Colligative Properties

Colligative Properties Kausar Ahmad Kulliyyah of Pharmacy http://staff.iiu.edu.my/akausar PHM1153 Physical Pharmacy 1 2010/11

Contents PHM1153 Physical Pharmacy 1 2010/11

Introduction PHM1153 Physical Pharmacy 1 2010/11

Definition PHM1153 Physical Pharmacy 1 2010/11

Colligative vs Non-colligative PHM1153 Physical Pharmacy 1 2010/11

Non-Colligative Properties PHM1153 Physical Pharmacy 1 2010/11

Examples of Colligative Properties All of these properties relate to the vapor pressure. PHM1153 Physical Pharmacy 1 2010/11

Effect of Solute on Vapour Pressure PHM1153 Physical Pharmacy 1 2010/11

Vapour pressure:Solution < pure solvent PHM1153 Physical Pharmacy 1 2010/11

Boiling point PHM1153 Physical Pharmacy 1 2010/11

Freezing Point PHM1153 Physical Pharmacy 1 2010/11

Osmotic Pressure PHM1153 Physical Pharmacy 1 2010/11

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

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

Raoult's Law 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 1 2010/11

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 1 2010/11

Total Vapour Pressure PHM1153 Physical Pharmacy 1 2010/11

Ideal & Non-Ideal/Real Solutions PHM1153 Physical Pharmacy 1 2010/11

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 1 2010/11

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 1 2010/11

Deviation from Raoult’sLaw PHM1153 Physical Pharmacy 1 2010/11

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: http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Manometer/Manometer.html 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 PHM1153 Physical Pharmacy 1 2010/11

Factors that affect the magnitude of the changes in melting point and boiling point. PHM1153 Physical Pharmacy 1 2010/11

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 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 1 2010/11

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 1 2010/11

ΔTb = iKbm 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. PHM1153 Physical Pharmacy 1 2010/11

Molal Boiling Point Elevation and Freezing Point Depression Constants at 1 Atm pressure 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 1 2010/11

Osmotic pressure PHM1153 Physical Pharmacy 1 2010/11

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 1 2010/11

Application of Raoult’s LawDistillation PHM1153 Physical Pharmacy 1 2010/11

DISTILLATION PHM1153 Physical Pharmacy 1 2010/11

Distillation of Binary MixtureIdeal 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 PHM1153 Physical Pharmacy 1 2010/11

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 1 2010/11

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 PHM1153 Physical Pharmacy 1 2010/11

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

Positively deviated solution mixturewith 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 1 2010/11

Distillation of positive azeotrope95.6% 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 1 2010/11

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

Negatively deviated solutionwith 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 1 2010/11

Distillation of negative azeotrope20.2% 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 1 2010/11

Application of Raoult’s Law in Aerosol Formulation PHM1153 Physical Pharmacy 1 2010/11

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? PHM1153 Physical Pharmacy 1 2010/11

Variation of Vapour Pressure with Temperature PHM1153 Physical Pharmacy 1 2010/11

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: Clausius-Clapeyron Equation • 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 1 2010/11

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 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 1 2010/11

Colligative Properties