# Colligative Properties

## Presentation on theme: "Colligative Properties"— Presentation transcript:

Colligative Properties
Kausar Ahmad Kulliyyah of Pharmacy PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Contents Effect of solute on vapour pressure Boiling point elevation Freezing point depression Osmotic pressure Lecture 1 Raoult’s law Deviation from Raoult’s law Lecture 2 Distillation Azeotropic mixtures Clausius-Clapeyron equation Lecture 3 PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Introduction Solutions have different properties than either the pure solvent or the solute. a solution of sugar in water is neither crystalline like sugar nor tasteless like water. Some of the properties unique to solutions depend only on the number of dissolved particles and not their identity. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Definition Properties of a liquid that may be altered by the presence of a solute. Depend only on the amount of solute in a solution Does not depend on the identity of the solute Colligative properties Depend on the identity of the dissolved solute and the solvent Non-colligative properties PHM1153 Physical Pharmacy /11

Colligative vs Non-colligative
Compare 1.0 M aqueous sugar solution to a 0.5 M solution of salt (NaCl) in water. both solutions have the same number of dissolved particles any difference in the properties of those two solutions is due to a non-colligative property. Both have the same freezing point, boiling point, vapor pressure, and osmotic pressure Compare 1.0 M aqueous sugar solution to a 0.5 M solution of table salt (NaCl) in water. Despite the concentrations, both solutions have precisely the same number of dissolved particles because each sodium chloride unit creates two particles upon dissolution - a sodium ion, Na+, and a chloride ion, Cl-. Therefore, any difference in the properties of those two solutions is due to a non-colligative property. Both solutions have the same freezing point, boiling point, vapor pressure, and osmotic pressure because those colligative properties of a solution only depend on the number of dissolved particles. PHM1153 Physical Pharmacy /11

Non-Colligative Properties
Sugar solution is sweet and salt solution is salty. Therefore, the taste of the solution is not a colligative property. Another non-colligative property is the color of a solution. A 0.5 M solution of CuSO4 is bright blue in contrast to the colorless salt and sugar solutions. Other non-colligative properties include viscosity, surface tension, and solubility. PHM1153 Physical Pharmacy /11

Examples of Colligative Properties
vapour pressure freezing point depression (melting) boiling point elevation osmotic pressure All of these properties relate to the vapor pressure. PHM1153 Physical Pharmacy /11

Effect of Solute on Vapour Pressure
When a nonvolatile solute is dissolved in a solvent, the vapor pressure of the resulting solution is lower than that of the pure solvent. The amount of the vapor pressure lowering is proportional to the amount of solute and not its identity. Therefore, vapor pressure lowering is a colligative property. PHM1153 Physical Pharmacy /11

Vapour pressure: Solution < pure solvent
On the surface of the pure solvent (shown on the left) there are more solvent molecules at the surface than in the right-hand solution flask. Therefore, it is more likely that solvent molecules escape into the gas phase on the left than on the right. Therefore, the solution should have a lower vapor pressure than the pure solvent. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Boiling point Boiling point elevation is a colligative property related to vapor pressure lowering. The boiling point is defined as the temperature at which the vapor pressure of a liquid equals the atmospheric pressure. Due to vapor pressure lowering, a solution will require a higher temperature to reach its boiling point than the pure solvent. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Freezing Point Every liquid has a freezing point - the temperature at which a liquid undergoes a phase change from liquid to solid. When solutes are added to a liquid, forming a solution, the solute molecules disrupt the formation of crystals of the solvent. That disruption in the freezing process results in a depression of the freezing point for the solution relative to the pure solvent. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Osmotic Pressure When a solution is separated from a volume of pure solvent by a semi-permeable membrane that allows only the passage of solvent molecules, the height of the solution begins to rise. The value of the height difference between the two compartments reflects a property called the osmotic pressure of a solution. If you add more solvent to a solution, the two mix together to form a more dilute solution. The same forces allowing that mixing serve to force solvent molecules from the pure solvent compartment across the membrane into the solution compartment causing the change in volume. The amount of osmotic pressure is directly related to the concentration of the solute. That is because more concentrated solutions have greater potentials for dilution. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Phase Diagrams and the effect of solutes on freezing and boiling points PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
end of lecture 1/3 PHM1153 Physical Pharmacy /11

Raoult's Law P1 = Po x X1 vapor pressure of a solution, P1,
Raoult's law states that the vapor pressure of a solution, P1, equals the mole fraction of the solvent, X1 , multiplied by the vapor pressure of the pure solvent, Po. P1 = Po x X1 PHM1153 Physical Pharmacy /11

A Visual Demonstration of Raoult's Law
Description: The intensity of color of bromine vapor is reduced (P↓) when a colorless volatile liquid is added (x↓). Source: Journal of Chemical Education - Vol. 67 Year : 1990 page: 598 PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Total Vapour Pressure In an ideal solution made up of two volatile components: P = p1 +p2 In an ideal solution made up of one volatile component: P = p1 PHM1153 Physical Pharmacy /11

Ideal & Non-Ideal/Real Solutions
Solutions that obey Raoult's law are called ideal solutions because they behave exactly as we would predict. Solutions that show a deviation from Raoult's law are called non-ideal solutions or real solutions because they deviate from the expected behavior. Very few solutions actually approach ideality, but Raoult's law for the ideal solution is a good enough approximation for the non- ideal solutions. PHM1153 Physical Pharmacy /11

Deviations from Raoult's law
the "law" is approximately obeyed by most solutions, some show deviations from the expected behavior. Deviations from Raoult's law can either be positive or negative. A positive deviation means that there is a higher than expected vapor pressure above the solution: P1 > P1o x X1 A negative deviation means that we find a lower than expected vapor pressure for the solution: P1 < P1o x X1 PHM1153 Physical Pharmacy /11

Reason for the deviation
In vapor pressure lowering we assumed that the solute did not interact with the solvent at all. If the solute is strongly held by the solvent, the solution will show a negative deviation from Raoult's law, because the solvent will find it more difficult to escape from solution. If the solute and solvent are not as tightly bound to each other as they are to themselves, then the solution will show a positive deviation from Raoult's law because the solvent molecules will find it easier to escape from solution into the gas phase. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Deviation from Raoult’s Law PHM1153 Physical Pharmacy /11

Vapor Pressure of a Mixture: Raoult's Law
The measurement of pressure exerted by a vapour is demonstrated using barometers. Vapor pressure varies with the strength of the intermolecular forces in the liquid. We can calculate the vapor pressure of a mixture using Raoult's law. Source: PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Example: Consider a solution that contains 0.6 mole fraction of decane and 0.4 mole fraction of diethyl ether. We can calculate the vapor pressure of a mixture using Raoult's law: P = P1o x X1 + P2o x X2 = (5 x 0.6) + (460 x 0.4) = 187 When diethyl ether is injected (into the open end of the barometer), the diethyl ether rises to the top and some vaporizes. The mercury is depressed to 275 millimeters. (The difference between the mercury levels before and after injection is the vapor pressure.) Here, the vapor pressure of diethyl ether is 460 millimeters of mercury. Let's look at how the vapor pressure will change when ether is mixed with another liquid such as decane, which has a vapor pressure of 5 millimeters of mercury. If we take a solution that contains 0.6 mole fraction of decane and 0.4 mole fraction of diethyl ether and inject it into the barometer, it depresses the mercury to only 552 millimeters. Therefore the vapor pressure of the solution is 183 mm, in between the vapor pressure of pure decane or pure ether. PHM1153 Physical Pharmacy /11

Factors that affect the magnitude of the changes in melting point and boiling point.
Concentration Effect of ionic compounds PHM1153 Physical Pharmacy /11

Effect of ionic compounds
0.1 mole of an ionic compound such as NaCl,, has an effect on the melting and boiling points that is almost twice what we would observe for 0.1 mole sugar. salt ionizes into Na+ and Cl- ions in water these ions act as independent particles on the vapor pressure of water. Thus NaCl, NaNO3, and CaCO3 would have multipliers of 2, while Na2SO4, and CaCl2 would have multipliers of 3. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Van’t Hoff factor In dilute solutions, ionic compounds have simple multiple effects, but as the solution concentration increases the multiplier effect diminishes. This phenomenon was first discovered by van't Hoff and is generally called the van't Hoff factor. As concentration increases, some of the ions floating in solution find one another and form ion pairs, in which two oppositely charged ions briefly stick together and act as a single particle. the higher the concentration, the more likely it is that two ions will find one another. PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11

Change in Boiling Point
One consequence of Raoult's law is that the boiling point of a solution made of a liquid solvent with a nonvolatile solute is greater than the boiling point of the pure solvent. For a solution, the vapor pressure of the solvent is lower at any given temperature. Therefore, a higher temperature is required to boil the solution than the pure solvent. The change in boiling point is ΔTb = iKbm PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11

Change in Freezing Point
In order for a liquid to freeze it must achieve a very ordered state that results in the formation of a crystal. If there are impurities in the liquid, i.e. solutes, the liquid is inherently less ordered. Therefore, a solution is more difficult to freeze than the pure solvent so a lower temperature is required to freeze the liquid. The change in freezing point is ΔTf = -iKfm Note that the sign of the change in freezing point is negative because the freezing point of the solution is less than that of the pure solvent. Q: Why can adding salt to ice water make the ice melt slower? Adding salt to the ice/water mix causes a temperature drop that slows the melting rate and increases the freezing rate [3]. The net result is that the ice melts more and more slowly after the initial addition of salt. Why does salt melt ice? In pure water, at 0°C, ice melts just as fast as water freezes. You won't see any of the ice melt as long as the freezing rate and melting rates are exactly equal [1]. Adding salt (or any foreign substance) to the water upsets the delicate balance between freezing and melting. Fewer water molecules reach the surface of the ice in a given time, so water freezes more slowly. The melting rate isn't changed by the salt, so melting "wins" [2]. Does adding salt to ice and water cause a temperature drop? Yes. This is how old-fashioned ice cream makers lowered the temperature of the ice cream below water's ordinary freezing point. A mixture of rock salt, ice, and water packed in the bucket around the ice cream mix can bring the temperature down as low as -21°C. Why does the temperature drop? Energy is required to snap the hydrogen bonds that hold the ice together. The melting ice draws that energy from the surrounding solution as heat. See these previous questions for more: "Why does salt melt ice?" (includes a Flash simulation of freezing point depression) Author: Fred Senese PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Molal Boiling Point Elevation and Freezing Point Depression Constants at 1 Atm pressure Compound Normal bp Kb (oC/m) Normal fp Kf (oC/m) Water, H2O 100.0 0.52 0.0 1.86 Benzene, C6H6 80.1 2.53 5.5 5.12 Ethanol, C2H5OH 78.4 1.22 -114.6 1.99 Carbon tetrachloride, CCl4 76.8 5.02 -22.3 29.8 Chloroform, CHCl3 61.2 3.63 -63.5 4.68 Thus the boiling point of water would increase 0.52 oC for a one molal solution, while the freezing point of this solution would decrease by 1.86 oC. PHM1153 Physical Pharmacy /11

Osmotic pressure P = ρgh
Solvent molecules flow into solution Volume of the solution rise Net flow through the membrane ceases due to the extra pressure exerted by the excess height of the solution chamber. Converting the difference in height into pressure gives the osmotic pressure P = ρgh When a solution and the pure solvent used in making that solution are placed on either side of a semipermeable membrane, more solvent molecules flow out of the pure solvent side of the membrane than solvent flows into the pure solvent from the solution side of the membrane. That flow of solvent from the pure solvent side makes the volume of the solution rise. When the height difference between the two sides becomes large enough, the net flow through the membrane ceases due to the extra pressure exerted by the excess height of the solution chamber. Converting the difference in height into of pressure gives the osmotic pressure P = rgh P stands for pressure, r is the density of the solution, and h is the height of the solution. Why more molecules flow from the solvent chamber to the solution chamber? More solvent molecules are at the membrane interface on the solvent side of the membrane than on the solution side. Therefore, it is more likely that a solvent molecule will pass from the solvent side to the solution side than vice versa. That difference in flow rate causes the solution volume to rise. As the solution rises, by the pressure depth equation, it exerts a larger pressure on the membrane's surface. As that pressure rises, it forces more solvent molecules to flow from the solution side to the solvent side. When the flow from both sides of the membrane are equal, the solution height stops rising and remains at a height reflecting the osmotic pressure of the solution. PHM1153 Physical Pharmacy /11

Effect of concentration on osmotic pressure
PV = inRT Since n / V gives the concentration of the solute in units of molarity, M P = iMRT End of lecture 2/3 PHM1153 Physical Pharmacy /11

Application of Raoult’s Law Distillation
PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
DISTILLATION Distillation is the process of boiling & condensing the vapour back to liquid A simple distillation: To change from liquid to vapour by boiling To change from vapour to liquid by condensing PHM1153 Physical Pharmacy /11

Distillation of Binary Mixture Ideal Solution
When a liquid and its vapour are in equilibrium, vapour is richer in the more volatile component compared to liquid mixture At equilibrium, liquid and vapour phase can be separated and analysed Example: A liquid composition C is in equilibrium with vapour of composition D At T (Tc), the liquid boils and the equilibrium vapour has composition D at temperature Tc, so that point D can be calculated The vapour composition D can be condensed to form liquid at temperature Td, which is the boiling point and this liquid D is in equilibrium with vapour composition E. Conversely, from the curve, the composition of the vapour in equilibrium with a liquid of known composition can be found As this is also at Td, the point ‘e’ can be plotted and so on until the vapour composition curve can be plotted Successive distillate: C, D, E, F result in distillate becomes richer and richer in the more volatile component B Eventually, it is possible to separate pure B which distill first and F last The above process is tedious and can be simplified by using a fractional distillation column or fractionating column PHM1153 Physical Pharmacy /11

Binary Mixtures Obeying Raoult’s Law Ideal Solution
Attractive forces between molecules of different component equal those of the same component. A-B = A-A = B-B Without a maximum or minimum at intermediate compositions. No change in properties of components (except dilution to form solution). Vapour pressure, refractive index, surface tension and viscosity of solution are averages of properties of pure individual constituents. No heat evolved or absorbed during mixing process. No change in solution temperature. No shrinkage or expansion. Final properties of solution are additive properties of individual constituents. E.g. methyl alcohol-water, benzene-toluene, methanol-ethanol. PHM1153 Physical Pharmacy /11

Definition - Azeotropic Mixture
Describes a mixture of miscible liquids which boils at a constant composition and thus the composition cannot be changed by simple distillation Composition of vapour similar to that of liquid The composition as well as the boiling point of an azeotropic mixture changes with pressure If a liquid mixture represented by a composition X1 is distilled, the vapour has composition X2 and condenses to form a liquid of that composition. Distillation starting at composition X1 produces an azeotropic mixture Z as the distillate, and the residue tends towards pure B Similarly, a mixture of composition Y1, yields an azeotropic mixture as distillate, and pure A as a residue Types of azeotropes Each azeotrope has a characteristic boiling point. The boiling point of an azeotrope is either less than the boiling points of any of its constituents (a positive azeotrope), or greater than the boiling point of any of its constituents (a negative azeotrope). A well known example of a positive azeotrope is 95.6% ethanol and 4.4% water (by weight). Ethanol boils at 78.4°C, water boils at 100°C, but the azeotrope boils at 78.1°C, which is lower than either of its constituents. Indeed 78.1°C is the minimum temperature at which any ethanol/water solution can boil. It is generally true that a positive azeotrope boils at a lower temperature than any other ratio of its constituents. Positive azeotropes are also called minimum boiling mixtures. An example of a negative azeotrope is 20.2% hydrogen chloride and 79.8% water (by weight). Hydrogen chloride boils at –84°C and water at 100°C, but the azeotrope boils at 110°C, which is higher than either of its constituents. Indeed 110°C is the maximum temperature at which any hydrochloric acid solution can boil. It is generally true that a negative azeotrope boils at a higher temperature than any other ratio of its constituents. Negative azeotropes are also called maximum boiling mixtures. Azeotropes consisting of two constituents, such as the two examples above, are called binary azeotropes. Those consisting of three constituents are called ternary azeotropes. Azeotropes of more than three constituents are also known. More than 18,000 azeotropic mixtures have been documented.[2] Combinations of solvents that do not form an azeotrope when mixed in any proportion are said to be zeotropic. When running a binary distillation it is often helpful to know the azeotropic composition of the mixture. PHM1153 Physical Pharmacy /11

Positive Deviation from Raoult’s Law
Vapour pressure greater than expected from Raoult’s law. The two components differ in properties e.g. polarity Attractive forces: A-B < A-A or B-B Escaping tendency higher A max is found in vapour pressure-composition curve Presence of azeotropic mixtures lead to min boiling point Examples: 1. ethyl, isopropyl, n-propyl alcohol - water, 2. volatile drug (methyl amphetamine) chloroform - ethanol PHM1153 Physical Pharmacy /11

Positively deviated solution mixture with a minimum boiling point
The mixture shows positive deviation from Raoult’s law A minimum boiling point is obtained The solution has an azeotropic mixture whose vapour pressure is the highest and boiling point is the lowest example of a positive azeotrope is 95.6% ethanol and 4.4% water (by weight). Ethanol boils at 78.4°C, water boils at 100°C, but the azeotrope boils at 78.1°C PHM1153 Physical Pharmacy /11

Distillation of positive azeotrope 95.6% ethanol and 4.4% water
distillation of any mixture will result in the distillate being closer in composition to the azeotrope than the starting mixture. E.g. if a 50/50 mixture of ethanol and water is distilled once, the distillate will be 80% ethanol and 20% water i.e. closer to the azeotropic mixture than the original. Distilling the 80/20% mixture produces a distillate that is 87% ethanol and 13% water. Further repeated distillations will produce mixtures that are progressively closer to the azeotropic ratio of 95.5/4.5%. increasing distillations will not give distillate that exceeds the azeotropic ratio. PHM1153 Physical Pharmacy /11

Negative Deviation from Raoult’s Law
Vapour pressure of solution less than that expected from Raoult’s law Attractive forces: A-B > A-A or B-B Escaping tendency lower A min is found in vapour pressure – composition curve Presence of azeotropic mixtures lead to max boiling point E.g. pyridine-acetic acid, chloroform-acetone (formation of loose compounds from hydrogen bonding), formation of hydrates, nitric acid-water, sulfuric acid-water. PHM1153 Physical Pharmacy /11

Negatively deviated solution with maximum boiling point
Mixtures showing negative deviation from Raoult’s law A maximum boiling point is obtained The solution has an azeotropic mixture whose vapour pressure is the lowest and the boiling point is the highest example of a negative azeotrope is 20.2% hydrogen chloride and 79.8% water (by weight). Hydrogen chloride boils at –84°C and water at 100°C, but the azeotrope boils at 110°C PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
Distillation of negative azeotrope 20.2% hydrogen chloride and 79.8% water distillation of any mixture of those constituents will result in the residue being closer in composition to the azeotrope than the original mixture. E.g. hydrochloric acid solution contains less than 20.2% hydrogen chloride, boiling the mixture will give a solution that is richer in hydrogen chloride than the original. If the solution initially contains more than 20.2% hydrogen chloride, boiling will give a solution that is poorer in hydrogen chloride than the original. Boiling of any hydrochloric acid solution long enough will cause the solution left behind to approach the azeotropic ratio. PHM1153 Physical Pharmacy /11

Application of Raoult’s Law in Aerosol Formulation
Vapour pressure of propellant control the spray As pressure increases, spray rate increases -> fine spray, propellant gas vapourises fast As pressure decreases, spray rate decreases -> coarse spray, propellant gas vapourises slowly -> wet Thus, improvise by using appropriate mixture of propellant Examples of components: HFA-125: pentafluoroethane CHCF5 HFC-134a: tetrafluoroethane CHCHF4 HFA-152: difluoroethane CH3CHF2 HFA-227: heptafluoropropane CHFCF3CF3 PHM1153 Physical Pharmacy /11

Exercise: Application of Raoult’s Law in Aerosol Formulation
The vapour pressure of pure propellant 11 (MW 137.4) at 21oC is P110 = 13.4 psi The vapour pressure of pure propellant 12 (MW 120.9) at 21oC is P120 = 84.9 psi A total of 100 g propellants consisting of 50:50 mixture by gram weight was used. What is the total vapour pressure? n11 = 50/137.4 = mole n12 = 50/120.9 = mole n11 + n12 = mole P11 = P110X11 = P110(n11/(n11 + n12) = 13.4 x 0.364/0.778 = 6.27 psi P12 = P120X12 = P120(n12/(n11 + n12) = 84.9 x 0.414/0.778 = 45.2 psi P = P11 + P12 = 51.5 psi Conversion: psi to psig (Subtract atmospheric pressure of 14.7 psi) Thus, P = 51.5 – 14.7 = 36.8 psig PHM1153 Physical Pharmacy /11

Variation of Vapour Pressure with Temperature
As T ↑, energy of molecules ↑ More escape into vapour phase increase in vapour pressure Clausius-Clapeyron Equation PHM1153 Physical Pharmacy /11

Clausius-Clapeyron Equation
Assuming that the vapour obeys ideal gas behaviour, PV = RT V = RT/P Thus, Vv = RT/P The equation becomes Assuming Hvap to be constant: The variation of vapour pressure with temperature in terms of molar enthalpy of the liquid, Hvap V is the difference in molar volume of the two phases Since molar volume of vapour is very much greater than the molar volume of liquid,  V approaches volume of vapour, Vv PHM1153 Physical Pharmacy /11

Application of Clausius-Clapeyron Equation
To estimate vapour pressure at any temperature. To calculate enthalpy of vaporisation based on the slope of plot To study phase transition – important to determine the extent of weight loss during processing or testing. End lecture 3/3 PHM1153 Physical Pharmacy /11

PHM1153 Physical Pharmacy 1 2010/11
References The required texts you shall seek, The recommended ones you may flirt, Revise! Revise! You’d better be quick! When you get your grades you won’t be hurt! PHM1153 Physical Pharmacy /11

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