Free energy-entropy relationships

Denoting the differences in Gibbs free energy, entropy and volume per unit mass between the two phases as Ag, As, Aco, we can write file above relationships as... 

Free energy is related to two other energy quantities, the enthalpy (the heat of reaction measured at constant pressure) and the entropy. S. an energy term most simply visualised as a measure of the disorder of the system, the relationship for a reaction taking place under standard conditions being... 

Further information on the effect of polymer structure on melting points has been obtained by considering the heats and entropies of fusion. The relationship between free energy change AF with change in heat content A// and entropy change A5 at constant temperature is given by the equation... 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) AH is constant and the AS terms are proportional for the series, (2) AS is constant and the AH terms are proportional, or (3) AH and AS are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. °... 

The complex substrate molecule (AB) is broken down to simpler product molecules (A and B). The substrate and the products each have both a free energy and an entropy. For this, and for all chemical reactions the following relationship applies ... 

Therefore, reaction series with constant entropy have been accorded great significance and have been investigated thoroughly. The condition in eq. (8) was even considered necessary for any linear free energy relationship to hold (16). However, as experimental data accumulated and precision improved, it was clear that for many theoretically important reaction series, this condition is not fulfilled (1, 17). It was also proved that a LFER can hold if entropy is not constant, but linearly related to enthalpy (18, 19). The linear equation... 

The second law of thermodynamics states that the total entropy of a system must increase if a process is to occur spontaneously. Entropy is the extent of disorder or randomness of the system and becomes maximum as equilibrium is approached. Under conditions of constant temperature and pressure, the relationship between the free energy change (AG) of a reacting system and the change in entropy (AS) is expressed by the following equation, which combines the two laws of thermodynamics ... 

The relationships presented thus far for partial, integral and relative partial molar free energies are applicable in a similar manner to entropy, enthalpy and also volume. 

It is perhaps interesting, in view of the very considerable success of Hammett plots, to say a word finally about the thermodynamic implications of linear free energy relationships in general. We have already mentioned (p. 359) the relationship between free energy change, AG, and log k or log K and each AG term is, of course, made up of an enthalpy, AH, and an entropy, AS, component ... 

It would be valuable if one could proceed with a reliable free energy calculation without having to be too concerned about the important phase space and entropy of the systems of interest, and to analyze the perturbation distribution functions. The OS technique [35, 43, 44, 54] has been developed for this purpose. Since this is developed from Bennett s acceptance ratio method, this will also be reviewed in this section. That is, we focus on the situation in which the two systems of interest (or intermediates in between) have partial overlap in their important phase space regions. The partial overlap relationship should represent the situation found in a wide range of real problems. 

It is well known that such quantities as the standard free energy, enthalpy and entropy display a remarkable tendency to be additive functions of independent contributions of part-structures of the molecule. This property, on which the mathematical simplicity of many extrathermodynamic relationships is largely based, is well illustrated, for example, by the enthalpies of formation at 298°K of several homologous series of gaseous hydrocarbons Y(CH2)mH, which are expressed by the relation (28) (Stull et al., 1969). In... 

Equation (1.27) relates the difference in free energy for a gas at any pressure and temperature to the standard state condition at constant temperature. Here dH = 0, and from Eq. (1.15) the relationship of the entropy to the pressure is found to be... 

O O Write a short paragraph, or use a graphic organizer, to show the relationship among the following concepts favourable chemical change, temperature, enthalpy, entropy, free energy. 

Like the free energy, the chemical potential can be separated into a contribution from enthalpy H and another contribution from entropy S the relationship is... 

Which is the correct formulation for the relationship between free energy, enthalpy and entropy ... 

In order for mixing and solution to occur, it is essential that the change in free energy, AG, which is the driving force in the solution process, decrease to below zero. A/f and AG are equal to the change in enthalpy and change in entropy, and for constant temperature the relationship is the classical Gibbs equation ... 

Solntions whose free energies follow Eq. (2.34) are said to be regular, to distinguish them from irregular solutions, wherein the entropy of mixing is governed by a relationship other than Eq. (2.30). The free energy for a mixtnre that behaves as an ideal solution (a = 0) reduces to... 

If we assume that the entropy and enthalpy are relatively independent of temperature, we can drop the subscript m on temperature in Eq. (3.32), thereby obtaining a more general relationship between the entropy and enthalpy of fusion as a function of temperature. Substitution of this modified form of Eq. (3.32) into Eq. (3.31) gives the following relation for the free energy ... 

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