Properties of solution
03
CHAPTER

3.1 Introduction

 A solution is defined as a homogeneous mixture of two or more components (elements or compounds). The components can be solid, liquid or gaseous. The major component (by mass or volume) of a solution is called solvent and the minor component of the solu­tion is called solute. A solution can have more than one solute. Nine different solute- solvent combinations are possible in terms of the states of the matter of the sol­ute and the solvent. An example is given below.

Table 3.1:

Possible solution combinations

Solvent

Solute

Example

Gas

Gas

Oxygen-helium (deep sea diver’s gas)

Gas

Liquid

Air-water (moisture in air)

Gas

Solid

Air-naphthalene (Naphthalene vapor)

Liquid

Gas

Water-carbon dioxide (Carbonated drink)

Liquid

Liquid

Acetic acid-water (Common vinegar)

Liquid

Solid

Water-mixed salt (Sea water)

Solid

Gas

Palladium-hydrogen (Gas stove lighter)

Solid

Liquid

Silver-mercury (dental amalgam)

Solid

Solid

Gold-silver (Gold alloy used in ornaments)

Liquid-solid, liquid-liquid, gas-gas solutions are one phase systems. A phase is defined as a space in which all the occupying molecules are homogeneously distribut­ed. A homogeneous mixture is defined as a mixture in which the composition of molecules is identical in any and all part of the mixture.

All pharmaceutical solutions have to be bio-compatible, which means that the pharmaceutical solutions have to have such a composition that is conducive to support cells and their growth. Consequently, all pharmaceu­tical solutions are polar and aqueous. This means that the pharmaceutical solutions have water primary and nearly exclusive as the solvent. The solutes can contain one or more liq­uids as minor component (solute). For example, some pharmaceutical solutions contain limited amounts of ethyl alcohol, and/or glycerol as additional liquid components in ad­dition to the drug that is solid. But, since these liquid components are not major components, they are also considered solute.

The properties of the solutions (solid mixtures are also called solution by definition) like melting point, boiling point, viscosity (resistance to flow), vapor pressure, solubility, osmotic pressure etc. are often different from those of the solvents. When the solution con­tains little amount of solute (dilute solution) the differ­ence in these properties between the solvent and the solution are often minute. But, for the concentrated solutions, the difference is often very significant. Fur­ther, the small differences in properties can also have serious consequences on the patients’ lives. One such example is the case of osmotic pressure and tonicity of the pharmaceutical solutions (especially large-vol­ume parenteral). Solution properties, thus, need to be studied carefully by pharmacists and pharmaceutical scientists.

3.2 Solubility

Solubility of a solute in a solvent is an important pa­rameter. In the context of pharmaceutical sciences and practice, the solubility of the drug molecules in water is of extreme importance; it determines how much drug can be put in a specific volume of water especially in case of injectable dosage forms. Gen­erally, only a few ml of solution of the drug solution are injected through intravenous bolus injections. The solubility of drug molecules in biological fluids like blood, interstitial fluid, tear etc. determines the drug distribution to different parts of the body and thus, the concentration in the target tissue. Solu­bility of drug molecules in water (or any solute for that matter in any solvent) also changes with many factors like temperature, polarity, ionization sta­tus of other solutes etc. The following equation correlates solubility of solute molecules that are non-electrolytes or weak electrolytes with temperature. The non-electrolytes are the mole­cules that are made up through covalent bonds and which do not ionize in aqueous solution. Examples of non-electrolytes include glucose, sucrose, glycerol etc. The weak electrolytes are the molecules which ionize only partially in aqueous solutions. Examples of such molecules include carbonic acid (H2CO3), acetic acid (CH3COOH), urea (NH3) etc. Ionization process of the weak electrolytes are shown below.

H2CO3↔H++HCO3–; CH3COOH↔CH3COO–+H+; NH3+H2O↔NH4++OH–

The double headed arrow in each of the above equa­tions mean that the ionization process is a reversable process and is never complete and the solute mole­cules always exist in partly ionized and partly unionized form.

In this equation, ST1 and ST2 are the initial and final concentrations at temperatures T1 (initial) and T2 (final) respectively where the temperatures T1 and T2 are measured in degrees Kelvin (°K) (273+°Celsius=° Kelvin). The symbol R refers to the universal gas constant that is equal to 1.987 calories*mole-1*degrees K-1. The term (ΔHSoln.) is known as heat of solution or latent heat of solution. ΔHSoln. Is usually measured in calorie per mole i.e. it is the energy that is absorbed by or eliminated from the solute molecules per mole during the dissolution process. Heat of solution can be both positive or negative.

When ΔHSoln. is positive, it means the solute molecules absorb heat for conversion from solute state to the dissolved state and the process is endothermic. In an endothermic dissolution process, the solutes take up heat from the surroundings and the solution becomes cold. The solubility of a solute increases with an increase in temperature if the dissolution pro­cess is endothermic. Examples of such solutes in­clude common salts like sodium chloride (NaCl), po­tassium chloride (KCl), potassium bromide (KBr).

When heat of solution is negative, it means the sol­ute molecules give off heat for conversion from solute state to the dissolved state and the process is exother­mic. In an exothermic dissolution process, the solutes give off heat to the surroundings and the solution be­comes warm or hot. The solubility of a solute de­creases with an increase in temperature if the dissolution process is exothermic. Examples of such solutes include concentrated mineral acids (sul­furic, nitric, hydrochloric acids), and salts like lithium chloride. It is always advised that the concentrated mineral acids are diluted by pouring a small amount of concentrated acid into a large volume of water to prevent hot splashing.

Very strong electrolytes like inorganic salts of metals with higher atomic weight have low solubility in wa­ter as water, as a solvent, is not polar enough for the salts to dissociate in it. For those strong electrolytes, the solubility is relatively independent of tempera­ture. The solubility of these salts are calculated with relation to their solubility products (written as Ksp) which is a theoretically (thermodynamically) derived quantity/parameter. The relationship between solu­bility product Ksp of a strong electrolyte salt and the ionization is expressed by the following equation be­low.

Ksp = [anion]n * [Cation]n

In this equation m and n are the coefficients of the dissociation equation of the salt. In this equation, the solubility product of the salt equals to the multiplica­tion product of the proportional concentrations of the ions, each raised to its coefficient. The point to be noted is that when the coefficient of the ion is 2, this number is both multiplied to S (the solubility of the solute) and again 2 is used as an exponent. The number 2 is just an example, could be 2 or 4 or any other small, non-zero, integral number.

In this equation, ST1 and ST2 are the initial and final concentrations at temperatures T1 (initial) and T2 (final) respectively where the temperatures T1 and T2 are measured in degrees Kelvin (°K) (273+°Celsius=° Kelvin). The symbol R refers to the universal gas constant that is equal to 1.987 calories*mole-1*degrees K-1. The term (ΔHSoln.) is known as heat of solution or latent heat of solution. ΔHSoln. Is usually measured in calorie per mole i.e. it is the energy that is absorbed by or eliminated from the solute molecules per mole during the dissolution process. Heat of solution can be both positive or negative.

When ΔHSoln. is positive, it means the solute molecules absorb heat for conversion from solute state to the dissolved state and the process is endothermic. In an endothermic dissolution process, the solutes take up heat from the surroundings and the solution becomes cold. The solubility of a solute increases with an increase in temperature if the dissolution pro­cess is endothermic. Examples of such solutes in­clude common salts like sodium chloride (NaCl), po­tassium chloride (KCl), potassium bromide (KBr).

When heat of solution is negative, it means the sol­ute molecules give off heat for conversion from solute state to the dissolved state and the process is exother­mic. In an exothermic dissolution process, the solutes give off heat to the surroundings and the solution be­comes warm or hot. The solubility of a solute de­creases with an increase in temperature if the dissolution process is exothermic. Examples of such solutes include concentrated mineral acids (sul­furic, nitric, hydrochloric acids), and salts like lithium chloride. It is always advised that the concentrated mineral acids are diluted by pouring a small amount of concentrated acid into a large volume of water to prevent hot splashing.

Very strong electrolytes like inorganic salts of metals with higher atomic weight have low solubility in wa­ter as water, as a solvent, is not polar enough for the salts to dissociate in it. For those strong electrolytes, the solubility is relatively independent of tempera­ture. The solubility of these salts are calculated with relation to their solubility products (written as Ksp) which is a theoretically (thermodynamically) derived quantity/parameter. The relationship between solu­bility product Ksp of a strong electrolyte salt and the ionization is expressed by the following equation be­low.

Ksp = [anion]n * [Cation]n

In this equation m and n are the coefficients of the dissociation equation of the salt. In this equation, the solubility product of the salt equals to the multiplica­tion product of the proportional concentrations of the ions, each raised to its coefficient. The point to be noted is that when the coefficient of the ion is 2, this number is both multiplied to S (the solubility of the solute) and again 2 is used as an exponent. The number 2 is just an example, could be 2 or 4 or any other small, non-zero, integral number.

Example 1 solubility of CaCO3 in water

The ionization equation is CaCO3↔Ca+++CO3— and the Ksp of CaCO3 =4.7*10-9 . So, if the solubility of CaCO3 is S moles in water Ksp,CaCO3 = (Ca++)1 * (CO3—)1=[S]*[S]=S2 and the solubility

Example 2 solubility of Mg(OH)2 in water

The ionization equation is Mg(OH)2↔Mg+++2(OH)— and the Ksp of Mg(OH)2 = 1.8*10-11 . So, if the solubility of Mg(OH)2 is S moles in KSP,Mg(OH)2 = [S]1*[2S]2=4S3 Or,

Resources for further practice

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3.3 Ionization of molecules and solubility

The solubility of strong electrolytes is often less import­ant for pharmacists as most of the drugs are not inorgan­ic salts but weak electrolytes. For weak electrolytes, the solubility of the compound in water depends on many factors in addition to the temperature. These factors in­clude the ionization status of the solute molecule. The ionization status of the solute molecule again depends on factors like acidity or basicity of the aqueous environ­ment (pH) and the propensity of ionization of the solute molecule (pKa or pKb). A proper understanding of the topic is only possible following a detailed discussion of the ionic equilibria. This topic will thus be discussed on a later chapter of this book.

3.4 Colligative properties

Colligative properties of solutions are the properties that are quantitatively dependent of on the concentra­tion of the solute particles in the solutions irrespective of the nature or identity of the solute molecules. Four colligative properties like freezing point depression, boiling point elevation, vapor pressure depression and osmotic pressure of the solution are of utmost impor­tance to scientists. Of all the four colligative properties, osmotic pressure is most important to the pharma­ceutical scientists and pharmacists. The concentration of particles refers to the concentration of independent entities of solutes that remain in solution. The concen­tration of particles is commonly measured by osmole (Osm) or milli osmole (mOsm). Osm is equal to concen­tration of particles of the solutes in molar terms per liter of solution. Colligative properties are the properties of solution. Theoretically speaking, all solutions including aqueous and non-aqueous solutions show colligative properties. But, only the colligative properties, especial­ly osmotic pressure of the aqueous solutions are of sig­nificance in the pharmaceutical discipline.

Non-electrolytes are the molecules which do not ionize in aqueous solutions. Examples include glucose (C6H12O6), Naphthalene (C10H8), ethanol (C2H5OH), carbon tetrachloride (CCl4), carbon disulfide (CS2) etc. Since the non-electrolytes do not ionize, one molecule produces one particle in solution and the concentra­tion of these solutes in solution in molar terms are equal to the concentration of particles. So, for non-electrolytes, one mole of the non-electrolytes in solu­tion, produces one Osm of particles in solution.

Strong electrolytes are the compounds which ionize completely (or almost completely) in aqueous or polar solutions. Examples include NaCl, KCl, MgCl2, CaSO4, AlCl3 etc. The ionization pattern of these strong electrolytes and the number of particles that they make in aqueous solutions and a rough estimate of the osmolar concentra­tion of the particles are given below. It is also to be noted that even the strong electrolytes (including sodium chlo­ride) do not always ionize quantitatively in aqueous solu­tions. Thus, an accurate measurement of osmolar con­centration of strong electrolytes need a correction factor which will be covered in a later section in table 7.1.

Weak electrolytes, on the other hand, have the pro­pensity to ionize in an aqueous solution only par­tially. Their ionization status or extent of ionization depends on other environmental factors like tem­perature, acidity or basicity (pH) etc. The osmolar concentration of particles of weak electrolytes, thus can be calculated only in a particular pH. Examples of weak electrolytes include weak acids or weak bases or their salts. Most of the drug molecules are weak electrolytes. It is more clinically relevant to calculate the osmolar concentration of drugs and other weak electrolytes in the physiological pH of 7.4. Another practical issue about the drug molecules is that their concentrations in the body fluids are usually so low that their osmolal contribution to the body are usu­ally insignificant. An example of a weak electrolyte phosphoric acid is given below. In this example, 50% the of phosphoric acid remains in unionized form and the other 50% of the phosphoric acid remains in monobasic phosphate form (two particles from one molecule) at pH 2.12. At pH 7.21, 50% of the phosphor­ic acid remains in monobasic phosphate form and the other 50% of the phosphoric acid remains in dibasic phosphate form (three particles from one molecule). At pH12.67, 50% of the phosphoric acid remains in dibasic phosphate and the other 50% of the phos­phoric acid remains in tribasic phosphate form (four particles from one molecule). This example serves the purpose of demonstrating the relationship of the ionization of weak electrolytes to the environment

Solute Ionization status Number of parti- cles/molecule Molar concentration of molecules Rough osmolar concentration of particles
NaCl NaCl↔Na++Cl– 2 1 2
KCl KCl↔K++Cl– 2 1 2
MgCl2 MgCl2↔Mg+++2Cl– 3 1 3
CaSO4 – CaSO4↔Ca+++SO4– 2 1 2
AlCl3 AlCl3↔Al++++3Cl– 4 1 4

i.e. pH (here). We can appreciate from this example how complex the particle concentration calculation (osmolar concentration) for a weak electrolyte can become.

H3PO4 ↔ (at pH 2.12) H2PO4 –+H+ ↔ (at pH 7.21) HPO4—+2H+ ↔ (at pH 12.67) PO4—+3H+

Calculation of particle concentration of a solution is important, it helps us quantitatively determine the ex­tent of osmotic pressure, lowering of freezing point, elevation of boiling point etc.

3.5 Osmotic pressure and tonicity

Osmotic pressure is the pressure exerted by the solute particles in a solution. This pressure is in addition to the hydrostatic pressure that results from the solvent and that is dependent on the depth of a point at which the pressure is being measured in the solution. For example, when a solute like glucose or common salt (NaCl) is added to water, a pressure is generated ev­erywhere in the solution in addition to the hydrostatic pressure of water. This pressure is called osmotic pres­sure. Osmotic pressure is dependent on the particle concentration of the solute (sugar or NaCl) in osmole or milliosmole and not the identity of the solute i.e. whether the solute is sugar or NaCl. It means that 300 mOsm solution of glucose or NaCl or KCl or MgCl2 or Ca3(PO4)2, all produces the same osmotic pressure be­cause osmotic pressure is a colligative property that depends on the particle concentration of the solutes, not on the property or identity of the solute com­pound. Osmotic pressure is calculated by the equation:

Π=imRT

where Π denotes the osmotic pressure, i is the van’t Hoff factor (also called the dissociation fac­tor), R denotes the universal gas constant (1.987 Cal­orie*mole-1*degree Kelvin-1 or 0.082 L*atm*mol-1*K-1) and m stands for the molal concentration of the sol­ute. The molal and molar concentrations of the solute are almost the same for the dilute solution of solutes which is usually the case for the biological fluids of im­portance. Osmotic pressure is uniform throughout the solution.

Eighty (80) % dissociation of inorganic salts is com­mon but not universal.

It is necessary to understand the idea of a semi-per­meable membrane to understand the effect of os­motic pressure on the body and biological fluids. A semipermeable membrane is one which allows the solvents to pass through it but does not allow the pas­sage of some or all of the solutes across. Cellophane paper, cell membrane are some common examples of semi-permeable membranes.

When salt water and pure water are kept in two adja­cent chambers that are separated by just a semi-per­meable membrane (like cell membrane or cellophane paper), the membrane does not allow the salt ions to pass through from one chamber to another, though the water molecules can freely travel across the semi-permeable membrane. The tendency of move­ment of molecules from a region of higher concentra­tion to a region of lower concentration is a property of all molecules in solution and is called diffusion. As shown in the diagram below, the left chamber contains salt water, while the right chamber contains pure wa­ter. Initially, the height of both the left and right arms of the U-tube are the same, it means that initially the hydrostatic pressure on both arms of the U-tube is same. If this system is allowed to remain undisturbed, the water column in the left arm of the U-tube be­comes higher. This happens because of the osmotic pressure due to the presence of salt particles in the left arm of the U-tube. As the osmotic pressure in the left-hand side is high and the salt particles cannot cross over to the right-hand side, water molecules that are free to cross the semi-permeable membrane rush in from the right-arm to dilute the salt water (and de­crease the osmotic pressure) to reach equilibrium. The excess water shows up in the left-arm of the U-tube after equilibrium is reached. It is to be understood that not all salt molecules are prevented from crossing the semi-permeable membrane.

Eighty (80) % dissociation of inorganic salts is com­mon but not universal.

It is necessary to understand the idea of a semi-per­meable membrane to understand the effect of os­motic pressure on the body and biological fluids. A semipermeable membrane is one which allows the solvents to pass through it but does not allow the pas­sage of some or all of the solutes across. Cellophane paper, cell membrane are some common examples of semi-permeable membranes.

When salt water and pure water are kept in two adja­cent chambers that are separated by just a semi-per­meable membrane (like cell membrane or cellophane paper), the membrane does not allow the salt ions to pass through from one chamber to another, though the water molecules can freely travel across the semi-permeable membrane. The tendency of move­ment of molecules from a region of higher concentra­tion to a region of lower concentration is a property of all molecules in solution and is called diffusion. As shown in the diagram below, the left chamber contains salt water, while the right chamber contains pure wa­ter. Initially, the height of both the left and right arms of the U-tube are the same, it means that initially the hydrostatic pressure on both arms of the U-tube is same. If this system is allowed to remain undisturbed, the water column in the left arm of the U-tube be­comes higher. This happens because of the osmotic pressure due to the presence of salt particles in the left arm of the U-tube. As the osmotic pressure in the left-hand side is high and the salt particles cannot cross over to the right-hand side, water molecules that are free to cross the semi-permeable membrane rush in from the right-arm to dilute the salt water (and de­crease the osmotic pressure) to reach equilibrium. The excess water shows up in the left-arm of the U-tube after equilibrium is reached. It is to be understood that not all salt molecules are prevented from crossing the semi-permeable membrane.

3.6.1 Iso-osmotic and iso-tonic, the difference

Polar non-ionic molecules (non-electrolytes) like glu­cose crosses the semi-permeable membrane. Macro­molecules like large proteins (albumen, hemoglobin etc.), long chain nucleic acid molecules (DNA or RNA etc.) and strong electrolytes and ions cannot cross semi-permeable membranes. The molecules that do not cross the semi-permeable membrane causes a permanent osmotic pressure differential across the semi-permeable membrane. The osmotic pressure that is created by the presence of impermeable solutes in the aqueous solution is called tonicity. Tonicity is distinctly different from osmotic pressure. For exam­ple, a glucose solution has an osmotic pressure over and above the hydrostatic pressure. But, the same glu­cose solution does not have any tonicity as glucose is a permeable solute, it quickly equilibrates across the semi-permeable membrane causing no permanent os­motic pressure differential. For example, 5% (w/v) dex­trose (D glucose, used in infusions) solution in water is iso-osmotic with 0.9 % (w/v) NaCl solution; both of them have a particle concentration of 298 mOsmole/L, both produces freezing point depression of -0.52°C. But the above two solutions are not isotonic as D5W does not produce a permanent osmotic pressure dif­ferential across the semi-permeable membrane (as glucose quickly equilibrates across the semi-perme­able membrane), while 0.9 % NaCl solution does pro­duce the permanent pressure differential in the same situation. Saline solution (0.9% sodium chloride solu­tion) is thus both iso-osmotic and isotonic.

Figure 3.1a:

3.6.2 Tonicity & Isotonicity- their importance

Now that we understand the term tonicity (osmot­ic pressure due to molecules that cannot cross the semi-permeable membranes), it is important to un­derstand the significance of tonicity and isotonicity. Isotonicity refers to the tonicity of the solutions that have the same osmotic pressure (due to imperme­able solutes) as those of biological fluids. Isotonic solutions are the solutions that have the same tonic­ity as that of biological fluids. Tonicity is a noun that refers to the nature of the solutions, while tonic is an adjective and refers to the quantitative aspect of to­ nicity (extent/magnitude of osmotic pressure due to impermeable solutes). So, an isotonic solution has the same tonicity as that of biological fluids. A hypo-tonic solution is one that has lower tonicity as compared to the biological fluids and a hypertonic solution is one which has higher tonicity than the biological fluids. All biological fluids as well as isotonic solutions have the following nature:

    • Osmotic pressure-around: 6.5 atmosphere
    • Particle concentration: 290-310 mOsm
    • Freezing point depression: 0.52°C
    • Sodium chloride equivalent: 0.9 % NaCl

Consequently, all isotonic solutions have the same above properties. All these properties go hand in hand, i.e. an isotonic solution will have roughly 6.5 atmosphere osmotic pressure, particle concentra­tion of around 300 mOsm, freezing point depres­sion of 0.52°C and will produce the same tonicity as 0.9% sodium chloride solution which is isotonic. All hypotonic solutions have osmotic pressure <6.5 atmosphere, particle concentration <300 mOsm, freezing point depression<0.52°C and sodium chlo­ride equivalent <0.9 sodium chloride solution. All hypertonic solutions will have these parameters higher than the numbers for isotonic solutions en­listed above.

Practical significance

The significance of tonicity is that all human and an­imal cells need roughly the same solution environ­ment to survive and thrive. It is to be noted that all biological fluids do not have the exact same tonici­ty, but the above numbers are very good practical approximations of isotonic solutions that pharma­ceutical scientists and pharmacists should strive to achieve in pharmaceutical solutions. The figure 3.1b describes what happens to cells (example of red blood corpuscles RBC) when they are subjected to treatment with isotonic, hypotonic and hypertonic solutions. The top panel is the schematic diagram of the fate of RBCs following treatment, while the bot­tom panel shows an actual microscopic picture of the fate of RBCs. In hypotonic solution i.e. plain wa­ter without any solute in it, the tonicity is zero. The tonicity and osmotic pressure within RBCs is higher due to high particle concentration as the cells con­tain a number of solute molecules like proteins and ions. Since these solute molecules cannot cross the cell membrane, water from the outside environment moves into the RBCs making them bigger and round­er. Eventually the RBCs burst open, losing their cel­lular content, and die. In isotonic solution, there is no large-scale movement of either water or solute molecules across the plasma membrane of the RBCs, and the cells remain healthy and functional. When the RBCs are put into hypertonic solution, the tonic­ity and osmotic pressure outside the cells are high. Ions cannot cross the plasma membrane of RBCs. Water molecules move out of the RBCs to lower the osmotic pressure in the environment outside the cells. The RBCs lose volume, shrink up and eventual­ly become dysfunctional and die. The same process occurs to every animal/human cell when treated with hypotonic, isotonic and hypertonic solutions, RBCs are just one example used to demonstrate the point. The take home point is that all pharmaceu­tical solutions, especially large volume par­enterals must be made isotonic. Small volume pharmaceutical preparations like injections (<5ml) should also be made isotonic, but they do not have

Figure 3.1b:

a systemic effect since the volume is small and they become isotonic when mixed with large volumes of body fluids like blood. Another point to note is that all pharmaceutical liquids by and large need to be of physiological pH (7.4) especially if they are in large volume. Only in rare cases, injectables are made in a pH that varies from 7.4 to address the inherent instability issues of the drug molecules. If the isoto­nicity of small volume injections, eye drops, vaginal or rectal preparations are not isotonic, significant irritation and pain may result.

Visualization of the process: https://url.linuslearning.com/DnvRS%20

3.7 Calculations involved and preparation of isotonic solutions

Isotonicity

There are four methods of adjusting isotonicity. Prepara­tions that are meant for use as intra-venous injections or for use in the eye or nasal tract or ear, the liquid must be isotonic with the body fluids. This adjustment of tonicity can be done by any one of four methods. It has to be understood that the drug solutions have some osmot­ic pressure and tonicity as most of the drug molecules do not cross the plasma membrane though almost any practical drug solution is hypotonic. The solutions are made isotonic by adding a tonicity adjuster solute in the solution. Sodium chloride is the most common tonicity adjuster though other solutes can and have been used in that role. A hypertonic solution can be made isotonic by diluting the solution proportionally with water.

1. Cryoscopic Method of tonicity adjustment:

Blood has a freezing point of –0.52° C. So, for any solution to be isotonic with blood, it must also have a freezing point depression (FPD)of 0.52 °C. The freezing point depression caused by a 1% solution of common drugs have been reported in contem­porary literature. Freezing point depression (FPD) is the difference in melting point of pure water and water with solute(s) in it. It is denoted as ΔTfx%, where ΔTf stands for freezing point depression and the superscript (x%) denotes the concentration of the solute due to which the ΔTf occurs. So ΔTf1% for sodium chloride means FPD due to 1% (w/v) of sodium chloride that is present in water as solute. For sodium chloride ΔTf 1% =0.576 °C. Freezing point depression is proportional; to the mOsm concentra­tion of solute particles; i.e. ΔTf 5% for any solute =5* ΔTf 1% of the same solute etc. ΔTf is a property of the solute, not that of the solvent or solution. Some­times ΔTf is expressed without any % indicated. If no % is indicated after ΔTf, the symbol in this case indicates the value of ΔTf for 1% solute in solution.

Van’t Hoff equation explains the relationship between the FPD, the ionization properties and the concentra­tion of the solute.

ΔTf = iKf m = Liso m

where i is the ionization factor that we have come across before. This is the property of the solute molecule (drug and salts for example). Kf is called the molal depression constant. It is a property of the solvent; for water Kf = 1.86. The molal depression constant Kf for other solvents have different values. But, since all the pharmaceutically relevant liquid preparations (other than topical preparations for which isotonicity calculations are irrelevant), we will restrict our discussion to water only and the value of Kf is always 1.86. The ‘m’ in the above equation stands for the molal concentration of the solute (drug or salt). The molal and molar concentration are virtually the same for dilute solutions. The ion­ization properties of the solute and the molal de­pression constant of the solvent (which is always water for isotonicity discussion) are often com­bined in the form of Liso, where Liso= iKf. Typical Liso

values for families of solutes are given below in table 8.2. The total FPD due to a solute can be calculated by using the Van’t Hoff equation. If there is more than one solute present in the aqueous solution, the FPDs caused by each of the solute component are added. Use of Liso or i and Kf in Van’t Hoff equation is a matter of convenience and is determined com­monly based on availability of data.

Compound Type by Valence and ionization Liso Value
Nonelectrolyte 1.86
Weak electrolyte 2.0
Di-divalent electrolyte (divalent cation and divalent anion) 2.0
Uni-univalent electrolyte (single charge on each) 3.4
Uni-divalent electrolyte 4.3
Di-univalent electrolyte 4.8

Table 3.2:

Number of Ions, Dissociation Factor (I), and Molecular Weight (MW) of Selected Compounds.

 

Ions

i

MW

Boric acid

1

1.0

62

Chlorobutanol

1

1.0

177

Dextrose, anhydrous

1

1.0

180

Dextrose, H2O

1

1.0

198

Mannitol Benzalkonium chloride

1

2

1.0

1.8

182

360

Cocaine HCI

2

1.8

340

Cromolyn sodium

2

1.8

512

Dipivetrin HCI

2

1.8

388

Ephedrine HCI Epinephrine bitartrate

2

2

1.8

1.8

202

333

Eucatropine HCI

2

1.8

328

Homatropine HBr

2

1.8

356

Oxymetazoline HCI Oxytetracycline HCI

2

2

1.8

1.8

297

497

Phenylephrine HCI

2

1.8

204

Procaine HCI

2

1.8

273

Scopolamine HBr 3H2O

2

1.8

438

Silver nitrate

2

1.8

170

Sodium chloride

2

1.8

58

Sodium phosphate, monobasic, anhydrous

2

1.8

120

Sodium phosphate, monobasic-H2O

2

1.8

138

Tetracaine HCI

2

1.8

301

Zinc sulfate-7H2O

2

1.8

288

Atropine sulfate, H2O

3

2.6

695

Ephedrine sulfate

3

2.6

429

Sodium phosphate, dibasic, anhydrous

3

2.6

142

Sodium phosphate, dibasic 7H2O

3

2.6

268

 

Example 1: solute NaCl, i=1.8, Kf =1.86, Liso=1.8*1.86=3.348 Example 2: solute glucose, i=1, Kf =1.86, Liso=1*1.86=1.86 Example 3: solute ZnCl2, i=2.6, Kf =1.86, Liso=2.6*1.86=4.836 The above tables list data for some of the families of molecules for Liso value, molecular weight and ionization factor for some of the drugs. The data from these tables can be used to calculate the so­dium chloride equivalent (E) and ΔTf1% values for practice.

How to use ΔTf for isotonic solution calculations

We can use the empirical formula given below for cal­culating the mass (in g) of the tonicity adjuster for 100 ml of isotonic solution.

W = weight of tonicity adjuster required for 100 ml of solution isotonic

a = sum total of freezing point depression due to one or more than one drug(s)

b = freezing point depression due to 1% (ΔTf 1%) of the tonicity adjuster

Steps:

    1. We find out the freezing point depression caused by the given amount of the drug in the prescription in the given volume of water.
    2. We subtract it from 0.52.
    3. For the remaining depression in freezing point, we add sufficient sodium chloride, know­ing that 1% sodium chloride has a FPD of 0.576 °C.

2. Sodium Chloride Equivalent Method:

The sodium chloride equivalent is also known as “ton­ically equivalent”. The sodium chloride equivalent of a drug is the amount of sodium chloride that is equivalent to (i.e., has the same osmotic/tonic effect as) 1 gram of the drug. The sodium chloride equivalent and ΔTf 1% values of many drugs are listed in handbooks. The following table lists these values of some of these drugs. This data can be used by the stu­dents to create problems for practice to understand the phenomenon completely.

Method 1 for calculating E value

In this method we find out the E value of the drug; ei­ther from tables or from the formula below.

E = 17 (Liso/MW)

Where E is sodium chloride equivalent value, while M is Molecular Weight, and Liso factor which depends on mass and ionization nature of the solute in water as discussed before.

Method 2 of calculating E value

Example of E value calculation of boric acid (weak acid, very little ionization)

How to use E value

w= amount of the tonicity adjuster in g needed for making 100 ml solution isotonic

a-sum total of the E values of all the drugs in 100 ml solution

b-the E value of the tonicity adjuster

If NaCl is used as the tonicity adjuster, which is usually the case, E=1

The steps are:
    1. We find the E value(s) of the drug(s).
    2. We multiply the quantity of the drug in g with its E value (ai=Wi*Ei). Here, Wi is the weight of the ith species of the drug in the prescription and Ei is the sodium chloride equivalent for that ith species of the drug in the prescription. We get the tonic equivalent of the drug(s) in terms of g of sodi­ um chloride (if there is more than one drug in the solution) represented by a (for three species, a= a1+a2+a3+… etc.) that is equivalent to sodium chloride with respect to osmotic pressure.
    3. Since, for every 100ml of solution, 0.9g of so­dium chloride is required for isotonicity, we subtract the amount obtained in step 2 (a) from 0.9g; let this be y.
    4. We add y of NaCl, to every 100ml of solution.

Table 3.3:

Sodium Choride Equivalents (E) and Freezing Point Depression (ΔT1%) Values of selected Compounds.

Substance

E

ΔT1%

Ammonium chloride

1.08

0.64

Apomorphine hydrochloride

0.14

0.08

Atropine sulfate

0.13

0.07

Boric acid

0.52

0.29

Chlorobutanol

0.18

0.14

Cocaine hydrochloride

0.16

0.09

Dextrose monohydrate

0.16

0.0

Ephedrine hydrochloride

0.30

0.18

Ephedrine sulfate

0.23

0.14

Epinephrine bitartrate

0.18

0.11

Epinephrine hydrochloride

0.29

0.17

Eucatropine hydrochloride

0.18

0.11

Fluorescein sodium

0.31

0.18

Glycerin

0.34

0.20

Naphazoline hydrochloride

0.27

0.16

Neomycin sulfate

0.11

0.06

Oxymetazoline

0.20

0.11

Phenol

0.35

0.2

Phenylephrine hydrochloride

0.32

0.18

Pilocarpine nitrate

0.22

0.14

Procaine hydrochloride

0.21

0.11

Scopolamine hydrobromide

0.12

0.07

Silver nitrate

0.33

0.19

Sodium chloride

1.00

0.58

Sulfacetamide sodium

0.23

0.14

Tetracaine hydrochloride

0.18

0.11

Zinc chloride

0.62

0.37

Zinc sulfate 7H₂O

0.15

0.09

 

3. Volumetric approach

In this approach, instead of adding a fixed volume of wa­ter, just enough water is added to the required amount of drug(s) to make the solution isotonic by the drug itself.

White – Vincent Method:

In this method, we add enough water to the drug to make the solution isotonic and then we add an isotonic sodium chloride solution to it to bring up the volume to the required level. No tonicity adjuster is re­quired to make the isotonic drug solution in this method as we are using only a restricted amount of water to begin with.

Here, Wi is the weight of the ith species of the drug in the prescription and Ei is the sodium chloride equiva­lent for that ith species of the drug in the prescription. For example, W1– the weight of drug component 1, E1 is the E value of the drug component 1.

W2– the weight of drug component 2, E2-the E value of the drug component 2

W3– the weight of drug component 3, E1-the E value of the drug component 3

111.1- this is the volume (in ml) of water that is needed to make 1g of NaCl isotonic.

Steps involved are

  1. Find the weight of the drug prescribed (w), the volume prescribed (v) and its sodium chloride equivalent value (E).
  2. Multiply the weight (w) with the sodium chlo­ride equivalent value (E) and add up for mul­tiple drugs in the same prescriptions (more than three is rare).

So X is the weight of sodium chloride osmotical­ly equivalent to the given weight W of the drug.

3. The volume V of isotonic solution that can be prepared from W g of drug is obtained by solving the equation

Explanation of the multiplication factor 111.1

For sodium chloride, 0.9 g in 100 ml is isotonic. So, us­ing proportion,

0.9 /100 =X/V or, V= ( X* 100 )/0.9 and V = X * 111.1

So X is the weight of sodium chloride osmotical­ly equivalent to the given weight W of the drug.

3. The volume V of isotonic solution that can be prepared from W g of drug is obtained by solving the equation

(This is the final equation, the above example is given to demonstrate how the multiplication factor 111.1 is derived).

  1. So V is the volume of solution that contains the prescribed amount of drug and is isotonic with blood. Dissolve W g of drug in V ml of water. This solution is isotonic.
  2. Usually this drug solution is small in volume, but since the drug solution is isotonic, it can bemixed with normal saline (isotonic) in any pro­portion, the diluted drug solution is still isotonic.

II Sprawls Method:

The Sprawl’s method is derived assuming that the drug amount in drug is 0.3 g, which is an arbitrary number. The amount of water to make 0.3 g of drug isotonic is calculated first by Sprawl’s method. The amount of water required to make any other amount of drug is then calculated by simple proportioning.

V = 111.1 * 0.3 * E

Disadvantages of Sprawl’s Method

    • In this method we make use of the V values which were defined and calculated for many drugs by Sprawl’s. Fixing the W as 0.3g for many drugs, and knowing their E values, he calculated the V values for many drugs. Dis­advantage1-volume of water for only one drug can be calculated at a time
    • The equation is set up only for 0.3 g of drug, for any other weight of the drug, the volume required needs to be proportioned

Steps :

    1. Multiply the E value of the drug with 111.1 and 0.3 successively. This is the volume of water that makes 0.3 g of the drug isotonic.
    2. Proportionate the volume if the prescription calls for any other amount of the drug (other than 0.3 g). Usually this drug solution is small in volume, but since the drug solution is isotonic, it can be mixed with normal saline (isotonic) in any proportion, the diluted drug solution is still isotonic.

Example Problem

The amount of tonicity adjuster required in g for 100 ml of solution using cryoscopic method,

So, to make the required drug solution isotonic, we dis­solve 1g of apomorphine hydrochloride and 0.76 g of sodium chloride in 100ml of water.

The amount of tonicity adjuster required in g for 100 ml of solution using sodium chloride method,

So, to make the required drug solution isotonic, we dis­solve 1g of apomorphine hydrochloride and 0.76 g of sodium chloride in 100ml of water.

Dissolve 1g of apomorphone hydrocloride in 15.5 ml of water and make up this solution to 100ml with 0.9% sodium chloride solution.

The amount water required to make the solu­tion isotonic by itself using volumetric method

(Sprawl’s)

Water required to make 0.3 g of apomorphone hydro­chloride

V = 111.1 * 0.3 * E

or, V = 111.1 * 0.3 * 0.14

or, V = 4.666 ml

Proportionating

Dissolve 1g of drug in 15.5 ml of water and make up the solution to 100ml with 0.9% sodium chloride solution.

References

    • Department of Biology | The University of New Mexico. (n.d.). http://biology.unm.edu/