Solubility of Drugs

chapter 1

Solubility of Drugs 

Introduction

• Solubility is the ability of one substance to fully dissolve in another substance under specified conditions. The word soluble comes from the fourteenth century, from the Latin word ‘solvere’ meaning to dissolve. The concentration of a solution is usually quoted in terms of mass of solute dissolved in a particular volume of solvent. The solubility is generally expressed in gram per litre. Therefore, solubility of a solute in a solvent at a particular temperature is the number of grams of the solute necessary to saturate 100 grams or mL of the solvent at that temperature. Most commonly encountered solutions are solids dissolved in liquids. The solid that dissolve in a liquid is the solute and the liquid in which it dissolves is solvent. A solute is the dissolved agent usually the less abundant part of solution whereas solvent is more abundant part of solution. If a solid can dissolve in a liquid, it is said to be soluble in that liquid, if not it is said to be insoluble. As we add more solids to a liquid the solution becomes more concentrated. The greater the solubility of a substance the more concentrated it is possible to make the solution. Solubility is measured after solute of interest has had sufficient contact time (however long it takes) with the solvent. 

• There are two types of solubility: one is called intrinsic solubility and the other one is apparent solubility. Intrinsic solubility is defined as the maximum concentration to which a solution can be prepared with a specific solute and solvent. It is often derived from calculation, and is a single numeric number (for example, 0.5 µg/mL) that is independent of the environmental factors. The apparent solubility is dependent on the environmental factor such as pH and ionic strength and is obtained from the experimental measurements. The rate of solubility is affected by many factors such as type of solvent, size and amount of solute particles, stirring speed and temperature. The concept of solubility is very important because it governs the preparation of solutions as dosage forms and a drug must be in solution before it can be absorbed by the body or have any biological activity. Since activity of drug depends on solubility, it is equally important to control environmental conditions which impact various types of solution.  

Solubility Expressions

• The solubility of a drug or other substance in a solvent can be expressed quantitatively in numerous terms viz. percent by mass, percent by volume, molality (m), molarity (M), mole fraction (x), and parts per million (ppm), etc. The particular terminology we use depends largely on the use to which we will put it. Solubility of substance is defined as the amount of solute dissolved in a specific amount of solvent at specific temperature. The British Pharmacopoeia and other official chemical and pharmaceutical compendia frequently use the term parts per parts of solvent (for example, parts per million, ppm). The expressions ‘insoluble’, ‘very highly soluble’ and ‘soluble’ also can be used to express solubility of solutes but being inaccurate often not found to be helpful. For quantitative work specific concentration terms must be used. Most substances have at least some degree of solubility in water and while they may appear to be ‘insoluble’ by a qualitative test, their solubility can be measured and quoted precisely. In aqueous media at pH 10, chlorpromazine base has a solubility of 8 × 10−6 mol/dm3 . It is very slightly soluble and it might be considered as ‘insoluble’ upon visual inspection due to lack of disappearance of solid.

• In many solutions the concentration has a maximum limit that depends on various factors, such as temperature, pressure, and the nature of the solvent. Relative concentrations of a solute/solvent system can often be expressed by the terms dilute and concentrated, or by the terms unsaturated, saturated, and supersaturated. Solutes in water are often categorized as either strong electrolytes, if completely ionized in water or weak electrolytes, if only partially ionized or non-electrolytes when non-ionized. In regard to solubility, general terms can be used when describing whether a compound is soluble or not. These terms are given in and are based on the part of solvent needed to dissolve 1 part of the solute for example, testosterone is considered insoluble in water but soluble in alcohol, ether or other organic solvents. Fortunately, when injected to body, insoluble testosterone is diluted, and the larger volume of body water permits testosterone to go into solution.

Saturated Solution

•  A solution in which dissolved solute is in equilibrium with the undissolved solute or solid phase is known as saturated solution. It is when no more of the solid will dissolve into the solution. When we add solute to a solvent a point is reached where no more solute dissolve under specified condition. The solution is saturated. The concentration of the solute in a saturated solution is the solubility of the solute in that solvent at that temperature. Saturation of solution also can be defined as the point where the solution is in equilibrium with undissolved solute. In a saturated solution containing undissolved solid solute, the rate at which the molecules or ions leave the solid surface is equal to the rate which the solvated molecules return to the solid 

• In KSOL is the rate constant at which solid is solvated and KPPT is the rate constant at which the solvated molecule is returned to the solid. The solubility of substance is ratio of these rate constants at equilibrium in a given solution. At equilibrium the rate of a solute precipitating out of solution is equal to the rate in which the solute goes into solution.

• Unsaturated Solution: An unsaturated solution is a solution containing the dissolved solute in a concentration less than a saturated solution. If less solute is added to the solvent, then the solution is said to be unsaturated. Most pharmaceutical solutions are considered to be unsaturated. 

• Supersaturated Solution: A solution which contains more concentration of solute than saturated solution is known as supersaturated solution. It requires an increase in temperature to make it possible to dissolve more solute into solvent than is required to produce a saturated solution. This yields a supersaturated solution. These solutions can be prepared by heating the saturated solutions at higher temperatures. The solute is dissolved into the solvent at a high temperature and then the solution is slowly cooled, such solution is unstable and the addition of small amount of solute cause all of the excess dissolved solute to crystallize out of the solution. A saturated potassium chloride solution at 10o C will have 31 grams of this substance dissolved in 100 grams of water. If there are 40 grams of potassium chloride in the container, then there will be 9 grams of undissolved potassium chloride remaining in the solution. Raising the temperature of the mixture to 30o C will increase the amount of dissolved potassium chloride to 37 grams and there will be only 3 grams of solid undissolved. The entire 40 grams can be dissolved if the temperature is raised above 40o C. Cooling the hot solution (40o C) will reverse the process. When the temperature decreased to 20o C the solubility will eventually be decreased to 34 grams. There is a time delay before the extra 6 grams of dissolved potassium chloride crystallizes. This solution is “supersaturated” and is a temporary condition. The “extra” solute will come out of solution when the randomly moving solute particles can form the crystal pattern of the solid. A “seed” crystal is sometimes needed to provide the surface for solute particles to crystallize on and establish equilibrium.

• Concentration Units: A wide range of units is commonly used to express solution concentration, and confusion often arises in the inter-conversion of one set of units to another. Wherever possible throughout this book we have used the SI system of units. Although this is the currently recommended system of units in Great Britain, other more traditional systems are still widely used and these are also used in latter sections. 

• Weight Concentration: Concentration is often expressed as a weight of solute in a unit volume of solution; for example, g/dm3, or % w/v, which is the number of grams of solute in 100 cm3 of solution. This is not an exact method when working at a range of temperatures, since the volume of the solution is temperature dependent and hence the weight concentration also changes with temperature. Whenever a hydrated compound is used, it is important to use the correct state of hydration in the calculation of weight concentration. Thus, 10% w/v CaCl2 (anhydrous) is approximately equivalent to 20% w/v CaCl2·6H2O and consequently the use of the vague statement ‘10% calcium chloride’ could result in gross error. The SI unit of weight concentration is kg/m3 which is numerically equal to g/dm3.

• Molarity and Molality: Molarity and molality are similar-sounding terms and must not be confused. The molarity of a solution is the number of moles (gram molecular weight) of solute in 1 litre (1 dm3 or 1000 mL) of solution. The molality is the number of moles of solute in 1 kg of solvent. Molality has the unit, mol/kg, which is an accepted SI unit. Molarity may be converted to SI units using the relationship 1 mol/L = 1 mol/dm3 = 1M= 1000 mol/m3 . Interconversion between molarity and molality requires knowledge of the density of the solution. Of the two units, molality is preferable for a precise expression of concentration because it does not depend on the solution temperature as does molarity; also, the molality of a component in a solution remains unaltered by the addition of a second solute, whereas the molarity of this component decreases because the total volume of solution increases upon the addition of the second solute.

• Milliequivalents: The unit milliequivalent (mEq) is commonly used clinically in expressing the concentration of an ion in solution. The term ‘equivalent’, or gram equivalent weight, is analogous to the mole or gram molecular weight. When monovalent ions are considered, these two terms are identical. A 1 molar solution of sodium bicarbonate, NaHCO3, contains 1 molar 1 Eq of Na+ and 1 mol or 1 Eq of HCO3 per litre (dm3) of solution. With multivalent ions, attention must be paid to the valency of each ion; for example, 10% w/v CaCl2·2H2O contains 6.8 mmol or 13.6 mEq of Ca2 in 10 cm3 . The Pharmaceutical Codex gives a table of milliequivalents for various ions and also a simple formula for the calculation of milli equivalents per litre. In analytical chemistry a solution which contains 1 Eq/dm3 is referred to as a normal solution. Unfortunately, the term ‘normal’ is also used to mean physiologically normal with reference to saline solution. In this usage, a physiologically normal saline solution contains 0.9 g NaCl in 100 cm3 aqueous solutions and not 1 equivalent (58.44 g) per litre. 

Mechanisms of Solute Solvent Interaction

• A solute dissolve in a solvent when it forms favorable interactions with the solvent. This dissolving process all depends upon the free energy changes of both solute and solvent. The free energy of solvation is a combination of several factors. The process can be considered in three stages:
  

• The solute must occupy the cavity created in the solvent. Placing the solute molecule in the solvent cavity requires a number of solutes–solvent contacts; the larger the solute molecule, the more contacts are created. If the surface area of the solute molecule is A, and the solute–solvent interface increases by γ12 A, where γ12 is the interfacial tension between the solvent1 and the solute2 then it leads to favorable solute-solvent interactions. This is entropically favorable as the mixture is more disordered than when the solute and solvent are not mixed.

• Dissolution often occurs when the solute-solvent interactions are similar to the solvent interactions, signified by the term ‘Like dissolves Like’. Hence, polar solutes dissolve in polar solvents, whereas non-polar solutes dissolve in non-polar solvents. Dissimilar nature of solute and solvent makes solute insoluble in the solvent. Substances dissolve when solvent solute attraction is greater than solvent-solvent attraction and solute-solute attraction. 

Ideal Solubility Parameters

• Regular solution theory characterizes non-polar solvents in terms of solubility parameter, δ1, which is defined as Where, ∆U is the molar energy and ∆H is the molar heat of vaporization of the solvent. The ∆H is determined by calorimetry at temperatures below the boiling point at constant volume and V is the molar volume of the solvent. The solubility parameter is thus a measure of the intermolecular forces within the solvent and gives us information on the ability of the liquid to act as a solvent. The ratio ∆U/V is the liquid’s cohesive energy density, a measure of the attraction of a molecule from its own liquid, which is the energy required to remove it from the liquid and is equal to the energy of vaporization per unit volume. As cavities have to be formed in a solvent by separating other solvent molecules to accommodate solute molecules the solubility parameter δ1 enables predictions of solubility to be made in a semiquantitative manner, especially in relation to the solubility parameter of the solute, δ2. By itself the solubility parameter can explain the behavior of only a relatively small group of solvents – those with little or no polarity and those unable to participate in hydrogen bonding interactions. The difference between the solubility parameters expressed as (δ1-δ2) will give an indication of solubility relationships. For solid solutes a hypothetical value of δ2 can be calculated from (U/V) 1/2, where U is the lattice energy of the crystal. In a study of the solubility of ion pairs in organic solvents it has been found that the logarithm of the solubility (log S) correlates well with (δ1/δ2) 2 .  

Solvation 

• The process of solvation is sometimes called dissolution. Solvation is a kinetic process and is quantified by its rate. It is the attraction and association of molecules of a solvent with molecules or ions of a solute. When a solute is soluble in a certain solvent, the solute's molecules or ions spreads out and became surrounded by solvent molecules. A complex formed of molecule or ion of solute in a solvent is known as a solvation complex. Solvation is the process of rearranging solvent and solute molecules into solvation complexes to distribute solute molecules evenly within the solvent. Solvation process is affected by hydrogen bonding and van der Waals forces (which consist of dipole-dipole, dipole-induced dipole, and induced dipole-induced dipole interactions). Which of these forces are at play depends on the molecular structure and properties of the solvent and solute. Insoluble solute molecules interact with other solute molecules rather than break apart and become solvated by the solvent, for example, solvation of functional groups on a surface of ion-exchange resin. In fact, solvation is an interaction of a solute with the solvent, which leads to stabilization of the solute species in the solution. Solvation of a solute by water is called hydration.

• Solvation is, in concept, distinct from solubility. Solubility quantifies the dynamic equilibrium state achieved when the rate of dissolution equals the rate of precipitation. The consideration of the units makes the distinction clearer. The typical unit for dissolution rate is mol/sec. The units for solubility express a concentration as mass per volume (mg/mL), molarity (mol/L) etc. The similarity between solvent and solute determines how well a solute can be solvated by a solvent.  

Association

• Association or ion association is a chemical reaction wherein ions of opposite electrical charge come together in solution to form a distinct chemical entity. Ion associates are classified, according to the number of ions that associate with each other, as ion pairs, ion triplets etc. Ion pairs are also classified according to the nature of the interaction as contact, solvent-shared or solvent-separated. The most important factor that determines the extent of ion association is the dielectric constant of the solvent. Ion associates have been characterized by means of vibrational spectroscopy. Ion pairs are formed when a cation and anion come together: An+ + Bm− AB(n−m)+ 

There are three distinct types of ion pairs depending on the extent of solvation of the two ions:

• In the above schematic representation, the circles represent spheres. The sizes are arbitrary and not necessarily similar as shown in Fig. 1.3, the cation is colored dark, and the anion is colored grey. The area surrounding ions represents solvent molecules in a primary solvation shell; secondary solvation is ignored. When both ions have a complete primary solvation sphere, the ion pair may be termed fully solvated. When there is about one solvent molecule between cation and anion, the ion pair may be termed solvent shared. Lastly, when the ions are in contact with each other, the ion pair is termed a contact ion pair. In contact ion pair the ions retain most of their solvation shell and the nature of this solvation shell is generally not known. In aqueous solution and in other donor solvents, metal cations are surrounded by between 4 and 9 solvent molecules in the primary solvation shell, but the nature of solvation of anions is mostly unknown. 

• Another name for a solvent-shared ion pair is an outer-sphere complex. Usage of outersphere complex is common in co-ordination chemistry and denotes a complex between a solvated metal cation and an anion. Similarly, a contact ion pair may be termed an innersphere complex. The major difference between these three types is the closeness with which the ions approach each other: The order of closeness is prevented as Fully solvated > Solvent-shared > Contact. With fully solvated and solvent-shared ion pairs the interaction is primarily electrostatic, but in a contact ion pair some covalent character in the bond between cation and anion is also present. 

• An ion triplet may be formed from one cation and two anions or from one anion and two cations. Higher aggregates, such as a tetramer (AB)4, may be formed. Ternary ion associates involve the association of three species. Another type, named intrusion ion pair, has also been characterized.  

Quantitative Approach to the Factors Influencing Solubility of Drugs 

• The solubility of most solid solutes is significantly affected by temperature. When some solid dissolves in a liquid a change in the physical state of the solid analogues (melting) takes place. Heat is required to break the bonds holding the molecules in the solid together. At the same time, heat is given off during the formation of new solute-solvent bonds. The typical solubility data for some common inorganic compounds at respective temperatures is given.
  

• Generally, increase in temperature increases solubility of solids in solvent. Although in many cases solubility increases with the rise in temperature and decreases with the fall of temperature, it is not necessary in all cases. It means there are exceptions that solubility decreases with increase in temperature.

CASE I: Increase in Solubility with Temperature 

•  In endothermic processes solubility increases with the increase in temperature and vice versa. For example, solubility of potassium nitrate increases with the increase in temperature. If the heat given off in the dissolving reaction is less than the heat required to break apart the solid, the net dissolving reaction is endothermic (energy required). Therefore, the heat is drawn from the surroundings. The addition of more heat facilitates the dissolving reaction by providing energy to break bonds in the solid. This is the most common situation where an increase in temperature produces an increase in solubility for solids. 

CASE II: Decrease in Solubility with Temperature 

•  In exothermic processes solubility decrease with the increase in temperature. For example, solubility of calcium oxide decreases with the increase in temperature. Gases are more soluble in cold solvent than in hot solvent. If the heat given off in the dissolving process is greater than the heat required to break apart the solid, the net dissolving reaction is exothermic (energy given off). The addition of more heat (increases temperature) inhibits the dissolving reaction since excess heat is already being produced by the reaction. This situation where an increase in temperature produces a decrease in solubility is not very common, for example, calcium hydroxide is more soluble at cold temperatures than at warm. When we dissolve a substance we must separate the intermolecular forces which surround the molecules. Separation of molecules requires a certain amount of energy which, in this case, can be provided in the terms of heat. There is also the possibility that compound will form a bond with the solvent resulting in energy release. However, care must be taken while supplying heat that may destroy a drug or cause other changes in the solution. For example, sucrose solution when we heat in presence of acid results in formation of invert sugar. The energy is supplied in the form of heat, providing a cooling effect. On the other hand, there is possibility of interaction between solute and solvent with formation of dipole-dipole type bond and this interaction will tend to give off heat. Based on which of these interactions are greater, we can get increase or decrease in temperature. A good example is mixture of chloroform and acetone. There exists a strong interaction between acetone and chloroform molecules. The heat produced by solute-solvent interaction is so much higher than the heat necessary to separate the molecules of acetone and chloroform, that the excess heat can be detected as rise in temperature of the liquid. 

Solubility Curves:

•  Solids are usually more soluble at higher temperatures; more salt will dissolve in warm water than in an equal amount of cold water. A graph showing the solubility of different solids as a function of temperature are very useful in chemical analysis. A curve drawn between solubility and temperature is called solubility curve. It indicates the effect of   temperature on solubility of substances. Substances such as calcium acetate and calcium chromate show decreased solubility with increase in temperature while sodium nitrate and lead nitrate show increase in solubility with increase in temperature. The solubility curve of sodium chloride shows very minute rise with increase of temperature. There are two types of solubility curves as shown.

Continuous Solubility Curve:

• Solubility curve of substance such as calcium salts of fatty acids, potassium chlorates, lead nitrate and sodium chloride are continuous solubility curves. They show no sharp break in the curves anywhere. The solubility curve of hydrated calcium sulphate shows a rise and then fall but it remains continuous at maximum point. 

Discontinuous Solubility Curve: 

•  The solubility curve which shows sudden change in direction is called as discontinuous solubility curve. For example, sodium sulphate, calcium chloride, ammonium nitrate etc. At the break a new solid phase appears, and another solubility curve of that new phase starts. The break in a solubility curve shows with sharp point where two different curves meet each other.

Diffusion Principles in Biological Systems

• Matter moves by diffusion along energy gradients from areas of high concentration to areas of lower concentration. The rate of diffusion depends on temperature, size of the particles, and the size of the concentration gradient. In biology, the selectively permeable cell membrane creates two special forms of diffusion namely: osmosis for the diffusion of water, and dialysis for the diffusion of solutes.

• Diffusion is one principal method of movement of substances within cells, as well as for essential small molecules to cross the cell membrane. Cell membranes act as barriers to most, but not all, molecules. A cell membrane that could allow some materials to pass while prevent the movement of other molecules is a major step in the development of the cell. The cell membrane functions as a semi-permeable barrier, allowing a very few molecules across it while holding majority of chemicals inside the cell. Cell membranes separate the inner cellular environment from the outer cellular (or external) environment. Most of the molecules move from higher to lower concentration, although there will be some molecules that move from low to high. The overall movement is thus from high to low concentration. If there is no energy input into the system, the molecules reach a state of equilibrium and gets uniformly distributed throughout the system.

• A cell membrane is composed of phospholipids and proteins. Absorption of drugs across the stomach lining/mucosa and the blood/brain barrier are two representative examples of transport phenomenon. Skin is another great example of a membrane for the entry of drugs. The transport of drug molecules through a non-porous membrane occurs by diffusion. Transport through porous cell membranes occurs by diffusion and convection. The rate of diffusion is expressed by equation (1.2). dM dt = DSK (C1 − C2) h .

• Where, M is amount of drug dissolved, t is time, D is diffusion coefficient of the drug, S is surface area of membrane, K is oil/water partition coefficient, h is thickness of the liquid film, C1 is the concentration of drug at donor side of membrane and C2 is the concentration of drug at receptor side and C1 – C2 is concentration gradient. However, C1 and C2 are not measured since these are values varies within the membrane.

• Typically, the gradient is measured as Cd − Cr , representing the partition at each phase, namely Ko/w = C1/Cd and Ko/w = C2/Cr . The rate of drug transport into diffusional system is predominantly dependent upon the magnitude of the concentration gradient considering the other parameters constant.

• Water, carbon dioxide, and oxygen are among the few simple molecules that can cross the cell membrane by diffusion (or a type of diffusion known as osmosis). Gas exchange in lungs operates by diffusion process. All cells because of cellular metabolic processes produce carbon dioxide. Since the source is inside the cell, the concentration gradient is constantly being replenished/re-elevated; leading to net flow of CO2 out of the cell. Metabolic processes in animals and plants usually require oxygen, which is in lower concentration inside the cell, have the net flow of oxygen into the cell through diffusion.  

Solubility of Gas in Liquids 

• Solubility of gas in liquids is the concentration of dissolved gas in the liquid when it is in equilibrium with the pure gas above the solution. The example of gas in liquid includes effervescent preparations containing dissolved carbon dioxide, ammonia water and hydrochloride gas. Aerosol products containing nitrogen or carbon dioxide as propellant are also considered to be solution of gases in liquids.

• Factors Affecting Solubility of Gas in Liquids: The solubility of gas in liquids depends on pressure, temperature, salt present, chemical reaction and micellar solubilization. 

Pressure: 

• Liquids and solids exhibit practically no change of solubility with changes in pressure. When considering solubility of gases in liquids, the pressure of the gas in contact with the liquid is important. At higher gas pressure, more gas is dissolved in liquids, Fig 1.6. For example, the soda bottle is packed at high pressure of carbon dioxide before sealing. When the cap of bottle is opened, the pressure above the liquid is reduced to 1 atm and the soda fizzes. This fizzing is just carbon dioxide that was dissolved in soda, is getting released. Therefore, if lower is the pressure less carbon dioxide is soluble. 

• The effect of pressure on the solubility of gas is given Henry’s law which states that in dilute solution the mass of gas which dissolves in each volume of liquid solvent at constant temperature is directly proportional to partial pressure of gas. Mathematically it is expressed as Sg = KHPg … (1.3) Where, Sg is solubility of gas, expressed as mol/L; KH is Henry law constant which is different for each solute-solvent system and Pg is partial pressure of the gas in mmHg. The amount of undissolved gas above the solution is obtained by subtracting the vapour pressure of the pure liquid from the total pressure of the solution. 

The solubility of a pure gas in water at 25 °C and at 1 atm pressure is 1.5 × 10−3 mol/L. What will be the concentration of the gas at same temperature at 0.5 atm? 

• Solution: Given that: Pressure = 1 atm = 101.3 kPa Concentration = 1.5 × 10−3 mol/L Solubility (Sg) = ? Sg = KHPg 1.5 × 10−3 = KH × 101.3 KH = 1.519 × 10 Now, at P = 0.5 atm = 0.5 × 101.3 kPa Sg = KHPg = 1.519 × 10−5 × 0.5 × 101.3 = 7.693 × 10-4 mole/L The concentration of gas at 25°C and at 0.5 atm pressure will be 7.693 × 10−4 mole/L.

Solubility of Liquids in Liquids 

Binary Solutions 

• It is very common for two or more liquids to be mixed together to make a solution. Therefore, we need to know what liquids can be mixed together without precipitation. Examples of pharmaceutical solutions of liquid dissolved in liquids are hydroalcoholic solutions, aromatic waters, spirits, elixirs, lotions, sprays and some medicated oils that contain mixture of two or more miscible oils. When two or more liquids mixed together, they can be completely miscible, partially miscible or practically immiscible. Completely miscible liquids mix uniformly in all proportions and hence do not get separated. Partially miscible liquids form two immiscible liquid layers, each of which is saturated solution of one liquid in the other. Such liquid pairs are called as conjugated liquid pairs.

• The mutual solubility of partially miscible liquids, being temperature specific, is affected by changes in temperature. For binary phase systems, such as phenol-water system, the mutual solubility of two conjugate liquid phase increases with increase in temperature called as conjugate temperature, where as above this temperature they are soluble in any proportions. Other examples of partial miscibility include conjugate liquid pair of nicotine and water, ether and water, and triethnolamine and water. Immiscibility refers to those systems which do not mix with each other at all such as water and liquid paraffin or water and oil. The dielectric constant of a substance also affects the solubility of substance.

• It is known fact that the polarity of solvent is dependent on the dielectric constant. Also, remember that LIKE DISSOLVES LIKE. The influence of a foreign substance on a liquid-liquid system is like the idea of three component system in the phase rule. Ternary systems are produced by addition of third component to a pair of partially miscible liquids to produce a solution. If added component is soluble in only one of the two components or if its solubility in the two liquids is markedly different, the mutual solubility of the liquid pair is decreased. If added solute is roughly soluble in both the liquids approximately to the same extent, then the mutual solubility of the liquid pair is increased. This is called blending. An example of this is when succinic acid is added to the phenol-water mixture. The succinic acid is soluble or completely miscible in each phenol and water therefore it causes a blending of the liquids making the mixture one phase. 

Ideal Solutions

• Dilute solutions consist of negligible amount of solute compared to pure solvents. These solutions are referred as ideal solutions. An ideal solution is one in which there is no change in the properties of the components other than dilution when they are mixed to form the solution. No heat is evolved or absorbed during the solution formation. The final volume of real solution is an additive property of the individual component. In another way it can be stated as a solution which shows no shrinkage or expansion when components are mixed to form solution. Ideal solutions are formed by mixing different substances having similar properties and therefore there is complete uniformity of attractive intermolecular forces. For example, when equal amounts of methanol and ethanol are mixed together, the final volume of the solution is the sum of the volumes of the methanol and ethanol.

• Solutions used in pharmacy consist of wide variety of solutes and solution. The basis of solubility and solution theory is based on ideal solution. In ideal solution there is a complete absence of attractive or repulsive forces and therefore the solvent does not affect solubility. The solubility in this case depends on temperature, the melting point of solute and the molar heat of fusion (∆Hf). In ideal solution heat of solution is equal to ∆Hf. Therefore, solubility in an ideal solution can be expressed by, − log Xi 2 = ∆Hf 2.303R      To − T ToT

• Where, Xi 2 is the ideal solubility in terms of mole fraction, R is gas constant; T is the temperature of solution and To is the temperature (Kelvin) of solute. The equation (1.4) can be used to calculate molar heat of fusion by plotting the log solubility versus reciprocal of absolute temperature which results in a slope of − ∆Hf/2.303R. Unfortunately, most of the solutions are non-ideal (real) because there may be interaction between solute and solvent. In these solutions mixing of solute and solvent can release or absorb heat into or from surroundings, respectively. While describing non-ideal solution, activity of solute must be considered. Activity of solute is defined as concentration of solute multiplied by the activity coefficient (X2). The activity coefficient is proportional to the volume of solute and to the fraction of the total volume occupied by the solvent. On substitution these values in equation (1.4) we get; − log X2 =      ∆Hf  2.303R      To − T To + log (µ2) 

• As activity approaches unity, the solution becomes more ideal. For example, as a solution become more dilute the activity increases and the solution becomes ideal. The log of activity coefficient (log X2) is the term that considers the work of solubilization, volume of solute and the volume of solvent. The work of solubilization includes the intermolecular forces of attraction removing molecule from the solid and integrating into the solvent. One more term solubility parameter (γ2) which is a measure of cohesive forces between like molecules is considered for solubility. It is expressed by following equation. − log γ2 = (ρ1 − ρ2) V2φ 2 1 2.303 … (1.6) Ρ =      (∆Hv − RT) V1 1/2 

• Where, ∆Hv is heat of vapourization of solute, V1 is volume/mole of solute as a liquid, V2 is the molar volume of solute and φ1 2 is the volume fraction of solvent, T is temperature (Kelvin) and R is gas constant.

• Example 10.2: The molar heat of fusion and melting point of benzoic acid is 4139 cal/mole and 122°C, respectively. Calculate ideal mole fraction solubility of benzoic acid at 25o C. Given: Gas constant = 8.134 J/K mole.

• Solution: Given that: To = 122 °C = 273 + 122 = 395 K T = 25 °C = 273 + 25 = 298 K R = 8.134 J/K.mole ∆Hf = 4139 cal/mole = 4139 × 4.184 = 17317.58 J/mole − log Xi 2 =      ∆Hf  (2.303R)      (To – T) (ToT) =      17317.58  (2.303 × 8.314)      (395 – 298) (395 × 298) =      17317.58 19.1471      97  117710 = 0.7453 X i 2 = antilog (− 0.7453) = 0.1798 The ideal mole fraction solubility of benzoic acid is 0.1798.     

Raoult’s Law 

• In ideal solution volume changes are negligible. Dilute solutions show colligative properties. These properties are the factors that determine how properties of a bulk solution change depending upon the concentration of the solute in it. Colligative properties are properties of a solution that depend mainly on the relative numbers of particles of solvent and solute molecules and not on the chemical properties of the molecules themselves. These can almost be referred as statistical properties because they can be understood solely based on relative number of different particles in a solution. There are four types of colligative properties namely:

1. Lowering of vapor pressure
2.  Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure.

• Colligative properties of non-electrolyte solutions are regular. The values of colligative properties are approximately equal for equimolar concentration of drugs. It is possible to determine the number of solute particles present in the solution by measuring these properties and comparing them with the corresponding properties of the pure solvent. If mass of solute present in known, the number average molecular weight can be calculated by dividing the mass of solute by number of particles present to obtain the average mass of particles. Osmotic pressure is the most important colligative property since it is related with physiological compatibility of parentral, ophthalmic and nasal solution. It is difficult and inconvenient to measure osmotic pressure and therefore other colligative properties are determined and related to osmotic pressure. In the following section equations for colligative properties of ideal solution are derived and are validated for this type of solutions. These equations can be applied to real solutions with respect to limit of small concentrations. While using these equations for real (non-ideal) solutions it requires correction to be made to these ideal equations because in real solutions there exist intermolecular interactions. 

Lowering of Vapour Pressure: 

• Lowering of vapour pressure is the simplest of the colligative properties and easiest to understand based on physical model. The pressure brought by vapour in equilibrium with its liquid at constant temperature is known as vapour pressure. It increases with temperature. The vapour pressure of solvent is due to its escaping tendency. Temperature at which the vapour pressure of the liquid is equal to the atmospheric pressure is called as normal boiling point. The vapour pressure of pure liquid solvent depends upon the rate of escape of molecule from the surface known as escaping tendency. Solvents with greater escaping tendencies have greater vapour pressure. The added solute is generally non-volatile which does not contribute directly to the vapour pressure of the solution. The solute interferes and prevents solvent molecules from escaping into the atmosphere. Therefore, the vapour pressure of solution is lower than that of pure solvent. The lowering of vapour pressure is proportional to the number of solute particles or ions. The effect of non-volatile solute on the vapour pressure may be determined in dilute solutions by applying Raoult’s law. It states that in an ideal solution the partial vapour pressure of each volatile constituent is equal to the vapour pressures of pure constituent at that temperature multiplied by its mole fraction in the solution. In equation form for two volatile constituent A and B, it can be expressed as PA = P° A XA … (1.8) PB = P° B XB

• where, PA and PB are partial vapour pressures, P° A and P° B are vapour pressures of pure constituents and XA and XB are mole fractions of the constituent A and B, respectively. The total vapour pressure of solution is sum of partial vapour pressure of each volatile constituent. Therefore

•  The partial vapour pressure of A and B and the total vapour pressure of solution is shown in Fig. 1.8. There are two ways to explain Raoult’s law. First, the simple visual way and the second one is a more sophisticated way based upon entropy. To describe using a simple way, consider that equilibrium is set-up where the number of molecules of solvent breaking and escaping away from the surface and some of them are sticking on to the surface again as shown in Fig. 1.9. An added solute molecule to the solvent replaces some of the solvent molecules present at the surface causing reduction in surface area. 

• A certain fraction of the solvent molecules has enough energy to escape from the surface. If these molecules are decreased as added solute replaces some of them causing reduction in the number of molecules escaping from the surface. The net result of this reduction in number is that the vapour pressure of the solvent is reduced. The composition of the solution in terms of mole fraction can be expressed as

• 
  XA + XB = 1 … (1.11) ∴ XA = 1 − XB … (1.12) Substituting equation (1.12) in equation (1.8) gives PA = P° A (1 − XB) … (1.13) Simplifying equation (1.13) we get XB = (P° A − PA) P ° A … (1.14) Substituting terms for mole fraction in equation (1.14) gives (P° A − PA) P ° A = nB (nA + nB) … (1.15) 

• where, nA and nB are number of moles of solute and solvent. Above equations (1.14) and (1.15) shows that relative lowering of vapour pressure of the solution is equal to the mole fraction of the solute. The mole fraction and vapour pressure in equation (1.14) and (1.15) has no units because these are relative expressions. Hence any units consistent with the system can be used. 

Deviations from Raoult’s Law: 

In real solutions, there is no complete uniformity of intermolecular attractive forces. There are many such liquid pairs that show greater cohesive forces than the attractive forces and greater attractive forces than the cohesive forces. It can be observed even when liquids are completely miscible in all proportions. Such mixtures of liquid pairs are real or non-ideal solutions. They do not adhere to the Raoult’s law over the entire range of concentrations and are represented as deviations. This behavior shown by liquid mixtures are called as positive deviation. 

Limitations of Raoult’s Law: 

• Raoult’s law work only for ideal solutions over entire range of concentrations. An ideal solution obeys Raoult’s law. While applying this law to real solutions it has following limitations.

Real Solutions: 

•  In real solution, the concentration of solute is high and thus intermolecular forces between solute-solute and solute-solvent are predominant that slows down the escaping of solvent molecules from the surface. This causes deviation from Raoult’s law because it is applicable only to dilute solutions where the forces between solute and solvent are exactly same as those between solvent-solvent molecules. 

Nature of the Solute: 

•  Raoult’s law is applicable only for solutes which are non-volatile in nature. Volatile solutes can contribute for vapour pressure above the solution which may cause the deviation from Raoult’s law. Raoult’s law does not apply if the added solute associates or dissociates in solvent. If association takes place the number of particles or molecules decreases causing reduction in lowering of vapour pressure. On the contrary, if solute gets dissociated a greater number of particles or ions are formed. For example, when 1 mole of solid sodium chloride is added to water it dissociates to produce two moles of ions as Na+ and Cl–. Na+ Cl− (solid) → Na + (aq) + Cl− (aq) If 0.1 mole of sodium chloride is added to water its dissociation takes place to form 0.2 moles of particles in solution. Thus, it increases lowering of vapour pressure of solution.   

Real Solutions 

• Real solutions show change in the total volume of the solution upon mixing its different components together. Also, there is absorption or evolution of heat during mixing and solution formation. For example, at room temperature when 100 mL of sulfuric acid is mixed with 100 mL of water, the total volume of solution becomes 180 mL rather than 200 mL. During mixing of acid and water considerable heat is evolved causing reduction in total volume of the solution

Partially Miscible Liquids

• Although three types of liquid/liquid systems are commonly encountered liquidliquid systems are mainly divided into two categories depending on the solubility of one substance in the other. The categories are complete miscibility and partial miscibility. Miscibility is the common solubilities of the components in liquid-liquid systems. Partial miscibility is when the substances only mix partially. When mixed, there are two layers formed each layer containing some of both liquids. Of these two mixed layers, each layer contains some of both the liquids for example, phenol and water. Some liquids are practically immiscible (for example, water and mercury), whilst others (for example, water and ethyl alcohol or acetone) mix with one another in all proportions.

• The mutual solubility or miscibility of two liquids is a function of temperature and composition. When two liquids (liquid A and liquid B) are partially soluble in each other, two liquid phases can be observed. At equilibrium, each phase contains liquid A and liquid B in amounts that reflect their mutual solubility. Some systems are totally miscible (i.e., they form a one-phase liquid) at high temperatures but separate into two liquid phases at lower temperatures. These systems have an upper consolette temperature, TUCT, in a plot of temperature versus mole fraction. Other systems are totally miscible at low temperatures but separate into two phases at higher temperatures giving rise to a lower convolute temperature, TLCT.

• Oil and water don’t mix. Pouring 10 mL of olive oil into 10 mL of water results in two distinct layers, clearly separated by a curved meniscus. Each layer has the same volume and essentially the same composition as the original liquids. Because very little mixing occurs apparently, the liquids are called “immiscible”. For example, pouring grain alcohol into the water results in a single liquid phase. No meniscus forms between the alcohol and the water, and the two liquids are considered “miscible”. Nearly any pair of liquids is miscible if only a trace amount of one of the liquids is present.

• Many liquid mixtures fall between these two extremes. Two liquids are “partially miscible” if shaking equal volumes of the liquids together results in a meniscus visible between two layers of liquid, but the volumes of the layers are not identical to the volumes of the liquids originally mixed. For example, shaking water with certain organic acids results in two clearly separate layers, but each layer contains water and acid (with one layer mostly water and the other, rich in acid.) Liquids tend to be immiscible when attractions between like molecules are much stronger than attractions between mixed pairs. Many examples are known, however, in which the liquids are partially miscible with one another. If, for example, water be added to ether or if ether be added to water and the mixture shaken, solution will form up to a certain point; beyond this point further addition of water on the one hand, or of ether on the other, will result in the formation of two liquid layers, one consisting of a saturated solution of water in ether and the other a saturated solution of ether in water. Two such mutually saturated solutions in equilibrium at a temperature are called conjugate solutions.

• A conjugate system has two partially miscible liquids in contact with each other. The proportionate quantities of these liquids are responsible for their existence as two liquids in contact with. Under this condition a saturated solution of one liquid in other or vice-versa is formed. The miscibility of such solution mixture can be increased by increasing temperature. For example, phenol – water, nicotine – water, triethanolamine – water etc.

• Phenol-water solution is characterized by increasing mutual solubility with rise of temperature. Thus, when phenol is added to water at the ordinary temperature, a homogeneous liquid is produced. When the concentration of the phenol in the solution has risen to about 8 %, the addition of more phenol results in the formation of a second liquid phase, which may be regarded as a solution of water in phenol. If now the temperature is raised, the second liquid phase will disappear, and more phenol must be added to produce a separation of the liquid into two layers. By increasing the amount of phenol in this way and observing the temperature at which the two layers disappear, the so-called solubility curve of phenol in water may be determined. In a similar manner, the solubility curve of water in liquid phenol may be obtained, and it is found that the solubility also increases with rise of temperature. Since with rise of temperature the concentration of water in the phenol layer and of phenol in the water layer increases. The compositions of the two conjugate solutions become more and more nearly the same and at a certain temperature the two solutions become identical in composition. The temperature at which the two layers become identical in composition and are in fact one layer is known as the critical solution temperature or the consulate temperature of the system. Above this temperature, the two liquids are miscible in all proportions. If the resulting mixture is represented by a point in the area enclosed by the solubility curve, separation into two layers will take place, whereas if the total composition of the mixture and the temperature is expressed by a point lying outside the solubility curve a clear homogeneous solution will result. 

Critical Solution temperature and its applications 

• A phase diagram is a plot describing conditions of temperature and pressure under which two or more physical states coexist in dynamic equilibrium. It means phase diagram is a graphical representation of chemical equilibrium. This diagram is also called as Pressure – Temperature graph.

• 
  In phase diagram of water there are three lines or curves that separate the area of each phase. Adjacent to each line there exist a different single phase of water. At any point on line there exist equilibrium between two phases shown by area i.e. solid/liquid, liquid/vapour and solid/vapour. The line OA, OB and OC represents equilibrium between liquid and vapour, solid and liquid and solid and vapour phases, respectively. The line OA represents vapourization curve and OC represent sublimation curve. For example, above line OA the liquid-water exist and below it water vapour exists. The liquid – vapour equilibrium curve has a top limit labeled as C in the phase diagram. This is known as critical point. Water has a critical point of 374°C. The temperature and pressure corresponding to this point is known as the critical temperature and critical pressure, respectively. The solid – liquid equilibrium line (m. p. line) slopes backwards (negative slope) rather than forward (positive slope). It means in case of water; the melting point gets lower at higher pressures. At solid – liquid equilibrium the ice is less dense than liquid water formed as it melts, and the water formed occupies a smaller space. At this equilibrium if pressure is increased the equilibrium move to reduce the pressure again. That means it moves to the side with smaller volume. To make the liquid water freeze again at this high pressure, we need to reduce the temperature. Higher pressure means lower melting point.

• The transition temperature (TUCT) of a system helps to determine percent purity of substances. The change in TUCT is proportional to the concentration of substance added. For example, in phenol-water system addition of sodium chloride or potassium chloride changes its TUCT depending upon concentration of these substances. If known different concentration solutions of sodium chloride are prepared and added separately to phenol-water mixtures having composition say 50:50, then TUCT of the system is determined by plotting a phase diagram by taking concentrations of sodium chloride on x-axis and UCT on y-axis. An unknown solution of sodium chloride is then added to phenol – water (50:50) system and again TUCT is determined. It is plotted on curve to obtain its concentration by extrapolating on x-axis. The TUCT is mostly used as criterion to test the purity of substances that form conjugate system with some other liquid. 

• Phenol USP is a necrotic agent having freezing point 17ºC. Thus, at room temperature it exists in solid crystalline form. The corrosive characteristic and solid nature of phenol makes it difficult to handle. The Liquefied Phenol BP contains 80% w/w of phenol in water. The presence of other substance or impurities solidifies phenol approximately at about 10°C. The miscibility curve of phenol-water system suggest that 76% w/w of phenol should be used in the preparation. At this concentration freezing point of phenol is 3.5°C. Such preparations remain in liquid form that can be handled easily. In India, we have wide variety of climatic conditions with diverse temperatures ranging from 10 – 40°C during different seasons. Hence, a preparation which is in dry powder state in winter or rainy season would become pasty during summer. The TUCT can also be used to determine percent compositions of each component in unknown mixtures. The temperature below which when system containing partially miscible liquids exist only as a single phase is known as lower consolute temperature (TLCT). For example, triethanolamine (TEA) - water system has TLCT of about 18.5°C at 13% w/w of TEA. The temperature – concentration plot of this system is shown in Fig. 1.12. Above 18.5°C mixture of these liquids forms two layers. The left upward curve shows decrease in miscibility of TEA in water whereas right upward curve shows decrease in miscibility of water in TEA with increase in temperature of system, respectively. At 50% by weight of TEA in water at 18.5°C forms single phase. This temperature is called TLCT of TEA – water system. The region outside the curve shows mutual solubility of TEA and water in each other. Other examples of liquid pairs that shows TLCT are dimethylamine – water (43°C, 13% w/w weight of dimethylamine), 1-methyl piperidine – water (48°C, 5% w/w of piperidine), polyethylene glycol – water, paraldehyde – normal saline, water – Tween 80, etc. 

• Phenol and water are partially miscible liquids at room temperature. In this system, addition of small amount of phenol to water or water to phenol significantly changes relative volumes of two layers but not their compositions.

• If temperature is increased by keeping composition constant the mutual solubility of both the liquids increases and at a specific temperature they become completely miscible and two layers becomes one. Thus, at a specific temperature the composition of both the components are fixed and both the liquids are miscible in all proportions with each other. The temperature at which two partially miscible liquids are in the state of one phase is known as critical solution temperature (CST) or upper consolute temperature (TUCT). This behaviour of critical solution temperature is shown by phenol-water system as represented in Fig. 1.13. At any temperature (say T°C) the points F and C represents the composition of two layers in equilibrium with each other. The two solutions A (phenol in water) and B (water in phenol) are in equilibrium at a temperature is known as conjugate solution temperature. At this temperature two solutions of different concentrations exist in equilibrium with each other. The line in phase diagram of phenol-water joining the points F and E is called as tie line. It is defined as the line which connects the compositions of the two layers in equilibrium on the phase diagrams of the system. At point C, the top of the dome shaped curve, two layers become identical, resulting in disappearance of second layer to form a single phase. The temperature at which this happens is called as TUCT of phenol – water system. At any temperature above TUCT both the liquids are completely miscible; whereas below this temperature they exist in separate layers as individual entities. 

Applications: 

•  Basically, CST allows the temperature limits for some reactions to be determined if it requires that two liquids are miscible. An important application of the CST is to determine the water content in substances such as methyl and ethyl alcohols. Here the system is usually the alcohol and a hydrocarbon, such as -hexane or dicyclohexyl. The water is, insoluble in the hydrocarbon. Thus, the methyl alcohol-cyclohexane system has a CST 45 - 50 °C and even presence of 0.1 % water produces a rise of 0-15 °C in the CST. The concept of TLCT is helpful in preparation of paradeladehyde in saline. If during preparation solution of paraldehyde is cooled, rapid solution formation takes place. At room temperature nicotine and water are miscible in all proportions with each other. As temperature is raised the mutual solubility of these liquids decreases. Further increase in temperature again at some higher temperature their mutual solubility increases. Nicotine - water system possess both TUCT and TLCT of 208 °C at 32 % w/w and 61 °C at 22% w/w of nicotine, respectively. Above TUCT and below TLCT system exist as single phase where as at any temperature between them it exists as two phase system (partial miscibility). The solubility curves of these two liquids are shown as closed curve. Pressure has effect on nicotine – water system that increase in pressure increases TLCT and decreases TUCT. At a specific pressure and above, these partially miscible liquids are completely miscible in all proportions with each other at all the temperatures. Other systems that show TUCT as well as TLCT are glycerin and m-toludine and β-picoline and water. The CST is affected by pressure and by the presence of impurities. Hence the CST may be taken as a criterion for the purity of a substance.   

Distribution Law 

• In pharmaceutical practice, often a single substance is dissolved in two immiscible phases’ i.e. two liquid phases in contact that do no not mix, such as chloroform and water. When an excess amount of solute is added to two immiscible liquid phases, it distributes itself between these phases until saturation, if mixed by shaking vigorously. If insufficient amount of solute is added it distributes in a definite ratio. The term partition coefficient is commonly refers to the equilibrium distribution of single substance between two solvent phases separated by a boundary. If third substance dissolves to some extent in both phases, the partition coefficient is the ratio of the amounts of the third substance dissolved in two phases. Partition coefficients’ are sometimes called distribution coefficient. The partition coefficient is a measure of drugs lipophilicity and is an indication of its ability to cross cell membranes. It is commonly determined using an oil phase of octanol or chloroform and water.

• If there is possible confusion with the extraction factor or mass distribution ratio the term concentration distribution ratio should be used. The terms distribution coefficient, extraction coefficient and, wherever appropriate, scrubbing coefficient, stripping coefficient are widely used as alternatives but are not recommended. If they must be used in a given situation the term ratio is preferable to coefficient. In equations relating to aqueous/organic systems the organic phase concentration is, by convention, the numerator and the aqueous phase concentration the denominator. In the case of stripping ratio, the opposite convention is sometimes used but should then be clearly specified. In the past, there has been much confusion between the distribution ratio as defined above, the value of which varies with experimental conditions, for example, pH, presence of complexing agents, extent of achievement of equilibrium etc. and the true partition coefficient which is by definition invariable or the partition coefficient or distribution constant which apply to a chemical species under specified conditions. For this reason, the terms distribution constant, partition constant, partition coefficient, partition ratio and extraction constant should not be used in this context. The use of the ratio of light phase concentration to heavy phase concentration is ambiguous and is not recommended. The distribution ratio is an experimental parameter, and its value does not necessarily imply that distribution equilibrium between the phases has been achieved.

Thermodynamic Deduction of Distribution Law: 

• Chemical potential of solute is at equilibrium in both aqueous and organic immiscible solvents. The chemical potential (µw) of solute in aqueous phase is expressed as: µw = µ° w + RT ln Cw.

• where, µ° w standard chemical potential of solute in aqueous phase, Cw is concentration of solute in aqueous phase, R is gas constant and T is absolute temperature. Similarly, the chemical potential of solute in organic phase is expressed as µorg = µ ° org + RT ln Corg … (1.17)

• where, Corg is concentration of solute in organic phase and µ° org is standard chemical potential of solute in organic phase. At the equilibrium upon distribution: µw = µorg … (1.18) µ° w + RT ln Cw = µ ° org + RT ln Corg RT ln (Cw/Corg) = µw − µorg … (1.19) 

• At given temperature, standard chemical potentials of solute in aqueous and organic phases are constant. RT ln (Cw/Corg) = Constant … (1.20).

• Therefore, ratio Cw/Corg is constant at given temperature. The ratio constant is called as distribution coefficient or partition coefficient and it depends upon amount of solute added. The equation (1.20) represents the Nernst distribution law.

• The ability of a drug to dissolve in a lipid phase when an aqueous phase is also present often referred to as lipophilicity, can be best characterized by a partition coefficient. The true or intrinsic partition coefficient can be defined as ratio of unionized drug distributed between the organic and aqueous phases at equilibrium. It is expressed for unionizable molecules as Ko/w = Co/Cw … (1.21).

• where, Co is concentration of unionized drug in organic phase and Cw concentration of unionized drug in aqueous phase. For ionizable molecules (acids, bases, salts) it is expressed as Ko/w = Co (1 − α)Cw … (1.22) .

• In equation (1.22) the term α is the degree of ionization in aqueous solution. Since partition coefficients are difficult to measure in living systems, they are usually determined in vitro using n-octanol as the lipid phase and a phosphate buffer of pH 7.4 as the aqueous phase. This permits standardized measurements of partition coefficients. The Ko/w is expressed in the form of log Ko/w as the measure of lipophilicity. If added solute has equal molecular weight in both the phases, then ratio of the concentration of solute in both phases is found to be constant. These concentrations of solute in aqueous and organic phases are expressed in g/liter or gram equivalent/liter. Being the ratio of two concentrations the constant, partition coefficient is dimensionless value. The value of Ko/w is unit less. It is necessary to specify in which of these two ways the partition coefficient is being expressed. No convention has been established with regard to whether the concentration in aqueous phase or in the organic phase should be placed in the numerator. Therefore, partition coefficient may be expressed as Ko/w = Cw/Co or K = Co/Cw (1.23).

• Partition coefficient is measured using low solute concentration, where K or Ko/w is a very weak function of solute concentration. Extensive data for the partitioning of drugs between octanol and water has been tabulated through the years, Table 1.3. For drugs having values of K much greater than 1 are classified as lipophilic whereas those with K smaller than 1 indicates a hydrophilic 

Limitations of Distribution Law 

• The selected solvent liquid pair must be immiscible with each other. Any mutual solubility must not affect distribution of solute if left aside for enough time to separate. 
• The experimental temperature must be maintained constant. As temperature has effect on solubility of solute, any change in temperature during determinations may change the findings.
•  The solute in question should be in same molecular state in both the solvents. If any chemical change is observed the concentration of species common to both solvents only should be considered. 
• Solute must present in the solvent at low concentrations. At high concentrations of solutes Nernst’s distribution law does not hold good. 
• Samples should be withdrawn for analysis only after achievement of equilibrium. Early equilibrium attainment can be possible by vigorous shaking.

Applications of Distribution Law

•  Partition coefficient first finds applications in medicinal chemistry and drug design.

• It has proved useful in other related areas such as drug absorption, bioavailability, toxicity, bioaccumulation and metabolism. Although it appears that the partition coefficient may be the best predictor of absorption rate, the effect of dissolution rate, pKa and solubility on absorption must not be neglected. 

• Partition coefficient values are helpful in knowing the hydrophobic drug receptor interactions.

• Partition coefficient help to understand the mechanism of preservative action of weak acids and determination of its optimum concentration for the effectiveness of action.

• From the partition coefficient general idea about the drugs solubility in solvent can be judged. It can be further useful in drugs solubility enhancement.

• For series of compounds, the partition coefficient can provide an empiric handle in screening for biologic properties. For drug delivery, the lipophilic/hydrophilic balance has been shown to be a contributing factor for the rate and extent of drug absorption. 

• Although partition coefficient data alone does not provide understanding of in-vivo absorption, it does provide a means of characterizing the lipophilic/hydrophilic nature of the drug. Since biological membranes are lipoidal in nature the rate of drug transfer for passively absorbed drugs is directly related to the lipophilicity of the molecule.

• Partition coefficient values are helpful in the extraction of drugs from mixtures such as blood, urine and crude plant extracts. Drugs depending upon its partition coefficient values extracts in organic or aqueous solvents. Efficient extraction is carried out by repeating steps several times.

• Partition coefficient has applications in drug separation by partition chromatography. This technique comprises of silica column soaked in water to which a mixture containing drugs is applied. A water immiscible solvent such as hexane is allowed to flow through column. The drugs in mixture partitions into hexane in order of their partition coefficient. The drug having high partition coefficient will partition first followed by other drugs in mixture with lower partition coefficient values. Each drug can be collected separately. 

• Partition coefficient values help to study structure activity relationship for series of compounds.

• To study release of drug from gels, ointments and creams partition coefficient is a very important consideration.