|8. Dissociation Constants
Please remember these concepts:
- Many processes can be at equilibrium.
But with changes in condition - concentration, temperature - the system will no
longer be at equilibrium and will adjust to try to get there again.
- The equilibrium concentrations of H3O+ and OH- are vanishingly small in pure water.
The dissociation constant is one of the most important
characteristics of a pharmaceutical compound. It is important to understand both how it is
calculated, and its significance. We will first concentrate on the basics: calculations
using the dissociation constant.
We saw a list of some drugs that are weak
acids or bases. Many additional drugs are weak acids or weak bases and like acetic
acid or like ammonia, they react with water to form conjugate pairs as we show below.
These are dissociation equations and the mathematical
expression of the extent of dissociation is called the dissociation
|Weak Acid Drug + Water <=> H3O+
+ Weak Base Drug Anion-
acid conjugate base
|Weak Base Drug + Water <=> OH-
+ H+Weak Base Drug
conjugate base conjugate
Proton transfer exists not only with water, but
occurs for all electrolytes that are in solution. We will concentrate our efforts mostly
on aqueous solutions, because water is the most desirable solvent for pharmaceutical
solutions. The dissociation constant is sometimes called the acidity constant or the
ionization constant. It is a numeric representative of the relative proton transfer for
that substance, or the likelihood of that compound donating a proton. It is calculated in
the same fashion as the equilibrium constant.
Drug pharmaceutics and the determination of useful dosage forms and
regimes for drugs depends upon an understanding of drug dissociation and the extent of
dissociation that will occur in the systems of the body. The dissociation constant
is one of the most important characteristics of a pharmaceutical compound. It is important
to understand both how it is calculated, and its significance. We will first concentrate
on the basics: calculations using the dissociation constant.
The dissociation constant is sometimes called the acidity
constant or the ionization constant. It is a numeric representative of the
relative proton transfer for that substance, or the likelihood of that compound donating a
proton. It is calculated in the same fashion as the equilibrium constant.
Lets take a look at our equation for the
protolysis of water by an acidic drug.
HA +H2O <==> H3O+
At equilibrium, the velocity of the reaction proceeding
to the ionized components (k1) is equal to the
velocity of the reaction resulting in the unionized HA and H2O (k2).
(k1) = [HA][H2O]
(k2) = [H3O+][A-]
Most drugs are weak acids and bases. They ionize only
slightly in the presence of water. That being the case, the concentration of water in the
above equation maybe taken as a constant, allowing us to rearrange the equation to yield:
ka = k2(55.53)/k1 =
where 55.53 is the number of moles of water per liter
This value, ka, gives us numeric value to express the
degree to which a compound ionizes, or dissociates, in aqueous solution. This dissociation
constant is an important characteristic of drug molecules, and provides a tool to
anticipate some of the "behaviors" of that compound. Dissociation constants are
determined by experimental data, and are unique to each molecule. Conductivity, freezing
point depression, pH of solution, and spectrophotometric data may be used to determine a
compound's dissociation constant.
What does the value of a dissociation constant mean?
The numeric value gives an indication of the degree to which the electrolyte will
dissociate, so acids with large ionization constants (ka) are more likely to ionize in
aqueous solution. Conversely, acids with smaller dissociation constants are less likely to
ionize. The order of magnitude is a good predictor of acid strength. Acetaminophen is an
acidic drug with a ka of 1.2x10-10, and is thus much less likely to ionize in aqueous
solution than aspirin (acetyl salicylic acid) which has a ka of 3.27x10-4. Be aware that
the numeric value is of far less importance than the exponent!
Often it is cumbersome to deal with exponential forms,
so another expression of a compound's acid strength may be used. The pka may be used to
describe the tendency of a weak acid to ionize. The following equation should be used to
calculate the pka of a substance.
pka = -log [A-][H3O+]/[HA]
Note the relationship to pKa and acid strength: The
smaller the pKa, the stronger the acid. It is just theopposite of the relationship to the
ka. Another point that should be made is that acids and bases have both ka and kb,
pka and pkb values. If you remember the equations, you can calculate one value if the
other is known.
Let's look at some examples of acidic and basic drugs:
HA +H2O <==> H3O+ + A-
|Acetylsalicylic Acid (Aspirin)
|Ascorbic Acid (vitamin C)
|Zidovudine (AZT, RetrovirŽ)
A + H2O <===> HA+ + OH-
|Zalcitabine (ddC, HividŽ)
It is clear by these examples that acidic and basic drugs may have pka values within
the same range. This is often quite confusing. It might help to remember that the ka and
pka represent the likelihood of a substance to ionize, not whether or not hydrogen ions
will be liberated when it does.
The pH, however, represents the hydronium concentration
in solution when the compound DOES
ionize. That is the way we can tell if a drug is an acid or a base!
Something to remember: