## Activity of ionised drugs

A large proportion of the drugs that are administered in aqueous solution are salts which, on dissociation, behave as electrolytes. Simple salts such as ephedrine hydrochloride (C6H5CH(OH)CH(NHCH3)CH3HCl) are 1:1 (or uni-univalent) electrolytes; that is, on dissociation each mole yields one cation, C6H5CH(OH)CH(N +H2CH3)CH3, and one anion, Cl0. Other salts are more complex in their ionisation behaviour; for example, ephedrine sulfate is a 1 : 2 electrolyte, each mole giving two moles of the cation and one mole of SO2- ions.

The activity of each ion is the product of its activity coefficient and its concentration, that is a+ = Y+m+ and a_ = y_

m using a theoretical method based on the Debye-Huckel theory. In this theory each ion is considered to be surrounded by an 'atmosphere' in which there is a slight excess of ions of opposite charge. The electrostatic energy due to this effect is related to the chemical potential of the ion to give a limiting expression for dilute solutions

The anion and cation may each have a different ionic activity in solution and it is not possible to determine individual ionic activities experimentally. It is therefore necessary to use combined terms, for example the combined activity term is the mean ionic activity, a&. Similarly, we have the mean ion activity coefficient, y&, and the mean ionic molality, m&. The relationship between the mean ionic parameters is then where z+ and z_ are the valencies of the ions, A is a constant whose value is determined by the dielectric constant of the solvent and the temperature (A = 0.509 in water at 298 K), and I is the total ionic strength defined by

where the summation is continued over all the different species in solution. It can readily be shown from equation (3.37) that for a 1:1 electrolyte the ionic strength is equal to its molality; for a 1:2 electrolyte I = 3m; and for a 2 : 2 electrolyte, I = 4m.

The Debye-Huckel expression as given by equation (3.36) is valid only in dilute solution (I < 0.02 mol kg1). At higher concentrations a modified expression has been proposed:

where ai is the mean distance of approach of the ions or the mean effective ionic diameter, and p is a constant whose value depends on the solvent and temperature. As an approximation, the product ai p may be taken to be unity, thus simplifying the equation. Equation (3.38) is valid for I less than 0.1 mol kg 1

More details of these combined terms are given in Box 3.4.

Values of the mean ion activity coefficient may be determined experimentally using several methods, including electromotive force measurement, solubility determinations and colligative properties. It is possible, however, to calculate Y& in very dilute solution

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