ChemCases.Com
Drug Pathways and Chemical Concepts

Prof. Sally Boudinot

8. Dissociation Constants

Please remember these concepts:

  1. 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.
  2. 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 constant.

Weak Acid Drug  + Water  <=>   H3O+ +  Weak Base Drug Anion-
      acid                base               conjugate acid            conjugate base         
Weak Base Drug  + Water  <=>   OH-  +  H+Weak Base Drug
      base                   acid              conjugate base            conjugate acid          

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.

Let’s take a look at our equation for the protolysis of water by an acidic drug.

HA  +H2O <==> H3O+ + A-

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 =   [A-][H3O+]/[HA]

where 55.53 is the number of moles of water per liter at 25°C.

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:

Acidic Drugs:
HA  +H2O <==> H3O+ + A-
ka kb* pka pkb*
Penicillin V 2.0x10-3 5.4x10-12 2.7 11.3
Acetylsalicylic Acid (Aspirin) 3.3x10-4 3.1x10-11 3.5 10.5
Ascorbic Acid (vitamin C) 5.0x10-5 2.0x10-10 4.3 9.7
Phenobarbital 3.9x10-8 2.6x10-7 7.4 6.6
Phenytoin (DilantinŽ) 7.9x10-9 1.3x10-6 8.1 5.9
Boric Acid 5.8x10-10 1.7x10-5 9.2 4.8
Zidovudine (AZT, RetrovirŽ) 2.0x10-10 5.0x10-5 9.7 4.3
Basic Drugs:
A + H2O <===> HA+ + OH-
       
Caffeine 2.5x10-4 4.0x10-11 3.6 10.4
Zalcitabine (ddC, HividŽ) 6.3x10-5 1.6x10--10 4.2 9.8
Theophylline (Theo-DurŽ) 3.4x10-6 1.6x10-9 5.2 8.8
Morphine 7.4x10-7 7.4x10-7 7.9 6.1
Erythromycin 2.0x10-9 6.3x10-6 8.8 5.2
Amphetamine 1.6x10-10 6.3x10-5 9.8 4.2


 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:

  • A weak acid or a weak base drug, in water, will disassociate to some extent.  The pH of the drug solution  will depend upon the pKa.

 

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Concept Map for this ChemCase

Case Study in Phenobarbitol
Or move on to
8a. The Henderson-Hasselbach Equation
13.  Drug Absorption/Effective Delivery
11.  Lab 1 - Determination of Dissociation Constant
12. Lab II: pH of Precipitation and the Henderson-Hasselbach
Equation
9.Calculations for Phenobarbital, the free acid
10.Calculations for Sodium Phenobarbital, the salt

 

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Prof. Sally Boudinot
College of Pharmacy
University of Georgia
Athens, GA
sallyb@rx.uga.edu