|8a. The Henderson-Hasselbach
Equation: A practical application
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.
- A weak acid or a weak base drug, in water,
will disassociate to some extent. The pH of the drug solution will depend upon
Let's begin our discussion of the Henderson-Hasselbach Equation with
a continuation of the dissociation constant derivation.
should be a familiar relationship . If we rearrange our
equation to provide the [H3O+] on the left side, we get
[H3O+] = Ka
(Notice that the ionized species of the acid is now
in the denominator.)
Taking the negative log of both sides gives us easier numeric values
to work with:
which can be rewritten
or more familiarly
This equation is one of the most valuable relationships described
for the student or practitioner of the pharmaceutical sciences.
Consider the concepts at the top of the page. If:
- H3O+ is
exceedingly small and
- systems adjust when changes occur and
- drugs produce or consume hydronium ions to give acidic or basic
then if we took drugs into our bodies and the fluids there were just
water, we would dramatically change the acidity of our bodies. And that's not good.
But biological systems are not pure water. Our fluids contain
other weak acids and bases that are present in rather high concentrations just
to adjust to the influxes of acids and bases and keep the pH approximately the same.
These weak acid and bases systems are called buffers.
Weak Acid + Water
<=> H3O+ + Weak Acid Anion-
Please look at the equation above. Suppose we
put .05M of this weak acid in water along with .05M of its salt. The system will
first equilibtrate and the concentrations of both acid and anion will change and the
system will reach a pH dependent upon the pKa. This combination of a weak acid and its anion or a weak base and its
protonated conjugate acid is the buffer.
If we add a small amount of drug to this buffered solution, the acid
produced by the ionization of the drug plays a role in a new equilibrium - one in which
the acid generated is a disruption to the buffer equilibrium. The additional acid
forces the buffer reaction in the direction that consumes acid and thus keeps the pH from
rising nearly as much as without the presence of the buffer.
We are buffered to pH=~7.4 in the blood and to various other pH
values in the rest of our systems. When we add the drug molecules, the pH does not
change significantly in the presence of buffers. Thus we can use the
Henderson-Hasselbach equation to determine important ratios of ionized to unionized
species by assuming the system pH does not change. This is a useful, good
approoximation - and approximations are with us all the time in science!
Drugs, most of which are weak organic acids and bases, are exposed
to biologic membranes in solution. Or drugs are dispersed in aqueous environments at
varying pH's, depending on the anatomy and physiology of that environment. Drugs are
administered usually in a buffered system. Biochemical reactions take place within the
very tightly buffered (in normal, healthy circumstances) environments. Th pH of the
solution indicates the concentration of the hydronium ion at that site, and will influence
the likelihood that a species will be found predominantly in the ionized form or the
unionized form. Its application is the basis for the ability that pharmaceuticists have to
predict drug absorption from the gastrointestinal tract. Use of the Henderson-Hasselbach
equation enables the calculation of the pH of stable drug solutions for the effective
administration of drugs. And its use provides a method of calculating pka.
One example of the implementation of the Henderson-Hasselbach
equation is in intravenous admixture solutions. Often a hospitalized patient is
administered drugs intravenously. This route of administration may be desirable for a
number of reasons. Intravenous drug administration eliminates the absorption phase that is
required of oral dosage forms. The drug is placed immediately in the systemic absorption,
often producing very rapid action. Some drugs are simply not suitable for other routes of
There are many factors to consider when administering a drug
intravenously. Not only does the physical and chemical characteristics of a drug molecule
play a role, but patient and disease related factors also influence iv drug
administration. A clinician must decide upon a fluid in which to administer the drug, and
the volume that should be administered. These factors, of course, influence the
concentration of the ionized and unionized drug in solution and whether or not the drug
will remain in solution or precipitate. The influence of all of these factors may be
predicted by the Henderson-Hasselbach equation.
|Let's look at an example.
Phenytoin is a drug (used an example on the dissociation
constant page) that is used to treat epilepsy. It is an acidic drug, and could be used
for intravenous administration to treat status epilepticus, or severe,
life-threatening seizures. The pKa of phenytoin is 8.1. Phenytoin must be
administered slowly, at a rate of 50 mg/min. For ease of administration, it would be
desirable to dilute the phenytoin sodium solution with a bag of intravenous fluid, and
adjust the rate of flow with an automated system. But most large volume parenteral
solutions are acidic within the range of 3.5-7. So at that pH, the unionized form of the
drug would predominate, and the Henderson-Hasselbach equation shows us how:
Substituting our values , assuming 4.5 is an average pH
for intravenous solutions, we get:
Solving we get :
which gives a ration of ionized to unionized drug of:
Stated differently, there is one part ionized phenytoin
for every 3981 parts unionized phenytoin.
The unionized species is water insoluble, and
thus will precipitate in this acidic environment.
One caveat: The concentrations of the species in
solution, by definition, are in molar concentration terms. Thus it is conceivable to
increase the volume of solution administered to increase the solubility. But in reality,
that is not a practical solution, as administration of large volumes of parenteral
solutions could create other problems for the patient.
Pharmaceuticists and practicing pharmacists, then,
must have an understanding of acid/base chemistry in order to decide the pH at which to
prepare solutions for the most stable dosage form. Thousands of references document the
importance of this phenomenon in intravenous admixtures.
Something to remember:
- Buffers stabilize pH. This stabilized
acidity determines the form of drug disassociation in systems. The
Henderson-Hasselbach equation conveniently handles drug ionization questions for buffered
systems like the body.