Entropy conventional

For those who are familiar with the statistical mechanical interpretation of entropy, which asserts that at 0 K substances are nonnally restricted to a single quantum state, and hence have zero entropy, it should be pointed out that the conventional thennodynamic zero of entropy is not quite that, since most elements and compounds are mixtures of isotopic species that in principle should separate at 0 K, but of course do not. The thennodynamic entropies reported in tables ignore the entropy of isotopic mixing, and m some cases ignore other complications as well, e.g. ortho- and para-hydrogen. 

Side chain generation is often a source of error. It will be most reliable if certain rules of thumb are obeyed. Start with structurally conserved side chains and hold them fixed. Then look at the energy and entropy of rotamers for the remaining side chains. Conventional conformation search techniques are often used to place each side chain. 

In the PPF, the first factor Pi describes the statistical average of non-correlated spin fiip events over entire lattice points, and the second factor P2 is the conventional thermal activation factor. Hence, the product of P and P2 corresponds to the Boltzmann factor in the free energy and gives the probability that on<= of the paths specified by a set of path variables occurs. The third factor P3 characterizes the PPM. One may see the similarity with the configurational entropy term of the CVM (see eq.(5)), which gives the multiplicity, i.e. the number of equivalent states. In a similar sense, P can be viewed as the number of equivalent paths, i.e. the degrees of freedom of the microscopic evolution from one state to another. As was pointed out in the Introduction section, mathematical representation of P3 depends on the mechanism of elementary kinetics. It is noted that eqs.(8)-(10) are valid only for a spin kinetics. 

Many of the conventional measures used in studying dynamical systems - power spectra, entropy, Lyapunov exponents, etc. - can in fact be used to quantify the difference among Regimes I-IV ([kaneko89a], [kaneko89c]). 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

Conventional Partial Molal Ionic Entropies. Correlation between Ionic Entropy and Viscosity. Conventional Partial Molal Entropy of (H30)+ and (OH)-. The Conventional and the Unitary Entropy of Solution. Solutes in Aaueous Solution. Solutes in Methanol Solution. 

Table 25. Conventional Paivtial Molal Entropies of Ions in Aqueous Solution...

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The Conventional and the Unitary Entropy of Solution. In Sec. 55 we discussed the free energy of solution, by considering the quantity (AF — 2RT In x). Again taking a uni-univalent solute, let us now fix attention on the quantity... 

The left-hand side of (165) or (166) gives the unitary part of the entropy of solution. In electrochemistry, however, it is the left-hand side of (167) which is the conventional entropy of solution at infinite dilution usually denoted by A[Pg.179]

With the usual 1000 grams of solvent as the b.q.s. we have in aqueous solution M = 55.51 thus 2R In M is equal to 16 e.u. To obtain the unitary part of the entropy of solution of a uni-univalent crystal in water at any temperature, we have to subtract 16.0 e.u. from the conventional... 

Accordingly, the conventional partial molal entropies of ions in solution are often said to refer to the ions in a one-molal solution (m = 1) hot in a real one-molal solution, but in a hypothetical ideal one-molal solution, where the contribution from the interionic forces is taken to be zero, and the cratic term replaces the communal term. 

Solutes in Aqueous Solution. As mentioned in See. 88, when we say that we expect to find a correlation between the /1-coefficients of viscosity of various species of ions, and their entropy of solution, this refers only to the unitary part of the entropy, the part associated with the ionic co-sphere. We are inclined to adopt the view that a negative //-coefficient for a pair of ions should be accompanied by a positive increment in entropy, while a positive //-coefficient should be accompanied by a decrease in entropy. The values of AS0, the conventional entropy of solution, to be found in the literature, do not, give a direct answer to this question, since they contain the cratic term, which in water at room temperature amounts to 16 e.u. This must be subtracted. 

The Number of Dipoles per Unit Volume. The Entropy Change Accompanying Proton Transfers. The Equilibrium between a Solid and Its Saturated Solution. Examples of Values of L and AF°. The Change of Solubility with Temperature. Uni-divalent and Other Solutes. Lithium Carbonate in Aqueous Solution. H2COj in Aqueous Solution. Comparison between HjCOj and Li2C03 in Aqueous Solution. Heats of Solution and the Conventional Free Energies and Entropies of Solution. 

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... 

Heats of Solution and the Conventional Free Energies and Entropies of Solution. Table 34 gives for various common salts the observed values of the heat of solution, and the conventional free energy... 

Table 35. Sion of the Conventional Fhee Knergy, Entropy, and Heat of...

The heat of solution tends at extreme dilution to the value +4207 cal/mole. Calculate the conventional free energy of solution at 25°C and the conventional entropy of solution. 

Table 45. Conventional Partial Molal Entropies of Ions in Water at 25°C...

The Caratheodory analysis has shown that a fundamental aspect of the Second Law is that the allowed entropy changes in irreversible adiabatic processes can occur in only one direction. Whether the allowed direction is increasing or decreasing turns out to be inherent in the conventions we adopt for heat and temperature as we will now show. 

Polymers undergoing dissolution show much smaller entropies of mixing than do conventional solutes of low relative molar mass. This is a consequence of... 

Since the reaction in the working electrode is an oxidation when the overall reaction is (7.14), the cell potential in (7.15) is defined as = ,ork - ref = anode Scaihode and the sign in this equation is opposite to that obtained with the more common convention that defines the cell potential as = caUiode - T anode ) From the temperature variation of the cell potential, the following equation can be written for the entropy of the overall reaction ... 

It should be clear that the most likely or physical rate of first entropy production is neither minimal nor maximal these would correspond to values of the heat flux of oc. The conventional first entropy does not provide any variational principle for heat flow, or for nonequilibrium dynamics more generally. This is consistent with the introductory remarks about the second law of equilibrium thermodynamics, Eq. (1), namely, that this law and the first entropy that in invokes are independent of time. In the literature one finds claims for both extreme theorems some claim that the rate of entropy production is... 

Conventional implementations of MaxEnt method for charge density studies do not allow easy access to deformation maps a possible approach involves running a MaxEnt calculation on a set of data computed from a superposition of spherical atoms, and subtracting this map from qME [44], Recourse to a two-channel formalism, that redistributes positive- and negative-density scatterers, fitting a set of difference Fourier coefficients, has also been made [18], but there is no consensus on what the definition of entropy should be in a two-channel situation [18, 36,41] moreover, the shapes and number of positive and negative scatterers may need to differ in a way which is difficult to specify. 

The free energy of activation can also be expressed in terms of an entropy and an enthalpy of activation in conventional thermodynamic fashion. 

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