An equilibrium is homogeneous when all components are either exclusively in the gas phase or exclusively in solution. For gas-phase equilibria, the ratio of the product concentrations for end and starting materials is constant at a given temperature (law of mass action of Guldberg and Waage, 1867). When the reaction partners are dissolved, the standard molar Gibbs energy of solvation, DG solv , is liberated due to the intermolecular interactions between solvent and solute. In general, this quantity is di¤erent for starting and end products. Thus, a displacement of the equilibrium can take place when going from the gas phase to solution [1][2][3][4][5][6][7]. An unchanged equilibrium constant can only be expected when DG solv is accidently the same for starting and end products. The e¤ect of the medium on the position of equilibrium can be considered from two points of view: (a) comparison of the gas-phase and solution equilibrium constants, and (b) comparison of the equilibrium constants for di¤erent solvents. Unfortunately, few equilibrium reactions have been studied both in the gas and liquid phases [5, 6]. These are primarily non-ionic reactions where the interaction between reacting molecules and solvent is relatively small (e.g. the Diels-Alder dimerization of cyclopentadiene). In this chapter, therefore, equilibria which have been examined in solvents of di¤erent polarity will be the main topic considered (except for acid-base reactions described in Section 4.2.2).
Let us consider a simple isomerization reaction A Ð B in the solvents I and II, whose abilities to solvate A and B are di¤erent. This corresponds to the Gibbs energy diagram shown in Fig. 4-1.
From Fig. 4-1, Eq. (4-1) can be immediately derived,
ðIIÞ þ DG t ðA; I ! IIÞ ¼ DG t ðB; I ! IIÞ þ DG ðIÞ ð 4-1Þ which, on rearrangement, leads to Eq. (4-2) [102]: DG ðIIÞ À DG ðIÞ ¼ DDG ðI ! IIÞ ¼ DG t ðB; I ! IIÞ À DG t ðA; I ! IIÞ ð 4-2Þ
Since, for equilibria, the logarithm of the equilibrium constant is proportional to the standard molar Gibbs energy change, DG , according to Eq. (4-3),
it follows from Eqs. (4-2) and (4-3) that the di¤erence in the molar transfer Gibbs energies of educt A and product B, DDG t ðI ! IIÞ, determines the solvent e¤ect on the position of this equilibrium. In the particular case of Fig. 4-1, DG t ðB; I ! IIÞ > DG t ðA; I ! IIÞ, so that the equilibrium is displaced towards B when the solvent is changed from I to II.