Entropy electron

Translational entropy Rotational entropy Vibrational entropy Electronic entropy Total... 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

AH and AS to various notional subprocesses such as bond dissociation energies, ionization energies, electron affinities, heats and entropies of hydration, etc., which themselves have empirically observed values that are difficult to compute ab initio. 

The reactivities of 4- and 2-halo-l-nitronaphthalenes can usefully be compared with the behavior of azine analogs to aid in delineating any specific effects of the naphthalene 7r-electron system on nucleophilic substitution. With hydroxide ion (75°) as nucleophile (Table XII, lines 1 and 8), the 4-chloro compound reacts four times as fast as the 2-isomer, which has the higher and, with ethoxide ion (65°) (Table XII, lines 2 and 11), it reacts about 10 times as fast. With piperidine (Table XII, lines 5 and 17) the reactivity relation at 80° is reversed, the 2-bromo derivative reacts about 10 times as rapidly as the 4-isomer, presumably due to hydrogen bonding or to electrostatic attraction in the transition state, as postulated for benzene derivatives. 4-Chloro-l-nitronaphthalene reacts 6 times as fast with methanolic methoxide (60°) as does 4-chloroquinoline due to a considerably higher entropy of activation and in spite of a higher Ea (by 2 kcal). ... 

Returning now to silver chloride, let us apply these ideas to its saturated aqueous solution at 25°. From the value given in Table 42, we see that in solid AgCl the entropy per ion pair is almost exactly 1 milli-electron-volt per degree, which is equivalent to 23.0 cal/deg/mole. It makes no difference whether we express the entropies per ion pair in electron-volts per degree or in the equivalent calories per degree per mole. In the electrochemical literature the calorie per degree per mole is used and is called one entropy unit. (This is abbreviated e.u.) ... 

Since the saturated solutions of AgT and AgCl are both very dilute, it is of interest to examine their partial molal entropies, to see whether we can make a comparison between the values of the unitary terms. As mentioned above, the heat of precipitation of silver iodide was found by calorimetric measurement to be 1.16 electron-volts per ion pair, or 26,710 cal/mole. Dividing this by the temperature, we find for the entropy of solution of the crystal in the saturated solution the value... 

Turning next to AgBr, we see from Table 33 that the value of L increases from 0.931 electron-volt at 15° to 0.935 at 35°, a difference of 0.004. Dividing by 20, we find that the average value of dL/dT in the neighborhood of 25° is 2 X 10 1 electron-volt/deg. Multiplying by 23,060, we find this is equivalent to 4.6 cal/mole. It follows that the value of the conventional entropy of solution AS0 in the neighborhood of 25°C is approximately... 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Eckart, criteria, 264, 298 procedure, 267 Effective charge, 274, 276 Effective Hamiltonian, 226 Elastic model, excess entropy calculation from, 141 of a solid solution, 140 Electric correlation, 248 Electric field gradient, 188, 189 Electron (s), 200... 

Variational principle on the correlation problem, 213, 318, 320, 326 Vibrational electronic modes, 12 Vibrational entropy in dilute solutions, 133... 

Under near-equilibrium conditions the shape of this curve is related to two contributions, the compositional dependence of the configurational entropy of the guest ions, and the contribution to the chemical potential from the electron gas [31]. 

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