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Acid-Base Properties of Drugs
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The Henderson-Hasselbach Equation
The use of conjugate acid/conjugate base terminology is expedient for the purpose of deriving a most useful equation in
pharmacology: the Henderson-Hasselbach equation.
A brief review of math principles regarding logarithms is in order:
The logarithm of the product of two numbers equals the sum of the logarithm of each number:
Log (a)*(b) = log a + log b
The logarithm of the quotient of two numbers equals the logarithm of the numerator minus the logarithm of the denominator:
Log (a)/(b) = log a - log b
Therefore:
Log (a)(b)/(c) = log a + log b - log c
Consider the general acid-base reaction in aqueous solution:
Eq.2.20.
Where CA is the "acidic form", or " protonated form" of any given drug, and CB is the "basic form ", or
"deprotonated form" of any given drug.
The pertinent equilibrium expression for the above reaction is:
Eq.2.21.
Taking the logarithm on both sides of the equation we obtain:
Log Ka = log [H + ][CB] /[CA]
or
Log Ka = log [H + ] + log [CB] - log [CA]
Multiplying both sides of the equation by -1 we obtain:
-log Ka = -log [H+ ] - log [CB] + log [CA]
Substituting "–log" by its equivalent, "p":
pKa = pH + log [CA] - log [CB]
And finally, combining logarithm parts of this equation we obtain the Henderson-Hasselbach equation:
Eq.2.22.
This equation can be used substituting equivalent terms for CA and/or CB, protonated/deprotonated form,
ionized/deionized forms. For example, another useful way of expressing the Henderson-Hasselbach equation is as follows
(Eq.23. and Eq.24):
For acids and bases:
Eq.2.23.
For acids:
Eq.2.24.
For bases:
Eq.2.25.
Please note the terminology used here and understand which of them are equivalent for acid-base reactions in aqueous
solutions:
CA= acidic form = protonated form = ionized form (if drug is a base that acquired a proton, BH+ )
CA= acidic form = protonated form = unionized form (if drug is an acid that has not yet donated its proton, HA)
CB= basic form = deprotonated form = ionized form (if drug is an acid that donated its proton, A - )
CB= basic form = deprotonated form = unionized form (if drug is a base that has not yet accepted a proton, B)
In summary, while CA is always the protonated form and CB is always the deprotonated form,
whether CA or CB will be an ionized or unionized species will depend on whether the original drug
molecule was an acid or a base to begin with.
You need to know which functional groups in drug molecules confer acidity or basicity, i.e., which functional groups in a
molecule are ionizable.
Write the reaction and equilibrium expression for the dissolution of chlorthiazide and pyrimethamine
in water.
Check your answer
The antimalarial drug pyrimethamine can be used to illustrate the effect of the ionization processes we have been
discussing on the distribution of drugs among different compartments in the body.
The urine typically has a pH of 6.0 while the blood has a pH of 7.4. Distribution of pyrimethamine between urine and
blood is illustrated in Fig.2.10.
Fig.2.10. A weak base like pyrimethamine is trapped in the urine when the latter
is more acidic than the blood. The diffusible uncharged form of the drug
equilibrates across the membrane, however, the total concentration (charged plus
uncharged) in the urine is almost eight times higher than in the blood.
Fig.2.10. shows a hypothetical equilibration of pyrimethamine across the renal tubule (nephron), with a concentration of
1 µM. The acid -base equilibrium for this drug (Fig.2.9.; Eq.2.28. see the Answer to previous Activity) will be established
on both sides of the membrane.
A weak base like pyrimethamine (pKa = 7.0) is trapped in the urine because at a pH of 6 (lower than its pKa) the
protonated, ionized form predominates, and the total concentration of both species is higher in the urine (11.0 µM) than
in the blood (1.4 µM). Therefore, if the goal is to enhance the excretion of pyrimethamine, one would administer an urine
acidifier, since lowering the pH in the urine will shift even further the equilibrium towards the ionized, water soluble form
of the drug. In the case of pyrimethamine, using the concentration values given in Fig.2.10. for the HendersonHasselbach equation, we obtain (in the urine):
pKa = 6 + log[protonated form]/[deprotonated form] = 7.0
log[protonated form]/[deprotonated form] = 1.0
[protonated form]/[deprotonated form] = 10 = [ionized form]/[unionized form]
This result tells us that for every 1 unionized pyrimethamine species in the urine, there are 10 ionized species.
A similar process for the equilibrium in the blood compartment yields the following:
pKa = 7.4 + log[protonated form]/[deprotonated form] = 7.0
log[protonated form]/[deprotonated form] = 7.0 – 7.4 = -0.4
[protonated form]/[deprotonated form] = 10 -0.4 = 0.398 = [ionized form]/[unionized form]
This result tells us that for every 1 unionized pyrimethamine species in the urine, there are 0.4 ionized species.
A similar partitioning process takes place among body compartments that differ in pH from that of the blood (~7.4). A list
of pH values in various body compartments is shown in Table 2.4.:
The principles discussed above for pyrimethamine apply to all weak bases:
Renal excretion of a weak base is enhanced by acidifying the urine.
On the other hand, the opposite is true of weak acids:
Renal excretion of a weak acid is enhanced by basifying the urine.
These statements are easily understood by a mathematical examination of the Henderson-Hasselbach equation, coupled
with an understanding of the acid-base properties of any given drug under consideration.
One of the most important application of the Henderson-Hasselbach equation is the manipulation of drug excretion by the
kidney. Virtually all drugs are filtered at the glomerulus, and if the drug is present mainly in the lipid-soluble non -ionized
form when it passes by the renal tubule, a significant fraction will be reabsorbed by passive diffusion. If the goal is to
enhance excretion of the drug, one must prevent its reabsorption from the renal tubules.
A list of common drugs that are weak acids or weak bases is given in Table 2.5.
It is important to note that the Henderson-Hasselbach equation expresses a relationship between the compartment pH
(not the drug’s), which is known for most body compartments, the drug’s pKa, which can be measured in the laboratory,
and provides the ratio of acidic and basic conjugates of the drug. The diagram below shows how the pH influences the
relative proportion of ionized and unionized forms of acidic and basic drugs.
Fig.2.7c.
Considering a hypothetical drug with a pKa of 8, at pHs lower than the pKa the protonated forms BH+ and HA
predominate, while at pHs higher than the pKa the unprotonated forms B and A - predominate. It is good to double check
any calculation using the Henderson-Hasselbach equation against this mental picture of what species, CA or CB, should in
larger proportion at any given pH under consideration.
In a later chapter we will discuss at greater length the effect of pKa and compartment pH on the distribution and
excretion of drugs.
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Last revised: 09/12/2003 15:45:09
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