2. Thermodynamics of electrolyte solutions

2.1. Species and components

All the entities existing in a system – ions, molecules, electrons etc. – are called species, while components are those species the amount of which can be varied independently. For example, an aqueous solution of acetic acid contains the species H+, OH–, H2O, CH3COO– and CH3COOH, but only two components, H2O and CH3COOH. A proton (or more like H3O+) and a hydroxyl ion OH– are coupled with the ionic product of water:

K^w = {[\text{H}^+]} [\text{OH}^-] =10^{-14} at 25 °C

(2.1)

The dissociation constant of acetic acid couples H+, CH3COO– and CH3COOH:

\ce{ ${K}_\ce{a}$=$\frac{[\ce{H+}][\ce{CH3COO-}]}{[\ce{CH3COOH}]}$ } =1.7378 \times10^{-5} \text{M}  at 25 °C

(2.2)

Furthermore, electrolyte solutions obey the very strong condition of (local) electroneutrality:


\displaystyle\sum\limits_{i}z_ic_i=0

(2.3)


The general statement is that if a system contains N species, bound by m reactions and p other contraints, the number of components, M, is

M = N - m - p

(2.4)

In acetic acid, N = 5, m = 2 and p = 1, hence M = 2. Equation (2.4) can be generalized to the Gibbs phase rule. Assume that acetic acid is distributed between an aqueous and an organic solvent phase (o). In addition to the above mentioned aqueous species, the entire system contains (at least in principle) the species H+(o), OH-(o), CH3COO-(o), CH3COOH(o) and the organic solvent, making N equal to 10. The mutual solubility of water and the organic solvent is assumed to be negligible. Yet an extra variable is the Galvani potential difference created across the phase boundary. The constraints are two reactions, the electroneutrality condition and four partition equilibria. The Galvani potential difference can be eliminated with the total mass balance of acetic acid. M thus is three, the components being water, acetic acid and the organic solvent. Electroneutrality in water implicitly implies electroneutrality in the organic phase too. Writing ionic equilibria similarly to (2.1) and (2.2) in the organic phase does not result in extra constraints either. Furthermore, it should be noted that the Gibbs-Duhem equation

\displaystyle\sum\limits_{i} \mu _idn_i=0, p, T constants

(2.5)

gives an extra constraint that in the both phases there is only one thermodynamically independent component, the solvent or acetic acid, hence two totally independent components.