Kinetic-molecular theory defined

Kinetic Molecular Theory model that defines an ideal gas and assumes the average kinetic energy of gas molecules is directly proportional to the absolute temperature... 

Rationalize the defining characteristics of the states of matter in terms of intermolecular forces and the kinetic molecular theory of matter. 

Define critical temperature and critical pressure. What is the relationship between critical temperature and intermolecular forces In terms of the kinetic molecular theory, why is it impossible for a substance to exist as a liquid above its critical temperature ... 

Z32 What is Henry s law Define each term in the equation, and give its units. How would you account for the law in terms of the kinetic molecular theory of gases Give two exceptions to Henry s law. 

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. 

Perhaps one of the most important consequences of the Boltzmann equation, discovered by Boltzmann himself, was that it led to a kinetic molecular theory basis for the law of entropy increase. This law is contained within the so-called Boltzmann -theorem. Here we will work directly with the Boltzmann entropy Sb rather than the i/-function used in Boltzmann s original work.1 We define a local Boltzmann entropy Ssfri, t) as... 

A prediction of kinetic molecular theory— which we already encountered in explaining how straws work—is the very existence of pressure. Pressure is the result of the constant collisions between the atoms or molecules in a gas and the surfaces around them. Because of pressure, we can drink from straws, inflate basketballs, and move air into and out of our lungs. Variation in pressure in Earth s atmosphere creates wind, and changes in pressure help predict weather. Pressure is all aroimd us and even inside us. The pressure exerted by a gas sample is defined as tiie force per unit area that results from the collisions of gas particles with surrounding surfaces. 

The different states of matter were defined in Section 1.4, and the gas laws and the kinetic theory of gases were defined in Chapter 5. Here we want to recall the salient features of those discussions and then compare gases, liquids, and solids. We especially want to compare how these states are viewed in terms of kinetic-molecular theory. 

It was during the first half of the 17th century that scientists began to study chemical reactions experimentally. Jan Baptista van Helmont laid the foundations of the law of conservation of mass. Van Helmont showed that in a number of reactions an aerial fluid was liberated which he defined as a gas. A new class of substances with their own physical properties was shown to exist. A kinetic-molecular theory of gases began to develop. Notable in this field were the experiments of Robert Boyle whose studies, later known as Boyle s law, provided an equation describing the inverse relation between pressure and volume of gas (see the ideal gas law in Chapter 3). 

It is quite simple to say that this article deals with Chemical Dynamics. Unfortunately, the simplicity ends here. Indeed, although everybody feels that Chemical Dynamics lies somewhere between Chemical Kinetics and Molecular Dynamics, defining the boundaries between these different fields is generally based more on sur-misal than on knowledge. The main difference between Chemical Kinetics and Chemical Dynamics is that the former is more empirical and the latter essentially mechanical. For this reason, in the present article we do not deal with the details of kinetic theories. These are reviewed excellently elsewhere " The only basic idea which we retain is the reaction rate. Thus the purpose of Chemical Dynamics is to go beyond the definition of the reaction rate of Arrhenius (activation energy and frequency factor) for interpreting it in purely mechanical terms. 

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

The Fermi surface plays an important role in the theory of metals. It is defined by the reciprocal-space wavevectors of the electrons with largest kinetic energy, and is the highest occupied molecular orbital (HOMO) in molecular orbital theory. For a free electron gas, the Fermi surface is spherical, that is, the kinetic energy of the electrons is only dependent on the magnitude, not on the direction of the wavevector. In a free electron gas the electrons are completely delocalized and will not contribute to the intensity of the Bragg reflections. As a result, an accurate scale factor may not be obtainable from a least-squares refinement with neutral atom scattering factors. 

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