Pharmaceutics: The Science of
`Dosage Form Design
`
`EDITED BY
`Michael E. Aulton BPharm PhD MPS
`
`Reader in Pharmacy, Leicester Polytechnic, Leicester, UK
`
`CHURCHILL LIVINGSTONE
`EDINBURGH LONDON MELBOURNE AND NEW YORK 1988
`
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`

`
`PRy OF CON%
`trcp\
`5 (cid:9)
`NOV 2 5 1987
`coPY
`—.
`C1P
`
`CHURCHILL LIVINGSTONE
`Medical Division of Longman Group UK Limited
`Distributed in the United States of America by
`Churchill Livingstone Inc., 1560 Broadway, New
`York, N.Y. 10036, and by associated companies,
`branches and representatives throughout the world.
`
`C) Michael Aulton 1988
`
`All rights reserved. No part of this publication may
`be reproduced, stored in a retrieval system, or
`transmitted in any form or by any means, electronic,
`mechanical, photocopying, recording or otherwise,
`without the prior permission of the publishers
`(Churchill Livingstone, Robert Stevenson House, 1-3
`Baxter's Place, Leith Walk, Edinburgh EH1 3AF).
`
`First published 1988
`
`ISBN 0-443-03643-8
`
`British Library Cataloguing in Publication Data
`Pharmaceutics: the science of dosage form
`design.
`1. Pharmaceutics
`I. Aulton, Michael E.
`615'.19 (cid:9)
`RS403
`
`Library of Congress Cataloging in Publication Data
`Pharmaceutics: the science of dosage form design.
`Replaces: Cooper and Gunn's tutorial pharmacy.
`6th ed. 1972.
`Includes bibliographies and index.
`1. Drugs — Design of delivery systems. 2. Drugs
`— Dosage forms. 3. Biopharmaceutics.
`4. Pharmaceutical technology. 5. Chemistry,
`Pharmaceutical. 6. Microbiology, Pharmaceutical.
`I. Aulton, Michael E.
`[DNLM: 1. Biopharmaceutics. 2. Chemistry,
`Pharmaceutical. 3. Dosage Forms. 4. Technology,
`Pharmaceutical. 5. Microbiology, Pharmaceutical.
`QV 785 P5366]
``1'46--1.9rr
`
`615.5'8 86-25888
`
`Produced by Longman Group (FE) Ltd
`Printed in Hong Kong
`
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`
`Preface
`
`The, first edition of Pharmaceutics has replaced the
`6th edition of Cooper and Gunn's Tutorial Phar-
`macy published by Pitman in 1972. Since then,
`there has been a change in editorship, a change
`in the title of the book, a change in some of the
`authors and a completely redesigned content. But
`all is not new and disjointed, the editorial link
`with Leicester School of Pharmacy continues.
`Sidney Carter recently retired as Deputy Head of
`Leicester School of Pharmacy and passed on the
`book to me. He in turn had inherited the book
`from one of its founders, the late Colin Gunn who
`was formerly Head of Leicester School of Phar-
`macy but sadly died on 25 February 1983.
`There are a greater number and a wider range
`of authors in this edition, each an accepted expert
`in the field on which they have written and, just
`as important, each has experience and ability in
`imparting that information to undergraduate phar-
`macy students.
`
`The philosophy of the subject matter which the
`book covers has changed because pharmaceutics
`has changed. Since the last edition of Tutorial
`Pharmacy there have been very marked changes
`in the concept and content of pharmaceutics.
`Those changes are reflected in this edition. The
`era of biopharmaceutics was in its infancy at the
`time of the previous edition. Since then we have
`become increasingly concerned with not merely
`producing elegant and accurate dosage forms but
`also ensuring that the optimum amount of drug
`reaches the required place in the body and stays
`there for the optimum amount of time, Now we
`are concerned much more with designing dosage
`forms and with all aspects of drug delivery. This
`book reflects that concern.
`
`Dr M E Aulton
`School of Pharmacy
`Leicester Polytechnic
`
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`3 (cid:9)
`
`H Richards
`
`Solutions and their properties
`
`DEFINITION OF TERMS
`Methods of expressing concentration
`Quantity per quantity
`Percentage
`Parts
`Molarity
`Molality
`Mole fraction
`Milliequivalents and normal solutions
`
`TYPES OF SOLUTION
`Vapour pressures of solids, liquids and
`solutions
`Ideal solutions; Raoult's law
`Real or non-ideal solutions
`
`IONIZATION OF SOLUTES
`Hydrogen ion concentration and pH
`Dissociation (or ionization) constants and,pKa
`Buffer solutions and buffer capacity
`
`COLLIGATIVE PROPERTIES
`Osmotic pressure
`Osmolality and osmolarity
`I so-osmotic solutions
`Isotonic solutions
`
`DIFFUSION IN SOLUTION
`
`38
`
`The main aim of this chapter and Chapter 5 is to
`provide information on certain physicochemical
`principles that relate to the applications and
`implications of solutions in pharmacy. For the
`purposes of the present discussion these principles
`have . been classified in a somewhat arbitrary
`manner. Thus, this chapter deals mainly with the
`physicochemical properties of solutions that are
`important with respect to systems and processes
`described in other parts of this book or in the
`companion volume, Dispensing 'for. Pharmaceutical
`Students by Carter (1975) (new edition in prep-
`aration). Chapter 5 on the other hand is concerned
`with the principles underlying the formation of
`solutions and the factors that affect the rate and
`extent of this dissolution process. Because of
`limitations of space and the number of principles
`and properties that need to be considered the
`contents of each of these chapters should only be
`regarded as introductions to the various topics.
`The student is encouraged, therefore, to refer to
`the bibliography cited at the end of each chapter
`in order to augment the present contents. The
`textbook written by Florence and Attwood (1981)
`is recommended particularly, because of the large
`number of pharmaceutical examples that are used
`to aid understanding of physicochemical
`principles.
`
`DEFINITION OF TERMS
`
`A solution may be defined as a mixture of two or
`more components that form a single phase, which
`is homogeneous down to the molecular level. The
`component that determines the phase of the
`solution is termed the solvent and usually consti-
`
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`tutes the largest proportion of the system. The
`other components are termed solutes and these are
`dispersed as molecules or ions throughout the
`solvent; i.e. they are said to be dissolved in the
`solvent. The extent to which the dissolution
`proceeds under a given set of experilnental
`conditions is referred to as the solubility of the
`solute in the solvent. Thus, the solubility of a
`substance is the amount of it that passes into
`solution when an equilibrium is established
`between the solution and excess, i.e. undissolved,
`substance. The solution that is obtained under
`these conditions is said to be saturated. Since the
`above definitions are general ones they may be
`applied to all types of solution. However, when
`the two components forming a solution are either
`both gases or both liquids then it is more usual
`to talk in terms of miscibility rather than
`solubility.
`
`Methods of expressing concentration
`Quantity per quantity
`
`Concentrations are often expressed simply as the
`weight or volume of solute that is contained in a
`given weight or volume of the solution. The
`majority of solutions encountered in pharmaceuti-
`cal practice consist of solids dissolved in liquids.
`Consequently, concentration is expressed most
`commonly by the weight of solute contained in a
`given volume of solution. Although the SI unit is
`kg rn-3 the terms that are used in practice are
`based on more convenient or appropriate weights
`and volumes. For example, in the case of a
`solution with a concentration of 1 kg m-3 the
`strength may be denoted by any one of the
`following concentration terms depending on the
`circumstances:
`1 g 1-1, 0.1 g per 100 ml, 1 mg ml-', 5 mg in 5 ml
`or 1 µg (cid:9)
`_
`
`Percentage
`
`The British and European Pharmacopoeias use the
`same method as a basis for their percentage
`expressions of the strengths of solutions. For
`example, the concentration of a solution of a solid
`in a liquid would be given by
`
`SOLUTIONS AND THEIR PROPERTIES 39
`concentration -= weight of solute
`in % w/v (cid:9)
`volume of solution X 100
`
`Per cent v/w, % v/v and % w/w expressions are
`also referred to in the General Notices of the British
`Pharmacopoeia (1980) together with the statement
`that the latter two expressions are used for
`solutions of liquids in liquids and solutions of
`gases in liquids, respectively.
`It should be realized that if concentration is
`expressed in terms of weight of solute in a given
`volume of solution then changes in volume caused
`by temperature fluctuations will alter the
`concentration.
`
`Parts
`
`The Pharmacopoeia also expresses some concen-
`trations in terms of the number of 'parts' of solute
`dissolved in a stated number of 'parts' of solution.
`Use of this method to describe the strength of a
`solution of a solid in a liquid infers that a given
`number of parts by volume (ml) of solution
`contain a certain number of parts by weight (g)
`of solid. In the case of solutions of liquids in
`liquids parts by volume of solute in parts by
`volume of solution are intended whereas with
`solutions of gases in liquids parts by weight of gas
`in parts by weight of solution are inferred.
`
`Molarity
`
`This is the number of moles of solute contained
`in 1 dm3 (or, more commonly in pharmacy, 1
`litre) of solution. Thus, solutions of equal molarity
`contain the same number of solute molecules in
`a given volume of solution. The unit of molarity
`is mol 1-1 (equivalent to 103 mol m-3 if converted
`to the SI unit). Although use of the term molar
`concentration and its symbol M to describe the
`molarity of a solution has been discouraged since
`the introduction of SI units the symbol M is still
`used in the current British and European
`Pharmacopoeias.
`
`Molality
`
`This is the number of moles of solute divided
`by the mass of the solvent, i.e. its SI unit is
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`40
`
`PHYSICOCHEMICAL PRINCIPLES OF PHARMACEUTICS
`
`mol kg-1. Although it is less likely to be encoun-
`tered in pharmaceutical practice than the other
`terms it does offer a more precise description
`of concentration because it is unaffected by
`temperature.
`
`Mole fraction
`This is often used in theoretical considerations and
`is defined as the number of moles of solute divided
`by the total number of moles of solute and
`solvent, i.e.
`
`mole fraction of solute (x1) =
`
`n1
`n1 + n2
`
`where n1 and n2 are the numbers of moles of solute
`and solvent, respectively.
`
`Milliequivalents and normal solutions
`
`The concentrations of solutes in body fluids and
`in solutions used as replacements for these fluids
`are usually expressed in terms of the number of
`millimoles (1 millimole = one thousandth of a
`mole) in a litre of solution. In the case of electro-
`lytes, however, these concentrations may still be
`expressed in terms of milliequivalents per litre. A
`milliequivalent (mEq) of an ion is, in fact, one
`thousandth of the gram equivalent of the ion,
`which is, in turn, the ionic weight expressed in
`grams divided by the valency of the ion.
`Alternatively,
`
`1 mEq —
`
`ionic weight in mg
`valency
`
`A knowledge of the concept of chemical equiv-
`alents is also required in order to understand the
`use of 'normality' as a means of expressing the
`concentration of solutions, because a normal
`solution, i.e. concentration = 1 N, is one that
`contains the equivalent weight of the solute,
`expressed in grams, in 1 litre of solution. It was
`thought that this term would disappear on the
`introduction of SI units but it is still encountered
`in some volumetric assay procedures, e.g. in
`British Pharmacopoeias preceding the 1980 edition
`and in the current European Pharmacopoeia. The
`student is referred to Beckett and Stenlake (1975)
`for an explanation of chemical equivalents.
`
`TYPES OF SOLUTION
`
`Solutions may be classified on the basis of the
`physical states, i.e. gas, solid or liquid, of the
`solute(s) and solvent. Although a variety of
`different types can exist, solutions of pharmaceuti-
`cal interest virtually all possess liquid solvents. In
`addition, the solutes are predominantly solid
`substances. Consequently, most of the comments
`given in this chapter and in Chapter 5 are made
`with solutions of solids in liquids in mind.
`However, appropriate comments on other types,
`e.g. gases in liquids, liquids in liquids and solids
`in solids are included.
`
`Vapour pressures of solids, liquids and
`solutions
`An understanding of many of the properties of
`solutions requires an appreciation of the concept
`of an ideal solution and its use as a reference
`system, to which the behaviours of real (non-ideal)
`solutions can be compared. This concept is itself
`based on a consideration of vapour pressure. The
`present section is included, therefore, as an intro-
`duction to the later discussions on ideal and non-
`ideal solutions.
`The kinetic theory of matter indicates that the
`thermal motions of molecules of a substance in its
`gaseous state are more than adequate to overcome
`the attractive forces that exist between the mol-
`ecules, so that the molecules undergo a completely
`random movement within the confines of the
`container. The situation is reversed, however,
`when the temperature is lowered sufficiently so
`that a condensed phase is formed. Thus, the
`thermal motions of the molecules are now insuf-
`ficient to overcome completely the intermolecular
`attractive forces and some degree of order in the
`relative arrangement of molecules occurs. If the
`intermolecular forces are so strong that a high
`degree of order, which is hardly influenced by
`thermal motions, is brought about then the
`substance is usually in the solid state.
`In the liquid condensed state the relative influ-
`ences of thermal motion and intermolecular
`attractive forces are intermediate between those in
`the gaseous and solid states. Thus, the effects of
`interactions between the permanent and induced
`
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`r
`
`dipoles, i.e. the so-called van der Waals forces of
`attraction, lead to some degree of coherence
`between the molecules of liquids. Consequently,
`liquids occupy a definite volume, unlike gases,
`and whilst there is evidence of structure within
`liquids such structure is much less apparent than
`in solids.
`Although solids and liquids are condensed
`systems with cohering molecules some of the
`surface molecules in these systems will occasion-
`ally acquire sufficient energy to overcome the
`attractive forces exerted by adjacent molecules and
`so escape from the surface to form a vaporous
`phase. If temperature is maintained constant an
`equilibrium will be established eventually between
`the vaporous and condensed phases and the
`pressure exerted by the vapour at equilibrium is
`referred to as the vapour pressure of the
`substance.
`All condensed systems have the inherent ability
`to give rise to a vapour pressure. However, the
`vapour pressures exerted by solids are usually
`much lower than those exerted by liquids, because
`the intermolecular forces in solids are stronger
`than those in liquids so that the escaping tendency
`for surface molecules is higher in liquids.
`Consequently, surface loss of vapour from liquids
`by the process of evaporation is more common
`than surface loss of vapour from solids via
`sublimation.
`In the case of a liquid solvent containing a
`dissolved solute then molecules of both solvent
`and solute may show a tendency to escape from
`the surface and so contribute to the vapour
`pressure. The relative tendencies to escape will
`depend not only on the relative numbers of the
`different molecules in the surface of the solution
`but also on the relative strengths of the attractive
`forces between adjacent solvent molecules on the
`one hand and between solute and solvent mol-
`ecules on the other hand. Thus, since the inter-
`molecular forces between solid solutes and liquid
`solvents tend to be relatively strong such solute
`molecules do not generally escape from the surface
`of a solution and contribute to the vapour
`pressure. In other words the solute is non-volatile
`and the vapour pressure arises solely from the
`dynamic equilibrium that is set up between the
`rates of evaporation and condensation of solvent
`
`SOLUTIONS AND THEIR PROPERTIES 41
`
`molecules contained in the solution. In a mixture
`of miscible liquids, i.e. a liquid in liquid solution,
`the molecules of both components are likely to
`evaporate and contribute to the overall vapour
`pressure exerted by the solution.
`
`Ideal solutions; Raoult's Law
`
`The concept of an ideal solution has been intro-
`duced in order to provide a model system that can
`be used as a standard, to which real or non-ideal
`solutions can be compared. In the model it is
`assumed that the strengths of all intermolecular
`forces are identical, i.e. solvent—solvent,
`solute—solvent and solute—solute interactions are
`the same and are equal, in fact, to the strength of
`the intermolecular interactions in either the pure
`solvent or pure solute. Because of this equality the
`relative tendencies of solute and solvent molecules
`to escape from the surface of the solution will be
`determined only by their relative numbers in the
`surface. Since a solution is homogeneous by
`definition then the relative numbers of these
`surface molecules will be reflected by the relative
`numbers in the whole of the solution. The latter
`can be expressed conveniently by the mole frac-
`tions of the components because, for a binary
`solution, i.e. one with two components, x1 + x2
`= 1, where xi and x2 are the mole fractions of the
`solute and solvent, respectively. Thus, the total
`vapour pressure (p) exerted by such a binary
`solution is given by Eqn 3.1:
`
`P (cid:9)
`Pi + P2 = PYX1 (cid:9)
`(3.1)
`P2X2 (cid:9)
`where pi and p2 are the partial vapour pressures
`exerted above the solution by solute and solvent,
`respectively, and pi and p`l are the vapour press-
`ures exerted by pure solute and pure solvent,
`respectively.
`If the total vapour pressure of the solution is
`described by Eqn 3.1 it follows that Raoult's law
`is obeyed by the system because this law states
`that the partial vapour pressure exerted by a
`volatile component in a solution at a given
`temperature is equal to the vapour pressure of the
`pure component at the same temperature, multi-
`plied by its mole fraction in the solution, i.e.
`
`Pi = P7x1
`
`(3.2)
`
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`
`42 PHYSICOCHEMICAL PRINCIPLES OF PHARMACEUTICS
`
`On'e of the consequences of the preceding
`comments is that an ideal solution may be defined
`as one which obeys Raoult's law. In addition, ideal
`behaviour should only be expected to be exhibited
`by real systems comprised of chemically similar
`components, because it is only in such systems
`that the condition of equal intermolecular forces
`between components, that is assumed in the ideal
`model, is likely to be satisfied. Consequently,
`Raoult's law is obeyed over an appreciable concen-
`tration range by relatively few systems in reality.
`Mixtures of benzene + toluene, n-hexane + n-
`heptane and ethyl bromide + ethyl iodide are
`commonly mentioned systems that exhibit ideal
`behaviour, whilst a more pharmaceutically inter-
`esting example is provided by binary mixtures of
`fluorinated hydrocarbons. These latter mixtures
`are used as propellants in therapeutic aerosols and
`their approximation to ideal behaviour allows Eqn
`3.1 to be used to calculate the total pressure
`exerted by a given mixture.
`
`Real or non-ideal solutions
`
`The majority of real solutions do not exhibit ideal
`behaviour because solute—solute, solute—solvent
`and solvent—solvent forces of interaction are
`unequal. These inequalities alter the effective
`concentration of each component so that it cannot
`be represented by a normal expression of concen-
`tration, such as the mole fraction term x that is
`used in Eqns 3.1 and 3.2. Consequently, devi-
`ations from Raoult's law are often exhibited by
`real solutions and the previous equations are not
`obeyed in such cases. The equations can be modi-
`fied, however, by substituting each concentration
`term (x) by a measure of the effective concen-
`tration, which is provided by the so-called activity
`(or thermodynamic activity), a. Thus, Eqn 3.2 is
`converted into Eqn 3.3,
`
`(3.3)
`
`Pi = (cid:9)
`which is applicable to all systems whether they be
`ideal or non-ideal. It should be noted that if a
`solution exhibits ideal behaviour then a = x,
`whereas a (cid:9)
`x if deviations from such behaviour
`are apparent. The ratio of activity/concentration
`is termed the activity coefficient (f) and it provides
`a measure of the deviation from ideality. (The
`
`student is encouraged to study relevant parts of
`the bibliography for further information on
`thermodynamic terms such as activity, activity
`coefficient, free energy and chemical potential.)
`If the attractive forces between solute and
`solvent molecules are weaker than those exerted
`between the solute molecules themselves or the
`solvent molecules themselves then the components
`will have little affinity for each other. The
`escaping tendency of the surface molecules in such
`a system is increased when compared with an ideal
`solution. In other words pi , p2 and p are greater
`than expected from Raoult's law and the thermo-
`dynamic activities of the components are greater
`than their mole fractions, i.e. al > x1 and a2 > x2.
`This type of system is said to show a positive
`deviation from Raoult's law and the extent of the
`deviation increases as the miscibility of the
`components decreases. For example, a mixture of
`alcohol and benzene shows a smaller deviation
`than the less miscible mixture of water + diethyl
`ether whilst the virtually immiscible mixture of
`benzene + water exhibits a very large positive
`deviation.
`Conversely, if the solute and solvent have a
`strong mutual affinity that results in the formation
`of a complex or compound then a negative devi-
`ation from Raoult's law occurs. Thus, pi, p2 and
`p are lower than expected and a l < x1 and
`a2 < x2. Examples of systems that show this type
`of behaviour include chloroform + acetone,
`pyridine + acetic acid and water + nitric acid.
`Even though most systems are non-ideal and
`deviate either positively or negatively from
`Raoult's law, such deviations are small when a
`solution is dilute because the effects of a small
`amount of solute on interactions between solvent
`molelcules are minimal. Thus, dilute solutions
`tend to exhibit ideal behaviour and the activities
`of their components approximate to their mole
`fractions, i.e. a l (cid:9)
`x1 and a2 = x2. Conversely,
`large deviations may be observed when the
`concentration of a solution is high. Knowledge of
`the consequences of such marked deviations is
`particularly important in relation to the distillation
`of liquid mixtures. For example, the complete
`separation of the components of a mixture by frac-
`tional distillation may not be achievable if large
`positive or negative deviations from Raoult's law
`
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`
`give rise to the formation of so-called azeotropic
`mixtures with minimum and maximum boiling
`points, respectively. Such knowledge is obviously
`important to the pharmaceutical chemist but is
`beyond the scope of the present chapter.
`
`IONIZATION OF SOLUTES
`
`Many solutes dissociate into .ions if the dielectric
`constant of the solvent is high enough to cause
`sufficient separation of the attractive forces
`between the oppositely charged ions. Such solutes
`are termed electrolytes and their ionization (or
`dissociation) has several consequences that are
`often important in pharmaceutical practice. Some
`of these consequences are indicated below whilst
`others that relate to solubilities and dissolution
`rates are referred to in Chapter 5.
`
`Hydrogen ion concentration and pH
`
`The dissociation of water can be represented by
`Eqn 3.4:
`
`H2O (cid:9) H + OH- (cid:9)
`
`(3.4)
`
`although it should be realized that this is a
`simplified representation because the hydrogen
`and hydroxyl ions do not exist in a free state but
`combine with undissociated water molecules to
`yield more complex ions such as H30+ and H7M
`In pure water the concentrations of H+ and
`OH- ions are equal and at 25 °C both have the
`values of 1 x 10-7 mol 1-1 . Since the
`Lowry—Bronsted theory of acids and bases defines
`an acid as a substance which donates a proton (or
`hydrogen ion) it follows that the addition of an
`acidic solute to water will result in a hydrogen ion
`concentration that exceeds this value. Conversely,
`the addition of a base, which is defined as a
`substance that accepts protons, will decrease the
`concentration of hydrogen ions.
`The hydrogen ion concentration range that can
`be obtained decreases from 1 mol 1-1 for a strong
`acid down to 1 x 10-14 mol 1-1 for a strong base.
`In order to avoid the frequent use of low values
`that arise from this range the concept of pH has
`been introduced as a more convenient measure of
`hydrogen ion concentration. pH is defined as the
`
`SOLUTIONS AND THEIR PROPERTIES 43
`
`negative logarithm of the hydrogen ion concen-
`tration [H-E] as shown by Eqn 3.5:
`
`pH = —logio[H+] (cid:9)
`
`(3.5)
`
`so that the pH of a neutral solution like pure water
`is 7, because the concentration of H+ ions (and
`OH-) ions. = 1 x 10-7 mol 1-1, and the pHs of
`acidic and alkaline solutions will be les's or greater
`than 7, respectively.
`pH has several important implications in phar-
`maceutical practice. For example, in addition to
`its effects on the solubilities of drugs that are weak
`acids or bases, as indicated in Chapter 5, pH may
`have a considerable effect on the stabilities of
`many drugs, be injurious to body tissues and affect
`the ease of absorption of drugs from the gastro-
`intestinal tract into the blood (see Chapter 9).
`
`Dissociation (or ionization) constants and pKa
`
`Many drugs may be classified as weak acids or
`weak bases which means that in solutions of these
`drugs equilibria exist between undissociated
`molecules and their ions. Thus, in a solution of
`a weakly acidic drug HA the equilibrium may be
`represented by Eqn 3.6:
`
`HA -,='• F11- + A-
`
`(3.6)
`
`although the proton H+ would be better
`represented by H30+ because it is always strongly
`solvated by a water molecule. Similarly, the
`protonation of a weakly basic drug B can be
`represented by Eqn 3.7:
`
`B + H+ ± BH+ (cid:9)
`
`(3.7)
`
`Such equilibria are unlikely to occur in solutions
`of most salts of strong acids or bases in water
`because these compounds are completely ionized.
`The ionization constant (or dissociation constant)
`Ka of a weak acid can be obtained by applying the
`Law of Mass Action to Eqn 3.6 to yield Eqn 3.8:
`
`Ka (cid:9)
`
`= (cid:9)
`
`[1-1-1[A-]
`[HA] (cid:9)
`
`(3.8)
`
`Taking logarithms of both sides of Eqn 3.8 yields
`
`log Ka = log [H+] + log [Al — log [HA]
`
`and the signs in this equation may be reversed to
`give Eqn 3.9:
`
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`44 PHYSICOCHEMICAL PRINCIPLES OF PHARMACEUTICS
`
`-log Ka = -log [H+] - log [A- ] + log [HA]
`(3.9)
`The symbol pKa is used to represent the negative
`logarithm of the acid dissociation constant Ka in
`the same way that pH is used to represent the
`negative logarithm of the hydrogen ion concen-
`tration [H+] and Eqn 3.9 may therefore be
`rewritten as Eqn 3.10:
`pKa = pH + log [HA] - log [A ] (3.10)
`
`or
`
`(3.11)
`
`pKa = pH + log [HA]
`[A-]
`Thus, a general equation, Eqn 3.12, that is appli-
`cable to any acidic drug with one ionizable group
`may be written, where cu and ci represent the
`concentrations of the unionized and ionized
`species, respectively. This equation is known as
`the Henderson-Hasselbalch equation.
`
`pKa = pH + log —ccu (cid:9)
`
`(3.12)
`
`From Eqn 3.7 it can be seen that the acid
`dissociation constant (Ka) of a protonated weak
`base is given by Eqn 3.13:
`
`Ka -
`
`[111[B]
`[BH+]
`Taking negative logarithms yields Eqn 3.14:
`-log Ka = -log [Hr] - log [B] + log [Bill
`(3.14)
`
`(3.13)
`
`or
`
`pKa = pH + log (cid:9)
`
`
`
`[B]
`The Henderson-Hasselbalch equation for any
`weak base with one ionizable group may therefore
`be written as shown by Eqn 3.15:
`
`pKa = pH + log —c (cid:9)
`i (cid:9)
`Cu
`
`(3.15
`)
`
`temperature at which the determination is
`performed should be specified because the values
`of the constants vary with temperature.
`Ionization constants are usually expressed in
`terms of pKa values for both acidic and basic drugs
`and a list of pKa values for a series of important
`drugs is given in the Pharmaceutical Handbook
`(1980).
`The degree of ionization of a drug in a solution
`can be calculated from the Henderson-Hasselbalch
`equations for weak acids and bases (Eqns 3.12 and
`3.15, respectively) if the pKa value of the drug and
`the pH of the solution are known. Such calcu-
`lations are particularly useful in determining the
`degree of ionization of drugs in various parts of
`the gastrointestinal tract and in the plasma (see
`Chapter 9). The following examples are therefore
`related to this type of situation.
`1 The pKa value of aspirin, which is a weak acid,
`is about 3.5, and if the pH of the gastric
`contents is 2.0 then from Eqn 3.12
`
`log —cu = pKa - pH = 3.5 - 2.0 = 1.5
`c,
`
`so that the ratio of the concentration of un-
`ionized acetylsalicyclic acid to acetylsalicylate
`anion is given by
`cu:ci = antilog 1.5 = 31.62:1
`2 The pH of plasma is 7.4 so that the ratio of
`unionized:ionized aspirin in this medium is
`given by
`
`log
`
`CL1
`T, (cid:9)
`
`pKa - pH = 3.5 - 7.4 = -3.9
`
`and
`cu:ci = antilog -3.9 = antilog 4.1
`= 1.259 x 10 -4:1
`3 The pKa of the weakly acidic drug sulphapyri-
`dine is about 8.0 and if the pH of the intestinal
`contents is 5.0 then the ratio of unionized:ionized
`drug is given by
`
`where ci and cu refer to the concentrations of the
`protonated and unionized species, respectively.
`Various analytical techniques, e.g. spectro-
`photometric and potentiometric methods, may be
`used to determine ionization constants but the
`
`log °
`c;
`
`and
`
`= pKa - pH = 8.0 - 5.0 = 3.0
`
`cu:ci = antilog 3.0 = 103:1
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`4 The pKa of the basic drug amidopyrine is 5.0,
`and in the stomach the ratio of ionized:unionized
`drug is shown from Eqn 3.15 to be given by
`ci
`log-- = pKa — pH = 5.0 — 2.0 = 3.0
`Cu
`
`and
`
`ci:cu = antilog 3.0 = 103:1
`while in the intestine the ratio is given by
`
`log— =- 5.0 — 5.0 0
`cu
`
`and
`
`ci:cu = antilog 0 = 1:1
`
`Buffer solutions and buffer capacity
`
`These solutions will maintain a constant pH even
`when small amounts of acid or alkali are added to
`the solution. They usually contain mixtures of a
`weak acid and its salt (i.e. its conjugate base)
`although mixtures of weak bases and their salts
`(i.e. their conjugate acids) may be used but suffer
`from the disadvantage that arises from the
`volatility of many of the bases.
`The action of a buffer solution can be appreci-
`ated by considering a simple system such as a
`solution of acetic acid and sodium acetate in
`water. The acetic acid, being a weak acid, will be
`confined virtually to its undissociated form
`because its ionization will be suppressed by the
`presence of common acetate ions produced by
`complete dissociation of the sodium salt. The p1-1
`of this solution can be described by Eqn 3.16,
`which is a rearranged form of Eqn 3.12:
`
`pH = pKa + log L. (cid:9)
`Cu
`
`(3.16)
`
`It can be seen from Eqn 3.16 that the pH will
`remain constant as long as the logarithm of the
`ratio ci/cu does not change. When a small amount
`of acid is added to the solution it will convert
`some of the salt into acetic acid but if the concen-
`trations of both acetate ion and acetic acid are
`reasonably large then the effect of the change will
`be negligible and the pH will remain constant.
`Similarly, the addition of a small amount of base
`will convert some of the acetic acid into its salt
`
`SOLUTIONS AND THEIR PROPERTIES 45
`
`form but the pH will be unaltered if the overall
`changes in concentrations of the two species are
`relatively small.
`If large amounts of acid or base are added to a
`buffer then changes in the log ci/cu term become
`appreciable and the pH alters. The ability of a
`buffer to withstand the effects of acids and bases
`is an im