09_1439PP_CH03 17/10/05 10:47 pm Page 55 3 Physicochemical properties of drugs in solution 3.1 Concentration units 56 3.5 Ionisation of drugs in solution 75 3.2 Thermodynamics – a brief 3.6 Diffusion of drugs in solution 89 introduction 57 Summary 90 3.3 Activity and chemical potential 62 References 91 3.4 Osmotic properties of drug solutions 69 In this chapter we examine some of the important physicochemical properties of drugs in aqueous solution which are of relevance to such liquid dosage forms as injections, solutions, and eye drops. Some basic thermodynamic concepts will be introduced, particularly that of thermo- dynamic activity, an important parameter in determining drug potency. It is important that parenteral solutions are formulated with osmotic pressure similar to that of blood serum; in this chapter we will see how to adjust the tonicity of the formulation to achieve this aim. Most drugs are at least partially ionised at physiological pH and many studies have suggested that the charged group is essential for biological activity. We look at the influence of pH on the ionisation of several types of drug in solution and consider equations that allow the calculation of the pH of solutions of these drugs. First, however, we recount the various ways to express the strength of a solution, since it is of fundamental importance that we are able to interpret the various units used to denote solution concentration and to understand their interrelationships, not least in practice situations. Physicochemical Principles of Pharmacy, 4th edition (ISBN: 0 85369 608 X) © Pharmaceutical Press 2006 09_1439PP_CH03 17/10/05 10:47 pm Page 56 3.1 Concentration units is an accepted SI unit. Molarity may be con- verted to SI units using the relationship 1 mol litre 01 # 1 mol dm 03 # 10 3 mol m 03. A wide range of units is commonly used to Interconversion between molarity and molal- express solution concentration, and confusion ity requires a knowledge of the density of the often arises in the interconversion of one solution. set of units to another. Wherever possible Of the two units, molality is preferable for a throughout this book we have used the SI precise expression of concentration because it system of units. Although this is the currently does not depend on the solution temperature recommended system of units in Great as does molarity; also, the molality of a com- Britain, other more traditional systems are still ponent in a solution remains unaltered by the widely used and these will be also described in addition of a second solute, whereas the this section. molarity of this component decreases because the total volume of solution increases follow- ing the addition of the second solute. 3.1.1 Weight concentration Concentration is often expressed as a weight of solute in a unit volume of solution; for 3.1.3 Milliequivalents example, g dm03, or % wv, which is the number of grams of solute in 100 cm3 of solu- The unit milliequivalent (mEq) is commonly tion. This is not an exact method when used clinically in expressing the concentration working at a range of temperatures, since of an ion in solution. The term ‘equivalent’, or the volume of the solution is temperature- gram equivalent weight, is analogous to the dependent and hence the weight concentra- mole or gram molecular weight. When tion also changes with temperature. monovalent ions are considered, these two Whenever a hydrated compound is used, terms are identical. A 1 molar solution of it is important to use the correct state of sodium bicarbonate, NaHCO3, contains 1 mol ! − or 1 Eq of Na and 1 mol or 1 Eq of HCO3 per hydration in the calculation of weight litre (dm03) of solution. With multivalent concentration. Thus 10% w v CaCl2 (anhy- drous) is approximately equivalent to 20% wv ions, attention must be paid to the valency of CaCl ·6H O and consequently the use of the each ion; for example, 10% w v CaCl2·2H2 O 2 2 2! vague statement ‘10% calcium chloride’ could contains 6.8 mmol or 13.6 mEq of Ca in 3 result in gross error. The SI unit of weight 10 cm . 1 concentration is kg m03 which is numerically The Pharmaceutical Codex gives a table of equal to g dm03. milliequivalents for various ions and also a simple formula for the calculation of milli- equivalents per litre (see Box 3.1). 3.1.2 Molarity and molality In analytical chemistry a solution which contains 1 Eq dm03 is referred to as a normal These two similar-sounding terms must not be solution. Unfortunately the term ‘normal’ is confused. The molarity of a solution is the also used to mean physiologically normal with number of moles (gram molecular weights) of reference to saline solution. In this usage, a solute in 1 litre (1 dm3) of solution. The molal- physiologically normal saline solution con- ity is the number of moles of solute in 1 kg of tains 0.9 g NaCl in 100 cm3 aqueous solution solvent. Molality has the unit, mol kg01, which and not 1 equivalent (58.44 g) per litre. Physicochemical Principles of Pharmacy, 4th edition (ISBN: 0 85369 608 X) © Pharmaceutical Press 2006 09_1439PP_CH03 17/10/05 10:47 pm Page 57 Thermodynamics – a brief introduction 57 (b) 9 g of sodium chloride are dissolved in Box 3.1 Calculation of milliequivalents 991 g of water (assuming density # 1gdm03). The number of milliequivalents in 1 g of substance is Therefore 1000 g of water contains 9.08 g of given by sodium chloride # 0.155 moles, i.e. molality # valency x 1000 x no. of specified 0.155 mol kg01. units in 1 atom/molecule/ion mEq = (c) Mole fraction of sodium chloride, x , is atomic, molecular or ionic weight 1 given by For example, CaCl2·2H2 O (mol. wt. # 147.0) n1 0.154 − 2 × 1000 × 1 x = = = × 3 2+ = 1 2.79 10 mEq Ca in 1 g CaCl2 · 2H2 O n + n 0.154 + 55.06 147.0 1 2 = 13.6 mEq (Note 991 g of water contains 99118 and moles, i.e. n2 # 55.06.) ! × × (d) Since Na is monovalent, the number of − 1 1000 2 ! mEq Cl in 1 g CaCl · 2H O = milliequivalents of Na # number of milli- 2 2 147.0 moles. = 13.6 mEq 03 that is, each gram of CaCl ·2H O represents 13.6 mEq Therefore the solution contains 154 mEq dm 2 2 ! of calcium and 13.6 mEq of chloride of Na . 3.1.4 Mole fraction 3.2 Thermodynamics – a brief introduction The mole fraction of a component of a solu- tion is the number of moles of that com- The importance of thermodynamics in the ponent divided by the total number of moles pharmaceutical sciences is apparent when it is present in solution. In a two-component realised that such processes as the partitioning (binary) solution, the mole fraction of solvent, of solutes between immiscible solvents, the # ! x1, is given by x1 n1 (n1 n2), where n1 and solubility of drugs, micellisation and drug– n2 are respectively the numbers of moles of receptor interaction can all be treated in solvent and of solute present in solution. thermodynamic terms. This brief section Similarly, the mole fraction of solute, x2, is merely introduces some of the concepts of # ! given by x2 n2 (n1 n2). The sum of the thermodynamics which are referred to through- mole fractions of all components is, of course, out the book. Readers requiring a greater ! # unity, i.e. for a binary solution, x1 x2 1. depth of treatment should consult standard texts on this subject.2, 3 EXAMPLE 3.1 Units of concentration Isotonic saline contains 0.9% wv of sodium 3.2.1 Energy chloride (mol. wt. # 58.5). Express the concen- tration of this solution as: (a) molarity; (b) Energy is a fundamental property of a system. molality; (c) mole fraction and (d) milliequiv- Some idea of its importance may be gained by alents of Na! per litre. Assume that the density considering its role in chemical reactions, of isotonic saline is 1 g cm03. where it determines what reactions may occur, how fast the reaction may proceed and in Answer which direction the reaction will occur. (a) 0.9% wv solution of sodium chloride Energy takes several forms: kinetic energy is contains 9 g dm03 # 0.154 mol dm03. that which a body possesses as a result of its Physicochemical Principles of Pharmacy, 4th edition (ISBN: 0 85369 608 X) © Pharmaceutical Press 2006 09_1439PP_CH03 17/10/05 10:47 pm Page 58 58 Chapter 3 • Physicochemical properties of drugs in solution motion; potential energy is the energy which changes in heat energy, which were not a body has due to its position, whether gravi- encompassed in the conservation law. tational potential energy or coulombic poten- It follows from equation (3.2) that a system tial energy which is associated with charged which is completely isolated from its sur- particles at a given distance apart. All forms of roundings, such that it cannot exchange heat energy are related, but in converting between or interact mechanically to do work, cannot the various types it is not possible to create or experience any change in its internal energy. destroy energy. This forms the basis of the law In other words the internal energy of an isolated of conservation of energy. system is constant – this is the first law of The internal energy U of a system is the sum thermodynamics. of all the kinetic and potential energy contri- butions to the energy of all the atoms, ions and molecules in that system.