Terminology pH Scale and pKa Definitions

This section introduces the terminology of pH and ionization, as a well as equations for calculating the pH of solutions of weak acids and bases, and for plotting distribution of species profiles. It also introduces ampholytes and zwitterions, and the concept of protonation microconstants.

5.16.1.1 Solution Equilibria

This chapter is concerned only with acid-base ionizations of organic molecules involving the gain or loss of hydrogen ions; this is the main class of ionization that can occur in solution. The terminology for ionization processes developed over more than 100 years of solution chemistry, with the result that many different words and phrases have been used to describe the same things. Thus, hydrogen ions are written as H+, but they are also referred to as protons. The acquisition of a hydrogen ion by a molecule is called protonation; the loss of a hydrogen ion is called deprotonation. Molecules that can gain or lose one proton may be called monobasic, though the word monoprotic is clearer; those that can gain or lose two are called diprotic, and so on. Molecules that can be protonated to create positively charged cations are called bases, and the protonated cations are called conjugate acids; molecules that can be deprotonated to create negatively charged anions are called acids, and the deprotonated anions are called conjugate bases. Some molecules can both gain and lose protons, existing as cations, anions, and unionized molecules, depending on pH. These are called either ampholytes or zwitterions; there is a tendency to use these terms interchangeably, but they represent distinctly different chemical forms, as explained later. The different forms of the molecule (unionized, ionized) are called species. Aside from mentioning these terms in this section, the remainder of the chapter will use a standardized set of terms that may be convenient for medicinal chemists, who are not on the whole concerned with the theories of solution chemistry but with the practical use of the numbers.

Ionizable drugs and drug-like molecules transform between their unionized and ionized states at pH values between 1 and 13. They are called weak acids and bases. The strength of the acid or base is denoted by its ionization constant, Ka. Besides ionization constant, this term has been called several other names in the literature, such as protonation constant, equilibrium constant, and dissociation constant. There is a related term, stability constant, which is equivalent to 1/Ka. Ka is usually expressed logarithmically as a pKa value, meaning -log10 Ka; where possible, the term pKa will be used throughout this chapter.

5.16.1.2 Definition of pH

Because pKa values are numbers on the pH scale, it is important to understand the concept of pH. The term pH is used to express the acidity of aqueous solutions, and was first introduced by S0rensen in 1909. In two important papers published simultaneously in German and French,1 he compared the usefulness of the degree of acidity with that of the total acidity, proposed the hydrogen ion exponent, set up standard methods for the determination of hydrogen ion concentrations by both electrometric and calorimetric means, with a description of suitable buffers and indicators, and discussed in detail the application of pH measurements to enzymatic studies.

S0rensen introduced a potential of hydrogen PH = — log CH+, which was subsequently modified to pH. Modern usage recognizes the following terms that are used in the so-called operational scale, pH = p«H = —log «h = — log10 [H+]g+ [1]

as well as a concentration pH, which is valid in solutions of constant ionic strength, pCH+ = —log [H+] = p[H+] [2]

In the above expressions, aH represents the activity of the hydrogen ion, g + represents the activity coefficient, and CH+ represents the concentration of hydrogen ions.

5.16.1.3 Concentration and Activity

Concentration expresses the amount of solute as a proportion of the amount of solvent or of solution, in units such as or moles per kilogram, moles per liter, grams per liter, etc. It is conventionally denoted by the use of square brackets in equilibrium expressions, so [S] means the concentration of S. The concept of activity was developed to relate concentration to thermodynamic activity as measured by solubility, vapor pressure, or electrochemical potential. For rough calculations, or in very dilute solutions that approach zero ionic strength, activity is more or less equal to concentration, but at higher concentrations activity (a) is shown as as = [%s [3]

where S denotes solute and gs is the activity coefficient of the solute. When considering molecules that ionize in solution, it would be easy to regard the ions as mere points of charge. However, this is not realistic, and the activity of ions is affected by a number of factors. One factor is temperature, and another is the dielectric of the solvent medium. Another significant factor is that hydrated ions occupy a volume of the solution in proportion to their size, and exclude other ions from this solution space. This competition for space inhibits the dissociation at high ionic strength. Ions self-associate to form ion pairs, so as the concentration of the solute increases, the activity of ions increases somewhat less. The equations to derive activity coefficients are complicated. However, two special cases are often used to avoid this complication. Results may be reported at zero ionic strength, where the activity coefficient is unity, though this introduces some practical difficulties. More usually, if the solute under study is dilute but the total ionic strength is high because an inert electrolyte has been added, then the activity coefficient of the solute ions will have a constant value at constant ionic strength.

Although the relationship between concentration and activity has been properly considered in fundamental work to establish the composition of primary buffer solutions, it is too complicated to apply in everyday measurement situations. For this reason, pH is measured and reported in units of activity. Values for p[H] can be obtained by measuring pH in solutions that have been adjusted to a constant ionic strength by adding a solution of an inert electrolyte; under these conditions, pH is proportional to p[H]. A constant ionic strength background of 0.15 M KCl is commonly used in the measurement of pKa values. The ionic strength of this solution is close to that of human blood; KCl is used in preference to NaCl because high concentrations of sodium ions interfere with the response of the glass electrode used to measure pH.

5.16.1.4 pH of Water

Liquid water is composed of molecules of H2O. Interactions between the molecules lead to complex metastable structures within liquid water, and a solvated ionized molecule (HgO^), as well as structures with additional solvation shells have been proposed.2 It is too complicated to include these hydration structures in written acid-base reactions. The ionization of water can be expressed in terms of the hydrated hydrogen ion H3O +,

or more simply using the proton H + itself (even though H + ions do not exist as free species in solution). Thus, the ionization of water can be written as

In terms of ionic activities an equation can be written containing the equilibrium constant K°:

The activities of H + and OH _ are proportional to their concentrations, but by convention the activity of H2O is proportional to the mole fraction of water in the solution. Thus, aH2O is close to 1.000 in dilute solutions, and may be included in the equilibrium constant K

If the activity coefficients are also included in the constant, the ionic product of water KW can be derived:

Values for Kw have been calculated from conductance data measured in water at varying temperatures and pressures, and a value of 10 — 13 997 (25 °C, 1 bar, zero ionic strength) is generally accepted. The corresponding value of pKw ( — log10 Kw) is 13.997 (i.e. close to 14.0 under standard conditions). The concentration of H + and OH — must be equal when water dissociates. Therefore, if [H + ] = [OH — ], and [H + ][OH — ] = 10 — 14 then [H + ] in pure water has a value of 10 — 7, and the pH ( — log10 10 — 7) of pure water is 7.0 at 25 °C. In fact, the pH of water at 25 °C is usually about 5.5, because water in equilibrium with air becomes saturated with carbon dioxide, thus forming a dilute solution of carbonic acid.

Note that pH varies with temperature, especially for solutions at high pH. This is because temperature affects the activity coefficients involved in the calculation of KJ (eqn [7]). The values of pKw vary from 14.96 at 0 °C to 13.26 at 50 °C.5 Note also that the value of Kw varies as a function of ionic strength. The values of the pKw of water at 25 °C vary between 13.997 at 0molL— 1 to 14.18 at 3.0molL— 1.6,7

5.16.1.5 pH of Strong Acids and Bases

Acids are molecules that are not ionized at low pH, but which become negatively charged ions at higher pH because they lose one or more hydrogen ions to the solution. Bases are not ionized at high pH, but become positively charged ions at lower pH because they gain one or more hydrogen ions from the solution. HCl and KOH are examples of a strong acid and base, respectively, meaning that they are fully ionized in aqueous solution; their unionized forms would only exist in solution outside the range of the aqueous pH scale. These definitions are in accordance with Br0nsted's concept that an acid is a species having a tendency to lose a proton.

The pH values of solutions of strong acids and bases in water can be easily calculated. In a solution of HCl of concentration C mol L- 1, the following equations may be defined:

Substituting for [Cl ] from eqn [9] and [OH ] from eqn [10] in eqn [11] gives the following equation, which has terms in units of [H + ] alone:

which reduces to a quadratic equation of the form

which could be solved for an explicit value of [H + ].

However, consider a solution of 10 — 1M HCl in water. The concentration of hydrogen ions supplied by the dissociation of the HCl is 10 — 1, and the term Kw/[H + ] in eqn is 10 — 13, which is very small compared with 10 and can be neglected. Equation [12] therefore reduces to

A similar series of equations can be defined for a strong base, such as a solution of KOH of C mol L 1:

Substituting for [K+ ] from eqn [16] and [OH ] from eqn [17] in eqn [18] gives the following equation that has terms in units of [H + ] alone:

which reduces to a quadratic equation of the form

which can be solved for an explicit value of [H + ].

However, in basic solutions the pH is higher than 7, and therefore [H + ] is less than 10 - 7. If C is much larger than 10 - 7 then [H + ]2 is negligible compared with C, and eqn [19] could be simplified to

which rearranges to p[H] = pKw + log C = 14.00 + log C [22]

In a solution of 10 - 1M KOH in water, log C = - 1, therefore pH = 13.

Solutions of HCl and KOH supply points at the extremes of the pH scale. On this logarithmic scale, a 0.1 M solution of HCl would have a pH of 1, and a solution of 0.1 M KOH would have a pH of 13. While solutions exist whose pH values are outside the range 1 to 13, they are not normally encountered in the human body, and these values represent the limits of the pH scale for most aspects of medicinal chemistry.

5.16.1.6 Weak Acids, Weak Bases, and Ionization Constants (pK)

Ionizable drugs are called weak acids and bases because their unionized forms exists in solution over at least a part of the pH range from about 1 to 13. A convenient nomenclature uses AH (and AH2, AH3, etc.) to represent weak acids, B to represent weak bases, and XH to represent ampholytes and zwitterions.

Consider a monoprotic (i.e., singly ionizing) acid AH that dissociates according to

The term Ka is the ionization constant such that at equilibrium,

The ionization of a monoprotic base B may be represented in a similar way:

From the above equations, when [A-] = [AH] or [B] = [BH + ], then [H + ] = Ka. Therefore, for monoprotic compounds the pKa ( = - log10 Ka) is the pH at which equal concentrations of neutral and ionized forms of the sample are present in the solution.

Equations [24] and [26] can be written in the following form, which is frequently cited as the Henderson-Hasselbalch equation:

In a series of acids with increasing pKa values, those with higher pKa values are said to be weaker, while acids with lower pKa values are stronger. In contrast, bases with higher pKa values are stronger, while bases with lower pKa values are weaker.

As with pH values, pTa values vary with temperature and ionic strength, so it is helpful if these conditions are cited along with the pTa value. Conditions of 25 °C and 0.15 M ionic strength are widely used for drugs. It is also important to know whether the pTa refers to an acidic or basic group.

5.16.1.7 Distribution of Species

The pTa and the type of compound (acid or base) provide a snapshot of the acid-base behavior of a molecule, and may be visualized graphically. For example, ibuprofen is a carboxylic acid with a pTa of 4.35. The relative concentration of unionized and ionized species as a function of pH may be plotted as a distribution of species graph (Figure 1). The graph consists of two lines plotted on the same axes. While these graphs conventionally plot the relative concentrations as percentages, they are based on the following equations. At any pH, the fraction of compound in the form A_ is expressed as

and the fraction in the form AH is expressed as

Figure 2 shows the distribution of species graph for carvedilol, a base with a pTa of 7.97. The fraction in the form B is expressed as

and the fraction in the form BH + is expressed as

5.16.1.8 Ionization Equations for Samples with up to Six pKa Values

Table 1 shows a general scheme for describing the ionization of compounds with up to six pTa values, together with equations for plotting the distribution of species. The equations in the table, as well as those used to draw the graphs and profiles of lipophilicity and solubility appearing in this chapter, are derived from principles of mass balance and

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