Kinetic energy relationship with temperature

The necessity of the statistical approach has to be stressed once more. Any statement in this topic has a definitely statistical character and is valid only with a certain probability and in certain range of validity, limited as to the structural conditions and as to the temperature region. In fact, all chemical conceptions can break dovra when the temperature is changed too much. The isokinetic relationship, when significantly proved, can help in defining the term reaction series it can be considered a necessary but not sufficient condition of a common reaction mechanism and in any case is a necessary presumption for any linear free energy relationship. Hence, it does not at all detract from kinetic measurements at different temperatures on the contrary, it gives them still more importance. 

Using a "home made" aneroid calorimeter, we have measured rates of production of heat and thence rates of oxidation of Athabasca bitumen under nearly isothermal conditions in the temperature range 155-320°C. Results of these kinetic measurements, supported by chemical analyses, mass balances, and fuel-energy relationships, indicate that there are two principal classes of oxidation reactions in the specified temperature region. At temperatures much lc er than 285°C, the principal reactions of oxygen with Athabasca bitumen lead to deposition of "fuel" or coke. At temperatures much higher than 285°C, the principal oxidation reactions lead to formation of carbon oxides and water. We have fitted an overall mathematical model (related to the factorial design of the experiments) to the kinetic results, and have also developed a "two reaction chemical model". 

As the gas is heated, the particles move with greater kinetic energy, striking the inside walls of the container more often and with greater force. This causes the pressure of the gas to increase. The relationship between the Kelvin temperature and the pressure is a direct one ... 

Lord Kelvin (1824-1907). The Kelvin temperature scale has an absolute zero. True comparisons can be made using the Kelvin scale. A substance at a temperature of 400 Kelvins contains particles with twice as much kinetic energy as a substance at 200 Kelvins. Absolute zero is the temperature where the random motion of particles in a substance stops. It is the absence of temperature. Absolute zero is equivalent to —273.16°C. How this value is determined is discussed shortly after we discuss our next gas law. The relationship between Kelvin and Celsius temperature is... 

The kinetic molecular theory (KMT see Sidebar 2.7) of Bernoulli, Maxwell, and others provides deep insight into the molecular origin of thermodynamic gas properties. From the KMT viewpoint, pressure P arises merely from the innumerable molecular collisions with the walls of a container, whereas temperature T is proportional to the average kinetic energy of random molecular motions in the container of volume V. KMT starts from an ultrasimplified picture of each molecule as a mathematical point particle (i.e., with no volume ) with mass m and average velocity v, but no potential energy of interaction with other particles. From this purely kinetic picture of chaotic molecular motions and wall collisions, one deduces that the PVT relationships must be those of an ideal gas, (2.2). Hence, the inaccuracies of the ideal gas approximation can be attributed to the unrealistically oversimplified noninteracting point mass picture of molecules that underlies the KMT description. 

In eqn. (54),feapp was considered to be a constant. In the determination of apparent activation energies and kinetic isotope effects, it is the variations in feapp as reflected in variations in vc with temperature or isotopic substitution while the concentrations are held constant that must be determined. The appropriate relationship becomes... 

Remember that kinetic energy is 1/2mv1. The Boltzmann constant k is equal to the ideal gas constant R divided by Avogadro s number. Avogadro s number is the number of molecules in a mole, so the Boltzmann constant treats individual molecules, while the ideal gas constant deals with moles of molecules. So, if we use the molecular mass (M), we need to use the ideal gas constant. Also, we re always safest in physics when we stick to SI units, so let s express the molecular mass in units of kg/mol and R in units of J/mol/K. So, on a molar scale, we can recast the relationship between kinetic energy and temperature as ... 

A certain amount of energy will be required to raise the molecules to a level of kinetic energy where they will escape. In the special case of a liquid passing to the vapor state, the energy put into the system to cause volatilization is the latent heat of vaporization. The property is characteristic for a given chemical and may vary with temperature. The temperature relationship of the latent heat of vaporization may be calculated by the Clausius-Clapyeron equation. 

Liquids are constantly evaporating at their surface. That is, the molecules at the surface of the liquid can achieve enough kinetic energy to overcome the forces between them and they can move into the gas phase. This process is called vaporization or evaporation. As the molecules of the liquid enter the gas phase, they leave the liquid phase with a certain amount of force. This amount of force is called the vapor pressure. Vapor pressure depends upon the temperature of the liquid. Think about a pot of water that is being heated in preparation for dinner. The water starts out cold and you do not see any steam. As the temperature of the water increases you begin to see more steam. As the temperature of the water molecules increases, the molecules have more kinetic energy, which allows them to leave the liquid phase with more force and pressure. You can then conclude that as the temperature of a liquid increases, the vapor pressure increases as well. This is a direct relationship. 

The crater volume increases with the projectile kinetic energy. This relationship for the snow sintered for 15 minutes at different temperatures is shown in Figure 5. The empirical equation shows that the crater volume is almost proportional to the root square of the projectile kinetic energy, which means that it is simply proportional to the impact velocity (Vj). Thus, we can describe the cratering efficiency as follows This... 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

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