Internal energy molecular interpretation

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

The relative stability of the delocalized, non-vertical radical cation relative to a localized, vertical isomer was demonstrated also in gas phase experiments [404]. The molecular ions of m/e 132 obtained by gas phase ionization of the [4 + 2] dimer exhibited a bimodal decay, a result which was interpreted as evidence for the presence of two isomeric ions with different structures. The possibility that the reactive ion is a species with excess internal energy was discounted, when equivalent decay curves were observed in experiments using 10 eV and 70 eV electron impact ionization energy. In dramatic contrast, the molecular ions derived from the [2 + 2] dimer fail to react apparently the ion population resulting in this experiment is homogeneous [404],... 

Loss of (C4H9)-from the molecular ion of rans-4- -butylcyclohexyl bromide at 10ps—Ins has been shown to proceed at higher rates than the corresponding loss from the molecular ion of the cis isomer [336]. The difference was interpreted in terms of a concerted reaction forming a cyclic bromonium ion. The comparison of rates is intermol-ecular, however, so that the differences could stem from differences in internal energy, P(E). 

The formation of molecular ions takes place with a range of internal energies, and more than one fragmentation path is possible for a given molecule. The mass spectrum is given as a chart showing the ion abundance (normalized to the most abundant ion) versus m/z of the fragments. For the interpretation of the mass spectra, two main questions should be answered, namely ... 

Molecular modeling techniques have been used to predict and interpret mechanical properties of polymers [88-95]. Theodorou and Suter [88, 89] found that the internal energy contribution to the elastic response is much more important than the entropic contribution for glassy polymers by a thermodynamic... 

Here k is Boltzmarm s constant, m is the mass of one molecule, hf is the total number of molecules present, v,- is the velocity of molecule i, and the angle brackets represent an average over molecules, as in (2.2.12). Boltzmann s constant is related to the gas constant Rhy k = RN, where is Avogadro s number therefore, k can be interpreted as the molecular gas constant. Note that temperature is simply proportional to the kinetic contribution to the molecular internal energy in (2.2.12). 

Interpreting Lennard-Jones parameters. Inter-molecular interactions are often described b> the Lennard-Jones potential u(r), which gives the internal energy- of interaction between two molecules as a function of intermolecular separation ... 

The shape of the energy profile of the ion-molecular reaction shown in Fig. 5.4a does not fit the interpretation by Brauman [100] of the data on reaction kinetics obtained with use of the ICR technique. Even though the reactions described by Eq. (5.10) are in the gas-phase extremely fast, their velocity is still 3-10 times lower than the collision frequencies of ions and molecules. As in the case of the 8 2 reactions of Eq. (5.2), this behavior may be explained by the emergence of an internal energy barrier for the nucleophilic substitution reaction. According to the scheme suggested in Ref [100], which rests on the calculations... 

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