Entropy calculations

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... 

The standard free energies, enthalpies, and entropies calculated from the experimental data for the reaction 4Me + Hj = 2Me2H (where Me = Pd or Ni), at 1 atm of hydrogen pressure and 298°K. 

One of the more interesting results of these calculations is the contribution to the heat capacity. Figure 10.10 shows the temperature dependence of this contribution to the heat capacity for CH3-CCU as calculated from Pitzer s tabulation with 7r = 5.25 x 10-47 kg m2 and VQ/R — 1493 K. The heat capacity increases initially, reaches a maximum near the value expected for an anharmonic oscillator, but then decreases asymptotically to the value of / expected for a free rotator as kT increases above Vo. The total entropy calculated for this molecule at 286.53 K is 318.86 J K l-mol l, which compares very favorably with the value of 318.94T 0.6 TK-1-mol 1 calculated from Third Law measurements.7... 

Because entropy is a state function, the change in entropy of a system is independent of the path between its initial and final states. This independence means that, if we want to calculate the entropy difference between a pair of states joined by an irreversible path, we can look for a reversible path between the same two states and then use Eq. 1 for that path. For example, suppose an ideal gas undergoes free (irreversible) expansion at constant temperature. To calculate the change in entropy, we allow the gas to undergo reversible, isothermal expansion between the same initial and final volumes, calculate the heat absorbed in this process, and use it in Eq.l. Because entropy is a state function, the change in entropy calculated for this reversible path is also the change in entropy for the free expansion between the same two states. 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

It should be pointed out that a finite residual entropy calculated for a substance from experimental data obtained at temperatures extending down to a certain temperature, with extrapolation below that point, may arise either from failure of the experimenter to obtain thermodynamic equilibrium in his calorimetric measurements or from error in the extrapolation. Measurements made under ideal conditions and extended to sufficiently... 

The seven-step problem-solving approach served us well in doing the thermodynamics examples of Chapter 6 and is equally valuable for quantitative entropy calculations. 

Schafer, H., Daura, X., Mark, A. E., and van Gunsteren, W. F. (2001). Entropy calculations on a reversibly folding peptide Changes in solute free energy cannot explain folding behavior. Proteins Strud. Fund. Genet. 43, 45-56. 

P° - reference pressure for entropy calculations, absolute units... 

The disordered nature of the a-AgI structure may be regarded as intermediate between that of a typical ionic solid in which every lattice site is occupied and a typical ionic liquid in which both anions and cations are disordered. This is borne out by entropy calculations based on heat capacity data (O Keeffe and Hyde, 1976). These show a large increase in entropy at the P (or y) to a transition and a similar increase in entropy on melting of the a polymorph at 557 °C ... 

This section includes the majority of physically adsorbed substances, and it is only in the exceptional cases that the loss of entropy can be attributed to the loss of particular degrees of freedom. In Table VII are given an extract of Foster s results for adsorptions on ferric oxide and silica gels together with the loss in entropy calculated for the loss of translational movement normal to the surface. In each case the area... 

This requires knowledge of the vibrational frequencies, the same information that is needed for entropy calculation and correction of the enthalpy for finite temperature. 

Godden, J. W., Stahura, F. L., Bajorath, J. (2000) Variabilities of molecular descriptors in compound databases revealed by Shannon entropy calculations. J Chem Inf Comput Sci 40, 796-800. 

The Hosoya index was applied 2,60 63) to correlations with boiling points, entropies, calculated bond orders, as well as for coding of chemical structures. 

The agreement obtained is remarkable for weak as well as strong lateral interactions, regarding the intrinsic difficulties of entropy calculation for polyatomic species at low temperatures. The shallow as well as the sharp minima for repulsive dimers in the cases (d) and (c) of Fig. 2 are accurately reproduced by this calculation. 

The enthalpy of ethylene oxide, measured calorimetrically, has been reported 817 to be 408 kcal./mole. Measurement of the enthalpy of ethylene oxide over a wide range of pressures has been conducted in at least two laboratories, 2 1181 and entropy calculations have been made from these results. The entropy of ethylene oxide vapor was likewise determined by Giauque and Gordon. 6 Their experimental value of 57.38 caL/degree-mole after a suitable correction for deviation from ideality is not far from the value 57.56 calculated from theory. 

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