Molecule entropy

Molecules/ Entropy (joules/mole/K) Hypothetical gases... 

Rigid molecule, entropy only at low surface coverage, (i.e., 6 < 0.2)... 

Rigid molecule, entropy only at high surface coverage... 

Entropy of formation of a pair electrode/molecule Entropy of formation of a molecular pair (rigid rotator)... 

Entropy corresponds, roughly, to the randomness of a system equilibrium tends to favor the side in which fewer restrictions are placed on the atoms and molecules. Entropy of activation, then, is a measure of the relative randomness of reactants and transition state the fewer the restrictions that are placed on the arrangement of atoms in the transition state—relative to the reactants—the faster the reaction will go. We can see, in a general way, how probability factor and entropy of activation measure much the same thing. A low probability factor means that a rather special orientation of atoms is required on collision. In the other language, an unfavorable (low) entropy of activation means that rather severe restrictions arc placed on the positions of atoms in the transition state. 

These indices encode information on the molecule entropy (thermodynamic entropy) and are useful in modeUing physico-chemical properties related to entropy and symmetry. 

For very large molecules, entropy, which is inversely related to the amount of structural organization of the total system, is oftentimes equally or more... 

Constant Z in the Arrhenius equation (also called frequency factor). The preexponential factor is associated with the frequency of collisions between molecules (entropy) and with the probability that these collisions result in a reaction. (See also Arrhenius equation and Activation energy .)... 

Each arrangement is called a microstate. Hence, at a higher temperature there is a greater number of vibrational microstates. When the number of microstates increases, entropy increases. When the number of microstates decreases, entropy decreases. Entropy is a measure of the number of ways that energy can be shared out among molecules. Entropy values calculated in this way are called statistical entropies. 

FIGURE 8.3 Processes with positive or negative entropic terms, (a) Two molecules react to give three molecules—entropy increases, (b) Two molecules combine to give one—entropy decreases in the Diels-Alder reaction. 

A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

It is of interest in the present context (and is useful later) to outline the statistical mechanical basis for calculating the energy and entropy that are associated with rotation [66]. According to the Boltzmann principle, the time average energy of a molecule is given by... 

Equation XVI-21 provides for the general case of a molecule having n independent ways of rotation and a moment of inertia 7 that, for an asymmetric molecule, is the (geometric) mean of the principal moments. The quantity a is the symmetry number, or the number of indistinguishable positions into which the molecule can be turned by rotations. The rotational energy and entropy are [66,67]... 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

The microcanonical ensemble is a set of systems each having the same number of molecules N, the same volume V and the same energy U. In such an ensemble of isolated systems, any allowed quantum state is equally probable. In classical thennodynamics at equilibrium at constant n (or equivalently, N), V, and U, it is the entropy S that is a maximum. For the microcanonical ensemble, the entropy is directly related to the number of allowed quantum states C1(N,V,U) ... 

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

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