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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 The Liquid State | 63 (vi) Molecular viscosity: Molecular viscosity is defined as the product of molecular surface and viscosity, i.e Molecular viscosity = Molecular surface × Viscosity = (M/d)2/3 × h The molecular surface is equal to (M/d)2/3 and is the surface area of one mole of the liquid Thorpe and Rodger showed molecular viscosity to be all additive and constitutive properties They prepared a table of values of molecular viscosity contributions by different atoms or structural factors as shown in the following table: Atom Molecular viscosity C H O (in -OH gp) O (in > C = 0) S -98 80 196 248 155 From these constants, the molecular viscosities of substances of known constitution could be calculated If the calculated and experimental values coincide, it is taken as a confirmation of the constitution of the substance For example, the structure of propionic acid is written as O || C H3 - C H2 - C - OH Its molecular viscosity can be calculated as follows: 6H = × 80 O (in OR) = × 196 O (in > C = 0) = × 248 3C = (-98) Total = 480 = 196 = 248 = -294 = 630 The experimental molecular viscosity of propionic acid is found to be 631.8 If the experimental and calculated values being the same, the structural formula assigned to propionic acid is correct MEMORY FOCUS Dunstan showed that viscosity coefficient (h) and molecule volume (d/M ) were related as: d × η × 106 = 40 to 60 M This expression holds only for normal (unassociated) liquids The product of molar surface and viscosity is termed molar viscosity M Molar viscosity = Molar surface × Viscosity = d 2/3 ×η Molar viscosity is an additive property at the boiling point The quantity [R] is termed Rheochor, M × η = [R] d The Rheochor may be defined as the molar volume of the liquid at the temperature at which its viscosity is unity Like parachor, rheochor is both additive and constitutive Chapter 02.indd 63 3/1/2012 1:28:45 PM 64 | Pharmaceutical Physical Chemistry Numerical Problems Example The water flow time for an Ostwald viscometer is 59.2 s at 25 °C If 46.2 s are required for the same volume of ethyl benzene (density = 0.867 g cm3) to flow through the capillary, calculate its absolute viscosity at 25 °C, that of water being 0.00895 poise at the same temperature Solution: Here, we are given that For water: For ethyl benzene: t1 = 59.2s, t2 = 46.2s, = 0.00895 poise, d1 = 1.0 g/cc = ?, d2 = 0.867 g/cc Substituting the values in the formula η2 = η1 d1t1 = , we get η2 d2 t η1 × d2t 0.00895 × 0.687 × 46.2 = = 0.00606 poise d1t1 × 59.2 Example At 20 °C, the density of water is 0.9983 g cm-3 and its viscosity is 0.010087 poise Explain how this figure shows that water is an associated liquid Solution: Here, we are given that d = 0.9983 g cm-3, M = 18 For H2O, ∴ h = 0.010087 poise Factor d 0.9983 η × 106 = × 0.010087 × 106 = 559.5 M 18 which is greater than 80 Hence, water is an associated liquid 2.6 REFRACTIVE INDEX When a ray of light travels from a less denser medium (i.e., air) to a more denser medium (i.e., liquid), the ray is bent towards the normal and the ratio of sine of the angle of incidence (sin i) to sin r of the angle of refraction (sin r) is constant and is called refractive index of the medium If n is the refractive index then, sin i n= sin r (2.13) Refractive index above is defined as n= velocity of light in vacuum um velocity of light in the mediu In addition, if x and y are refractive indices of less dense (liquid) and more dense media, respectively, i Liquid (x) Solid (y) Incident Ray r Reflected Ray sin i y = sin r x Chapter 02.indd 64 3/1/2012 1:28:53 PM The Liquid State | 65 2.6.1 Measurement of Refractive Index Refractive index depends upon the temperature as well as the wavelength of light used Generally, the D-line of sodium is used for standard measurements Refractive indices of liquids can be measured directly by means of an instrument known as refractometer One such refractometer is Abbe’s refractometer Fig 2.6 The principle of Abbe’s refractometer can be discussed with the help of Fig 2.7 A beam of light from a suitable source is reflected by a mirror M, passes through a lower prism P and illuminates its upper surface AB The surface of the prism is ground and thus it serves as a diffusing screen providing rays in every direction The small space between the lower prism P and the upper prism R contains a very thin layer of experimental liquid (the refractive index of the liquid should be smaller than that of the prism P, so as to allow the critical angle phenomenon) The rays after passing through the diffused surface AB enter into the liquid medium at different angles of incidence A particular ray going along the grazing incidence, i.e., at an angle only slightly less that 90 °, will pass through the prism R at an angle e which is equal to the critical angle According to critical angle phenomenon, n sin e = N Telescope Scale Magnifying Glass Compensating Prism Arm, R Water Jacket C Prism, R Prism, P H Mirror Figure 2.6 Abbe’s refractometer (2.14) where N is the refractive index of the prism R and n that of the liquid (Fig 2.7) The critical ray coming out from the face AC at an angle a is observed through a telescope T It can be seen that the refractive index of the liquid and the angle a are related by the equation: n = sin ABC (n sin α - sin2 α ) - cos BAC (2.15) All rays entering the liquid at angles less than the grazing incidence will pass through the prism R at angles less than the critical angle All other rays will suffer the phenomenon of total internal reflection; therefore, they will not pass through the prism R at all Thus, the band of light viewed through the telescope finishes sharply at the point where the critical angle emerges out of the face AC Therefore, the angle a can be accurately measured In experimental practice, the telescope is fixed and the prism box is rotated such that the critical ray coincides with the cross wire of the eye piece The setting of the prism at this position corresponds to a certain critical angle and, therefore, to a definite value of refractive index This value can be read directly from the scale made on the instrument Within the apparatus, there is an arrangement to remove chromatic aberration when white light is used The temperature of the liquid can be varied by Chapter 02.indd 65 T a C A R e P B D M Figure 2.7 Principle of Abbe’s refractometer 3/1/2012 1:28:56 PM 66 | Pharmaceutical Physical Chemistry flowing water at the required temperature through a jacket surrounding the prism box Refractive indices of some liquids are given in Table 2.5 Table 2.5 Refractive indices of some liquids at 293 K for D-sodium line Liquid Methyl alcohol Acetone Water Ethyl acetate Ethylene glycol Refractive Index 1.3289 1.3585 1.3330 1.3725 1.4314 Liquid Benzene Toluene Aniline Ethyl alcohol Cyclohexanol Refractive Index 1.5005 1.4950 1.5859 1.3611 1.4663 2.6.2 Refractive Index and Chemical Constitution Attempts have been made to relate the chemical constitution of a substance with its refractive index Thus, a number of new terms have been put forward as explained in the following list: (i) Specific refractivity (Rs): According to Lorentz and Lorentz, n2 - 1 (2.16) n2 + d where Rs = specific refraction of the substance, n = the index of refraction and d = the density of the liquid at the same temperature For any given substance, specific refraction is constant and independent of temperature (ii) Molar refractivity: Multiplying the specific refractivity by the molecular mass M of the substance, we get what is known as molar refractivity or molar refraction R Thus, Rs = n2 - M (2.17) Rm = r × M = n + d The above formula is applicable to gases, liquids as well as to solid To determine the molar refractivity of a solid, it is dissolved in a suitable solvent and the refractive index n and density d of the solution are measured The molar refractivity, R, of the solution is then given by the formula n2 - N1 M1 + N M2 Rs = n + d where N1 and N2 are the mole fractions of the solvent and solute, respectively, and M1 and M2 are their molecular masses However, the total molar refractivity of the solution is the sum of the contributions made by the solute (solid) and the solvent Hence, Rs = N1 R1 + N R2 where R1 is the molar refractivity of the solvent and R2 is that of the solid Thus, knowing R1, R2 can be calculated Like parachor, the molar refractivity has been found to be additive as well as constitutive The additive nature is supported again by the facts that (i) the difference in the molar refractivity of the successive Chapter 02.indd 66 3/1/2012 1:29:00 PM The Liquid State | 67 members of a homologous series is nearly constant and (ii) the isomeric compounds with the similar structures (e.g isopropyl alcohol and n-propyl alcohol) are found to have nearly same value of the molar refractivity Similarly, the constitutive nature is supported by the fact that in case of compounds containing double bond, triple bond or a closed ring etc., the observed value of molar refractivity is higher than the value obtained by simply adding the atomic refractivities The values of atomic refractivities have been calculated in a manner similar to that done for parachor Tables are available for consulting these values However, while calculating the molar refractivity, the following two points must be kept in mind: The atomic refractivity of oxygen atom is different in alcohols, ethers and ketones When a compound contains more than one double or triple bond, the molar refractivity depends not only on the number of double or triple bonds but also on their relative position in the molecule When the double bonds or triple bonds are present in conjugated position, e.g -CH = CH-CH = CH-, the molar refractivity is higher than the calculated value This is known as optical exaltation Thus for 1, 2, hexatriene, CH2 = CH-CH = CH-CH = CH2 Calculated value of [R] = 28.52 Experimental value of [R] = 30.58 Optical exaltation = 30.58 - 28.52 = 2.06 The application of molar refractivity in deciding chemical constitution of a substance may be illustrated with the help of example given below However, even this method has found only limited application in deciding chemical constitution Numerical Problems Example A substance having the formula C3H6O might be either acetone H3 C H3 C C O or allyl alcohol CH2=CH-CH2-OH) Determine which substance it actually is if its molar refractivity is found to be 16.974 by experiment Given that refractivity for C = 2.418, H = 1.100, O (carbonyl) = 2.211, O (hydroxyl) = 1.525 and C=C double bond = 1.733 Solution: Acetone Carbon = × 2.418 = 7.254 Hydrogen = × 1.100 = 6.600 Carbonyl oxygen = 2.211 16.065 Allyl Alcohol Carbon Hydrogen Double bond (C=C) Hydroxyl oxygen = 7.254 = 6.600 = 1.733 = 1.525 17.112 The value for double bond in the carbonyl group (>C = O) is included in the atomic refractivity of oxygen Chapter 02.indd 67 3/1/2012 1:29:01 PM 68 | Pharmaceutical Physical Chemistry Example Calculate the molar refraction of acetic acid (CH3COOH) at temperature at which its density is 1.046 g cm-3 The experimentally observed value of refractive index at this temperature is 1.3715 Solution: Here, we are given d = 1.046 g cm-3; n = 1.3715 Molecular mass of CH3COOH is M = 60 n2 - M , we get Substituting this value in the formula Rm = n + d Rm = (1.3715)2 - 60 ⋅ = 13.021 cm mol -1 (1.3715)2 + 1.046 Example Density of acetic acid at 25 °C is 1.046 g/ml Calculate the refractive index of acetic acid Value of Rm (molecular refractivity) for C = 2.42, H = 1.10, O in OH = 1.50, O in CO = 2.21 Solution: First step: To calculate the value of Rm for CH3COOH Here, we are given RC = 2.42, RH = 1.10 RO in -OH = 1.50 RO in > CO = 2.21 O || Rm for C H3 - C - OH = R C + R H + R O in - OH + R O in > CO = × 2.42 + × 1.10 + 1.50 + 2.21 = 12.95 cm3 mol-1 Second step: To calculate the value of n In addition, we are given d = 1.046 g/ml Molecular mass of CH3COOH (M) = 60 n2 - M Substituting this value in the formula Rm = , we get n + d n2 - 60 12.95 = n + 1.046 or n2 - = 0.2258 n2 + or n2 - = 0.2258 n2 + 0.4516 or 0.7742 n2 = 1.4516 or n2 = ∴ Chapter 02.indd 68 1.4516 = 1.8753 0.7742 n = 1.369 3/1/2012 1:29:11 PM The Liquid State | 69 MEMORY FOCUS The refractive Index (n) of a substance is defined as the ratio of the velocity of light in vacuum or air to that in the substance: n= Velocity of light in substance Velocity of light in air The refractive index of the liquid with respect to air is given by Snelle’s law According to it, sini n= sinr Molar refraction is defined as the product of specific refraction and molecular mass RM = n2 - M ⋅ n2 + d The value of molar refraction is characteristic of a substance and is temperature-independent The molar refraction (RM) is an additive and constitutive property The molar refraction of a molecule is thus a sum of the contributions of the atoms (atomic refractions) and bonds (bond refractions) present On comparing the calculated and experimentally observed value of RM, the structure of compounds can be confirmed Optical exaltation A compound containing conjugated double bonds (C = C - C = C) has a higher observed RM than that calculated from atomic and bond refractions The molar refraction is thus said to be exalted (raised) by the presence of a conjugated double bond and the phenomenon is called optical exaltation For example, for hexatriene, CH3 = CH - CH = CH - CH = CH2 The observed value of RM is 30.58 cm3mol-1 as against the calculated value 28.28 cm3mol-1 If present in a closed structure as benzene, the conjugated double bonds not cause exaltation 2.7 OPTICAL ACTIVITY Plane polarized light: According to wave theory of light, ordinary light consists of waves vibrating in all plane perpendicular to its path of propagation When, by a special device, the waves in all plane except one are cut off, the light radiations vibrating only plane are called plane polarized light The device which is capable of producing plane polarized light is named Nicol prism or polarizer Nicol prism is made by cutting a rhombohedron piece of calcite diagonally and cementing them along the diagonal by means of Canada balsam When light falls on one side of the prism, all other waves are reflected from the interface to one side and the waves vibrating in one plane pass through it Even monochromatic light, such as light emitted by a sodium lamp, is composed of waves which are vibrating in a number of different planes If such a beam is passed through a Nicol prism, it is converted into plane polarized light (Fig 2.8) Chapter 02.indd 69 3/1/2012 1:29:13 PM 70 | Pharmaceutical Physical Chemistry Slit Light in all Planes Nicol Prism Reflected Light Light in one Plane Interact Plane Polarized Light Sodium Lamp Figure 2.8 How to obtain plane polarized light 2.7.1 Optical Activity There are certain substances, such as quartz, turpentine oil or sugar solution, which when placed in the path of plane polarized light, rotate the plane of polarized light towards left or right Such substances which rotate the plane of polarized light towards right (clockwise) or towards left (anticlockwise) are called optically active substances and the property is called optical activity A substance which rotates the plane of polarized light to right (clockwise) is called dextrorotatory (Latin: dextro meaning right) and the one capable of rotating the plane of polarized light to left (anticlockwise) is termed as laevorotatory (Latin: laevous meaning left) The dextro- and laevorotatory compounds are also represented as d- and l- (or + and -) forms respectively The phenomenon of the rotation of plane of polarized light can be observed experimentally as explained below Allow the plane polarized light after coming out of the polarizer to pass through another Nicol prism with its axis parallel to that of the first (polarizer) The light in this case will be visible Now, rotate the second prism so that its axis is at right angle to the first In this case, no light will get through and the field of view will be dark If a glass cell containing some turpentine oil or a solution of cane sugar is placed between two Nicol prisms The field gets lighted up and the second prism has to be rotated through a certain angle for ‘extinction’ of light This clearly indicates that after passing through the optically active substance, the plane of polarized light gets rotated 2.7.2 Specific Rotation The angle in degrees through which the plane of polarized light gets rotated on passing through the solution of an optically active compound is known as angle of rotation The angle of rotation produced by an optically active compound depends upon: (i) (ii) (iii) (iv) (v) (vi) the nature of the optically active compound, the concentration of the solution (in g/ml), the length of the liquid column through which the light passes, the nature of the solvent, the temperature of the solution, and the wavelength of light used Chapter 02.indd 70 3/1/2012 1:29:13 PM The Liquid State | 71 If g grams of an optically active substance are dissolved in v ml of the solution and the solution taken in a glass tube of length l cm, then optical rotation produced will be found proportional to the concentration of the solution (g/ml) and length of the tube (in decimetres), i.e., m v ∝l m α∝ l v (the concentration of solution) α∝ or t α = [α ]λ or (the length of the tube in decimetres) m×l v (2.18) t where [α ] λ is a constant characteristic of the substance under conditions of temperature (1 °C) and wavelength of light used (l) Since d light of sodium flame at 25 °C is generally used It is generally 25° expressed as [α ]D and in known specific rotation of the substance From Eq (2.18), we get t v α [α ]λ = × (2.19) l m If m = g, v = ml and l = dm, t then [α ] λ = α Thus, specific rotation of a substance may be defined as the angle of rotation produced when the plane polarized light passes through the decimetre length of a solution containing one gram per millilitre of the optically substance If c grams of substance are dissolved in 100 ml of the solution, then Eq (2.19) reduces to t 100 × α [α ] λ = l ×c In case of pure solids or liquids, the above expression may be written as t α [α ] λ = (2.20) l ×d where d is the density of pure substance at temperature t °C 2.7.3 Optical Activity and Chemical Constitution Optical activity is an important property for determining the structure of different substances even in these days of highly developed electronic techniques It is purely a constitutive property which depends upon the arrangements of atoms within the molecule It is found, in general, that optically active organic compound consist of molecules which have at least one asymmetric carbon atom, i.e., a carbon atom attached to four different atoms or groups Lactic acid represents a very simple case of optically active compounds It contains an asymmetric carbon atom (marked with asterisks) attached to four different atoms or groups CH3 H *C OH COOH Chapter 02.indd 71 3/1/2012 1:29:22 PM 72 | Pharmaceutical Physical Chemistry It is observed that lactic acid exists in two forms; one of which rotates the plane of polarized light towards right and is called dextrorotatory (d-form) and the other rotates the plane of polarized light towards left and is called laevorotatory (l-form) Both the forms have the same constitution, i.e., contain an asymmetric carbon atom attached to four different atoms or groups but differ in their arrangements of atoms or groups in space Such forms, which otherwise, have the same molecular formula but differ only in their arrangement of atoms or groups in space are called optical isomers Vant’ Hoff and Le bel explained the relationship between optical activity and molecular asymmetry They pointed out that in all such compounds, the asymmetric carbon atom is present at the centre of a regular tetrahedron and four different atoms or groups attached to it are present at the corners of a tetrahedron In such a case, it can be shown by models that there are two ways of arranging the groups about the central carbon atom as shown in Fig 2.9 CH3 CH3 *C C* H OH HOOC CH3 CH3 *C H H HO COOH C* OH HO COOH H HOOC Mirror Figure 2.9 Two space models of latic acid Evidently, these two arrangements, although having similar structure or constitutions, cannot be superimpose on each other One structure is the mirror image of other and they are related to each other just as the right hand is to left hand of a person Neither of the two structures has a plane of symmetry, i.e the structures cannot be divided into two identical halves by a single plane In a simple way, the above two forms can be represented as follows The arrangement from H to OH is clockwise in the first form, while it is anticlockwise in the second form Therefore, if one of them is dextrorotatory, the other must be laevorotatory (Fig 2.10) However, simply by seeing its configuration, it is not possible to distinguish as to which one of them is dextro- or laevorotatory These two forms of lactic acid are also known as enantiomorphs If d- and l- forms of a compound are mixed with one another in equimolar quantities, the resulting Clockwise Anti-clockwise product is optically inactive This is due to mutual or external compensation of the two constituents, i.e., the CH3 CH3 rotation produced by one form completely nullifies the C* C* H OH HO H equal rotation in the opposite direction produced by the second form The optically inactive products thus COOH COOH obtained are called racemic mixtures and are repreFigure 2.10 Two forms of lactic acid sented as dl form or ± form Chapter 02.indd 72 3/1/2012 1:29:22 PM The Liquid State | 73 It is interesting to note that whenever any optically active comCOOH pound is synthesized in the laboratory, the product obtained in most of the cases is a racemic mixture This is because that there *C H OH are equal chances of the formation of two enantiomers The racemic mixtures obtained above can be separated into d- and l- forms by suitable physical and chemical methods This process of separation *C H OH of racemic mixture into d- and l- forms is called resolution In case of certain compounds, which contain more than COOH one asymmetric carbon atoms, another form is found to exist In this form, the rotation caused by one half of the molecule Figure 2.11 Meso form of tartaric acid is exactly cancelled by equal and opposite rotation caused by other half of the molecule (Fig 2.11) and the molecule on the whole becomes optically inactive Such a form which becomes optically inactive due to internal composition is called mesoform From above discussion, it appears as if only the organic compounds containing an asymmetric carbon atom show optical isomerism However, there are certain inorganic compounds, which contain other asymmetric atoms such as cobalt, silicon and sulphur and show optical isomerism Lastly, it may appear from above that the presence of an asymmetric carbon atom is the essential condition for a compound to be optically active However, this is not so 2,3-pentadiene, for example, does not contain an asymmetric carbon atom, yet it is optically active This is because, the molecule, as a whole, is asymmetric and does not possess any plane of symmetry We may conclude from above discussion that: (a) Optical activity can be used to prove a structure but cannot be used to disprove any structure (b) In general, optical activity can be used to test the presence of asymmetry in the molecules MEMORY FOCUS Some substances possess a special property of rotating the plane of polarized light.These substances are said to be optically active substances and this property is called optical activity Ordinary light has vibrations in all the planes perpendicular to the path of light When the vibrations are restricted in a single plane, it is said to be plane polarized light If the plane polarized light is rotated towards right, the compound is called dextrorotatory (d or + form) If the plane polarized light is rotated towards left, the compound is called laevorotatory (l or - form) Specific rotation is defined as, ‘the angle of rotation of the plane of polarized light by a liquid, which in a volume of ml contains gram of active substance when the length of the column through which the light passes is one decimetre’ With one tetrahedral chiral centre, a molecule is always chiral CHBrCIF is a chiral molecule containing one chiral centre With two or more chiral centres, a molecule may or may not be chiral To distinguish chiral and achiral compounds, keep in mind the followings: (i) A plane of symmetry is a mirror plane that cuts a molecule in half, so that one half of the molecule is a reflection of the other (ii) Achiral molecules usually contain a plane of symmetry, i.e., they can be cut into two identical halves by a simple plane, but chiral molecules not (Continued ) Chapter 02.indd 73 3/1/2012 1:29:23 PM 74 | Pharmaceutical Physical Chemistry MEMORY FOCUS (Continued ) For n chiral centres, the maximum number of stereoisomers is 2n (i) When n = 1, 21 = With one chiral centre, there are always two stereoisomers and they are enantiomers (ii) When n = 2, 22 = With two chiral centres, the maximum number of stereoisomers is four These isomers include enantiomers, diastereomers and meso-compounds 10 A meso-compound is an achiral compound that contains tetrahedral chiral centres Mesocompounds generally have a plane of symmetry; therefore, they possess two identical halves 11 Because two enantiomers have identical physical properties, they cannot be separated by common physical techniques such as distillation 12 Diastereomers and constitutional isomers have different physical properties, and therefore they can be separated by common physical techniques 2.8 POLARITY OF BONDS Covalent bonds are of two types: (i) Non-polar covalent bond (ii) Polar covalent bond (i) Non-polar covalent bond: In the non-polar covalent bonds, the two atoms have equal electronegativity, i.e., equally attract the pair of shared electrons Thus, the electron pair is shared equally between two atoms, e.g., the covalent bond in H2 and Cl2 is non-polar As a result, the molecule is neutral or non-polar : Cl : Cl : H:H Hydrogen Chlorine molecule molecule (ii) Polar covalent bond: In the case of polar covalent bonds, the two atoms have unequal electronegativities or the electron pair is shared unequally For example, in HCl, the electron pair is more attracted or displaced towards chlorine, as it is more electronegative than hydrogen Due to this, chlorine end of the molecule appears negative and the hydrogen end appears positive Such molecules having the oppositely charged poles are called polar molecules and the bond is said to be a polar covalent bond Displaced to Cl atom δ δ– δ+ δ– H – – Cl or H : Cl H : Cl : : Similarly, BrCl molecule is a polar molecule, as chlorine is more electronegative than bromine The shared electron pair is more attracted towards chlorine than towards bromine As a result, the chlorine end of the molecule is negative and the bromine end is positive If there is a single bond in a molecule, the molecular dipole moment is the same as that of the individual bond, e.g., molecular dipole moment of HCl is the same as that of single HCl bond, i.e., 1.03 D In case of the molecule having more than one polar bond, the molecular dipole moment is not measured by the values of individual bonds but by the arrangement of the polar bonds in space δ δ– xx : Br x Cl xx Br– – Cl xx Chapter 02.indd 74 3/1/2012 1:29:24 PM The Liquid State | 75 2.8.1 Polar Character of Covalent Bond When a covalent bond is formed between two dissimilar atoms, one of which has larger value of electronegativity and the bonding pair of electrons is displaced towards the more electronegative atom In other words, electron cloud containing the bonding electrons gets distorted and the charge density gets concentrated around the more electronegative atom and it acquires a partial negative charge (indicated by δ-), where as less electronegative atom acquires a partial positive charge (indicated as δ+) Such a bond is called a polar covalent bond and it develops a partial ionic character It is represented by an arrow pointing towards the more electronegative atom as shown in the case of hydrochloric acid δ H Cl Whereas the covalent bond between two similar atoms is called non-polar covalent bond, as the shared pair of electrons lies midway between the nuclei of two atoms (Fig 2.12) δ+ or A A - A B Symmetrical Non-polar Distorted Electron Bond Covalent Bond Electron Bond +d or A −d A Polar Covalent Bond Figure 2.12 Polarity of covalent bond The extent of ionic character in a covalent bond depends upon the difference of electronegativities of the atoms forming a covalent bond A bond is considered to be ionic if it has more than 50% ionic character If the difference in electronegative values of the two bonded atoms is more than 2, it is primarily ionic The difference of about 1.17 gives 50% ionic character 2.9 DIPOLE MOMENT The degree of polarity developed in polar molecule is expressed in terms of dipole moment Dipole moment may be defined as the product of the magnitude of charge on either atom and the distance between the centres of the nuclei of boding atoms forming a polar covalent bond Dipole moment is represented by Greek letter m and is expressed as: Dipole moment, = e × d (2.21) where e is the charge on either atom and d is the distance between them 2.9.1 Unit of Dipole Moment Since charge is of the order of 10-10 esu and distance is of the order of 10-8 cm, dipole moment is of the order of 1018 esu-cm and this unit is known as Debye unit (D), i.e D = 10-18 esu-cm In S.I system, the unit of dipole moment is coulomb metre, C-m D = 3.336 × 10-30 C-m Dipole moment is a vector quantity and can be determined experimentally It can be represented by an arrow pointing towards negative charge with a small tail at the positive charge, e.g., δ+ δ- H F Chapter 02.indd 75 or H F 3/1/2012 1:29:25 PM 76 | Pharmaceutical Physical Chemistry 2.9.2 Dipole Moment and Molecular Structure (i) Diatomic molecules: Dipole moment is a vector quantity, i.e., it has magnitude as well as direction As a polar diatomic molecule has only one polar bond, the dipole moment of that molecule is equal to the dipole moment of the polar bond Thus, the greater the electronegativity difference between the bonded atoms is, the greater is the dipole moment For example, the dipole moments of hydrogen halides are in the order: H-F > H-CI > H-Br H-I (1.91 D) (1.03 D) (0.78 D) (0.38 D) (2) Polyatomic molecules: As polyatomic molecule has more than one polar bond, the dipole moment of the molecule is equal to the resultant dipole moment of all the individual bonds (called bond moments) The dipole moments of lone pairs also make their contribution to the resultant dipole moment The magnitude of the resultant dipole moment not only depends upon the values of individual moments but also on their arrangements in space i.e shape For example, CO2 has linear structure because the dipole moment of one C = O and is cancelled by that of the other C = O bond Water has angular V-shaped structure It has a net value of dipole moments (= 1.85 D), which the resultant of two O-H bonds The effect of two lone pairs on the oxygen atom is cancelled mutually Ammonia molecule has pyramidal shape and has a net resultant value of dipole moment (= 1.46 D) due to unsymmetrical structure Cl O O C (M = 0d) Carbon Dioxide C H H H (m = 1.84D) Net Dipole Moment Net Dipole Moment O H (The Dipole Moment of chloro methane arises mainly from highly polar carbon-chlorine bond) N H H (m = 1.85D) Since dipole moment of the long pair and bond pairs are in the opposite directions, therefor dipole moment of NF3 is very low N F F (m = 0.24D) H H (m = 1.49D) F 2.9.3 Application of Dipole Moments (i) To distinguish polar and non-polar molecules: The molecules having zero dipole moment are non-polar, e.g., O2, CO2, CCl4, CH4, CS2, SiF4, SnCl4 and BF3 The bonds of such molecules may be polar or non-polar The molecules having dipole moments are polar, e.g., NH3, H2O and HF Chapter 02.indd 76 3/1/2012 1:29:25 PM The Liquid State | 77 (ii) To predict degree of polarity: Dipole moments help in determining the degree of polarity developed in molecules More the dipole moment is, the more will be the degree of polarity in molecules For example, HF has more dipole moment than HCl Thus, HF is more polar than HCl (iii) To predict the shape or the symmetry of molecules: Dipole moment helps to determine the shape of the molecules Tri and polyatomic molecules having zero double moment have symmetrical structure F H Cl B C C F H H H Methane m = 0.0 Symmetrical Tetrahedral Structure F Boron Trifluoride m = 0.0D Plane Triangular Structure Cl Cl Cl Carbon Tetrachloride m = 0.0D Symmetrical Tetrahedral Structure The bonds in such molecules (being polar in nature) have some dipole moment However, the resultant dipole moment becomes zero due to symmetrical structure (iv) To distinguish cis- and trans-isomers: Trans-isomer has almost zero dipole moment, whereas cis-isomer has significant dipole moment, e.g., H H Cl Cl C C C C H Cl Cl H (v) To distinguish ortho-, meta- and para-isomer: The position of the two electronegative atoms/ groups in the benzene ring, i.e., o-, m- and p-isomers Cl Cl Cl Cl Cl m = 2.54 D Chapter 02.indd 77 m = 1.48 D Cl m=0D 3/1/2012 1:29:26 PM .. .Pharmaceutical Physical Chemistry Theory and Practices S K Bhasin Prelims.indd i 3/6/2012 1:09:17 PM Copyright © 2012... 3/5/2012 4:15:02 PM 12 | Pharmaceutical Physical Chemistry (vi) Derivation of ideal gas equation: PV = = mnu2 21 mnu2 = (K.E.) 32 = kT = k ′T ∴ ∴ [∵ K.E ∝ T, ∴ K.E = kT , where k is constant... and postgraduate students in chemistry and 15 years of teaching in professional institutes He is a ‘life fellow’ of four professional bodies, namely, the International Congress of Chemistry and