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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 higher precision as more parameters of (with ) become available.[8]

Small molecules carrying an acid and/or a basic group tend to be soluble in pure water and exhibit a certain degree of ionization (Section 1.1.6) or dissociation (Section 1.1.5). The ionization or dissociation of the acid HA in aqueous solutions (H₂O + HA ⇌ A⁻ + H₃O⁺) at a given temperature is characterized by the acid ionization constants and . They are defined as:

(1.14)

where is the activity of the species . The activity of water is approximately constant at a given temperature and with the low solute concentrations normally used in the ESTs. Therefore, it is assumed that . Equivalently, the conjugated acid BH⁺ of base B, produced by the equilibrium reaction H₂O + BH⁺ ⇌ B + H₃O⁺, has the following acid ionization constants:

(1.15)

These acid ionization constants are better represented by , where .

The ranges defined for very strong (), strong (), medium, weak, and very weak acids are poorly defined. Nevertheless, it is safe to say that acids with a of between 4 and 10 are weak acids and that acids with can be considered as very weak acids. The opposite occurs for bases, as for a base to be very strong the of the conjugated acid BH⁺ (equation 1.15) must be above 14 (), with strong bases exhibiting . Similar to weak acids, weak bases also exhibit of between 4 and 10; however, in this case the very weak bases exhibit .

It is important to note that significantly changes with temperature for some functional groups: , where is expected to be a smooth and slowly varying function of temperature. The of the great majority of amines decreases with temperature, while carboxylic acids exhibit a much smaller change, usually negative, but there are some exceptions and it depends on the temperature range. These temperature sensitivities have important practical implications for method development within the field of ESTs, as they affect the mobility of the analytes and the pH of the buffers.[9–11] Moreover, they are used to promote cyclic band compression in the toroidal layouts, which is an interesting way to get some control of band spreading along the separation mediums (see Appendix G).