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Pharmaceutical Physical Chemistry Theory and Practices S K Bhasin Prelims.indd i 3/6/2012 1:09:17 PM Copyright © 2012 by Dorling Kindersley (India) Pvt Ltd Licensees of Pearson Education in South Asia No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent This eBook may or may not include all assets that were part of the print version The publisher reserves the right to remove any material present in this eBook at any time ISBN 9788131765272 eISBN 9788131775981 Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India Prelims.indd ii 3/6/2012 1:09:21 PM Dedicated to All Those Who Toiled in Shaping Me into What I Am Today Prelims.indd iii 3/6/2012 1:09:21 PM This page is intentionally left blank Prelims.indd iv 3/6/2012 1:09:22 PM Contents Preface xxi About the Author xxii Behaviour of Gases 1.1 Introduction 1.2 Gas Laws 1.2.1 Boyle’s Law 1.2.2 Charles Law 1.2.3 Avogadro’s Law 1.2.4 The Combined Gas Law Equation or the Gas Equation 1.2.5 Graham’s Law of Diffusion 1.2.6 Dalton’s Law of Partial Pressure 1.3 Kinetic Theory of Gases 1.3.1 Postulates (Assumptions) of Kinetic Theory 1.4 Derivation of Kinetic Gas Equation 1.5 Derivation of Gas Laws from Kinetic Equation 1.5.1 Some Useful Deductions from Kinetic Theory of Gases 12 1.6 Ideal and Real Gases 17 1.6.1 Ideal Gases 17 1.6.2 Real Gas 17 1.7 Deviations of Real Gases from Gas Laws 18 1.7.1 Deviations from Boyle’s Law 18 1.8 Causes of the Derivations from Ideal Behaviour 20 1.9 van der Waals’ Equation (Reduced Equation of State) (Equation of State for Real Gases) 20 1.9.1 Units of van der Waals’ Constants 23 1.9.2 Significance of van der Waals’ Constant 24 1.10 Explanation of Behaviour of Real Gases on the Basis of van der Waals’ Equation 24 1.11 Isotherms of Carbon Dioxide—Critical Phenomenon 28 1.12 Principle of Continuity of States 30 1.13 Critical Constants 31 1.13.1 Relations Between van der Waals’ Constants and Critical Constants 1.13.2 Derivation of PcVc = RTc from van der Waals’ Equation 33 Prelims.indd v 31 3/6/2012 1:09:22 PM vi | Contents 1.13.3 Calculation of van der Waals’ Constants in terms of Tc and Pc 1.14 Law of Corresponding States 34 1.14.1 Significance of Law of Corresponding States 35 1.15 Limitations of van der Waals’ Equation 36 34 Revision Questions 36 Multiple Choice Questions 39 Answers 42 The Liquid State 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Introduction 44 General Characteristics of Liquids 44 Classification of Physical Properties of Liquids 46 Surface Tension 46 2.4.1 Some Important Results 47 2.4.2 Effect of Temperature on Surface Tension 48 2.4.3 Measurement of Surface Tension 48 2.4.4 Surface Tension in Everyday Life 51 2.4.5 Surface Tension and Chemical Constitution (Parachor) Viscosity 57 2.5.1 Coefficient of Viscosity 58 2.5.2 Measurement of Viscosity 59 2.5.3 Effect of Temperature on Viscosity 60 2.5.4 Factors Affecting Viscosity 61 2.5.5 Viscosity and Chemical Constitution 62 Refractive Index 64 2.6.1 Measurement of Refractive Index 65 2.6.2 Refractive Index and Chemical Constitution 66 Optical Activity 69 2.7.1 Optical Activity 70 2.7.2 Specific Rotation 70 2.7.3 Optical Activity and Chemical Constitution 71 Polarity of Bonds 74 2.8.1 Polar Character of Covalent Bond 75 Dipole Moment 75 2.9.1 Unit of Dipole Moment 75 2.9.2 Dipole Moment and Molecular Structure 76 2.9.3 Application of Dipole Moments 76 43 52 Revision Questions 80 Multiple Choice Questions 81 Answers 83 Prelims.indd vi 3/6/2012 1:09:22 PM Contents | vii Solution 85 3.1 Introduction 86 3.2 Modes of Expressing Concentration of Solutions 87 3.3 Raoult’s Law 89 3.3.1 For a Solution of Volatile Liquids 89 3.3.2 For a Solution of Non-volatile Solute 90 3.4 Ideal Solution 90 3.4.1 Non-ideal Solution 91 3.4.2 Solutions Showing Positive Deviations 91 3.4.3 Solutions Showing Negative Deviations 91 3.4.4 Factors Responsible for Deviations 92 3.4.5 Distinction Between Ideal and Non-ideal Solutions 93 3.4.6 Difference Between Solutions of Positive and Negative Deviations 93 3.5 Colligative Properties of Dilute Solution 95 3.6 Lowering of Vapour Pressure 95 3.6.1 Determination of Molecular Masses of Non-volatile Solute 96 3.7 Elevation in Boiling Point 99 3.7.1 Expression for the Elevation in Boiling Point 99 3.7.2 Calculation of Molecular Masses 101 3.8 Depression of Freezing Point 102 3.8.1 Expression for the Depression in Freezing Point 103 3.8.2 Calculation of Molecular Masses 104 3.9 Osmotic Pressure 105 3.9.1 Difference Between Osmosis and Diffusion 105 3.9.2 Osmotic Pressure 105 3.9.3 Determination of Osmotic Pressure Berkley and Hertley’s Method 106 3.9.4 Osmotic Pressure is a Colligative Property 107 3.9.5 Isotonic Solutions 107 3.9.6 Calculation of Molecular Masses from Osmotic Pressure 108 3.10 Abnormal Molecular Masses 112 3.10.1 Modified Equation for Colligative Properties in Case of Abnormal Molecular Masses 114 Revision Question 115 Multiple Choice Questions 117 Answers 118 Thermodynamics 119 4.1 Introduction 119 4.1.1 Objective of Thermodynamics 120 4.1.2 Limitation of Thermodynamics 120 Prelims.indd vii 3/6/2012 1:09:22 PM viii | Contents 4.2 Some Common Thermodynamics Terms 121 4.2.1 Thermodynamic Equilibrium 122 4.2.2 Thermodynamic Processes 122 4.2.3 Reversible and Irreversible Processes 123 4.2.4 Thermodynamic Properties 124 4.3 Zeroth Law of Thermodynamics 126 4.3.1 Absolute Scale of Temperature 126 4.4 Work, Heat and Energy Changes 127 4.4.1 Work 127 4.4.2 Heat 129 4.4.3 Equivalence Between Mechanical Work and Heat 130 4.4.4 Internal Energy 130 4.5 First Law of Thermodynamics 131 4.5.1 Mathematical Formulation of First Law of Thermodynamics 132 4.5.2 Some Special Forms of First Law of Thermodynamics 132 4.5.3 Limitations of the First Law of Thermodynamics 133 4.6 The Heat Content or Enthalpy of a System 135 4.7 Heat Capacities at Constant Pressure and at Constant Volume 136 4.7.1 Heat Capacity at Constant Volume 137 4.7.2 Heat Capacity at Constant Pressure 137 4.7.3 Relationship Between Cp and Cv 138 4.8 Joule-Thomson Effect 138 4.9 Reversible-Isothermal Expansion of an Ideal Gas 140 4.9.1 Maximum Work 141 4.10 Second Law of Thermodynamics 142 4.10.1 Spontaneous Processes and Reactions (Basis of Second Law) 143 4.10.2 Spontaneous Reactions 143 4.11 Entropy 145 4.11.1 Mathematical Explanation of Entropy 145 4.11.2 Entropy Change in Chemical Reaction 147 4.11.3 Units of Entropy 147 4.11.4 Physical Significance of Entropy 147 4.11.5 Entropy Change Accompanying Change of Phase 147 4.11.6 Entropy Changes in Reversible Processes 148 4.11.7 Entropy Changes in Irreversible Processes 149 4.11.8 Entropy as Criterion of Spontaneity 150 4.11.9 Entropy Changes for an Ideal Gas 150 Revision Questions 154 Multiple Choice Questions 156 Answers 157 Prelims.indd viii 3/6/2012 1:09:22 PM Contents | ix Adsorption and Catalysis 159 5.1 5.2 5.3 5.4 5.5 Adsorption 160 Types of Adsorption 161 Factors Affecting Adsorption of Gases on Solids 162 Adsorption Isobar (Effect of Temperature on Adsorption) 163 Adsorption Isotherm (Effect of Pressure) 163 5.5.1 Explanation of Type I Isotherm 164 5.5.2 Freundlich Adsorption Isotherm 164 5.5.3 The Langmuir Adsorption Isotherm 165 5.5.4 Verification 166 5.5.5 Explanation of Type II and III Isotherms 167 5.5.6 Explanation of Type IV and V Isotherms 167 5.6 Theory of Adsorption 168 5.7 Gibbs’ Adsorption Equation 169 5.8 Applications of Gibbs’ Adsorption Equation 173 5.9 Equation for Multi-Layer Adsorption (B.E.T Equation) 176 5.9.1 Determination of Surface Area of the Adsorbent 178 5.10 Catalysis 179 5.10.1 Positive and Negative Catalyses 179 5.11 Homogeneous and Heterogeneous Catalyses 179 5.12 How Does a Catalyst Work? 180 5.12.1 Characteristics of Catalytic Reactions 181 5.12.2 Acid–Base Catalysis 182 5.12.3 Enzyme Catalysis 183 5.13 Mechanism of Homogeneous and Heterogeneous Catalyses 184 5.13.1 Significant Characteristics of Heterogeneous Catalysis 186 5.13.2 Facts Explained by Adsorption Theory 187 Revision Questions 188 Multiple Choice Questions 190 Answers 192 Photochemistry 6.1 Introduction 193 6.2 Thermochemical and Photochemical Reactions 194 6.3 Laws Governing Light Absorption — Lambert’s Law and Beer’s Law 6.3.1 Limitations of Lambert–Beer’s Law 198 6.4 Laws of Photochemistry 201 6.4.1 Grotthus–Drapper Principle of Photochemical Activation: (First Law of Photochemistry) 201 6.4.2 Stark–Einstein’s Law of Photochemical Equivalence— The Second Law of Photochemistry 201 Prelims.indd ix 193 195 3/6/2012 1:09:22 PM 104 | Pharmaceutical Physical Chemistry 3.8.2 Calculation of Molecular Masses If WB g of solute of molecular mass MB is dissolved in WA g of solvent, the number of moles of the solute present in the solution is equal to WB/ MB The molality (m) of the solution, i.e., the number of moles of the solution dissolved is 1000 g of solvent W 1000 = B × M B WB Substituting the value of molality in the formula, ∆T = K f m ∆T f = K f K f × WB × 1000 M B = ∴ WB 1000 M B WA (3.12) Thus, knowing the depression in freezing point, it is possible to determine the molecular mass of the dissolved solute ∆T f × WA Numerical Problems Example The freezing point of pure nitrobenzene is 278.8 K When 2.5 g of an unknown substance is dissolved in 100 g of nitrobenzene, the freezing point of the solution is found to be 276.8 K If the freezing point depression constant of nitrobenzene is 8.0 K kg mol-1, what is the molar mass of the unknown substance? Solution: Depression in freezing point of nitrobenzene (∆Tf ) = 278.8–276.8 =2.0 K Applying the relation, MB = MB (molar mass of unknown substance) = 1000K f WB ∆T f WA 1000 × 8.0 × 2.5 = 100 amu 2.0 × 100 Example A solution containing 25.6 g of sulphur dissolved in 1000 g of naphthalene, whose melting point is 80.1 °C gave the freezing point lowering of 0.680 °C Calculate the formula of sulphur (Kf, for naphthalene = 6.8 K/m and atomic mass of sulphur = 32) Solution: Molecular mass of sulphur can be calculated from the formula 1000K f WB MB = Putting the given values, we get M B = Atomic mass of S = 32 ∆T f WA 1000 × 6.8 × 25.6 = 256 0.68 × 1000 The number of atoms of sulphur in one molecule = Therefore, the formula of sulphur = S8 Chapter 03.indd 104 256 =8 32 3/5/2012 4:11:51 PM Solution | 105 3.9 OSMOTIC PRESSuRE Semipermeable membrane is a membrane which allows the passage of solvent molecules through it but not that of solute when a solution is separated from the solvent by it These membranes are of two types: (i) Natural semipermeable membranes: Vegetable membranes and animal membranes are the examples of the natural semipermeable membranes, which are just found under the outer skin of plants and animals The pig’s bladder is the most common animal membrane (ii) Artificial semipermeable membranes: Some of the examples of artificial semipermeable membrane are parchment paper, cellophane, collodion and certain freshly precipitated inorganic substance, e.g., copper ferrocyanide, silicate of iron, cobalt, nickel etc If the two solutions of different concentrations are kept in contact, the molecules of the solute and solvent both move from the region of higher concentration to the region of lower concentration till a uniform concentration is obtained The spontaneous mixing of the particles of solute and solvent to form a homogeneous mixture is called diffusion in solutions A different phenomenon has been observed whenever a solution and a pure solvent or two solutions of different concentrations are kept in contact through a semipermeable membrane In this case, only the solvent molecules penetrate through the membrane while the solute particles are held back The solvent molecules pass through the semipermeable membrane from the solvent to the solution side or from the less concentrated solution to the more concentrated solution till an equilibrium is attained This process of flow of the solvent molecules from the solvent to the solution or from a less concentrated to a more concentrated solution through a semipermeable membrane is called osmosis 3.9.1 difference Between Osmosis and diffusion The main differences between osmosis and diffusion are: (i) Osmosis can be carried out only with the help of semipermeable membrane, but no such external agency is required for diffusion to take place (ii) In diffusion, the movement of the molecules is from both sides The solute molecules move in one direction, whereas the solvent molecules in the other direction However, in osmosis, the movement of molecules is one sided (iii) In diffusion, the molecules of solute move from solution of higher concentration to the lower concentration giving a homogeneous mixture, whereas in osmosis, the solvent molecules move from the solution of lower concentration to that of the higher Thistle funnel concentration making it dilute Sugar solution (iv) Osmosis occurs in biological systems Distilled water h (v) Osmosis can be stopped by applying pressure to the solution; however, diffusion cannot be stopped 3.9.2 Osmotic Pressure The phenomenon of osmosis can be illustrated by a simple experiment Let a solution of sugar in water be kept in contact with water through a semipermeable membrane in a thistle funnel as shown in Fig 3.7 Here, water is separated from sugar solution with the help of a semipermeable membrane It is observed that water enters the Chapter 03.indd 105 Semi permeable membrane (a) Initial State (b) Final State Figure 3.7 Osmosis and osmotic pressure 3/5/2012 4:11:52 PM 106 | Pharmaceutical Physical Chemistry Piston given solution through the semipermeable membrane and the level of water in the funnel rises gradually Thus, experiment illustrates osmosis A stage is ultimately reached Narrow tube when the level of the solution becomes constant At this stage, the hydrostatic pressure developed is just sufficient to prevent the inflow of the solvent into the solution The equilibrium hydrostatic pressure developed on the solution side due to the net flow of the solvent molecules through a Solvent Solution semipermeable membrane is called the osmotic pressure The term osmotic pressure of a solution is, however, not strictly correct A solution does not, in itself, have any osmotic pressure Osmotic pressure is the hydrostatic pressure developed by osmosis under the conditions given Semi permeable membrance above Thus, we see that, it is osmosis that develops osmotic pressure and not the osmotic pressure, which develops Figure 3.8 Concept of osmotic pressure osmosis Osmotic pressure is a measure of the force, which produces osmosis This flow of solvent into the solution may also be stopped by the application of sufficient pressure with the help of a piston as illustrated in Fig 3.8 This extra pressure which must be applied to a solution in order to stop the flow of the solvent into it through a semipermeable membrane separating the two is a measure of osmotic pressure of the solution 3.9.3 determination of Osmotic Pressure Berkley and Hertley’s Method The measurement of osmotic pressure involves essentially the determination of the excess pressure that has to be applied upon the solvent to produce a state of equilibrium in the system (i.e., to stop osmosis) The method commonly employed for the determination of osmotic pressure is due to Pressure Gauge R Berkley and Hartley (1904) In this method, the Gun Metal Vessel osmotic pressure is balanced by a counter pres- M sure, which prevents the passage of the solvent into the solution The apparatus employed, shown in Fig 3.9, consists of a fine uniformly textured Solution porcelain tube A, within the pores of which the semipermeable membrane of copper ferrocyanide is deposited electrolytically towards its outer T Solvent surface This porcelain tube A is fitted into a gunmetal jacket B, with liquid-tight joints The outer vessel is provided with an air-tight piston One end of the porcelain tube is attached with capillary tube, T, and the other end is attached with a Porous tube with funnel, F, provided with a stopcock The porcesmipermeable membrance lain tube is completely filled with water while the outer vessel B is filled with the solution External Figure 3.9 Berkeley and Hartley’s apparatus Chapter 03.indd 106 3/5/2012 4:11:52 PM Solution | 107 pressure, which is measured by a pressure gauge, is applied on the solution by working the piston C so as to prevent the entrance of water into the solution, which is indicated when the level of water in the capillary tube T remains stationary This pressure measures the osmotic pressure of the solution So long as the hydraulic pressure is less than the osmotic pressure, the level of the solvent in the capillary tube will fall When the hydraulic pressure exceeds the osmotic pressure, the liquid in the capillary tube remains constant, which indicates that the two opposing pressures balance each other This method has following advantages: (i) The equilibrium is established very quickly and so it gives the results in very short time (ii) Since the external pressure applied balances the osmotic pressure, there is a little strain on the semipermeable membrane (iii) The concentration of the solution does not change during the determination of osmotic pressure Learning Plus Silica gardens When small crystals of copper sulphate, nickel sulphate etc are added to 5% sodium silicate solution, the so-called silicate gardens or chemical gardens are produced because of the diffusion of metal ions from crystals to form precipitate of metal silicate These precipitates act as semipermeable membrane around the crystal The osmosis takes place and water flows from dilute sodium silicate solution to stronger salt solution The membrane bursts at its weaker points so as to liberate more metal ions and these ions further give rise to new membrane As a result, the growth of metal ions looks like gardens around the crystals 3.9.4 Osmotic Pressure is a Colligative Property It has been observed that behaviour of non-electrolyte substances in dilute solutions is very much similar to the behaviour of gases Vant Hoff pointed out that substances in dilute solutions obey certain laws, which are very much similar to the gas laws Just like gas equation, we have a Vant Hoff equation for dilute solutions pV = n RT, where p is the osmotic pressure of the solution at temperature T containing n moles of the solute dissolved in V litres of the solution R is a constant called solution constant The value of the constant R is the same as for the gas constant The value is taken as 0.0821 litre atm per degree per mole or 8.3141 K-1 mole-1 n From the preceding equations, we have π = RT V means the number of moles per litre of the solution, which may be taken as the molar concentration (C) of the solution (3.13) π = C RT ∴ It is clear that osmotic pressure (p) is proportional to the concentration of the solute and not upon the nature of the solute Therefore, osmotic pressure is a colligative property 3.9.5 Isotonic Solutions It is evident from the equation = CRT that, if two solutions have the same value of C and T, they must have the same value of p It means that the solutions of equimolar concentrations at the same temperature must have same osmotic pressure Such solutions, which have the same osmotic pressure at the same temperature, are called isotonic solutions Chapter 03.indd 107 3/5/2012 4:11:55 PM 108 | Pharmaceutical Physical Chemistry 3.9.6 Calculation of Molecular Masses from Osmotic Pressure According to Vant Hoff equation for dilute solutions, we have πV = n RT If WB of the solute is dissolved in V litres of the solution and MB is the molecular mass of the solute, then n= WB MB Substitute the value of n in the preceding equation, we get W πV = B RT MB WB RT (3.14) πV Thus, measuring the osmotic pressure (p) of the solution of known concentration at a given temperature (T), the molecular mass (MB) of the solute can be calculated The value of R is taken as 0.0821 litre atm/degree/mole or 8.314 JK-1 mol-1 It may be noted that osmotic pressure method for determining the molar masses of bio-molecules such as proteins and polymers such as polythene and PVC are preferred to other colligative properties because of the following reasons: MB = (i) The magnitude of other colligative concentrations may be too low to be measured accurately due to very big size of the particles (ii) The experimental determination may require high temperature at which the big molecules get decomposed, e.g., in case of elevation in boiling point MEMORY FOCuS The spontaneous flow of solvent, through a semipermeable membrane, from a solution of low concentration or solvent to a solution of high concentration is called as ‘Osmosis’ The excess pressure that must be applied to a solution to prevent the flow of the solvent into it through a semipermeable membrane is known as osmotic pressure The equilibrium hydrostatic pressure from the solution to the solvent side, when the two are separated by a semipermeable membrane is called osmotic pressure The negative pressure which must be applied to the solvent in order to just stop the osmosis is equal to the osmotic pressure of that solution Solutions having same osmotic pressure are said to be isotonic with each other Isotonic solutions must have same molar concentrations When isotonic solutions are separated by a semipermeable membrane, no transfer of solvent takes place If the given solution has lower osmotic pressure than the one under consideration, then the given solution is said to be hypotonic solution If the given solution has higher osmotic pressure than the one under consideration, then the given solution is said to be hypertonic solution 10 Solutions having same osmotic pressure with reference to a perfect semipermeable are said to isosmotic Only for a perfect semipermeable membrane, isotonic solutions are isosmotic (Continued ) Chapter 03.indd 108 3/5/2012 4:11:59 PM Solution | 109 MEMORY FOCuS (Continued ) 11 12 Osmotic pressure of a solution is proportional to: (a) concentration of solute at constant temperature and (b) the absolute temperature at constant concentration The osmotic pressure of a dilute solution is equal to the pressure in which the solute would exert if it existed as a gas at the same temperature and occupied the same volume as the solution This statement is called as Vant Hoff ’s theory of dilute solutions 13 Swelling of resins (dried grapes) when put in water for sometime is another example of osmosis in everyday life Numerical Problems Example 10 A solution of sucrose (molecular mass = 342) is prepared by dissolving 68.4 g of it per litre of solution What is its osmotic pressure at 300 K? nRT Solution: We know π= V 68.4 g = 0.2 mol 342 g mol -1 Here, n= Putting the values, we get R = 0.0821 litre atom K -1 mol -1 and V = litre 0.2 × 0.0821 × 300 = 4.92 atm where R is expressed as 8.314 KPa dm2 K-1 mole-1 0.2 × 8.314 × 330 π= = 448.84 KPa π= Example 11 Osmotic pressure of a solution containing g of dissolved protein per 100 mol of the solution is 0.0392 atm at 310 K What is the molecular mass of the protein? The value of R is 0.8 litre deg-1 mol-1 Solution: We know that πV = n RT p = 0.0329 atm nB = , V = 100 mol = 0.1 litre MB R = 0.0820, T = 310 K Putting the value in the expression, × 0.0820 × 310 MB × 0.0820 × 310 = 46.387 MB = 0.1 × 0.0329 0.0329 × 0.1 = or Chapter 03.indd 109 3/5/2012 4:12:09 PM 110 | Pharmaceutical Physical Chemistry Example 12 A 6% sucrose (C12H22O11) is isotonic with a 3% solution of an unknown organic substance Calculate the molecular mass of the unknown substance Solution: Since the two solutions are isotonic, therefore, they are equimolar, i.e., they have same mol concentration Now, molecular mass of sucrose = 342 1000 60 ∴ Molar concentration of sucrose = × = 100 342 342 Let MB be the molecular mass of the unknown substance × 1000 30 = Then, molar concentration of unknown substance = 100 × M B M B 60 30 = Thus, we have 342 M B 30 × 342 or MB = = 171 60 Hence, the molecular mass of unknown organic substance = 171 amu Example 13 An aqueous solution freezes at 272 K, while pure water freezes at 273.0 K Determine (i) the molality of the solution, (ii) the boiling point of the solution and (iii) the lowering of vapour pressure of water at 298 K [Given Kf = 1.86 K kg mol-1, Kb = 0.512 K kg mol-1 and vapour pressure of water at 298 K = 23.75 mm Hg] Solution: (i) From the given values, We know ∆T f = (273 K = 272.4 K ) = 0.6 K ∆T f = K f m or m = Molality (m) = (ii) ∆T f kf 0.06 K mol -1 = 0.3225 mol kg -1 1.86 K kg mol -1 ∆Τb = kb × m = 0.512 K kg mol -1 × 0.3225 mol kg -1 = 0.1612 K ∴ (iii) we know that Tb = 373 K + 0.1612 K = 373.1612 K PA0 - PA PA0 PA0 - PA ∴ or Chapter 03.indd 110 = xB = nB nB + nA 0.3225 0.3225 = 27.756 0.32 + 55.55 55.8725 0.3225 × 23.756 = 0.137 mm Hg PA0 - PA = 55.8725 = 3/5/2012 4:12:24 PM Solution | 111 Example 14 A solution or sucrose (molar mass = 342 g) has been prepared by dissolving 68.4 g of sucrose in one kg of water Calculate the following: (i) the vapour pressure of the solution at 298 K, (ii) the osmotic pressure of the solution at 298 K and (iii) the freezing point of the solution [Given: the vapour pressure of water at 298 K = 0.024 atm, Kf for water = 1.86 K kg mol–1, R = 0.082 L atm mol-1 K-1] Solution: 68.4 = 342 1000 The number of moles of water = = 55.55 18 (i) The number of moles of sucrose = PA0 - PA = xB PA0 We know that 0.024 - PA nB 0.2 = = 0.024 nA + nB 55.55 + 0.2 0.024 × 55.75 - PA × 55.75 = 0.2 × 0.024 1.338 - 55.75 × PA = 0.0048 or (ii) We know -55.75PA = -1.338 + 0.0048 -55.75PA = -1.3332 1.3332 = 0.0239 atm 55.75 W RT 68.4 × 0.082 × 298 π= B = 342 × M BV 1671.4224 = atm = 4.8872 atm 342 PA = (iii) We know that ∆Τ f = K f m = 1.86 × 0.2 = 0.372 K ∴ Τ f = 273 - 0.372 = 272.628 K Example 15 1% solution of KCl is dissociated to the extent of 80% What would be osmotic pressure at 27 °C (R = 0.0821 L atm K-1 mol-1?) Solution: 0 1- α α α KCl → K + + Cl i = - α + α + α = + α = + 0.80 = 1.80 1000 C= × = 0.34 74.5 100 T = 273 + 27 = 300 K Now Chapter 03.indd 111 π = iC R T = 1.80 × 0.134 × 0.0821 × 300 = 5.98 atm 3/5/2012 4:12:42 PM 112 | Pharmaceutical Physical Chemistry nOTEwORTHY POInTS Osmotic pressure is the best colligative property to determine the molecular mass of a nonvolatile substance Substances having high vapour pressure (e.g petrol) evaporate more quickly than the substances of low vapour pressure (e.g motor oil) Kb and Kf are also called ebullioscopic constant and cryoscopic constant, respectively Ethylene glycol is commonly added to car radiators to depress the freezing point of water It is known as antifreeze NaCl or CaCl2 (anhydrous) is used to clear snow on roads It depresses the freezing point of water and reduces the temperature at which ice is expected to be formed Raoult’s law is applicable for only dilute solutions Konowaloff ’s rule: In case of non-ideal solutions, the vapour is relatively richer in the component whose addition to the required mixture results in an increase of total vapour pressure Babo’s law: It states that the vapour pressure of a liquid gets decreased when a non-volatile solute is added, the amount of decrease being proportional to the amount of solute dissolved Relative lowering of vapour pressure is measured by Ostwald and Walker method Elevation in boiling point by Landsberger method, depression in freezing point by Beckmann method and osmotic pressure by a Berkeley and Hertley’s method 3.10 ABnORMAL MOLECuLAR MASSES We know that colligative properties depend upon the molar concentration of the solute in solution These properties depend upon the number and not upon the nature of the solute particles in solution Therefore, in many cases where the solute associate or dissociate in solution, certain abnormal values of colligative properties are obtained The values of molecular masses calculated based on colligative properties in such cases will also be abnormal (i) Association: If a solute associates in the solution, the number of particles present in the solution will be less than the actual number dissolved and hence the value of osmotic pressure and other colligative properties will be smaller and consequently the molecular mass indicated will be higher than the true molecular mass For example, carboxylic acids such as acetic acid and benzoic acid associate in benzene to form dimers due to hydrogen bonding O 2CH3 COOH H3C H O C C O H Dimmer CH3 O (ii) Dissociation: If a solute dissociates in the solution, the number of particles in the solution will be more than that actually dissolved and the value of colligative properties will be higher and hence the molecular masses observed will be smaller than the true molecular mass For example, the electrolyte such as NaCl dissociates in solution and exists as Na+ and Cl– ions NaCl (a ) Water → Na + (aq ) + Cl + (aq ) Chapter 03.indd 112 3/5/2012 4:12:44 PM Solution | 113 Vant Hoff’s factor (i ) To account for the abnormal results, Vant Hoff introduced a factor (i) known after his name It is given by the expression: Observed value of the colligative property i= Calculated or normal value assuming no dissociation or association For example, the osmotic pressure observed in the case of electrolytes is much greater than what could come out from the equation πV = n RT Vant Hoff explained this abnormally by modifying the equation by putting factor (i), thus π obsV = in RT (3.15) Now, the equation in case of calculated osmotic pressure is π calV = n RT (3.16) π obs =i π cal Dividing Eq (3.15) by Eq (3.16), Osmotic pressure of the solution is proportional to the vapour pressure (∆P), elevation in boiling point (∆Tb) and depression in freezing point (∆Tf) Hence, Vant Hoff ’s factor can be expressed as i= π obs ∆Pobs ∆Tb obs ∆Tf obs = = = π cal ∆Pcal ∆Tb cal ∆Tf cal Each colligative property is inversely proportional to the molecular mass of the solute Therefore, i= i= Observed colligative property Normal or calculated colligaative property Normal Molecular mass (3.17) Observed Molecular mass Since a colligative property is directly proportional to the number of moles and inversely proportional to the molar mass of the solute, Vant Hoff ’s factor (i) may also be expressed as i= Number of particles after dissoiaton or association Normall number of particles (3.18) In case of association, since the observed molecular mass is more than the normal molecular mass, the factor i has a value less than In case of dissociation, since the observed molecular mass is less than the normal molecular mass, the factor i has a value greater than In case there is no association or dissociation, the value of i is equal to Degree of Dissociation Equation (3.14) can be used to determine the degree of dissociation of solutes in different solutions (i) Dissociation: Let a molecule of an electrolyte when dissolved in a solvent gives n ions and a is the degree of dissociation Chapter 03.indd 113 3/5/2012 4:12:52 PM 114 | Pharmaceutical Physical Chemistry mole AB 0 Water + A (aq ) + B (aq ) α (1- α ) mole α Before dissociation After dissociation The number of moles before dissociation = mole The number of moles after dissociation = - α + n α = 1(n - 1) α i= Therefore, 1(n - 1) α or i -1 =α n -1 Thus, a can be calculated (ii) Association: Let n molecules of solution ‘A’ associate to form one molecule and a is the degree of association 0 n A → ( A )n 1- α α n Before dissociattion After dissociation when n = factor of association Total number of moles after association α n α 1-α + n i= n α = (1 - i ) n -1 =1-α + Therefore, or 3.10.1 Modified Equation for Colligative Properties in Case of Abnormal Molecular Masses (i) Elevation of boiling point, ∆Τb = iK b m (ii) Depression in freezing point, ∆Τ f = iK f m (iii) Osmotic pressure, or πV = i n RT π =i n RT = iCRT V MEMORY FOCuS When the solute undergoes either dissociation or association, abnormalities are observed in the colligative properties Colligative properties are inversely proportional to the molecular mass of the solute and directly proportional to the number of solute particles If the solute undergoes association, (a) molecular mass increases (b) the number of particles decreases (c) observed colligative property is less than the theoretical value (Continued ) Chapter 03.indd 114 3/5/2012 4:13:04 PM Solution | 115 MEMORY FOCuS (Continued ) If the solute under goes dissociation, (a) molecular mass decreases (b) the number of particles increases (c) observed colligative property is higher than the theoretical value To explain the abnormal values of colligative properties and consequently molecular masses, a correction factor known as Vant Hoff ’s factor (i) is employed Vant Hoff ’s factor (i) = Observed colligative property Calculated colligative propertty Vant Hoff ’s factor for binary electrolytes such as NaCl and CuSO4 is close to 2, whereas of ternary electrolytes such as CaCl2 and Na2SO4 is close to Vant Hoff ’s factor (i) for acetic acid or benzoic acid in benzene is close to 0.5 Vant Hoff ’s factor is useful to calculate the degree of dissociation or association and the number of particles (ions) produced by complex salts in solution nOTEwORTHY POInTS Plasmolysis: When a plant cell is placed in a hypertonic solution, the fluid from the plant cell comes out and the cell shrinks This phenomenon is called plasmolysis and is due to osmosis Reverse Osmosis: When the external pressure applied on the solution is more than the osmotic pressure, the solvent will start following from the solution to the pure solvent It is called reverse osmosis It is used in the desalination of sea water to obtain pure water Bursting of red blood cells when placed in water is due to osmosis A 0.91% solution of pure NaCl is isotonic with human RBC’s Association generally occurs in the non-aqueous solvents because in the aqueous solution, the high dielectric constant of water helps in the dissociation of the associated molecules When outflow of water occurs from a cell, it is called exo-osmosis and when inward flow of water into a cell takes place, it is called endo-osmosis Gelatinous Cu2[Fe(CN)6] and gelatinous Ca3(PO4)2 are artificial semipermeable membranes Semipermeable membrane of Cu2[Fe(CN)6] does not work in non-aqueous solutions because it gets dissolved in non-aqueous solvents For solutes showing dissociation, i >1 and in case of association, i < 10 The phenomenon of osmosis was first observed by Abbe Nollet REVISIOn QuESTIOn Define or explain the following terms: (a) Colligative properties (b) (c) Molecular mass (d) (e) Boiling point constant (f) (g) Freezing point depression (h) Chapter 03.indd 115 Raoult’s law Boiling point elevation Molal elevation constant Electrolytes 3/5/2012 4:13:04 PM 116 | Pharmaceutical Physical Chemistry Explain the following: (a) Vapour pressure of a liquid does not depend upon the size of the container (b) Boiling point of a liquid increase on adding non-volatile solute in it (c) Vapour pressure of a liquid varies with temperature (a) What are isotonic solutions? Explain (b) Write a note on Vant Hoff ’s factor Differentiate ideal and real solutions State Raoult’s law and write about the solubility of gases in liquids Write briefly a short note on Raoult’s law and azeotropes What you understand by colligative properties of solutions? List important colligative properties Define osmosis and osmotic pressure How does it differ from diffusion? What you understand by relative lowering of vapour pressure and mole fraction of solute? Describe an experimental method for determining the molecular weight of solute by measuring the lowering of vapour pressure 10 Derive the expression for determining the elevation of boiling point 11 Describe the method used for determining the molecular weight of a non-volatile solute by the boiling point method 12 Derive a relationship between the depression of freezing point and the molecular weight of a non-volatile solute 13 Define depression of freezing point and describe any one method to determine it 14 Explain what is meant by molal depression constant of solvent? How it is related to latent heat of fusion? Describe a method for determining the molecular weight of a substance by depression in freezing point 15 Write short notes on the following: (a) Abnormal molecular weights or abnormal solutes (b) Vant Hoff ’s factor (c) Isotonic solutions 16 (a) Explain the term lowering of vapour pressure and relative lowering of vapour pressure (b) What are the colligative properties? Explain Why electrolytes have abnormally high value of colligative properties? 17 Explain the following by giving reasons: (a) Addition of non-volatile solute lowers the freezing point and elevates the boiling point of a solvent (b) Equimolar solutions of sucrose and sodium chloride in water are not isotonic 18 State and explain Van’t Hoff theory of dilute solutions 19 (a) State and explain Henry’s Law (b) Write a note on ideal solution (c) Write a short note on depression in freezing point 20 (a) Explain the following terms (i) Molarity (ii) Molality (iii) Normality (iv) Mole fraction (b) What is fractional distillation? Explain it for binary liquid solutions (c) Write a short note on reverse osmosis and depression in freezing point Chapter 03.indd 116 3/5/2012 4:13:04 PM Solution | 117 MuLTIPLE CHOICE QuESTIOnS Very dilute solutions which show deviations (positive or negative) from Raoult’s law are called (a) Ideal solution (c) Non-ideal solutions (b) True solution (d) Colloidal solutions Colligative properties of a solution depend upon (a) Nature of solute (b) Nature of solvent (c) The relative number of solute and solvent particles (d) None of these If 5.85 g of NaCl is dissolved in 90 g of water, the mole fraction of NaCl is (a) 0.1 (c) 0.2 (b) 0.01 (d) 0.0196 The freezing point of a solution containing 18 g of a non-volatile solute dissolved in 200 g of water is 0.93 °C Find the molecular weight of the solute K for water is 1.86 ° C/mole (a) 160 (c) 210 (b) 320 (d) 180 In an equimolar solution of (A) electrolyte and (B) non-electrolyte, (a) Freezing point of A is greater than that of B (b) Freezing point of B is greater than that of A (c) Osmotic pressure of B is greater than that of A (d) Boiling point of B is greater than that of A How many grams of CH3OH would have to be added to water to prepare 150 ml of a solution that is 2.0 MCH3OH? (a) 9.6 (c) 9.6 × 104 (b) 2.4 (d) 4.3 × 102 At 25 °C, the highest osmotic pressure is exhibited by 0.1 M solution of (a) CaCl2 (c) Glucose (b) KCl (d) Urea 10 ml of conc H2SO4 (18 molar) is diluted to litre The approximate strength of dilute acid could be (a) 0.18 N (c) 0.36 N (b) 0.09 N (d) 1800 N Chapter 03.indd 117 Equal volumes of 0.1 M AgNO3 and 0.2 M NaCl are mixed The conc of NO3 ions in the mixture will be (a) 0.1 M (c) 0.2 M (b) 0.05 M (d) 0.15 M 10 Addition of common salt to a sample of water will (a) increase its freezing point and increase the boiling point (b) decrease its freezing point and increase the boiling point (c) increase both the boiling and freezing points (d) decrease both the boiling and freezing points 11 Partial vapour pressure of a solution component is directly proportional to its mole fraction This statement is known as (a) Henry’s law (b) Raoult’s law (c) Ostwald dilution law (d) Distribution law 12 The law which states that the mass of a gas dissolved in a given mass of a solvent at any temperature is directly proportional to the pressure of the gas above the solution is called (a) Joule’s law (c) Charle’s law (b) Boyle’s law (d) Henry’s law 13 Vant Hoff ’s factor for 0.1 M ideal solution is (a) 0.1 (c) 0.01 (b) (d) none of the three 14 The depression in freezing point of 0.01 M aqueous solutions containing urea, sodium chloride and sodium sulphate is in the ratio of (a) 1:1:1 (c) 1:2:4 (b) 1:2:3 (d) 2:2:3 15 The solution of sugar in water contains (a) free atoms (b) free molecules (c) free ions (d) free atoms and free molecules 16 Vant Hoff ’s factor more than unity indicates that the solute has 3/5/2012 4:13:04 PM 118 | Pharmaceutical Physical Chemistry 17 18 19 20 22 23 (a) dissociated (b) associated (c) both (d) cannot say anything Isotonic solutions have same (a) molar concentration (b) molality (c) normality (d) none of these Unit of molarity is (a) g/litre (c) kg/litre (b) mole/litre (d) none of these When mango is placed in very dilute aqueous solution of hydrochloric acid, it (a) shrinks (c) bursts (b) swells (d) nothing happens 4.0 g of caustic soda is dissolved in 100 cc of solution; the normality of solution is (a) (c) 0.5 (b) 0.1 (d) 4.0 Molecular weight of urea is 60 A solution of urea containing g of urea in one litre is a (a) molar (c) 0.1 molar (b) 1.5 molar (d) 0.01 molar Which of the following solution in water possesses the lowest vapour pressure? (a) 0.1 (M) NaCl (c) 0.1 (M) KCl (b) 0.1 (M) AlCl3 (d) None of these 2N−HCl will have the same molar concentration as (a) 0.5 N−H2SO4 (c) 2N−H2SO4 (b) 1.0N−H2SO4 (d) 4N−H2SO4 24 The relationship between osmotic pressure at 273 K when 10 g of glucose (P1) 10 g of urea (P2) and 10 g of sucrose (P3) are dissolved, respectively, in 250 ml of water is (a) P1 > P2 > P3 (c) P2 > P1 > P3 (b) P3 > P1 > P2 (d) P2 > P3 > P1 25 Lowering of vapour pressure is the highest for (a) Urea (c) 0.1 M MgSO4 (b) 0.1 M glucose (d) 0.1 M BaCl2 26 Which of the following 0.10 M aqueous solution will have the lowest freezing point? (a) Al2(SO4)3[ (c) Kl (b) C2H10O5 (d) C12H22O11 27 Which is not affected by temperature? (a) Normality (c) Molarity (b) Formality (d) Molality 28 A 5% solution of cane sugar (molecular weight = 342) is isotonic with 1% solution of a substance X The molecular weight of X is (a) 34.2 (c) 68.4 (b) 171.2 (d) 136.8 29 If the increase in the boiling point of sucrose solution is 0.1 K, then what is the increase in boiling point of the same concentration of NaCl solution? (a) 0.1 K (c) 0.4 K (b) 0.2 K (d) 0.58 K 30 An ideal solution is formed, when its constituent components (a) have only zero heat of mixing (b) have only zero volume change (c) are converted into ideal gases (d) both ‘a’ and ‘b’ AnSwERS (c) (c) (d) (d) (b) Chapter 03.indd 118 10 (a) (a) (c) (b) (b) 11 12 13 14 15 (b) (d) (b) (b) (b) 16 17 18 19 20 (a) (a) (b) (b) (a) 21 22 23 24 25 (c) (b) (d) (c) (d) 26 27 28 29 30 (a) (d) (c) (d) (d) 3/5/2012 4:13:04 PM ... Gases obey gas laws at high temperature and low pressure usually and are called real gases In this chapter, we will discuss the deal gas behaviour in terms of kinetic theory of gases and also... This implies that Vt ∝ T if pressure remains constant or simply V ∝ T if pressure constant pressure Thus, the Charles Gay-Lussac? ?s law may also be defined as follows: Pressure remaining constant,... conferences and workshops and has acted as resource person in many conferences He has presented his research papers in international conferences abroad—two research papers in Kuwait in 2007 and one