefficient of the reactants and products in a catalytic reaction, which can be determined from NMR, is often rate limiting. Relaxation studies can also determine surface coverage by the sorbed species and provide information about the distribution of adsorption energy between the different sites on the surface of a catalyst. For these reasons a great deal of NMR work has been done with adsorbed species in zeolites in the course of the last twenty years. From the applied viewpoint the emphasis is on water and hydrocarbons as guest molecules from the fundamental viewpoint species such as Xe, SF6, H2, CH4, and NH3 are of special interest. 

We now proceed to develop a specific expression for the rate constant for reactants where the velocity distributions /a( )(va) and /B(J)(vB) for the translational motion are independent of the internal quantum state (i and j) and correspond to thermal equilibrium.4 Then, according to the kinetic theory of gases or statistical mechanics, see Appendix A.2.1, Eq. (A.65), the velocity distributions associated with the center-of-mass motion of molecules are the Maxwell-Boltzmann distribution, a special case of the general Boltzmann distribution law ... 

The kinetic theory of gases deals with the translational motions of gaseous molecules. Translational motion of molecules can be considered separately from rotational and internal motions and has energy... 

The delocalized state can be considered to be a transition state, and transition state theory [105], a well-known methodology for the calculation of the kinetics of events, [12,88,106-108] can be applied. In the present model description of diffusion in a zeolite, the transition state methodology for the calculation of the self-diffusion coefficient of molecules in zeolites with linear channels and different dimensionalities of the channel system is applied [88], The transition state, defined by the delocalized state of movement of molecules adsorbed in zeolites, is established during the solution of the equation of motion of molecules whose adsorption is described by a model Hamiltonian, which describes the zeolite as a three-dimensional array of N identical cells, each containing N0 identical sites [104], This result is very interesting, since adsorption and diffusion states in zeolites have been noticed [88],... 

How does a gas exert pressure In a sense, it cannot exert measurable pressure in the same way that a solid or liquid can. The pressure of a gas is determined by the kinetic motion of its component molecules. Suppose hundreds of billions of gas molecules are in random motion, striking the entire inner surface of their container. Each collision exerts a force on the container s inner surface. 

Thus, the molecular velocity of any gas is proportional to the square root of the absolute temperature. The molecular motion is, therefore, often termed as thermal motion of molecules. At absolute zero (i.e., T = 0), kinetic energy is zero. In other words, thermal motion ceases completely at absolute zero. 

Kinetic Molecular Theory Set of rules that are assumed to govern the motion of molecules. 

Internal energy All energy possessed by a system other than kinetic and potential energy, such as energy due to the motion of molecules relative to the center of mass of the system, to the rotational and vibrational motion and the electromagnetic interactions of the molecules, and to the motion and interactions of the atomic and subatomic constituents of the molecules. 

There are certain essential differences between solid state reactions and reactions involving gaseous or liquid phases. In the latter case, the kinetic motion of the reactant molecules ensures that they are available to one another for reaction under conditions which can be defined by statistical laws. Solid state reactions occur between apparently regular crystal lattices, in which the kinetic motion is very restricted and depends on the presence of lattice defects. Interaction can only occur at points of contact between the reacting phases and is therefore dependent on particle size and particle size distribution. The factors which govern the rate of a solid state reaction are (/) the rate of the boundary phase processes which lead to the consumption of the original lattices, and (ii) the rate of particle transfer through the product layer. 

An increase in the temperature of a substance is always accompanied by an increase in the random motion of its particles. Recall that the kinetic energy of molecules increases with temperature. Increased kinetic energy means faster movement, more possible arrangements, and increased disorder. Therefore, the entropy of any substance increases as its temperature increases, and > 0. 

We first use the kinetic theory of gases to find a relation among pressure, volume, and the motions of molecules in an ideal gas. Comparing the result obtained with the ideal gas law (PV = nRT) provides a deeper understanding of the meaning of temperature. 

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