Solubility expression Physical Pharmaceutics

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 the mass of solute dissolved in a  particular volume of solvent. 

The solubility is generally expressed in grams per liter.  Therefore, the 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. The most commonly encountered solutions are solids dissolved in liquids.

The solid that dissolves in a liquid is the solute and the liquid in which it dissolves is solvent. A solute is a dissolved agent usually the less abundant part of the solution whereas solvent is the more abundant part of the 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 the 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 the 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 environmental factors 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 the activity of drugs depends on solubility, it is equally important to control environmental conditions which impact various types of solutions.

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 a substance is defined as the amount of solute dissolved in a  specific amount of solvent at a 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 the solubility of solutes but being inaccurate is 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 Table 1.1 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 into the 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 a 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 dissolves under specified conditions.  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 the 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 at which the solvated molecules return to the solid.

In Fig. 1.1, 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 a substance is the 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 at 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 that contains more concentration of solute than the saturated solution is known as a 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 a small amount of solute causes all of the excess dissolved solute to crystallize out of the solution.

A saturated potassium chloride solution at 10oC 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  30oC  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 40oC. Cooling the hot solution (40oC) will reverse the process.  When the temperature decreased to 20oC 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 the 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 the 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 cm3of solutions. 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 liter (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 the 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 a 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 1Eq of Na+ and 1 mol or 1 Eq of HCO3 per liter (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 milliequivalents per liter.  In analytical chemistry, a solution that 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 liter.

The Phase Rule:

Solubility can be described in a concise manner by the use of the Gibbs phase rule, which was described on: 

Where F is the number of degrees of freedom, that is, the number of independent variables (usually temperature, pressure, and concentration) that must be fixed to completely determine the system, C is the smallest number of components that are adequate to describe the chemical composition of each phase, and P is the number of phases.

Notes credit:

Mr. Sumeet Manohar Kharat
PSPS’s Indira Institute of Pharmacy, Sadavali
Physical Pharmaceutics I

Solubility expression Video Lecture

Video credits:

Dr. Govind Kailash Lohiya
Gurunanak Collge of Pharmacy, Nagpur
Physical Pharmaceutics

What is Intrinsic 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 the calculation and is a single numeric number (for example,  0.5  µg/mL) that is independent of the environmental factors

What is apparent solubility?

The apparent solubility is dependent on environmental factors such as pH and ionic strength and is obtained from the experimental measurements.

What is the importance of solubility?

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 the activity of drugs depends on solubility, it is equally important to control environmental conditions which impact various types of solutions

What are types of Solubility?

There are two types of solubility one is called intrinsic solubility and the other one is apparent solubility.

What is the unit of solubility?

The solubility is generally expressed in grams per liter