Free energy change equilibrium

Extension to a nonideal system Minimization of free energy Thermodynamics of reactions in solution Partial molar properties Medium and substituent effects on standard free energy change, equilibrium constant, and activity coefficient General considerations Solvent and solute operators Comments... 

If we consider the case of a gas in adsorption equilibrium with a surface, there must be no net free energy change on transporting a small amount from one region to the other. Therefore, since the potential represents the work done by the adsorption forces when adsorbate is brought up to a distance x from the surface, there must be a compensating compressional increase in the free energy of the adsorbate. Thus... 

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

It is known that the order of acidity of hydrogen halides (HX, where X = F, Cl, Br, I) in the gas phase can be successfully predicted by quantum chemical considerations, namely, F < Cl < Br < I. However, in aqueous solution, whereas hydrogen chloride, bromide, and iodide completely dissociate in aqueous solutions, hydrogen fluoride shows a small dissociation constant. This phenomenon is explained by studying free energy changes associated with the chemical equilibrium HX + H2O + HjO in the solu-... 

When two or more substituents are present on a cyclohexane ring, the interactions between the substituents must be included in the analysis. The dimethylcyclohexanes provide an example in which a straightforward interpretation is in complete agreement with the experimental data. For 1,2-, 1,3-, and 1,4-dimethylcyclohexane, the free-energy change of the equilibrium for the cis trans isomerization is given below. ... 

Estimation of the free-energy change associated with a reaction permits the calcula-aon of the equilibrium position for a reaction and indicates the feasibility of a given chemical process. A positive AG° imposes a limit on the extent to which a reaction can x cur. For example, as can be calculated using Eq. (4.2), a AG° of 1.0 kcal/mol limits conversion to product at equilibrium to 15%. An appreciably negative AG° indicates that e reaction is thermodynamically favorable. 

At equilibrium, the ratio of concentrations is an equilibrium constant, so we can write the standard free energy change for the process as... 

In any of these forms, this relationship allows the standard-state free energy change for any process to be determined if the equilibrium constant is known. More importantly, it states that the equilibrium established for a reaction in solution is a function of the standard-state free energy change for the process. That is, AG° is another way of writing an equilibrium constant. 

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so... 

Hexokinase catalyzes the phosphorylation of glucose from ATP, yielding glncose-6-P and ADR Using the values of Table 3.3, calculate the standard-state free energy change and equilibrium constant for the hexokinase reaction. 

The free-energy change of the glycogen phosphorylase reaction is AG° = +3.1 kj/mol. If [P ] = 1 mM, what is the concentration of glncose-1-P when this reaction is at equilibrium ... 

The production of ammonia is of historical interest because it represents the first important application of thermodynamics to an industrial process. Considering the synthesis reaction of ammonia from its elements, the calculated reaction heat (AH) and free energy change (AG) at room temperature are approximately -46 and -16.5 KJ/mol, respectively. Although the calculated equilibrium constant = 3.6 X 108 at room temperature is substantially high, no reaction occurs under these conditions, and the rate is practically zero. The ammonia synthesis reaction could be represented as follows ... 

The magnitude of AG, the free energy change, of a specific corrosion reaction provides a measure of the spontaneity of the reaction and of the extent to which it will proceed before equilibrium is attained if AG 0... 

The driving force of the reaction is the free energy change AC which is related to the reversible or equilibrium e.m.f. of the cell by the relationship... 

The standard free-energy change for a reaction M + X - MX is also related to the equilibrium constant for the corresponding reaction... 

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. 

Because the equilibrium constant, Keq, and the standard free-energy change, AG°, both measure whether a reaction is favored, they are mathematical related by the equation... 

What typically happens for an energetically unfavorable reaction to occur is that it is "coupled" to an energetically favorable reaction so that the overall free-energy change for the two reactions together is favorable. To understand what it means for reactions to be coupled, imagine that reaction 1 does not occur to any reasonable extent because il has a small equilibrium constant and is energetically unfavorable that is, the reaction has AG > 0. 

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