Entropy cratic

The entropy of a solution is itself a composite quantity comprising (i) a part depending only on tire amount of solvent and solute species, and independent from what tliey are, and (ii) a part characteristic of tire actual species (A, B,. ..) involved (equal to zero for ideal solutions). These two parts have been denoted respectively cratic and unitary by Gurney [55]. At extreme dilution, (ii) becomes more or less negligible, and only tire cratic tenn remains, whose contribution to tire free energy of mixing is... 

Suppose that we arbitrarily set the partial molal entropy of the K+ ion equal to zero. This means that we assign to the Cl- ion the whole of the partial molal entropy of the ion pair (K+ + Cl-) that is to say, we assign to the Cl- ion, not only the unitary term for the Cl- ion, but also the cratic term for both ions, and also the unitary term for the potassium ion. 

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. 

Table 27 contains data for some uni-univalent solutes for which both the entropy of solution at 25°C and the viscosity //-coefficient in aqueous solution at 18 or 25° are known. In column 3 from the entropy of solution 16.0 e.u. have been subtracted for the cratic term. 

Consider an ionic crystal in which the anion is a molecular ion. The orientation of this anion in the crystal is completely determined, or determined to a large extent, by the crystal structure and furthermore, its freedom of libration is severely limited by the intense fields of the adjacent ions. When this ion goes into solution, it will have a greater number of possible orientations, and its freedom of libration will be greater. Hence the AS0 for a molecular anion will contain a considerable increment in entropy over and above the cratic term (which is all that we subtract in the case of an atomic ion). This additional increment in entropy is likely to be somewhat different for different species of anion. The best we can do at present is to subtract an amount that is of the right order of magnitude. The question is whether we can, by sub-... 

Taking the values for the Ag+ ion and the Cl" ion from Table 25, and adjusting the cratic term, find the value of the partial molal entropy of silver chlorido in an aqueous solution having a molality equal to 10 8. 

Cantor and SchimmeP provide a lucid description of the thermodynamics of the hydrophobic effect, and they stress the importance of considering both the unitary and cratic contributions to the partial molal entropy of solute-solvent interactions. Briefly, the partial molal entropy (5a) is the sum of the unitary contribution (5a ) which takes into account the characteristics of solute A and its interactions with water) and the cratic term (-R In Ca, where R is the universal gas constant and ( a is the mole fraction of component A) which is a statistical term resulting from the mixing of component A with solvent molecules. The unitary change in entropy 5a ... 

In the case of water, the situation is complicated because of the anisotropic nature of the potential. Thus, we have effective harmonic potential for translation, rotation, and librational motions. Each is characterized by a force constant and contributes to the partition function, free energy, and entropy. Furthermore, a water molecule can be categorized by the number of HBs it forms. Since these quantities can be considered as thermodynamic, they make a contribution as the entropy of mixing, also known as the cratic contribution. 

For the sphere and DAPI both the NLPB and limiting law models (infinite length polymer at infinite dilution) give a slope with salt concentration close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model, there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the cratic entropy of ion release in the limiting law model. 

The thermodynamics of solute-solvent interactions is most conveniently described in terms of unitary quantities. The unitary free energy and unitary entropy changes accompanying some process (such as the transfer of hydrocarbon from nonpolar solvent to water or the transfer of hydrocarbon from pure hydrocarbon to water) are the standard free-energy and entropy changes corrected for any translational entropy terms (the cratic entropy) that are not intrinsic to the interaction under consideration. The cratic entropy is simply the entropy of mixing the solute and solvent into an ideal solution. With the cratic contribution removed, the unitary free energy and entropy contain only contributions to the thermodynamics of the process that come from the interaction of the individual solute molecules with the solvent. 

A very large cratic entropy is associated with the uniform dispersal... 

The outcome of the competition between cratic and unitary entropies, as the temperature and concentration are varied, thus gives rise to the broad features of the phase diagram shown in Fig. 4. This situation is somewhat analogous to existence of an ordered nematic state in the hard rod model. In this case, the two kinds of entropy in competition are the cratic and orientational entropies. 

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