Free entropy

Now, classical thermodynamics gives another expression for the standard free energy which separates it into two parts, the standard free enthalpy and the standard free entropy. 

Figure 9. Graph of Standard Free Entropy against Standard Free Enthalpy for an Ether, Thioether and Amine...

Introducing the functions for standard free enthalpy and standard free entropy. 

It is seen from equation (22) that there will, indeed, be a temperature at which the separation ratio of the two solutes will be independent of the solvent composition. The temperature is determined by the relative values of the standard free enthalpies of the two solutes between each solvent and the stationary phase, together with their standard free entropies. If the separation ratio is very large, there will be a considerable difference between the respective standard enthalpies and entropies of the two solutes. As a consequence, the temperature at which the separation ratio becomes independent of solvent composition may well be outside the practical chromatography range. However, if the solutes are similar in nature and are eluted with relatively small separation ratios (for example in the separation of enantiomers) then the standard enthalpies and entropies will be comparable, and the temperature/solvent-composition independence is likely be in a range that can be experimentally observed. 

Finally, it is necessary to select values for the thermodynamic constants that are to be used in equation (9). The data selected were that published by Beesley and Scott [2], for the two enantiomers, (S) and (R) 4-benzyl-2-oxazolidinone. The values for the standard free enthalpy and standard free entropy for the (R) isomer were... 

AHo) is the Excess Free Enthalpy (ASo) is the Excess Free Entropy. 

In addition to the calculations of changes in the free entropy mixing, Flory introduced the interaction parameter, %, to account for the intermolecular interactions between polymer and solvent molecules, thus giving [53]... 

Let us first consider the changes in entropy and calculate the free entropy of mixing per unit volume, AS instead of AS [66-68]. 

Disposing the Flory-Huggins modified equation, including the free entropy of mixing per total volume, AS , as a function of conversion and the enthalpy term expressed with the interaction parameter [66-68,72] ... 

Temperature used = 298.15 K N = number of ligands AG°= standard free energy AH°= standard free enthalpy AS°= standard free entropy EDF = equilibrium driving force. 

From eq, (15.10) it can be seen that AH03 (the partial free enthalpy of formation) and AS02 (the partial free entropy of formation) may be derived from curves of the types shown in Fig. 15.2. AHqz/R may be obtained from the slopes of the curves and ASoz/R ff m the intercepts. 

Figure 15.5. The panial free entropy of formation. - So2, as a function of log(x) in for...

Figure 15.6. The panial free entropy of formation. -ASoj. as a (unction of log(x-t-y) in CC. 2yGdjyOn,, > for y = 0.0.1 and 0.2. The data are taken from a literature review. ...

The present author has the impression from the literature on the stability of diazomethane relative to diazirine that two different physico-chemical phenomena were called (thermal) stability in some of the publications, namely the thermodynamic stability, as defined by the free energy of formation AGf and the free enthalpy of formation A//f for the (hypothetical) formation of a compound from the elements in a gas phase reaction under standardized conditions (298 K, 1 mol). AGf and A//f are related to one another by the free entropy A5f in the Gibbs-Helmholtz equation AGf = A/ff-TASf. The absolute values of AGf, A/ff and ASf do not give definite information on the stability of a compound, as this word is used in the everyday language of a chemist, because it is related to an unrealistic chemical process, namely the formation from the elements. If A/ff is known, however, for a given compound and for a real product of one of its reactions, the difference in magnitude of the two free enthalpies tells us whether this reaction is likely to take place, but we cannot depict at all, at least in principle, the half-life of such a reaction. 

To achieve a separation between two substances, thermodynamics has shown that their standard free energy of distribution must differ. As the difference between enantiomers are solely spatial and not structural, any separation must be achieved by primarily changing the relative standard free entropy contribution to the standard free energy of each isomer. It will be seen later that this does not exclude a significant contribution from a change in free enthalpy as well, but the primary effect must be entropic in order to realize the corresponding change in free enthalpy. This will be better understood when actual separations are discussed. Thus, in order to obtain some selectivity between enantiomers, the structure of the stationary phase must be such that one isomer will fit... 

In addition, the effect of temperature on column efficiency, is now being frequently exploited, particularly in size exclusion chromatography (SEC) and in other separations where the standard free entropy dominates the separation (i.e. all chiral separations and the separation of all closely eluting isomers). 

The same type of molecular forces are involved as those in GC, except that, as the solutes no longer need to be volatile, ionic interactions can now be used to control retention, in addition to dispersive and polar interactions, as in GC. It will be seen that temperature can also be used to control retention in LC, in a somewhat similar manner to GC. The distribution coefficient of a solute between the two phases in LC will always result from both standard free entropy and enthalpy changes during distribution, as in GC. In addition, the separation of enantiomers will also depend primarily on a difference in the standard free entropy between the two isomers, that results from spatial variations and which are then augmented by standard free enthalpy differences. 

Calculate the standard enthalpy and Gibbs free entropy of reaction from tabulated values. 

The respective rate and equilibrium constants (k, K) are related to the changes in the free energy of the reactions, AAG. The linear Hammett relationships hence imply linear relationships between the free energies of the equilibrium and the rate processes, AGeq im,rium rate- Such linearity should occur only if the changes in the free enthalpy, A AH, and in the free entropy, AA5, are constant and if a linear relation exists between AH and A5. Even in those cases when LFERs have been obtained, these criteria are... 

E = fluorescence enhancement AG = free energy AH = free enthalpy Ka = association constant Kd = dissociation constant n = hydration number Pm = fractional population at site M R = the gas constant r = internuclear distance AS" = free entropy Ti = longitudinal relaxation time Tim = longitudinal relaxation time in a paramagnetic complex... 

---