Henderson Hasselbach Equation

At a given temperature the thermodynamic ionization constants are independent of concentration, and at a pH value equal to pKa the activity of ionized and neutral forms is equal. In many measurement techniques we measure concentration rather than activity, such as in the use of spectroscopic methods. In such instance:

where values in brackets are observed concentration from spectroscopic measurements based on the Beer-Lambert law. The "Thermodynamic" Ionization Coefficient is related to the "Concentration" Ionization Coefficient by:

FIGURE 1 Typical Bransted acids and their conjugate bases.

where f is the activity coefficient.

The pKa values are also temperature dependent, often in a nonlinear and unpredictable way. Samples measured by potentiometry are therefore held at a constant temperature bath and therefore pKa value should be quoted at a specific temperature. Often a temperature of 25°C is chosen to reflect room temperature whereas this may be quite different from the body temperature.

The Henderson-Hasselbach equation defines the relationship between ionization and pH; it is understood in equation (3). This equation relates the pKa to the pH of the solution and the relative concentrations of the dissociated and undissociated parts of a weak acid:

where [A] is the concentration of the dissociated species and [HA] is the concentration of the undissociated species. This equation can be manipulated into the form given by equation (4) to yield the percentage of a compound that will be ionized at any particular pH.

One simple point to note about equation (5) is that 50% dissociation (or ionization) pKa = pH. It should also be noted that, usually, piCa values are preferred for bases instead of pKb values (piCw = pKa + pKb). As a result, the extent of ionization of a compound will depend on the pH of medium. Figure 2 shows pH values of common fluids.

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