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84 BASIC CONCEPTS IN MEDICINAL CHEMISTRY
11. Shown below is the structure of clonidine, an α2 adrenergic agonist that can be used to
treat hypertension. Clonidine contains a guanidine functional group (highlighted in bold)
that has a pKa of 8.3. Other guanidine functional groups, such as that seen with arginine,
are much more basic with a pKa of 12.5. Provide a chemical explanation for this difference.
12. For each of the drug molecules shown below, determine if it is an acidic drug molecule, a
basic drug molecule, an amphoteric drug molecule, or a nonelectrolyte.
Drug Molecule Acid/Base Character of Drug Molecule
Hydrocortisone
Oxacillin
Dorzolamide
Diltiazem
Amobarbital
SOLVING pH AND
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4
pKa PROBLEMS
LEARNING OBJECTIVES
After completing this chapter, students will be able to
• Explain the similarities, differences, and interrelationships between the pKa of a functional
group and the pH of an environment.
• Explain how the Henderson-Hasselbalch equation was constructed and how it can be used
to calculate pH values, pKa values, and the ratio of ionized to unionized functional groups.
• Solve both qualitative and quantitative pH/pKa problems.
• Explain how the pH of a given environment and the pKa of a given functional group can
influence the solubility, duration, and binding properties of a drug molecule.
• Explain how the pH of a given environment and the pKa of a given functional group can
prevent or contribute to a drug interaction.
The relative acidity or basicity of the functional groups discussed in Chapter 3 can be measured by
comparing their respective pKa values, while the relative acidity or basicity of the environments
in which they reside can be measured by comparing their respective pH values. The Henderson-
Hasselbalch equation provides a mathematical relationship among the pK
group, the pH of the environment in which it resides, and the ratio that exists between the ionized
and the unionized form of the functional group.
This chapter focuses on strategies to solve two basic types of problems: those that determine if a functional group is primarily ionized or primarily unionized at a given pH (i.e., qualitative
problems) and those that determine the actual percent that is ionized (i.e., quantitative problems).
Within the discipline of medicinal chemistry, the ability to solve qualitative problems and/or estimate the percent to which a functional group is ionized is much more important than the ability to
solve quantitative problems. As such, this chapter places a greater emphasis on qualitative problems and the ability to predict or estimate the extent of functional group ionization. This chapter
reviews the Henderson-Hasselbalch equation and how to use it to solve both types of problems.
This is then followed with descriptions of how to intuitively solve these same types of problem
without actually using the Henderson-Hasselbalch equation. For sake of completeness, examples
are also provided for the calculation of pH and pKa values. The chapter ends with a discussion that
highlights the importance of pH, pK
DOI 10.37573/9781585286959.004
, and functional group ionization in the practice of pharmacy.
a
85
value of a functional
a
86 BASIC CONCEPTS IN MEDICINAL CHEMISTRY
p
]=−
+
=− =−−=Solution 1:pHlog[0.1](1) 1
=− =−−=Solution 2:pHlog[0.00001](5) 5
+−
A]
The concepts discussed in this chapter with regard to the Henderson-Hasselbalch equation and
the relationship among pH, pKa, and functional group ionization are also applicable to discussions
of drug delivery, permeation, buffering formulations, product stability, and dosage form selection.
Most of these topics lie outside the discipline of medicinal chemistry and, therefore, the focus of
this text. Additionally, they often require more complicated quantitative calculations than discussed
here. Readers interested in any of these topics are referred to either Martin’s Physical Pharmacy and
Pharmaceutical Sciences, 7th edition (Wolters Kluwer, 2017) or Aulton’s Pharmaceutics: The Design
and Manufacture of Medicines, 4th edition (Churchill Livingstone/Elsevier, 2013).
DEFINING pH AND pK
a
By definition, pH is equal to the negative log of the hydrogen ion concentration in a solution.
Hlog[H
A very important fact to remember is that a pH value is a property of the environment in which
drug molecules reside and is determined by the solutes present in the solution. Thus, aqueous environments such as water, blood, urine, intravenous preparations, and ophthalmic preparations have a
pH, while drug molecules and functional groups do not. A second key point in using, evaluating, and
comparing pH values is that lower pH values indicate more acidic solutions. As an example, consider
two solutions, one with a hydrogen ion concentration of 0.1 M and another with a concentration of
0.00001 M. By simply comparing these concentrations, it is obvious that the solution with the 0.1 M
hydrogen ion concentration is the more acidic solution. Using these molar concentrations and the
above equation, the respective pH values can be calculated. Please note that the more acidic solution has a lower pH value.
By definition, pKa is equal to the negative log of the Ka, the dissociation constant for an acid in
an aqueous environment. While it appears to be a concentration value, Ka is actually a dimensionless term. This is due to a simplification of the actual equilibrium equation to one that excludes the
molecule of water.
=− =
pK logK ,where K
aa a
[H ][
[HA]
Similar to the previous discussions regarding pH, it is very important to remember that a pKa
value is a property of a specific functional group and is affected by the steric and electronic factors
that surround or are connected to the functional group. Thus, functional groups such as carboxylic
acids, sulfonamides, and aliphatic amines all have pKa values, while the solutions in which they
reside do not.
The pKa values of functional groups can be used to compare their relative acidity and basicity.
In examining acidic functional groups, a stronger acidic functional group dissociates more than a
weaker one, resulting in a higher hydrogen ion concentration and a higher Ka value. Because the pKa
is equal to the negative log of the Ka, a larger Ka value results in a lower pKa value. As an example,
consider two hypothetical acidic functional groups. Functional group A is a stronger acid and is 10%
ionized, or dissociated, in a given environment, while functional group B is a weaker acid and is only
CH 4 - SOLVING pH AND pKa PROBLEMS 87
+−
=− =F
a
+−
1]
=− =F
a
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1% ionized, or dissociated, in the same environment. Using 1.0 M concentrations for the drug molecules that contain these functional groups, the pKa values can be calculated as follows:
[H ][A]
unctionalGroup A:pKlog
=− =−
a
[HA]
unctionalGroup A:pKlog0.01 2
[H ][A]
unctionalGroup B:pKlog
=− =−
a
[HA]
unctionalGroup B:pKlog0.0001 4
[0.1][0.1]
log
[0.01][0.0
log
[0.9]
[0.99]
Math Review
For Functional Group A: Because 10% of a 1.0 M concentration is ionized, 0.9 M exists as
HA and 0.1 M exists as H+ A−. Therefore, the [HA] = 0.9, while the [H+] = [A−] = 0.1. The Ka is
a dimensionless term (as previously discussed), so the numbers 0.9 and 0.1 are used in the
equation without the molar designation.
For Functional Group B: Because 1% of a 1.0 M concentration is ionized, 0.99 M exists as HA
and 0.01 M exists as H+ A−. Therefore, the [HA] = 0.99, while the [H+] = [A−] = 0.01.
Similar to acidic functional groups, pKa values can be used to measure the relative strength of
basic functional groups. A strongly basic functional group has a higher pKa than a weakly basic functional group because the pKa value of a basic functional group is based on the dissociation of B:H+,
the conjugate acid of the basic functional group (see Chapter 3 for further discussion of conjugate
acids and bases).
In reviewing this equilibrium, it is important to note that a low pKa value indicates that the
equilibrium lies to the right and that the basic functional group is predominantly not bound to the
proton. Conversely, a high pKa value indicates that the equilibrium lies to the left and that the basic
functional group is predominantly bound to the proton.
Key Summary Points for pH and pK
a
• A pH value is a property of the environment, or solution, in which drug molecules and
functional groups reside. The pH of a solution can change based on what is added or
removed from the solution.
• Low pH values indicate acidic environments, while high pH values indicate basic envi-
ronments. A pH at or about 7.0 indicates a neutral environment.
• A pKa value is a property of a specific acidic or basic functional group. Although excep-
tions can occur, pKa values should generally be treated as constants (i.e., the secondary amine of epinephrine has a pKa of 10, regardless of whether it is in the stomach
fluid, the blood, or the urine).
• Low pKa values indicate either strongly acidic functional groups or weakly basic func-
tional groups. In comparing functional groups, the one with the lower pKa value is the
stronger acid or the weaker base.
• High pKa values indicate either weakly acidic functional groups or strongly basic func-
tional groups. In comparing functional groups, the one with the higher pK
value is the
a
weaker acid or the stronger base.
88 BASIC CONCEPTS IN MEDICINAL CHEMISTRY
+−
A]
HA
aa
==
+
THE HENDERSON-HASSELBALCH EQUATION
First described by Lawrence Henderson in 1908 and later revised with logarithmic terms in 1916 by
Karl Hasselbalch, the Henderson-Hasselbalch equation is very useful for solving a variety of pH, pKa,
and ionization problems. Examples include calculating the pH change of a buffered solution upon
the addition of an acid or base, calculating the molar ratio of salt to acid concentrations required to
prepare a buffer solution for a particular pH, and calculating the percent to which a functional group
is ionized. This chapter primarily focuses on this latter use; however, it provides a few examples of
other applications.
The following equations are also discussed in Chapter 3 and are used to review how the equation
is derived. To maintain consistency between acidic and basic functional groups, the equations are
written such that the acid and base designations lie on the same side of the equations, regardless of
the acid/base nature of the functional group.
This same consistency can also be maintained if the groups are designated as protonated (seen
on the left) or unprotonated (seen on the right). In contrast, the terms ionized and unionized would
not provide consistency because the ionized forms of acidic and basic functional groups lie on opposite sides of their respective equations.
Why Is Consistency Between Acids and Bases Important?
When using the Henderson-Hasselbalch equation, maintaining consistency between acidic
and basic functional groups eliminates confusion and allows the same equation to be used
regardless of the acid/base nature of the functional group. Although ionized/unionized designations can be used with the Henderson-Hasselbalch equation, this requires similar but
different equations depending on whether the functional group is an acid or a base. Adding an
additional step that requires the selection of the appropriate version of the equation is often
the root of mistakes on ionization questions.
Derivation of the Henderson-Hasselbalch Equation
To correctly understand and use the Henderson-Hasselbalch equation, it is important to review how
it is derived.
Step 1: Starting with Ka, the acid dissociate constant for an acid, substitute the terms Base Form
for A− and Acid Form for HA.
[H ][Base Form]
[AcidForm]
[H ][
=
K
a
or K[H]
+
[BaseForm]
[AcidForm]
Step 2: Take the log of each side of the equation.
[BaseForm]
[AcidForm]
[BaseForm]
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CH 4 - SOLVING pH AND pKa PROBLEMS 89
gK log[H] log
a
+
=+
Step 3: Rearrange the equation.
+
log[H] logK log
=− +
a
[AcidForm]
Step 4: Substituting the terms pH for –log [H+] and pKa for –log Ka gives the Henderson-
Hasselbalch equation.
pHpKlog
=+
a
[BaseForm]
[AcidForm]
Using the descriptors previously identified (i.e., Base Form = unprotonated form and Acid Form
= protonated form), the equation can alternatively be designated as shown here. Both representa-
tions of the Henderson-Hasselbalch equation are valid for both acidic and basic functional groups.
pHpKlog
=+
[UnprotonatedForm]
a
[ProtonatedForm]
Another form of the equation that compares the concentration of the ionized form to the concentration of the unionized form is often used; however, it often leads to erroneous calculations, and
the authors of this text highly discourage its use. The equation is shown below and is valid for monoprotic acidic functional groups such as the carboxylic acid shown in Figure 4-1. Because monoprotic
FIGURE 4-1.Equilibria for monoprotic acidic functional groups, diprotic acidic functional
groups, and basic functional groups.
90 BASIC CONCEPTS IN MEDICINAL CHEMISTRY
[Ionized Form]
[Unionized Form]
acids have only one proton capable of dissociation, the designations base form, unprotonated
form, and ionized form are all compatible, and any one of these could be used for the HendersonHasselbalch equation.
HpKlog
=+
a
[Unionized Form]
In the case of diprotic acids, such as the phosphate group shown in Figure 4-1, the use of this
equation can become problematic. This is because diprotic acids have two protons capable of dissociation and two pK
values. The use of ionized and unionized designations becomes very confusing
a
when evaluating an equilibrium between the mono-ionized and the di-ionized forms of a phosphate
group because both forms are ionized. Finally, since the pKa value of a basic functional group is determined by its conjugate acid (as discussed in Chapter 3), the ionized form of a basic functional group
lies on the opposite side of an equilibrium equation as compared with an acidic functional group. As
such, the following analogous version of the Henderson-Hasselbalch equation is required for basic
functional groups. Please note the presence of the negative log.
quationfor basicfunctionalgroupsONLY:pHpKlog
=−
a
[Ionized Form]
These last two equations using the ionized and unionized designations are presented here solely
for sake of completeness and are not used or mentioned in any subsequent sections of this or other
chapters. Although they are mathematically correct, their use is highly discouraged because they
can be confusing and can lead to erroneous calculations.
SOLVING pH AND pKa PROBLEMS
The Henderson-Hasselbalch equation can be used to solve a variety of pH/pKa problems. For medicinal chemistry, this equation is most commonly used to determine the percent ionization of one or
more functional groups present within the structure of a drug molecule. As mentioned previously,
there are two types of problems that you are likely to encounter: qualitative problems and quantitative problems. Qualitative problems seek to identify the most predominant form of the functional
group. In other words, is the functional group primarily ionized or primarily unionized? Quantitative
problems go one step further and seek to identify what percent of the functional group is ionized
and/or unionized.
Regardless of the type of problem, the initial goal is to identify the acidic and basic functional
groups for the structure in question and correctly assign any given pKa values. Questions provided
in this text do not require memorization or research of specific pKa values; however, it is strongly
encouraged that you be familiar with the general pKa ranges provided in Chapter 3.
Solving Qualitative pH and pKa Problems Using the
Henderson-Hasselbalch Equation
The overall goal for these types of problems is to determine whether a specific functional group is primarily ionized or primarily unionized in a given environment. Although the Henderson-Hasselbalch
equation can be used to solve these types of problems, it usually is not necessary. For the sake
of both comparison and completeness, let us first solve a sample problem using the HendersonHasselbalch equation.
CH 4 - SOLVING pH AND pKa PROBLEMS 91
[BaseForm]
m]
[AcidForm]
[BaseForm]
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Question: Captopril has a functional group with a pKa of 3.7. Will this functional group be primar-
ily ionized or primarily unionized in the urine at a pH of 5.9?
Analysis and Answer: The initial step is to match the given pKa value with the appropriate func-
tional group. In evaluating the structure, it is easy to identify that the pK
carboxylic acid. The remainder of the molecule consists of an amide, aliphatic and alicyclic hydrocarbons, and a thiol. While the aliphatic thiol is weakly acidic, its normal pKa range is between 10
and 11 and does not match a pK
of 3.7. The remaining functional groups, the hydrocarbons, and the
a
amide are neutral functional groups.
Inserting the given pH and pKa values into the Henderson-Hasselbalch equation gives the fol-
lowing equation:
value belongs to the
a
enderson-HasselbalchEquation:pHpKlog
=+
93.7 log
=+
[BaseFor
a
[AcidForm]
Rearranging the equation (i.e., subtracting 3.7 from each side of the equation) gives the following information, which is all that is required to determine if the functional group will be primarily
ionized or unionized.
=
2log
[AcidForm]
The fact that the number on the left has a positive value indicates that the base form (i.e., the
conjugate base of the carboxylic acid) is predominant. The question asks if the functional group will
be primarily ionized or primarily unionized at a urine pH of 5.9. Since the predominant form is the
conjugate base form of a carboxylic acid, the functional group is predominantly ionized.
As you work to become proficient in solving these types of problems, assigning the pKa value to
the appropriate functional group is an important initial step in this process. Let’s evaluate another
sample problem that emphasizes this key point. Shown below is the structure of procainamide.
92 BASIC CONCEPTS IN MEDICINAL CHEMISTRY
This drug has a functional group with a pKa of 9.2. Is this functional group primarily ionized or unionized at physiologic pH?
Only one pKa value is given in this problem; therefore, the first step is to match this pKa value
with the appropriate functional group. In evaluating the structure, you should be able to identify
three specific functional groups: an aromatic amine, an amide, and a tertiary amine. Because amides
are neither acidic nor basic (i.e., neutral), the pKa value must belong to either the aromatic amine or
the tertiary amine. As discussed in Chapter 3, aliphatic amines have a general pKa range of 9 to 11
while aromatic amines have a general pKa range of 2 to 5. Thus, the given pKa value of 9.2 must be a
property of the tertiary amine.
Key Point: To become proficient at solving these types of problems, it is strongly suggested
that this initial step be done prior to proceeding with the question. For the question involving procainamide, it is sufficient to know that the drug molecule is basic without identifying the most basic
functional group; however, other questions may require you to draw the most predominant form
(i.e., ionized or unionized) of the functional group or the drug molecule at a given pH. In this case,
it is essential that a thorough structural evaluation be conducted. Assigning the pKa value to either
the amide or the aromatic amine would result in the wrong ionized form being drawn. It is important
to develop good habits and thoroughly evaluate the functional groups within a given structure prior to
solving a pH/pKa problem.
Solving Qualitative pH and pKa Problems Without the
Henderson-Hasselbalch Equation
In most instances, it is possible to solve qualitative problems without using the HendersonHasselbalch equation and without using all of the steps previously outlined. While the principles
governing the Henderson-Hasselbalch equation are implicit within the method to be described, the
actual equation does not need to be used. To be consistent, let us return to the previous sample
problem involving captopril and examine it from a different perspective.
CH 4 - SOLVING pH AND pKa PROBLEMS 93
Y
0
Y
3
Y
3
Y
1
Y
Y
[BaseForm]
[AcidForm]
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For these types of problems, a structure, a pH, and a pKa are given. As before, it is first necessary
to correctly assign the pKa to the appropriate functional group and determine if the functional group
is acidic or basic. This has already been determined for this sample problem, so we can now move
to the second step, in which the pH is compared with the pKa. In doing this, one of three possible
scenarios arises. The pH will be less than the pKa, greater than the pKa, or equal to the pKa.
Math Review
The log of the ratio between two values, X and Y, can be greater than, less than, or equal to
zero. As examples, let us use the following three equations:
X
tion 1: log
tion 2: log
tion 3: log
Calculating the antilog of each side or each equation gives the following:
tion 1:
tion 2:
tion 3:
=
X
=+
0.
X
=−
0.
X
=
X
2=
X
0.5=
When each side of each equation is then multiplied by “Y,” the following relationships
are revealed:
Therefore:
• As shown with Equation 1, when the log of a ratio between X and Y is equal to zero,
then the values of X and Y are the same.
• As shown with Equation 2, when the log of a ratio between X and Y is greater than
zero, then the value of X is greater than the value of Y.
• As shown with Equation 3, when the log of a ratio between X and Y is less than zero,
then the value of X is less than the value of Y.
These relationships are directly applicable when using the Henderson-Hasselbalch equa-
tion and comparing pH and pK
values because the value of “pH − pKa” is greater than, less
a
than, or equal to zero.
HpKlog
−=
a
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