Translational energy of molecules

Clausius had shown in 1857 that if K is the translational energy of molecules of a gas and H is the total kinetic energy, then... 

Molecular entropies For a perfect monoatomic gas, there is only translational motion. According to quantum mechanics, the translational energy of molecules in a box is quantized and the size of the quantum is proportional to the reciprocal of the atomic weight. Heavier gases have smaller gaps and the number of states available and degeneracies are greater. 

Thermal energy, the energy contained in the heat of a chemical substance, is essentially the translational energy of molecules. There are two forms of kinetic energy which play an important role in photophysics the rotational and vibrational energies of molecules. 

Let (f,) be the average translational energy of molecules as the internal energy is the sum of all the mean energies of the different modes, we can... 

The van t Hoflf equation reveals the exponential dependence of the reaction rate on temperature. Arrhenius, while working on the hydrolysis rate of sugar cane by mineral acids [9], found that the temperature dependence of the rate cannot be determined by the translational energy of molecules or the viscosity of the medium. He discovered that in a reaction, there are both active as well as inactive molecules which are always in equilibrium and this equilibrium is exponentially dependent on the temperature, as predicted by Van t Hoff in his study. 

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

Fig. 3-11 shows that, foi watei, entropy and heat capacity ai e summations in which two terms dominate, the translational energy of motion of molecules treated as ideal gas paiticles. and rotational, energy of spin about axes having nonzero rnorncuts of inertia terms (see Prublerris). 

Translational energy, which may be directly calculated from the classical kinetic theory of gases since the spacings of these quantized energy levels are so small as to be negligible. The Maxwell-Boltzmann disuibution for die kinetic energies of molecules in a gas, which is based on die assumption diat die velocity specuum is continuous is, in differential form. 

In porous media, liquid-gas phase equilibrium depends upon the nature of the adsorbate and adsorbent, gas pressure and temperature [24]. Overlapping attractive potentials of the pore walls readily overcome the translational energy of the adsorbate, leading to enhanced adsorption of gas molecules at low pressures. In addition, condensation of gas in very small pores may occur at a lower pressure than that normally required on a plane surface, as expressed by the Kelvin equation, which relates the radius of a curved surface to the equilibrium vapor pressure [25],... 

The displacement of the center of mass of a molecule gives rise to the external or translation energy of the molecule. It corresponds to the energy associated with the movement in three-dimensional space of a particle whose mass is equal to that of die molecule. In each of the three directions in space the problem can be treated as a particle in a box. as presented in Section 5.4.1. It was shown that the energy is given by... 

Diffusion is defined as the random translational motion of molecules or ions that is driven by internal thermal energy - the so-called Brownian motion. The mean movement of a water molecule due to diffusion amounts to several tenth of micrometres during 100 ms. Magnetic resonance is capable of monitoring the diffusion processes of molecules and therefore reveals information about microscopic tissue compartments and structural anisotropy. Especially in stroke patients diffusion sensitive imaging has been reported to be a powerful tool for an improved characterization of ischemic tissue. 

At high T (low X,), reduces to Il,(l/X,). Because the potential energies of molecules dilfering only in isotopic constituents are alike, one can define a separative elfect based on the partition function ratio / of isotopically heavy and light molecules ((T and Q°, respectively) in such a way that the rotational and translational contributions to the partition function cancel out ... 

In a pore the overlapping potentials of the walls more readily overcome the translational energy of an adsorbate molecule so that condensation will occur at a lower pressure in a pore than that normally required on an open or plane surface. Thus, as the relative pressure is increased, condensation will occur first in pores of smaller radii and will progress into the larger pores until, at a relative pressure of unity, condensation will occur on those surfaces where the radius of curvature is essentially infinite. Conversely, as the relative pressure is decreased, evaporation will occur progressively out of pores with decreasing radii. 

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