Determination of free-energy changes

AG° may of course be determined from observed equilibrium constants. However, we often wish to be able to do the opposite and predict equilibrium constants from standard free energies. To do this we make use of the equation (Section 4.2) 

For a reaction AH0 can be measured either directly by the use of calorimetry or indirectly by making use of Hess s Law. For any reaction we also have 

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The determination of free-energy changes Determine equilibrium constant and use... 

Problem 46 Use the chart of standard free energies of formation (Table l4-6) to determine the free energy change in the following reaction and report whether the reaction will proceed. 

Although there are some aspects of micellization that we have not taken into account in this analysis —the fact that n actually has a distribution of values rather than a single value, for example —the above discussion shows that CMC values expressed as mole fractions provide an experimentally accessible way to determine the free energy change accompanying the aggregation of surfactant molecules in water. For computational purposes, remember Equation (3.24), which states that x2 n2/n, for dilute solutions. This means that CMC values expressed in molarity units, [CMC], can be converted to mole fractions by dividing [CMC] by the molar concentration of the solvent, [solvent] x2 [CMC]/[solvent] for water, [solvent] = 55.5 mole liter... 

There is another type of free energy change that can be considered within the overlap volume in addition to the concentration effect considered by the Flory-Krigbaum theory. This additional contribution to AGlens is likely to be more important for d < 5RS and should be considered when the outcome of the encounter is not determined by the initial approach of the colliding particles. This contribution arises from an elastic response by the adsorbed polymer, effectively pushing the approaching particles apart. 

The free energy change of a system is dependent on changes in both the entropy and enthalpy that is, AG = AH-T AS. For a micellar system at normal temperatures the entropy term is by far the most important in determining the free energy changes (T AS constitutes approximately 90-95% of the AG value). Micelle formation entails the transfer of a hydrocarbon chain from an aqueous to a nonaqueous environment (the interior of the micelle). To understand the changes in enthalpy and entropy that accompany this process, we must first consider the structure of water itself. 

Another procedure for testing the third law of thermodynamics is to combine heat content with entropy data for a given reaction, and so to determine the free energy change, the value of which is known from direct measurement. The standard free energy change for the formation of silver oxide, i.e., for the reaction 2Ag(s) + = Ag20(s), can be derived from... 

Heatburst Microcalorimetry, Principle and Methods of, and Determination of Free Energy, Enthalpy, and Entropy Changes... 

Summary This chapter has presented a set of variations on the theme of free energy changes. We have seen how accurate values of AG° may be derived at any temperature, how this data may be summarized either as free energy functions or in terms of Ellingham diagrams, and how the data may be applied in a few instances. In virtually all cases, we have seen that activity can simplify the calculations of equilibrium constants and that allowances can always be made for non-ideal behaviour, assuming that activity coefficient data are available. Complete thermodynamic data have been published for relatively few compounds, however, and there are for example many common organic compounds for which only an enthalpy of formation has been determined. As more complete information is circulated, the number of applications of chemical... 

We can determine the free energy change of any reaction if we have the free energies of formation of all the substances in the reaction, analogous to AH° ... 

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