Solution, free energy changes

Let us consider mixing of two gases A and 5to form a homogeneous mixture (a solution). Free energy changes of the constituents involved are... 

We now consider briefly the matter of electrode potentials. The familiar Nemst equation was at one time treated in terms of the solution pressure of the metal in the electrode, but it is better to consider directly the net chemical change accompanying the flow of 1 faraday (7 ), and to equate the electrical work to the free energy change. Thus, for the cell... 

Let us define the respective basicity by — AG in the gas phase and — AG" in aqueous solution. For discussions concerning the relative strength in basicity of a series of methyl-amines, only the relative magnitudes of these quantities are needed. Thus the free energy changes associated with the protonation of the methylamines relative to those of ammonia are defined as... 

Free energy changes of methylamines m aqueous solution upon protonation refeiTed to... 

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes AG and AG" upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of —AG and — AG" for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution. 

Figure 7 Free energy changes of halo-substituted carboxyl acid in aqueous solution upon deproto-nation referred to acetic acid.

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-... 

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

In Section 8.2 solvation energy AGsoiv was defined as the free energy change upon transferring a solute from the gas into a solvent. We can now relate the transfer free energy to solvation energies ... 

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. 

Equation (3.12) shows that the free energy change for a reaction can be very different from the standard-state value if the concentrations of reactants and products differ significantly from unit activity (1 Mfor solutions). The effects can often be dramatic. Consider the hydrolysis of phosphocreatine ... 

Even this set of equations represents an approximation, because ATP, ADP, and Pi all exist in solutions as a mixture of ionic species. This problem is discussed in a later section. For now, it is enough to note that the free energy changes listed in Table 3.3 are the group transfer potentials observed for transfers to water. 

Calculate the free energy change for acetyl phosphate hydrolysis in a solution of 2 mM acetate, 2 mM phosphate, and 3 iiM acetyl phosphate. 

There is negligible reaction with water and steam at moderate temperatures and pressures, as indicated by the free-energy change for the solution 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. 

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... 

Proceeding as in Sec. 55, we can consider AF, the free energy change per mole accompanying the solution of this crystal in a certain solvent... 

The equation just written is generally applicable to any system. The equilibrium constant may be the K referred to in our discussion of gaseous equilibrium (Chapter 12), or any of the solution equilibrium constants (Rw Ra, Rj, K, . . . ) discussed in subsequent chapters. Notice that AG° is the standard free energy change (gases at 1 atm, species in solution at 1M). That is why, in the expression for K, gases enter as their partial pressures in atmospheres and ions or molecules in solution as their molarities. 

AG° is the standard free energy change (gases at I atm, species in solution at 1M) for the reaction. 

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