PCT 213 Lecture notes on Solutions.docx

**PHARMACEUTICAL SOLUTIONS, SOLUBILITY, COLLIGATIVE PROPERTIES OF SOLUTIONS AND PHASE EQUILIBRIA**. **Dr. Allen A. Iboi, PharmD, MSc, mPSN** **Department of Pharmaceutics and Pharmaceutical Technology** **Faculty of Pharmacy, University of Benin.** **Learning Objectives** At the end of this lec...

**PHARMACEUTICAL SOLUTIONS, SOLUBILITY, COLLIGATIVE PROPERTIES OF SOLUTIONS AND PHASE EQUILIBRIA**. **Dr. Allen A. Iboi, PharmD, MSc, mPSN** **Department of Pharmaceutics and Pharmaceutical Technology** **Faculty of Pharmacy, University of Benin.** **Learning Objectives** At the end of this lecture, students should be able to; i. Appreciate the concept of solutions dissolution and solubility, understand the factors affecting solubility and its relevance in preparation of pharmaceutical solutions. ii. Explain the mechanism of dissolution and factors affecting dissolution rate. iii. Understand the application of colligative properties of solutions in drug formulation and appreciate the concept of phase equilibrium. iv. Apply the knowledge gained to solve practical pharmaceutical problems in real time. **SOLUTIONS** A solution can be defined as a homogenous mixture of two or more components. The component that determines the phase of the solution is called the **solvent** while the other component(s) which are dispersed as molecules or ions throughout the solvent are termed **solute(s)**. The solvent usually (but not necessarily) constitutes the largest portion of the system. Solutions are usually homogenous down to the molecular level. In physicochemical terms, solutions may be prepared from any combination of the three states of matter (i.e solid, liquid and gas). For example, a solid solute may be dissolved in another solid, a liquid or a gaseous medium, this can also be the case for a liquid solute as well as a gaseous solute. Thus, there are nine possible types of homogenous mixtures and they are shown in the table below. **Table 1.1: Types of Homogenous Mixtures** **Solute** **Solvents** ------------ -------------- Gas Gas Liquid Gas Solid Gas Gas Liquid Liquid Liquid Solid Liquid Gas Solid Liquid Solid Solid Solid In Pharmacy however, our interest in solutions is for the most part limited to preparations of solid and liquid solutes in a liquid solvent and less frequently a gas solute in a liquid solvent. **PHARMACEUTICAL SOLUTIONS** In Pharamaceutical terms, solutions are "liquid" preparations that contain one or more chemical substances **dissolved** in a suitable solvent or a mixture of mutually miscible solvents. **Classification of Pharmaceutical Solutions** Pharmaceutical solutions may be classified based on its mode of application as oral, otic, ophthalmic or topical. It can also be classified based on its dosage form into: - Syrups- aqueous solutions containing a sugar - Elixirs- sweetened solutions containing water and ethanol (sweetened hydroalcoholic solutions). - Spirits/ Aromatic water- solutions of aromatic materials are termed spirits if the solvent is alcoholic or termed aromatic water if the solvent is aqueous. - Tinctures- solutions prepared by extracting the active constituents from crude drugs. Tinctures may also be solutions of chemical substances dissolved in alcohol or in a hydroalcoholic solvent. - Parenteral solutions- these are solutions intended to be administered as injections or infusions and are prepared to be sterile and pyrogen free. Although other examples could be cited, it is apparent that a solution as a distinct type of pharmaceutical preparation is much further defined than the physicochemical definition of the term solution. **ORAL SOLUTIONS** Syrups, elixirs, spirits and tinctures are prepared and used for the specific effects of the medicinal agents they contain. In these preparations, the medicinal agents are intended to provide systemic effects. The fact that they are administered in solution form indicates that they are soluble in aqueous systems and their absorption from the gastrointestinal tract into the systemic circulation may be expected to occur more rapidly than from suspension or solid dosage forms of the same medicinal agent. Solutes other than the medicinal agent are usually present in orally administered solutions and these additional agents are included to provide colour, flavour, sweet taste or stability. In formulating a pharmaceutical solution, the Pharmacist must apply the information on the solubility and stability of each solute with regards to the solvent or solvent system. Combinations of medicinal agents or active ingredients that will result in chemical or physical interactions which affect the quality or pharmaceutical stability of the product must be avoided. For single-solute solutions and especially for multiple-solute solutions, the Pharmacist must be aware of the solubility characteristics of each of the solutes and the features of the common pharmaceutical solvents because each chemical agent has its own solubility in a given solvent. For many medicinal agents, their solubilities in the usual solvents are stated in the United States Pharmacopeia- National Formulary (USP-NF) as well as other reference books. **DISSOLUTION** In order to appreciate the concept of solubility, it is important to first take a look at dissolution. The transfer of molecules or ions from solid state into solution is known as **dissolution.** Fundamentally, this process is controlled by the relative affinity between the molecules of the solute and that of the solvent. The extent to which the dissolution proceed under a given set of conditions is referred to as the **solubility** of the solute in the solvent. The solubility of a substance is the amount of it that passes into solution when equilibrium is established between the solute in solution and the excess (undissolved) solute. The solution that is obtained under these conditions is called a **saturated solution**. A solution with a concentration less than this at equilibrium is said to be undersaturated. Solutions with concentration greater than the concentration at equilibrium can be obtained and these are known as **supersaturated solutions.** Supersaturated solutions are however unstable and the excess undissolved solute can be precipitated out of solution easily. **Mechanisms of Dissolution** The majority of drugs and excipients are crystalline solids although liquid, semi-solid and amorphous drugs and excipients do exist but in minority. At this level, we will restrict our discussion to dissolution of crystalline solids into liquid solvents. Also, for simplicity, it will be assumed that the drug is molecular in nature and that most solid crystalline materials whether drugs or excipients will dissolve in a similar manner. The dissolution of a solid in a liquid may be regarded as being composed of two consecutive stages. 1. First, there is an interfacial reaction that results in the liberation of solute molecules from the solid phase into the liquid phase. This involves a phase change so that molecules of the solid becomes molecules of solute in the solvent in which the crystal is dissolving. 2. After this, the solute molecules must migrate through the boundary layers surrounding the crystal to the bulk of the solution. These stages and the associated solution concentration changes are illustrated in the figure 1.1 below: Figure 1.1: diagram of boundary layers and concentration change surrounding a dissolving particle. **Interfacial reaction:** - **Leaving surface**- dissolution involves the replacement of crystal molecules by solvent molecules. The process of removal of drug molecules from a solid and their replacement by solvent molecules is determined by the relative affinity of the various molecules involved. The solvent-solute forces of attraction must overcome the cohesive forces of attraction between the molecules of the solid. Figure 1.2 below gives a pictorial representation of this process.  Figure 1.2: Schematic representation of the replacement of crystal molecules with solvent molecules during dissolution. - **Moving into liquid**- on leaving the solid surface the drug molecule must become incorporated in the liquid phase i.e within the solvent. Liquids are thought to contain a small amount of so-called 'free volume' (interstitial space) in the form of 'holes' that at a given instance are not occupied by the solvent molecules themselves (see the figure below). Individual solute molecules are thought to occupy these spaces as shown in figure 1.3 below. Figure 1.3: the theory of cavity creation in the mechanism of dissolution The process of dissolution may be considered therefore, to involve the relocation of solute molecules from an environment where they are surrounded by other identical molecules, with which they form intermolecular attractions into a cavity in a liquid where it is surrounded by non-identical molecules with which it may interact to a different degree. - **Diffusion through the boundary layer**- this step involves transport of the drug molecules away from the solid-liquid interface into the bulk of the liquid phase under the influence of diffusion. Boundary layers are static or slow-moving layers of liquid that surround all solid surfaces that are surrounded by liquid. Mass transfer takes place more slowly usually by diffusion through these static or slow-moving layers that limit the movement of solute molecules from the surface of the solid into the bulk of the solution. The solution in contact with the solid will be saturated (because it is in direct contact with undissolved solute). During diffusion, the concentration of the solution in the boundary layers changes from being saturated (C~S~) at the crystal surface to being equal to that of the bulk of the solution (C) at its innermost limit. **Dissolution Rates of Solids in Liquids** Like any reaction that involves consecutive stages, the rate of dissolution will depend on the slowest step (the rate-limiting step or rate-determining step). In dissolution, the interfacial step is virtually instantaneous and so the rate of dissolution will most frequently be determined by the rate of the slowest step of diffusion of dissolved solute through the boundary layer of liquid that exists at a solid-liquid interface. On rare occasions when the release of the molecules from the solid into solution is slower than the transport of dissolved solute across the boundary to the bulk solution, dissolution is said to be interfacially controlled. The rate of diffusion will obey Fick's law of diffusion which states that "*the rate of change in concentration of dissolved material with time is directly proportional to the concentration difference between the two sides of the diffusion layer",* i.e, [\$\\frac{\\text{dC}}{\\text{dt}}\$]{.math.inline} α ∆C..................................1.1 Or [\$\\frac{\\text{dC}}{\\text{dt}}\$]{.math.inline} = k∆C.................................1.2 Where C is the concentration of solute in solution at any point and at time t, and k is the rate constant. In this context, ∆C is the difference in concentration of solution at the solid-liquid interface (C~1~) and the bulk of the solution (C~2~). At equilibrium, the solution in contact with the solid (C~1~) will be saturated (C~S~). Hence C~1~ = C~S~ Thus, ∆C= C~1~ -- C~2~ = C~S~ -- C An equation known as the Noyes-Whitney (1897) equation was developed to define the dissolution from a single spherical particle. This equation has found great usefulness in the estimation or prediction of the dissolution of pharmaceutical particles. The rate of mass transfer of solute molecules or ions through a static diffusion layer ([\$\\frac{\\text{dm}}{\\text{dt}}\$]{.math.inline} ) is directly proportional to the area available for molecular or ionic migration (A), the concentration difference (∆C) across the boundary layer is inversely proportional to the thickness of the boundary layer (h). Hence, [\$\\frac{\\text{dm}}{\\text{dt}}\$]{.math.inline} = [\$\\frac{K1A\\mathrm{\\Delta}C\\ }{h}\$]{.math.inline}....................................... 1.3 [\$\\frac{\\text{dm}}{\\text{dt}}\$]{.math.inline} = [\$\\frac{K1\\text{A\\ }\\left( Cs - C \\right)\\ }{h}\$]{.math.inline}.................................. 1.4 The constant K~1~ is known as the diffusion coefficient, usually given the symbol D and has the unit of M^2^/S. If the volume of the solvent is large or solute is removed from the bulk of the dissolution medium by some process at a faster rate than it passes into solution, then C remains close to zero and the term (C~S~ -- C) in equation 1.4 above may be approximated to C~S~. In practice, if the volume of the dissolution medium is so large that C is not allowed to exceed 10% of the value of C~S~, then the same approximation could be made. In either of these circumstances' dissolution is said to occur under 'sink' condition. Equation 1.4 may then be simplified into [\$\\frac{\\text{dm}}{\\text{dt}}\$]{.math.inline} = [\$\\frac{\\text{DACs\\ }}{h}\$]{.math.inline}............................. 1.5 Sink condition may arise invivo when a drug is absorbed into the body from its solution in the gastrointestinal fluids at a faster rate than it dissolves in those fluids from a solid dosage form such as a tablet. The phrase is illustrative of a solute disappearing down a sink. If solute is allowed to accumulate in the dissolution medium to such an extent that the above approximation is no longer valid i.e when C \> [\$\\frac{\\text{Cs}}{10}\$]{.math.inline} , then 'non-sink' conditions are said to be in operation. When C builds up to such an extent that it equals C~S~, the dissolution medium is saturated with solute and the overall dissolution rate will be zero. **FACTORS AFFECTING DISSOLUTION RATE** These factors may be derived from a consideration of the terms that appear in the Noyes-Whitney equation and the knowledge of the factors that in turn affect these terms. Let us look at equation 1.4 again, [\$\\frac{\\text{dm}}{\\text{dt}}\$]{.math.inline} = [\$\\frac{K1\\text{A\\ }\\left( Cs - C \\right)\\ }{h}\$]{.math.inline}.................................. 1.4 An increase in the factors at the top right-hand side of the Noyes-Whitney equation will increase the rate of diffusion (and therefore dissolution), whereas, an increase in the factors at the bottom of the equation will result in a decrease in the rate of dissolution. **Surface Area of Undissolved Solid (A)** - Size of solid particles -- the surface area of isodiametric particles is inversely proportional to their particle size. In general, milling or other means of particle size reduction will increase the rate of dissolution of sparingly soluble drug. Note that particle size will change during dissolution process because large particles will become smaller and small particles will eventually disappear into solution. Compact masses of solid may be also disintegrate into smaller particles thus increasing the surface area available for dissolution as the disintegration process progresses. - Dispersibility of powdered solid in dissolution medium -- if particles tend to cluster or form coherent masses in the dissolution medium, then the surface area available for dissolution is reduced. This effect may be overcome by the addition of a wetting agent to improve the dispersion into primary powder particles. - Porosity of the solid particle -- pores in some materials, particularly granulated ones may be large enough to allow access of the dissolution medium and outward diffusion of dissolved solute molecules. **Saturation Solubility of Solid in Dissolution Medium (C~S~)** - Temperature -- dissolution may be an exothermic or an endothermic process and so temperature changes will influence the energy balance and thus the energy available to promote dissolution. - Nature of dissolution medium -- factors such as solubility parameters, co-solvents and pH will affect the rate of dissolution. - Molecular structure of solute -- factors such as the use of salts of either weakly acidic or weakly basic drugs or esterification of neutral compounds can influence solubility and dissolution rate. - Crystalline form of solid -- the presence of polymorphs, hydrates, solvates or the amorphous form of the drug can all have an influence on dissolution rate. - Presence of other compounds -- the common ion effect, complex formation and the presence of solubilizing agents can affect the rate of dissolution. **Concentration of Solute in Solution at time, t (C)** - Volume of dissolution medium -- if volume of the dissolution medium is small, C can approach C~S~. if it is large then C may be negligible with respect to C~S~ and thus 'sink' conditions will operate. This can be controlled in vitro but must be taken into account in vivo as the volume of the stomach contents can vary greatly. Also, the volume of the fluid in the rectum and vagina can be small and so this consideration can be important in drug delivery from suppositories and pessaries. - Any process that removes dissolved solute from the dissolution medium -- for example, adsorption onto insoluble adsorbent, partition into a second liquid that is immiscible with the dissolution medium, removal of solute by dialysis or by continuous replacement of solution by fresh dissolution medium. **Dissolution Rate Constant (K)** - Thickness of boundary layer -- affected by degree of agitation which depends in turn on the speed of stirring or shaking, shape, size and position of stirrer, volume of dissolution medium, shape and size of container, viscosity of dissolution medium. - Diffusion coefficient of solute in the dissolution medium -- the diffusion coefficient of the solute in the dissolution medium is affected by the viscosity of the dissolution medium and the molecular characteristics and size of diffusing molecules. **SOLUBILITY** The solution produced when equilibrium is established between undissolved and dissolved solute in a dissolution process is termed a saturated solution. The amount of substance that passes into solution in order to establish this equilibrium at constant temperature thereby producing a saturated solution is known as the solubility of the substance. Solubility may be expressed in concentration terms such as; - Quantity per quantity (weight of solute per volume of solution) - Percentage concentration in %w/v = [\$\\frac{\\text{weight\\ of\\ solute}}{\\text{volume\\ of\\ solution}}\$]{.math.inline} X 100 - Parts - Molarity - Molality - Mole Fraction - Multiequivalents and normal solutions **Table 1.2: Descriptive Solubilities** **Description** **Approximate weight of solvent (g) necessary to dissolve 1g of Solute** ----------------------- -------------------------------------------------------------------------- Very Soluble \< 1 Freely Soluble Between 1 and 10 Soluble Between 10 and 30 Sparingly Soluble Between 30 and 100 Slightly soluble Between 100 and 1000 Very slightly soluble Between 1000 and 10 000 Practically insoluble \> 10 000 **Solubility Of Solids in Liquids** In pharmaceutical practice, solutions of solids in liquids are the most common type of solution encountered. Hence, it is important that the pharmacist must be aware of the general method of determining the solubility of a solid in a liquid and the various precautions that should be taken during such determinations. **Factors affecting the Solubility of Solids in Liquids** The knowledge of these factors is important to pharmaceutical scientists as it provides information which may be used to improve the solubilities and bioavailability of a drug. These factors are discussed briefly below: - **Temperature** -- the dissolution process is usually an endothermic one which implies that heat is usually absorbed when dissolution occurs. In this type of system, a rise in temperature will lead to an increase in the solubility of a solid with a positive heat of solution. Conversely, in a system that exhibits exothermic dissolution, an increase in temperature will result in a decrease in solubility (systems that exhibit exothermic dissolution are however uncommon). Plots of solubility versus temperature referred to as **solubility curves** are often used to describe the effect of temperature on a given system. This is shown in figure 1.4 below.  Figure 1.4: Solubility curve for various substances in water. Most of the curves are continuous ones. However, abrupt changes in slope may be observed in some systems if a change in the nature of the dissolving solid occurs at a specific transition temperature. For example, sodium sulphate exists as the decahydrate Na~2~SO~4~.10H~2~O up to 32.5^o^C and its dissolution in water is an endothermic process. Its solubility therefore increases with a rise in temperature until 32.5^o^C is reached. Above this temperature, the solid is converted into the anhydrous form (Na~2~SO~4~) and the dissolution of this compound is exothermic. The solubility therefore exhibits a change from a positive to a negative slope as the temperature exceeds the transition value. - **Molecular structure of solute** -- the nature of solute and solvent is of paramount importance in determining the solubility of a solid in a liquid. It should be noted that even a small change in the molecular structure of a compound can have a marked effect on its solubility in a given liquid. For example, the introduction of a hydrophyllic hydroxyl group can produce a large improvement in water solubility as evidenced by the more than 100- fold difference in the solubility of phenol compared with benzene. Also, the conversion of a weak acid to its sodium salt leads to much greater degree of ionic dissociation of the compound when it dissolves in water. The overall interaction between solute and solvent is increased markedly and the solubility rises consequently. A specific example of this effect is provided by a comparison of the aqueous solubilities of salicylic acid and its sodium salt (sodium salicylate) which are 1 in 500 and 1 in 1 respectively. A reduction in the aqueous solubility of a parent drug may be achieved by esterification. Such reduction in solubility may be useful in pharmaceutical formulations to achieve the following: 1. Masking the taste of a parent drug. For example, chloramphenicol palmitate has been used in paediatric suspensions rather than the more soluble but very bitter chloramphenicol base. 2. Protecting the parent drug from excessive degradation in the gut e.g, erythromycin propionate is less soluble and consequently less readily degraded than erythromycin. 3. Increasing the ease of absorption of drugs from the gastrointestinal tract, e.g erythromycin propionate is also more readily absorbed than erythromycin. - **Nature of Co-solvents** -- the use of mixtures of solvents as a dissolution medium is common in pharmaceutical practice. Such mixtures are often employed in order to obtain aqueous based systems that contain solutes in excess of the solubilities in pure water. Such mixtures of solvents are called **co-solvents**. Ethanol or propylene glycol mixed with water act as better solvents for some solutes than water alone. For example, the aqueous solubility of metronidazole is about 100mg in 10ml. The solubility of this drug can be increased exponentially by the incorporation of one or more water-miscible co-solvents so that a solution containing 500mg in 10ml can be obtained (this solution is suitable for parenteral administration in the treatment of anaerobic infection). - **Crystal characteristics (polymorphism and solvation)** -- different crystalline forms of the same substance which are known as polymorphs possess different lattice energies which is reflected by changes in other properties. For example, the polymorphic form with the lowest free energy will be most stable and possess the highest melting point. Other less stable (or metastable) forms will tend to transform into the more stable one at rates that depend on the energy difference between the metastable and stable forms. Many drugs exhibit polymorphism e.g steroids, barbiturates and sulfonamides. The effect of polymorphism on solubility is particularly important from a pharmaceutical point of view because it provides a means of increasing the solubility of a crystalline material and hence its rate of dissolution by using a metastable polymorph. The absence of crystalline structure that is usually associated with an amorphous powder may lead to an increase in the solubility of a drug when compared with that of its crystalline form. In addition to the effect of polymorphism, the lattice structure of crystalline materials may be altered by the incorporation of molecules of the solvent from which crystallization occurred. The resultant solids are called solvates and the phenomenon is referred to correctly as solvation. The alteration in crystal structure that accompanies solvation will affect the internal energy balance of the solid so that the solubilities of solvated and unsolvated crystals will differ. If water is the solvating molecule (i.e a hydrate or aqueous solvate), then the interaction between the substance and water that occurs at the crystal phase reduces the amount of energy liberated when the solid hydrate dissolves in water. Consequently, hydrated crystals tend to exhibit a lower aqueous solubility than their non-hydrated forms. This decrease in solubility can lead to precipitation from solutions of drugs. In contrast, the aqueous solubilities of other non-aqueous solvates are often greater than those of the unsolvated forms. - **Particle size of solids** -- the changes in interfacial free energy that accompany the dissolution of a particle of varying sizes cause the solubility of a substance to increase with decreasing particle size as indicated in equation 1.6 below. [\$\\log\\frac{S}{\\text{So}}\$]{.math.inline} = [\$\\frac{2\\gamma M}{2.303RT\\rho r}\$]{.math.inline}.......................................1.6 Where S is the solubility of small particles of radius r, S~O~ is the normal solubility (solubility of a solid consisting of fairly large particles) [*γ*]{.math.inline} is the interfacial energy, M is the molecular weight of the solid, [*ρ*]{.math.inline} is the density of the bulk solid, R is the gas constant and T is the thermodynamic temperature. The increase in solubility with particle size ceases when the particles have a very small radius (less than about 1 µM) and any further decrease in size causes a decrease in solubility. - pH -- many drugs behave as weak acids or weak bases hence; their solubilities are therefore affected by the pH of an aqueous solvent. For example, a weakly acidic drug such as acetylsalicylic avid (ASA) will be more soluble in alkaline solution since it will be converted to the more soluble salt form (e.g sodium salicylate). This drug however is better absorbed in the acidic environment of the stomach. Non-ionic or unionized form of a drug is better absorbed than the ionic form. ASA also exists an the unionized form in the acidic region of the stomach, hence its absorption in this environment. - **Additional Substances** -- these are; i. Common Ion Effect -- the solubility of a sparingly soluble electrolyte is decreased by the addition of a second electrolyte that possess a similar ion to the first. AB A^+^ + B^-^ (Solid) (ions) ii. Effect of indifferent electrolytes -- the solubility of a sparingly soluble electrolyte may be increased by the addition of a second electrolyte that does not possess ions common to the first i.e an indifferent electrolyte. iii. Effect of non-electrolytes on the solubility of electrolytes -- the solubility of electrolytes depends on the dissociation of dissolved molecules into ions. The ease of this dissociation is affected by the dielectric constant of the solvent which is a measure of the polar nature of the solvent. Liquids with a high dielectric constant (e.g water) are able to reduce the attractive forces that operate between oppositely charged ions produced by dissociation of an electrolyte. If a water soluble non-electrolyte , such as alcohol is added to an aqueous solution of a sparingly soluble electrolyte, the solubility of the latter is decreased because the alcohol lowers the dielectric constant of the solvent and ionic dissociation of the electrolyte becomes more difficult. iv. Effect of electrolytes on the solubility of non-electrolytes -- non-electrolytes do not dissociate into ions in aqueous solution and in dilute solution the dissolved species therefor consists of single molecules. Their solubility in water depends on the formation of weak intermolecular bond (hydrogen bonds) between their molecules and those of water. The presence of a very soluble electrolyte, the ions of which have a marked affinity for water will reduce the solubility of a non-electrolyte by competing for the aqueous solvent and breaking the intermolecular bonds between the non-electrolytes and water. This effect is important in the precipitation of proteins. v. Effect of complex formation -- the apparent solubility of a solute in a particular liquid may be increased or decreased by the addition of a third substance which forms an intermolecular complex with the solute. The solubility of the complex will determine the apparent change in the solubility of the original solute. For example, HgI~2~ which is not very soluble in water is made more soluble by dissolving in an aqueous solution of potassium iodide resulting in the formation of a water soluble complex, K~2~(HgI~4~). vi. Effect of surface acting agents (solubilizing agents) -- these substances are capable of forming large aggregates at certain concentration in aqueous solution. Organic compounds with low water solubility are taken into the interior of these aggregates and the apparent water solubility of the organic compounds are increased. This phenomenon is referred to as solubilization. **Application of Solubility in Pharmacy** i. The knowledge of solubility is required in the formulation or preparation of medicines. ii. The knowledge of solubility is essential in the understanding and prediction of the absorption of drugs from biological systems. iii. This knowledge is also necessary to effect separation of a substance in qualitative and quantitative analysis. iv. The accurate determination of the solubility of a substance is one of the best methods for determining its purity. **COLLIGATIVE PROPERTIES OF SOLUTION** Generally, solutions have properties which are classified as **additive,** **constitutive** and **colligative**. Additive properties depend on the total contribution of the atoms in the molecule or on the sum of the properties of the constituents of the solution. An example is molecular weight. Constitutive properties depend on the arrangement and to a lesser extent the number and kind of atoms in a molecule. Examples are refraction of light, electrical properties, surface and interfacial properties. Colligative properties on the other hand depend primarily on the number of particles in solution. The colligative properties include changes in vapour pressure, boiling point, freezing point and osmotic pressure. **Vapour Pressure Lowering** -- a vapour in equilibrium with its pure liquid at a constant temperature will exert vapour pressure. When a solute is added to the pure liquid, it will alter the tendency of the molecules to escape the original liquid thus the vapour pressure of the solvent is lowered. This is due to the reduction in the surface available for the evapourating solvent by the solute molecules which have little if any vapour pressure of their own. For an ideal solution of non-electrolytes, the vapour pressure of the solution follows Roult's Law which states that; P~A~ = X~A~P~A~^o^..................................1.12 Where, P~A~ = Vapour pressure of solution X~A~ = Mole fraction of solvent P~A~^o^ = Vapour pressure of pure solvent From this equation, the vapour pressure of solution is proportional to the number of molecules of solvent in the solution. The sum of the mole fractions of solvent and solute in solution (X~A~ + X~B~) = 1 Therefore, X~A~ = 1 - X~B~ Substituting, P~A~ = P~A~^o^ (1 - X~B~ ) \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-- eqn 1 Thus, P~A~ = P~A~^o^ -- P~A~^o^X~B~ \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-- eqn 1a OR P~A~^o^ -- P~A~ = P~A~^o^ X~B~ \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-- eqn 1b The absolute lowering of vapour pressure of the solution is defined by: P~A~^o^ -- P~A~ = X~B~P~A~^o^ **Example:** Calculate the lowering of vapour pressure at 20^o^C of a solution containing 50g of anhydrous dextrose (mol. Wt = 180.16) in 1000g of water (mol.wt = 18.02). The vapour pressure of water at 20^o^C in the absence of air = 17.535 mmHg. **Solution:** No of moles of dextrose in 50g of dextrose = [\$\\frac{50}{180.16}\$]{.math.inline} = 0.2775 moles No of moles of water in 1000g of water = [\$\\frac{1000}{18.02}\$]{.math.inline} = 55.49 moles Total number of moles in solution = 55.49 + 0.2775 = 55.77 moles Mole fraction of Solution X~B~ = n~B~ n~A~ + n~B~ Where n~A~ = number of moles of solvent n~B~ = number of moles of solute So, X~B~ = [\$\\frac{0.2775}{55.77}\$]{.math.inline} = 0.00498 Therefore, the vapour pressure lowering, P~A~^o^ -- P~A~ = X~B~P~A~^o^ X~B~P~A~^o^ = 0.00498 x 17.535 = 0.0873 mmHg Thus, P~A~^o^ -- P~A~ = 0.0873 mmHg The vapour pressure of the solution (P~A~) = P~A~^o^ -- 0.0873 P~A~ = 17.535 -- 0.0873 P~A~ = 17.448mmHg **Boiling Point Elevation** -- the boiling point of a liquid is the temperature at which the vapour pressure of the liquid comes into equilibrium with the atmospheric pressure. Since the vapour pressure is reduced when a non-volatile solute is added to a solvent, the resulting solution must reach a higher temperature to re-establish the equilibrium (boiling point) hence an increase in the boiling point. **Freezing Point Depression** -- the freezing point of a pure liquid is the temperature at which the solid and liquid phases are in equilibrium at a fixed external pressure (760 mmHg or 1 atmosphere). At this temperature, the solid and the liquid forms have the same vapour pressure. The freezing point of a solution is the temperature at which the solid phase of pure solvent and the liquid phase of solution are in equilibrium at 1 atmospheric pressure. When a solute is added to a solvent, the freezing point decreases and this decrease in freezing point is proportional to the concentration of the solute. The freezing point depression of a dilute solution of non-electrolytes can be used to determine the molecular weight of the solute. Freezing point depression is more advantageous than boiling point elevation in such determination owing to its larger magnitude. **Osmotic Pressure** -- the pressure that must be applied to a more concentrated solution to prevent the flow of pure solvent into the solution separated by a semi-permeable membrane is called **Osmotic pressure** and it is proportional to the concentration of the solute or the attractive force (between the solute and the solvent) in the solution. For dilute solution of a non-electrolyte, the relationship can be expressed as follows; PV = nRT..........................................1.13 Where, P is the pressure (atm) V is the volume (L) n is the number of moles of solute R is the gas constant T is the absolute temperature in ^o^C. For dilute solution of an electrolyte, the Van't Hoff term (i) is introduced thus; PV = inRT..........................................1.14 This is in consideration to the fact that electrolytes exert more pressure than non-electrolytes and the term i denotes the number of ionic species present. The osmotic pressure is the most important of all the colligative properties of solution in Pharmacy **PHASE EQUILIBRIA** A phase is any homogenous and physically distinct part of a system that is separated from other parts of the system by definite boundaries. For example, ice, water and water vapour are three separate phase system each being physically distinct and there are definite boundaries between them. Pure liquids or solutions constitute homogenous phases but two immiscible liquids (or solutions) constitute two phases since there are definite boundaries between them. A mixture of gases always constitutes one phase because the mixture is homogenous and there are no boundaries between the different gases in the mixture. **The Phase Rule** The conditions relating to physical equilibria between various states of matter in a system are conveniently expressed by the phase rule which was derived by J. Willard Gibbs in 1876. This rule is applied to relate the effect of the least number of independent variables (e.g the concentration pressure) upon the various phases (Solid, liquid and gas) that can co-exist in equilibrium in a system containing a given number of components. The phase rule can be expressed quantitatively as follows: F = C -- P + X Where, F is the number of degrees of freedom C is the number of components P is the number of phases X is a variable dependent upon selected considerations of the phase diagram (1, 2, 3). 1. Number of components (C): this is the smallest number of independent chemical constituents by which the composition of each phase in the system at equilibrium can be expressed. For example, in the three-phase system ice, water and water vapour, the number of components is one since each phase can be expressed in terms of H~2~O. A mixture of salt and water is a two-component system since both chemical species are independent. 2. Degrees of Freedom (F): this is the number of variable conditions (such as temperature, pressure, concentration) that is necessary to state in order that the condition of the system at equilibrium may be completely defined. **A One Component System** Water existing in three phases (solid water, liquid water and water vapour) is often used to describe this system. This phase diagram is shown below:  Figure 1.5: Phase diagram of Water. **Multi-Component System (Eutectic Mixtures)** pure A Composition Pure B Figure 1.6: Temperature -- Composition Diagram The phase diagram or temperature-composition diagram above represents the melting point as a function of composition for a two-component mixture. The two components are completely miscible in the liquid state but immiscible or distinct in the solid state (i.e no solid-solid solution or additional compound is formed in the solid state). As is evident in this phase diagram, starting from the extremes of either pure component A or pure component B, as the second component is added, the melting point of the pure component decreases. There is a point on the phase diagram at which the minimum melting point occurs. This is called the 'eutectic point'. The four regions or phases in the diagram represent the following: I. Solid A + Solid B II. Solid A + Melt III. Solid B + Melt IV. Melt Each Phase is a homogenous part of the system, physically separated by distinct boundaries. **EUTECTIC MIXTURES** A eutectic mixture is a specific composition of at least two solid components that produces a change of phase to liquid at a certain temperature. The eutectic point temperature corresponds to the minimum melting temperature of the different possible compositions. Thus, the melting point of pure component (A or B) is higher than that of the eutectic mixture. Eutectic mixture formation is usually governed by the following factors; a. The components must be miscible in liquid state and mostly immiscible in the solid state. b. Intimate contact between eutectic forming materials is necessary for contact induced melting point depression. c. The components should have chemical groups that can interact to form physical bonds such as intermolecular hydrogen bonding. d. The molecules which are in accordance to modified Van't Hoff's equation can form eutectic mixtures. **Application of Eutectic Mixtures in Pharmacy** Eutectic mixtures can be formed between active pharmaceutical ingredients (APIs), between APIs and excipients or between excipients; thereby providing a vast scope for its applications in the pharmaceutical industry. Some of the applications are provided below; - During pre-formulation stage, compatibility studies between APIs and excipient play a crucial role in excipient selection. - Testing for eutectic mixture formation can help in anticipation of probable physical incompatibility between drug and excipient molecules. - Eutectic mixtures are commonly used in drug designing and delivery process for various routes of administration. - During manufacturing of pharmaceutical dosage forms, it is extremely necessary to anticipate the formation of eutectics and avoid manufacturing problems of any. For example, during tableting compaction, the heat produced in the punch and die cavities may lead to fusion or melting of tablet powder compacts leading to manufacturing defects. This knowledge of eutectic points of powder components may help to avoid these problems. - During pharmaceutical analysis, understanding of eutectic mixtures can help in the identification of compounds having similar melting points.