Free energy unitary

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... 

If in a dilute solution we carry out q proton transfers according to (28), there will be a change in the cratic term, and at the same time the free energy will receive the contribution qj, that is to say, q units each equal to J Since each of the quantities qD, qL, qY, and qj consists of q equal units, we may call them unitary quantities, in contrast to the cratic term, which is a communal quantity, depending as it does on the amount of solvent as well as the amount of solute present. 

We may say then that in each of those processes the change AF in the free energy consists of two parts, a unitary part and a communal part. When an ionic solution is not extremely dilute, the free energy of the solution receives a contribution from the interionic forces this quantity depends on the concentration of the solute and is a communal quantity. When, however, the solution is extremely dilute, the interionic contribu-... 

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. 

The Unitary Part of a Free Energy Change. In this way we can obtain values for the unitary terms characteristic of processes of each of the four types discussed in Chapters 1 and 2. At this point it will be convenient to review what was said in those chapters and to relate that discussion to (71) and (72). In Sec. 11 the dissociation energy D was introduced by analogy with the dissociation energy T3tac, defined for the Bame molecule in a vacuum. In solution (as in a gas or vapor) the parts... 

The same remarks can be made about each part of the c.m.f., separately. The unitary part of the e.m.f., expressed in volts, is numerically equal to the unitary change in the free energy, expressed in electron-volts per ion pair. At the same time, the cratic term in the e.m.f., expressed in volts, is numerically equal to the cratic change in the free energy, expressed in electron-volts per ion pair. A similar statement can be made about the interionic part but we are usually interested in the value of the e.m.f., extrapolated to extreme dilution, where this part is negligibly small. 

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... 

We shall discuss now in greater detail the process depicted in Fig. 11, where ions are taken from the surface of a solid into a solvent. In Sec. 52 we defined a unitary quantity L, which will play a role similar to that played by D and J. The equilibrium between a solid and its saturated solution is an examplo of the equilibria considered in Sec. 51. If a few additional pairs of ions are taken into this solution, the value of dF/dn is zero. We now say that this zero value can come about only when the communal part and the unitary part have values that are equal and opposite. A saturated solution is, in fact, the solution that provides these equal and opposite values. The communal term ill the free energy differs from the cratic term by the value that d has in the saturated solution. When this value is known, AF° and L can be evaluated. Let m.ai, y. t, and x,ai refer to the concentration of the saturated solution. Then, writing AF = 0 in (108), we obtain for the standard free energy... 

On closing the external circuit between the two Ag electrodes, when a current flows, the net result will be simply to transfer an amount of solute from one solvent to the other, and the measured e.m.f. will be equal to the change in free energy associated with the transfer of a kome of ions from one solvent to the other. This quantity will contain, in addition to the usual communal term, a unitary term arising from the fact that, in the co-sphere of each positive ion and each negative ion, the amount of free energy lost by the dipoles of one solvent will be different from that lost by the dipoles of the other solvent. 

We shall be interested in pairs of cells, in which the mole fraction of the solute in one solvent is equal to its mole fraction in the other solvent. Suppose then that a series of such pairs of cells is made up, with the solute at progressively greater dilutions. When the members of these pairs of cells are placed back to back, the resultant e.m.f. s will contain progressively smaller contributions from the intcrionic forces and, on extrapolation to extreme dilution, this contribution will be negligibly small. Since the mole fraction on each side is the same, the difference between the eratic terms will be zero. In any such scries of cells, the measured e.m.f. s when extrapolated to extreme dilution thus yield the unitary part of the change in free energy. 

There is an additional, more fundamental, issue involved in applying the standard diabatic formalism. The solvent reorganization energy and the solvent component of the equilibrium free energy gap are bilinear forms of A ab and (Fav (Eqs. [45] and [47]). A unitary transformation of the diabatic basis (Eq. [27]), which should not affect any physical observables, then changes A b and v, affecting the reorganization parameters. The activation parameters of ET consequently depend on transformations of the basis set ... 

The thermodynamic equilibrium constants are related to the overall standard unitary free energy changes associated with the transfer of the solutes from the mobile to the stationary phase such that... 

Hydrophobic interactions have been correlated with unitary free energy changes, A/ , of relatively simpler processes such as (Kauzmann, 1959) ... 

Unitary Free Energy Changes for the Transfer of Benzene to Varioits Solvents"... 

Presumably this is a reasonable model for a peptide bond, and formation of the dimer and higher polymers can be detected easily by examination of the N-H stretching frequency by ir spectroscopy. The degree of association of N-methylacetamide is affected by the solvent (Table II). In aqueous solutions die association is extremely weak, with positive values for the unitary free energy change associated with hydrogen bond formation. That is, monofunctional hydrogen bonds in aqueous solution do not appear to be stable (15). 

Figure 3 Free energy profile for the simulated reaction vs the constrained NO distance. Energy in KJmol distances in A. The free energy zero has been arbritarily set at a value of the constraint of 4.0 A. Chemical formula in the panel represent the content of each P-cage at the beginning and at the end of the reaction. The free energy profile refers to a unitary cell (two / -cages).

Eq. [5.5.37] gives the free energy with respect to a IM standard state, because the unit of Kn is M . To calculate the unitary (mole fraction) free energy change we write, instead of eq. [5.5.37], eq. [5.5.38] ... 

There seems to be a reasonably good correlation between complex stability and the planar area of interactants. Cohen and Connors have plotted the standard unitary free energy change for complex formation in aqueous solution against estimated maximal overlap area for fifty complexes. The dispersion of points in the plot was considered to be a second-order effect, possibly correlatable with specific structural features in substrate and ligand. 

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. 

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