on the potential barriers, but if then the reaction will not occur (the specified quantity of solute is not soluble). Generally it is easy to estimate ; however, it is very difficult to evaluate in most real situations. Dissociation of a salt, for instance, increases the number of states available to the sub-system salt, as solvation occurs, but decreases the number of states available to the sub-system water molecules. This works as a trade off: as the entropy of the salt ions increases the entropy of the water molecules is consequently decreased. When the overall entropy change is negative then lower temperatures favor the occurrence of the dissolution. By contrast, if the entropy change is positive then higher temperatures will favor dissolution. It is necessary to note that lower temperatures generally decrease the velocity of reactions, since a lower thermal energy decreases the probability of reactants overcoming the energy potential barriers of the intermediate products. Remember that entropy is proportional to the logarithm of the number of states available to the system, within the constrains (volume and total energy) imposed by the system. A didactic explanation of enthalpy, entropy, and Gibbs free energy is given by Connors (2002) [6] and a quantitatively rigorous approach is described by Reif (1965) [1]. The above presented theory is also valid for the solubilization processes of hydrophobic solutes (and colloids) in aqueous solutions with the aid of micelles (surfactants) or microemulsions (stabilized submicron droplets of oil). The same can be told with the inverse, the solubilization of hydrophilic solutes in hydrophobic solvents.
1.1.9 Acid Ionization Constants
From reaction 1.3, the ionization constants and of water can be written as:
(1.9)
where the multiplication operation is explicitly denoted by to avoid confusion, at 25 C and represents dimensionless variables called chemical activities. The activity of a chemical species is defined as:
(1.10)
where is a dimensionless parameter called the activity coefficient, which depends on the units of concentration of the variables , , and . These are standard states of solute concentrations with the following units, respectively: amount concentration (molar), molality (molal), and mass concentration (g ). They should not be confused with the standard solutions used in analytical chemistry, nor with the standard conditions of a system (e.g., standard temperature and pressure of a gas). These standard states are standard quantities of a thermodynamic variable and in the present case could be 1 M, 1 molal, and 1 g L−1.
The activity coefficients express the deviation from an ideal behavior. When the activity coefficient of a chemical species is close to one for a given range of concentration amount or other unit, then this species exhibits an almost ideal behavior according to Henry's law in this range and the same is expected up to infinite dilutions of the solute.
The equilibrium constant is called the autoprotolysis constant, [7] the water dissociation constant, the ionization constant or self-ionization constant of water. From the definition shown in equation 1.9 it may also be seen as the ionic product of water. These are small numbers that are difficult to handle. Therefore it is more practical to apply the mathematical operator “p”, which stands for “”, to them. Consequently we obtain:
In reality it is more common to use the simplified notations of pH and pOH instead of and , respectively. For all other entities the notation , where denotes any charged or neutral species, is used. For example, , , , ,…, and so on.
From the mathematical point of view it is incorrect to write or , because the transcendental functions (exponential, logarithmic, and trigonometric) must be handled with dimensionless arguments. Second, from a chemical point of view, the cited expressions are not very informative. To illustrate this, let us suppose that the pH of a solution is exactly . From equation 1.10 we can see that this is much more information rich, as it leads to the following relationships:
(1.11)
(1.12)
(1.13)
These allow the content of H3O+ to be known in many more units (including, but not limited to, molar, molal, and g ) and with much
