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(BQ) Part 2 book Essentials of physical chemistry has contents: Physical properties and chemical constitution, solutions, theory of dilute solutions, theory of dilute solutions, theory of dilute solutions, distribution law, distribution law, chemical kinetics,...and other contents.
482 13 PHYSICAL CHEMISTRY 13 Physical Properties and Chemical Constitution C H A P T E R C O N T E N T S SURFACE TENSION AND CHEMICAL CONSTITUTION USE OF PARACHOR IN ELUCIDATING STRUCTURE VISCOSITY AND CHEMICAL CONSTITUTION (1) Dunstan Rule (2) Molar Viscosity (3) Rheochor DIPOLE MOMENT Determination of Dipole moment BOND MOMENT DIPOLE MOMENT AND MOLECULAR STRUCTURE Dipole moment and Ionic character MOLAR REFRACTION AND CHEMICAL CONSTITUTION OPTICAL ACTIVITY AND CHEMICAL CONSTITUTION MAGNETIC PROPERTIES Paramagnetic Substances Diamagnetic substances MOLECULAR SPECTRA ELECTROMAGNETIC SPECTRUM Relation between Frequency, Wavelength and Wave number Energy of Electromagnetic Radiation MOLECULAR ENERGY LEVELS Rotational Energy Vibrational Energy Electronic Energy ABSORPTION SPECTROPHOTOMETER ROTATIONAL SPECTRA VIBRATIONAL SPECTRA VIBRATIONAL-ROTATIONAL SPECTRA How are IR spectra recorded and interpreted ? IR SPECTROSCOPY UV-VIS SPECTROSCOPY NMR SPECTROSCOPY MASS SPECTROSCOPY RAMAN SPECTRA P hysical properties of a substance depend on the intermolecular forces which originate in the internal structure or the constitution of the molecule Thus the determination of properties such as surface tension, viscosity, refractive index etc., can give valuable information about the structure of molecules In the modern times the molecular spectra of substances recorded by spectroscopic techniques have proved extremely helpful in elucidating the structure of organic molecules Physical properties may be classified into the following types : (1) Additive Property When a property of a substance is equal to the sum of the corresponding properties of the constituent atoms, it is called an additive property For example, molecular mass of a compound is given by the sum of the atomic masses of the constituent atoms (2) Constitutive Property A property that depends on the arrangement of atoms and bond structure, in a molecule, is referred to as a constitutive 482 PHYSICAL PROPERTIES AND CHEMICAL CONSTITUTION 483 property Surface tension and viscosity and optical activity are examples of constitutive property (3) Additive and Constitutive Property An additive property which also depends on the intramolecular structure, is called additive and constitutive property Surface tension and viscosity are such properties In this chapter we will discuss the application of some important physical properties for elucidating the constitution of molecules SURFACE TENSION AND CHEMICAL CONSTITUTION What are Parachors ? From a study of a large number of liquids, Macleod (1923) showed that γ1/ (1) =C D–d where γ is the surface tension, D its density and d the density of vapour at the same temperature, C is a constant Sugden (1924) modified this equation by multiplying both sides by M, the molecular weight of the liquid, M γ1/ (2) = MC = [ P ] D–d The quantity [P], which was constant for a liquid, was given the name Parachor As d is negligible compared to D the equation (2) reduces to M 1/ γ = [ P] D or Vmγ1/4 = [P] (3) where Vm is the molar volume of the liquid If surface tension (γ) is unity, from equation (3), we may write [P] = Vm Thus, the parachor [P] may be defined as the molar volume of a liquid at a temperatures so that its surface tension is unity Use of Parachor in Elucidating Structure Sugden examined the experimental parachor values of several organic compounds of known molecular structure He showed that the parachor is both an additive and constitutive property That is, the parachor of an individual compound can be expressed as a sum of : (1) Atomic Parachors which are the contributions of each of the atoms present in the molecule (2) Structural Parachors which are the contributions of the various bonds and rings present in the molecule By correlating the experimental values of parachor with molecular structure, Sugden (1924) calculated the atomic and structural parachors listed in Table 13.1 These values were further revised by Vogel (1948) on the basis of more accurate measurements of surface tension TABLE 13.1 SOME ATOMIC AND STRUCTURAL PARACHORS Atom C H O N Cl Parachor Sugden Vogel 4.8 17.1 20.0 12.5 54.3 8.6 15.7 19.8 — 55.2 Bond or Ring Single bond Double bond Coordinate bond 3- membered ring 6- membered ring Parachor Sugden Vogel 23.2 –1.6 17.0 6.1 19.9 12.3 1.4 484 13 PHYSICAL CHEMISTRY We can now illustrate the usefulness of parachor studies in the elucidation of molecular structure (1) Structure of Benzene (Vogel) If the Kekule formula for benzene be accepted, the value of its parachor can be calculated by using Vogel’s data H H H C C C C C C H 6C × 8.6 = 51.6 6H × 15.7 = 94.2 (=) × 19.9 = 59.7 H 6-membered ring = 1.4 H Kekule formula Parachor of benzene = 206.9 The experimental value of the parachor of benzene is 206.2 Since the calculated parachor tallys with that determined by experiment, the Kekule structure for benzene is supported (2) Structure of Quinone (Sugden) The two possible structural formulas proposed for quinone are : C C HC HC CH HC CH HC O CH CH C C O A O B The parachors calculated for the two structures are : Structure A 6C 4H 2O (=) six-membered ring × 4.8 × 17.1 × 20.0 × 23.2 × 6.1 = = = = = 28.8 68.4 40.0 92.8 6.1 Structure B 6C × 4.8 = 4H × 17.1 = 2O × 20.0 = (=) × 23.2 = six-membered rings × 6.1 = Total = 236.1 28.8 68.4 40.0 69.6 12.2 Total = 219.0 The experimental value of parachor for quinone is 236.8 This corresponds to the parachor calculated from structure A Therefore, the structure A represents quinone correctly (3) Structure of Nitro group (Sugden) The parachor has also been found useful in providing information regarding the nature of bonds present in certain groups The nitro group (–NO2), for example, may be represented in three ways : O N O N N O I O O II O III PHYSICAL PROPERTIES AND CHEMICAL CONSTITUTION 485 The calculated parachors are : Structure I 1N 2O 3-membered ring Structure II × 12.5 = 12.5 × 20.0 = 40.0 × 17.0 = 17.0 1N 2O (=) Total = 69.5 × 12.5 = 12.5 × 20.0 = 40.0 × 23.2 = 46.4 Total = 98.9 Structure III 1N 2O (=) (→) × 12.5 = × 20.0 = × 23.2 = × (– 1.6) = 12.5 40.0 23.2 – 1.6 Total = 74.1 The experimental value of parachor for – NO2 group has been found to be 73.0 This approximates to the calculated parachor for structure III which is, therefore, the appropriate structure of – NO2 group VISCOSITY AND CHEMICAL CONSTITUTION Viscosity is largely due to the intermolecular attractions which resist the flow of a liquid Therefore, some sort of relationship between viscosity and molecular structure is to be expected Viscosity is also dependent on the shape, size and mass of the liquid molecules The following general rules have been discovered (1) Dunstan Rule Dunstan (1909) showed that viscosity coefficient (η) and molecular volume (d/M) were related as: d × η × 106 = 40 to 60 M This expression holds only for normal (unassociated) liquids For associated liquids this number is much higher than 60 For example, the number for benzene (C6H6) is 73, while for ethanol (C2H5OH) it is 189 This shows that benzene is a normal liquid, while ethanol is an associated one Thus Dunstan rule can be employed to know whether a given liquid is normal or associated (2) Molar Viscosity The molar surface of a liquid is (M/d)2/3 The product of molar surface and viscosity is termed molar viscosity That is, Molar Viscosity = Molar surface × Viscosity 2/ ⎛M ⎞ =⎜ ⎟ ×η ⎝ d ⎠ Thorpe and Rodger (1894) found that molar viscosity is an additive property at the boiling point They worked out the molar viscosity contributions of several atoms (C, H, O, S, etc) and groups From these, they calculate the molar viscosity of a liquid from its proposed structure By comparing this value with the experimental one, they were able to ascertain the structure (3) Rheochor Newton Friend (1943) showed that if molecular volume (M/d) be multiplied by the eighth root of the coefficient of viscosity, it gives a constant value [R] The quantity [R] is termed Rheochor M × η1/ = [ 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 However it has not proved of much use in solving structural problems 486 13 PHYSICAL CHEMISTRY DIPOLE MOMENT In a molecule such as HCl, the bonding electron pair is not shared equally between the hydrogen atom and the chlorine atom The chlorine atom with its greater electronegativity, pulls the electron pair closer to it This gives a slight positive charge (+q) to the hydrogen atom and a slight negative charge (– q) to the chlorine atom H Cl or +q –q H Cl Such a molecule with a positive charge at one end and a negative charge at the other end is referred to as an electric dipole or simply dipole The degree of polarity of a polar molecule is measured by its dipole moment, μ (Greek mu) μ = θr q +q r Figure 13.1 An electric dipole of the magnitude = r The dipole moment of a polar molecule is given by the product of the charge at one end and the distance between the opposite charges Thus, μ = q×r The dipole moment (μ) is a vector quantity It is represented by an arrow with a crossed tail The arrow points to the negative charge and its length indicates the magnitude of the dipole moment Thus a molecule of HCl may be represented as H Cl Unit of Dipole Moment The CGS unit for dipole moment is the debye, symbolised by D, named after the physical chemist Peter Debye (1884-1966) A debye is the magnitude of the dipole moment (μ) when the charge (q) is × 10–10 esu (electrostatic units) and distance (r) is 1Å (10–8 cm) μ = q × r = × 10–10 × 10–8 = × 10–18 esu cm Thus D = × 10–18 esu cm In SI system, the charge is stated in Coulombs (C) and distance in metres (m) Thus dipole moment is expressed in Coulomb metres (Cm) The relation of debye to SI units is given by the expression coulomb: D = 3.336 × 10–30 Cm Determination of Dipole Moment Electric condenser The dipole moment of a substance can be experimentally determined with the help of an electric condenser (Fig 13.2) The parallel plates of the condenser can be charged by connecting them to a storage battery When the condenser is charged, an electric field is set up with field strength equal to the applied voltage (V) divided by the distance (d) between the plates Polar molecules are electric dipoles The net charge of a dipole is zero When placed between the charged plates, it will neither move toward the positive plate nor the negative plate On the other hand, it will rotate and align with its negative end toward the positive plate and positive end toward the negative plate Thus all the polar molecules align themselves in the electric field This orientation of dipoles affects the electric field between the two plates as the field due to the dipoles is opposed to that due to the charge on the plates PHYSICAL PROPERTIES AND CHEMICAL CONSTITUTION 487 Storage battery Condenser plate Figure 13.2 Polar molecules rotate and align in electric field The plates are charged to a voltage, say V, prior to the introduction of the polar substance These are then disconnected from the battery On introducing the polar substance between the plates, the voltage will change to a lower value, V' Just how much the voltage changes depends on the nature of the substance The ratio ε = V/V' is a characteristic property of a substance called the dielectric constant The experimentally determined value of dielectric constant is used to calculate the dipole moment Use of Rotational Spectra The rotational spectrum of a polar molecule is examined in the gas phase It is found that the spectral lines shift when the sample is exposed to a strong electric field From the magnitude of this effect (Stark effect), the dipole moment can be determined very accurately The dipole moments of some simple molecules are listed in Table 13.2 TABLE 13.2 DIPOLE MOMENTS OF SOME SIMPLE MOLECULES IN THE VAPOUR PHASE μ(D) Formula H2 Cl2 HF HCl HBr HI BF3 μ(D) Formula 0 1.91 1.08 1.80 0.42 CO2 CH4 CH3Cl CH2Cl2 CCl4 NH3 H2O 0 1.87 1.55 1.47 1.85 BOND MOMENT Any bond which has a degree of polarity has a dipole moment This is called Bond moment The dipole moment of H—H bond is zero because it is nonpolar The dipole moment of the H—Cl bond is 1.08 D because it is polar In a diatomic molecule, the bond moment corresponds to the dipole moment of the molecule The dipole moments of the halogen halides shown below also indicate their bond moments 1.91D H 1.80 D 1.08 D F H Cl H 0.42 D Br H The bond moment decreases with decreasing electronegativity of the halogen atom I 13 PHYSICAL CHEMISTRY 488 When a molecule contains three or more atoms, each bond has a dipole moment For example, 1.5 D 0.4 D C H C 1.5 D 1.3 D H Cl H O N The net dipole moment of the molecule is the vector resultant of all the individual bond moments If a molecule is symmetrical having identical bonds, its dipole moment is zero That is so because the individual bond moments cancel each other out DIPOLE MOMENT AND MOLECULAR STRUCTURE Dipole moment can provide important information about the geometry of molecular structure If there are two or more possible structures for a molecule, the correct one can be identified from a study of its dipole moment (1) H2O has a Bent Structure Water molecule (H2O) can have a linear or bent structure Net dipole moment H O H H O H (a) (b) The dipole moments of the two O—H bonds in structure (a) being equal in magnitude and opposite in direction will cancel out The net dipole moment (μ) would be zero In structure (b) the bond moment will add vectorially to give a definite net dipole moment Since water actually has a dipole moment (1.85 D); its linear structure is ruled out Thus water has a bent structure as shown in (b) (2) CO2 has a Linear Structure and SO2 a Bent Structure Carbon dioxide has no dipole moment (μ = 0) This is possible only if the molecule has a linear structure and the bond moments of the two C = O units cancel each other Net dipole moment S O C μ=0 O O O μ = 1.63 D On the other hand, SO2 has a dipole moment (μ = 1.63) Evidently, here the individual dipole moments of the two S = bonds are not cancelled Thus the molecule has a bent structure The vector addition of the bond moments of the two S = units gives the net dipole moment 1.63 D (3) BF3 has a Planar and NH3 a Pyramid Structure The dipole moment of boron trifluoride molecule is zero This is possible if the three B—F bonds are arranged symmetrically around the boron atom in the same plane The bond moments of the three B—F bonds cancel each others effect and the net μ = PHYSICAL PROPERTIES AND CHEMICAL CONSTITUTION F 489 Lone pair B N F H F Net dipole moment H H Ammonia, NH3 (μ = 1.47 D) Boron trifluoride, BF3 (μ = 0) Ammonia molecule (NH3) has a dipole moment (μ = 1.47 D) This is explained by its pyramidal structure The three H atoms lie in one plane symmetrically with N atom at the apex of the regular pyramid The dipole moments of the three N—H bonds on vector addition contribute to the net dipole moment In addition, there is a lone pair of electrons on the N atom Since it has no atom attached to it to neutralise its negative charge, the lone pair makes a large contribution to the net dipole moment Thus the overall dipole moment of ammonia molecule is the resultant of the bond moments of three N—H bonds and that due to lone-pair It may be recalled that the high dipole moment of water (H2O) can also be explained by the presence of two lone-pairs of electrons on the oxygen atom H H 0.4 D 109.5 C H H o C H o 70.5 H H H 0.4 D (a) (b) Figure 13.3 Dipole moment of methane molecule (4) CH4 has Tetrahedral Structure Methane (CH4) has zero dipole moment, despite the fact that each C—H bond possesses a dipole moment of 0.4 D This can be explained if the molecule has a symmetrical tetrahedral structure (Fig 13.3) μ (μ cos 70.5) to the resultant dipole moment Thus the net dipole moment of CH3 group is equal to μ This acts in a direction opposite to that of the fourth C—H bond moment, thereby cancelling each other (5) Identification of cis and trans Isomers The dipole moment can be used to distinguish between the cis and trans isomers The cis isomer has a definite dipole moment, while the trans isomer has no dipole moment (μ = 0) For example, Each C—H bond in the pyramidal CH3 group contributes H H C H C Cl C Cl cis-Dichloroethylene (μ = 2.96 D) Cl C Cl H trans-Dichloroethylene (μ = 0) In the cis isomer, the bond moments add vectorially to give a net dipole moment The trans isomer is symmetrical and the effects of opposite bond moments cancel so that μ = 490 13 PHYSICAL CHEMISTRY (6) Identification of ortho, meta and para Isomers Benzene has a dipole moment zero Thus it is a planar regular hexagon Let us examine the dipole moments of the three isomeric dichlorobenzenes (C6H4Cl2) Since the benzene ring is flat, the angle between the bond moments of the two C—Cl bonds is 60° for ortho, 120° for meta and 180° for para On vector addition of the bond moments in each case, the calculated dipole moments are ortho 2.6 D, meta 1.5 D and para D These calculated values tally with the experimental values Thus the above structures of o-, m - and p-isomers stand confirmed In general, a para disubstituted benzene has zero dipole moment, while that of the ortho isomer is higher than of meta isomer This provides a method for distinguishing between the isomeric ortho, meta and para disubstituted benzene derivatives Cl Cl Cl Cl 60 o o 120 o 180 Cl μ = 2.6 D μ = 1.5 D Cl μ=0 Figure 13.4 Dipole moments of ortho, meta and para dichlorobenzenes Dipole Moment and Ionic Character The magnitude of the dipole moment of a diatomic molecule determines its ionic character Let us consider an HBr molecule whose measured dipole moment (μexp) is 0.79 D and bond distance (r) = 1.41Å If the molecule were completely ionic (H+Br–), each of the ions will bear a unit electronic charge, e (4.8 × 10–10 esu) Thus the dipole moment of the ionic molecule (μionic) can be calculated μionic = e × r = (4.8 × 10–10 esu) (1.41 × 10–8 cm) = 6.77 D But the experimental dipole moment (μexp) of Hδ+—Brδ–, which determines its actual fractional ionic character, is 0.79 D Therefore, % ionic character of HBr = μ expt μionic × 100 0.79 D × 100 = 11.6 6.77 D Hence HBr is 12% ionic in character = MOLAR REFRACTION AND CONSTITUTION 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 PHYSICAL PROPERTIES AND CHEMICAL CONSTITUTION 491 refractions) present From the observed values of RM of appropriate known compounds, the atomic refractions of different elements and bonds have been worked out Some of these are listed in Table 13.3 TABLE 13.3 SOME ATOMIC AND BOND REFRACTIONS IN cm3 mol–1 FOR D LINE (VOGEL 1948) Atom C H O (in C = O) O (in –O–) O (in –O–H) Cl Br Ratomic Bond Rbond 2.591 1.028 2.010 1.643 1.518 5.844 8.741 C–H C=C C≡C 6C ring 5C ring 4C ring 1.676 4.166 1.977 – 0.15 – 0.10 0.317 The molar refraction of the proposed structure of a molecule can be computed from the known atomic and bond refractions If this value comes out to be the same as the experimental value, the structure stands confirmed Some examples are given below for illustrating the use of molar refractions in elucidating molecular structure (1) Acetic acid The accepted structural formula of acetic acid is H H O C C O H H The molar refraction (RM) may be computed from the atomic refractions of the constituent atoms as 2C 4H l O (in OH) l O (in C = O) × 2.591 × 1.028 × 1.518 × 2.010 = = = = 5.182 4.112 1.518 2.010 Total RM = 12.822 cm3 mol–1 The value of molar refraction of acetic acid found by determination of its refractive index is 13.3 cm3 mol–1 There is a fairly good agreement between the calculated and experimental values It confirms the accepted formula of acetic acid (2) Benzene The molar refraction of benzene (C6H6) on the basis of the much disputed Kekule formula may be calculated as : H C HC CH HC CH C H Kekule formula for benzene 6C × 2.591 = 15.546 6H × 1.028 = 6.168 3C=C × 1.575 = 4.725 = – 0.150 16 C ring Total RM = 26.289 cm3 mol–1 The observed values of RM for benzene is 25.93 This is in good agreement with the calculated value Hence the Kekule formula for benzene is supported INTRODUCTION TO COMPUTERS 18 19 20 21 22 23 24 25 (a) 500 MB (b) 500 GB (c) 700 MB (d) 700 GB (e) None of these Answer (c) Which of the following is not a GUI based software ? (a) Windows (b) UNIX (c) MS-Office (d) Corel Draw (e) Pagemaker Answer (b) The number of digits used in a number system is known as its (a) Power (b) Weight (c) Radix (d) Base (e) Either (c) or (d) Answer (e) Number System is used by the computer systems (a) Decimal (b) Binary (c) Octal (d) Hexadecimal (e) None of the these Answer (b) Hexadecimal Number System has a base of _ (a) (b) (c) (d) 10 (e) 16 Answer (e) Number System has a base of (a) Binary (b) Decimal (c) Octal (d) Hexadecimal (e) None of the these Answer (c) The octal equivalent of (111)2 is (a) (b) (c) (d) (e) None of the these Answer (d) The hexadecimal equivalent of (1111)2 is (a) (b) A (c) C (d) F (e) None of the these Answer (d) In Binary Addition, + is equal to _ (a) (b) (d) with carry (c) with carry (e) None of the these Answer (c) 1131 Appendix A Physical Constants Quantity Symbol Traditional units SI units th Atomic mass unit ( 12 mass of 12C atom) amu 1.6606 × 10–2 g 1.6606 × 10–27 kg Avogadro’s number N 6.022 × 1023 6.022 × 1023 particles/mol particles/mol Bohr radius a0 0.52918 Å 5.2918 × 10–13 m Boltzmann constant k 1.3807 × 10–16 erg/K 1.3807 × 10–23 J/K Charge-to-mass ratio of electron e/m 1.7588 × 108 Coulomb/g 1.7588 × 1011 C/kg Electron rest mass me 9.1095 × 10–28 g 9.1095 × 10–31 kg 0.00054859 amu Faraday constant F 96,487 coulombs/mole–1 96,487 J/V mol–1 Gas constant R 0.08206 Gravitational acceleration g 980.6 cm/s 9.906 m/s Molar volume (STP) Vm 22.414 L/mol 22.414 × 10–3 m3/mol Neutron rest mass mn 1.67495 × 10–24 g 1.67495 × 10–27 kg L atm mol K 8.3145 Pa dm3 mol K 1.008665 amu Planck’s constant h 6.6262 × 10–27 erg sec 6.6262 × 10–27 Proton rest mass mp 1.6726 × 10–27 erg sec 1.6726 × 10–27 kg 1.0077277 amu Velocity of ligh (in vaccum) c 2.9979 × 1010 cm/s 186,281 miles/s 2.9979 × 108 m/s Rydberg constant Rz 3.289 × 1015 cycles/s 1.0974 × 107 m–1 2.1799 × 10–11 erg 2.1799 × 10–18 J 1132 Appendix B Conversion Factors cm in in 2.54 cm cm3 in3 in3 2.54 cm3 cm in ft ft 12 in in 2.54 cm in cm 2.54 cm in in2 cm2 (2.54 cm)2 (1 in)2 km m2 (1000)2 (1 km)2 km mi 0.6214 m km km mi 0.6214 mi km laps lap 0.250 mi m mm ft in 12 in 1ft mm 0.001 m m 1m 39.37 in in cm dm3 m3 2.54 cm in cm3 in3 (0.1 m)3 (1 cm)3 (1 in)3 (1 dm)3 (0.01 m)3 (2.54 cm)3 1133 Appendix B L qt cu cu qt 1.057 qt 1L g mL L mL 0.84 g 1L 1000 mL cm3 g mL cm3 mL cm3 1.32 g kg g cm3 cm3 0.752 1000 g kg kg g 1000 g kg cm3 cm3 mL mL 1cm3 0.789g K °C K = °C + 273 °C K K = °C + 273 °F °C °C = [°F – 32] 1.8 °C °F °C = [°F – 32] 1.8 K °C K = °C + 273 d Cal cal 1000 cal Cal °F [°F – 32] 1.8 m d = v °C = m, V J 4.184J cal 1134 L 1L 100 mL Appendix C Dissociation constants of acids at 25ºC Name Formula Ka1 Ka2 Acetic acid CH3COOH 1.8 × 10–5 Arsenic acid H3AsO4 5.6 × 10–3 Arsenious acid H3AsO3 6.0 × 10–10 Benzoic acid C6H5COOH 6.5 × 10–5 Boric acid H3BO3 5.8 × 10–10 Carbonic acid H2CO3 4.3 × 10–7 Chloroacetic acid CICH2COOH 1.4 × 10–3 Formic acid HCOOH 1.8 × 10–4 Hydrocyanic acid HCN 4.9 × 10–10 Hydrofluoric acid HF 6.8 × 10–4 Hydrogen peroxide H2O2 2.4 × 10–12 Hydrogen sulphate ion HSO−4 1.2 × 10–2 Hydrogen sulphide H2S 5.7 × 10–8 Hypobromous acid HBrO 2.0 × 10–9 Hypochlorous acid HClO 3.0 × 10–8 Hypoiodous acid HIO 2.0 × 10–11 Lactic acid CH3(OH)COOH 1.4 × 10–4 Malonic acid CH3(OH)COOH 1.4 × 10–4 Malonic acid CH2(COOH)2 1.5 × 10–3 Nitrous acid HNO2 4.5 × 10–4 Oxalic acid (COOH)2 5.9 × 10–2 Phenol C6H5OH 1.3 × 10–10 Phosphoric acid H3PO4 7.5 × 10–3 Propionic acid CH3CH2COOH 1.3 × 10–5 Sulphuric acid H2SO4 strong acid 1.2 × 10–2 Sulphurous acid H2SO3 1.7 × 10–2 6.4 × 10–8 Tartaric acid (CHOHCOOH)2 1.0 × 10–3 4.6 × 10–5 1135 1.0 × 10–7 Ka3 3.0 × 10–12 5.6 × 10–11 2.0 × 10–6 6.4 × 10–5 6.2 × 10–8 4.2 × 10–13 1136 PHYSICAL CHEMISTRY Index Abbe refractometer, 436 Anisotropy, 448 Bar code reader, 1105 Anode compartment, 99 Barometric method, 564 Absolute zero, 1065 Anode, 999 Base peak, 514 Absorption coefficient, 1045 Antibonding orbitals, 219 Bases, 932 Absorption Antilogarithm, 1071 Beckmann thermometer, 572 Applications of Beckmann’s method, 576 spectrophotometer, 500 adsorption, 850 Becquerel, 115 Absorption, 844 colloids, 828 Acid rain, 953 ion-exchange adsorption, 852 Berkeley and Hartley’s method, 598 spectrum, 17, 497 Acid-base indicators, 963 Beryllium chloride, 180 Acid-base titrations, 1023 Arrhenius concept, 932 Beta rays, 104 Acids, 932 Arrhenius equation, 757 Binary Actinium series, 111 Arrhenius theory of ionisation, 883 addition, 1125 Artificial kidney machine, 830 digits, 1107 Associated colloids, 825 division, 1127 Aston’s mass spectrograph, 85 multiplication, 1126 Asymmetry effect, 913 number system, 1114 Activation energy, 767, 789 Adiabatic expansion, 258 process, 241 reversible compression, 312 reversible expansion, 260 reversible expansion, 312 systems, 239 Adsorption isotherms, 846 Adsorption theory, 792 Adsorption, 843 Aggregation methods, 813 Algorithm, 1113 Alpha particles, Alpha rays, 104 Aluminium chloride, 165 Aluminium oxide, 158 Ammonia, 161, 170 Ammonium ion, 164, 182 Amorphous solid, 448 Atomic subtraction, 1125 bomb, 133 Binding energy, 126 number, 11 Birkeland-Eyde process, 658 parachors, 483 BIT, 1107 spectra, 17 Body-centred cubic structure, 469 Aufbau principle, 65 Andrews isotherms, 395 Anionic exchange, 852 Bohr Autocatalysis, 788 atom, 12 Auto-ionisation of water, 940 atom, 23 Average life, 118 radius, 26 Average velocity, 375 Bohr’s theory, 23 Avogadro’s law, 362 Bohr-Bury scheme, 33 Avogadro-van’t Hoff law, 605 Boiling-point elevation, 570 Axis of symmetry, 450 Bomb calorimeter, 292 Azeotropes, 540 Bond Azimuthal quantum number, 54 energy, 195, 290 formation, 195 Ampere, 862 Analog computers, 1100 arithmetic, 1125 Balmer equation, 18 Balmer series, 18 1136 moment, 487 order, 220 Bonding electrons, 152 INDEX Born-Haber cycle, 462 catalytic reactions, 784 Colloids, 807 Boron trifluoride, 180 covalent compounds, 162 Combined gas law, 361 Boyle’s law, 358, 373 Compton effect, 23 Boyle-van’t Hoff law, 603 hydrogen-bonded compounds, 172 Bragg’s equation, 456 ionic compounds, 158 Concentration cells, 1027 1137 Common-ion effect, 915 Bravais unit cells, 452 Charles’ law, 373, 359 Concentration of solution, 528 Bredig’s are method, 811 Charles-van’t Hoff law, 604 Bronsted-Lowry concept, 934, 977 Chemical Conditions for hydrogen bonding, 169 Conductance Brownian movement, 817 actinometer, 1046 Bubble pressure method, 430 adsorption, 845 cell, 871 Buckminsterfullerene, 466 bond, 151 equation, 913 Bucky balls, 466 bonding, 151, 193 measurement, 872 Buffer solution, 953 equilibrium, 241, 621, 623 of electrolytes, 865 kinetics, 731 titrations, 898, 901 potential, 341 Congruent melting point, 717 shifts, 508 Conjugate acid-base pairs, 935 Cache memory, 1108 Calcium oxide, 157 Chemiluminescence, 1055 Consecutive reactions, 760 Calomel electrode, 1014 Chemiluminescent reaction, 1055 Constant of integration, 1086 Capillary-rise method, 425 Chemisorption, 845, 846 Contact process, 658 Carbon dioxide, 162, 180 Chiral, 492 Coordinate bond, 163 Carbon monoxide, 166 Chirality, 493 Coordination number, 456 Carbon-12, 94 Chloesteric liquid crystals, 473 Cottrell smoke precipitator, 829 Carbon-13, 94 Chlorine, 161 Cottrell’s method, 572 Carbon-14, 94 cis and trans isomers, 489 Coulomb, 862 Carnot cycle, 311, 316 Clapeyron equation, 330 Covalent bond, 160 Carnot theorem, 314 Classification of crystals, 459 Criteria for equilibrium, 241 Catalysis, 767, 781, 789 Claude’s method, 403 Criteria of spontaneity, 304 Catalytic poisoning, 787 Clausius-Clapeyron equation, 331 Cathode compartment, 999 Cleansing action of soap, 826 Criterion for spontaneous process, 328 Cathode rays, Closed system, 239 Critical Cathode, 999 Cloud chamber, 106 constants, 398 Cationic exchange, 851 Coagulation, 821 density, 399 CD-R, 1110 Coefficient of viscosity, 431 phenomenon, 395 CD-ROM, 1109 Cold light, 1055 state, 395 CD-RW, 1110 Cold packs, 277 temperature, 399 Cell potential, 1000 Colligative properties, 559 Cell reaction, 1000 Collision volume, 399 Crystal Celsius scale, 1065 diameter, 382 defects, 469 Centipoise, 432 frequency, 383 lattice, 452 Centre of symmetry, 450 properties, 380 Cesium chloride crystal, 462 Characteristics of theory of reactions rates, 756 Colloid mill, 811 structure, 451 Crystalline solid, 447 Cubic close-packed structure, 468 1138 PHYSICAL CHEMISTRY Cubic unit cells, 453, 454 Displacement-time graphs, 1073 Curie, 115 Dissociation constant method, 986 affinity, 73, 155 Dissolution, 547 microscope, 816 Distribution law, 672, 673, 675 sea model, 176 Cyclic process, 242 Dalton’s law, 364 Electron configuration, 63 Distribution of electrons, 61 Electronegativity values, 75 Daniel cell, 999 DOS, 1111 Electronegativity, 74 Davison experiment, 45 Dosimeter, 107 Electronic energy, 499 de Broglie’s equation, 44 Dot matrix printers, 1105 Electronic spectra, 500 de Broglie’s wavelength, 44 Downfield shift, 512 Electron-pair bond, 160 Debye-Huckel theory, 912 Drop-number method, 428 Electroosmosis, 820 Decimal number system, 1114 du Nouy tensiometer, 429 Electrophoresis, 819 Degree of dissociation, 579, 638, 914, 916 Dunstan rule, 485 Electrophoretic effect, 913 DVD drive, 1110 Electrovalent compounds, 154 Degree of hydrolysis, 979, 986 DVD-ROM, 1110 Emf, 1000 Deionization of water, 852 Dyanmic Emission spectra, 17 Demineralized water, 852 allotropy, 705 Emulsification, 827 Dempster’s mass spectrograph, 85 equilibrium, 623 Emulsifier, 827 method, 422 Emulsions, 826 Derivation of pH, 980 Derivation of Raoult’s law, 611 Enantiomers, 492 Desalination of sea water, 602 Egg experiment, 594 Enantiotropy, 704 Desilverization of lead, 688 Eigen-functions, 52 Determination of Endothermic reaction, 273 Eigen-values, 52 Endothermic processes, 274 association, 689 Einstein, 1051 Enthalpy of a reaction, 272, 278, 281 dipole moment, 486 Einstein’s equation, 125 Enthalpy of a system, 272 dissociation, 689 Electrical double layer, 819 Entropy of formation, 310 emf of a half-cell, 1006 Electrical properties of sols, 818 Entropy, 305, 306 molecular mass, 562 Electrical units, 861 Enzyme catalysis, 797 molecular weights, 833 Electrochemical cells, 997 Equilibrium concentrations, 634 osmotic pressure, 597 Electrode, 999 Equilibrium constant, 627 pH, 1017 Electrodialysis, 814 Equivalent conductance, 866 solubility, 549, 689 Electrical conductance, 860 Equivalent protons, 509 surface tension, 425 Electrolysis, 860 Eutectic system, 711 transport number, 889 Electrolyte, 999 Examples of Dialysis, 814 Electrolytes, 860 adsorption, 844 Diamagnetic substances, 494 Electrolytic cell, 860 colloids, 808 Differentiation, 1080 Electromagnetic emulsions, 827 Digital computers, 1100 radiations, 13, 498 first order reaction, 740 Dipole moment, 486 separation, 90 Dipole-dipole attractions, 416 spectrum, 15 hydrogen-bonded compounds, 170 Dipping calomel electrode, 1015 spectrum, 497 hydrolysis, 977 Dispersion methods, 811 isotopes, 91 INDEX Heterogeneous polar covalent bonds, 168 Geiger-Muller counter, 107 second order reaction, 744 Gels, 828 catalysis, 783 third order reactions, 745 Geometries of molecules, 179 equilibria, 650 Exothermic processes, 274 Ghosh’s formula, 911 Exothermic reaction, 273 Gibb’s Helmholtz equations, 326 Exponential functions, 1072 Gibbs Duhem equation, 342 Expressing concentration, 529 Glass electrode, 1016 Extensive properties, 239 Gold number, 822 Gouy balance, 494 1139 systems, 237 Heteronuclear diatomic molecules, 225 Hexagonal close-packed structure, 468 Hittorf’s method, 889 Homogeneous catalysis, 782 Factorial of an integer, 1088 Gradient of a line, 1078 Fahrenheit scale, 1066 Graphical method, 753 Faraday’s laws of electrolysis, 862 Grothus-Draper law, 1047 Homonuclear diatomic molecules, 221 Group displacement law, 111 Hot packs, 277 Graham’s law, 366, 374 Faraday’s method, 402 Fingerprint region, 505 First law of thermodynamics, 236, 249 First order reactions, 739 Floppy disk, 1109 Fluorescence, 1053 Fluoroborate ion, 164 Formation of ionic bond, 154 Fractional distillation, 540 Fractional electrolysis, 91 Fractionating columns, 541 Freezing mixtures, 716 Haber process, 656, 785 Homogeneous system, 237 Homogenizer, 827 How to determine the order of a reaction, 752 HTML, 1112 Habit of a crystal, 449 Hund’s rule, 61 Half reactions, 996 Hybrid computers, 1100 Half-cell, 999 Hybridization, 200 Half-life, 114, 746 Hydrogen Hard disk, 1109 bomb, 137, 138 Heat engines, 311 bonding, 169 Heat of bonding, 417 combustion, 283 fluoride, 170 formation, 281 spectrum, 28 fusion, 286 Hydrogen, 160 neutralisation, 284 Hydrogenation of ethene, 792 reaction, 278, 281 Hydrolysis constant, 978, 979 solution, 284 Hydrolysis, 976 Froth flotation process, 850 sublimation, 286 Hydronium ion, 164 Fugacity, 339 transition, 286, 289 Fundamental particles, vapourisation, 286 Fuos-mead osmometer, 833 adsorption, 845 Freezing-point depression, 573 Frequency, 13 Freundlich adsorption isotherm, 847 Fusion reaction, 137 Galvanic cell, 998 Ideal gas equation, 363 Heisenberg’s uncertainty principle, 48 Infrared spectroscopy, 504 Helmholtz double layer, 819 Integration, 1086 Henderson-Hasselbalch equation, 956 Intensive properties, 239 Gamma rays, 105 Henry’s constant, 678 Gas laws, 358 Henry’s law equation, 678 Gaseous state, 355 Henry’s law, 534, 677 Gay Lussac’s law, 361 Hess’s law, 286 Ink jet printers, 1106 Interfacial angles, 449 Intermolecular forces, 415, 419 Intermolecular hydrogen bonding, 171 1140 PHYSICAL CHEMISTRY Internal energy, 248, 271 experiment, 257 Interstitial defect, 469 Intramolecular hydrogen bonding, 172 Kelvin scale, 1065 Intrinsic energy, 271 Kidney dialysis, 597 Ion-exchange adsorption, 851 Kinetic Ionic gas equation, 369 bond, 153 molecular theory , 367 character, 490 properties of sols, 817 crystals, 459 Kirchoff’s equations, 278 equilibria, 909 Kohlrausch’s law, 894 Ionisation chamber, 106 energy, 155, 69 Irreversible Lamber law, 1045 Lamber-Beer law, 1045 expansion, 247 Landsberger-Walker method, 571 processes, 242, 243 Isobaric processes, 241 Langmuir adsorption isotherm, 847 Isobars, 96 Langmuir scheme, 31 Liquid-liquid chromatography, 687 Liquids, 415 Lodge’s moving boundary experiment, 884 Logarithmic functions, 1069 Logarithms, 1070 London dispersion forces, 417 Lyophilic sols, 810, 811 Macromolecules, 831 Magnesium chloride, 157 Magnetic balance, 494 disk, 1108 properties, 494 quantum number, 55 tape, 1108 Isochoric processes, 242 Laplacian operator, 52 Manometric method, 564 Isolated system, 238 Laser printers, 1106 Mantissa, 1070 Isothermal processes, 241 Laser separation, 91 Manufacture of Isothermal reversible compression, 312 Lattice energy, 155, 462 nitric acid, 658 Law of corresponding states, 400 sulphuric acid, 658 Isothermal reversible expansion, 312 Law of mass action, 626 Isotones, 96 Isotonic solutions, 600 Isotopes of chlorine, 93 hydrogen, 92 Neon, 92 oxygen, 93 uranium, 93 Isotopes, 85 Isotopic effects, 95 Isotropy, 448 Laws of osmotic pressure, 603 defect, 126 LCAO method, 213 number, 11 Le Chatelier’s principle, 652 of electron, Lewis concept, 938 spectrometer, 515 Lewis symbols, 152 spectroscopy, 514 Ligand, 164 Mathematical concepts, 1069 Linde’s method, 403 Maxima, 1084 Lindeman’s theory, 767 Mean free path, 380 Linear Measurement of equations, 1077 electrolytic conductance, 871 hybrid, 201 emf, 1002 molecules, 180 Linus Pauling, 154 Joule-Kelvin effect, 257 Joule-Thomson coefficient, 258 effect, 257 Mass pH, 945, 946 Mechanical Linux, 1112 dispersion, 811 Liquefaction of gases, 395 equilibrium, 241 Liquid crystals, 472 Liquid systems, 648 Mechanism of adsorption, 844 electrolysis, 861 INDEX 1141 Memory stick, 1110 Negative catalysis, 789 Orbitals, 201 Meso form, 493 Nematic liquid crystals, 473 Order of a reaction, 734, 737 Metal alloys, 470 Neptunium series, 112 Order of filling of electrons, 62 Metallic bonding, 176 Nernst equation, 1011 Osmometer, 599 Metallic crystals, 465 Nernst’s partition law, 673 Osmosis, 592 Methane, 161, 181 Neutrons, Osmotic pressure method, 833 Milikan’s oil-drop experiment, Nicotine-water system, 538 Osmotic pressure, 596, 607, 611 Miller indices, 450 Nitrogen, 162 Ostwald method, 432 Millipoise, 432 Nitromethane, 165 Minima, 1084 Nitrophenol, 171 Ostwald and Walker’s dynamic method, 564 Molal depression constant, 335 Nonbonding electrons, 152 Ostwald viscometer, 433 Molality, 532 Non-equivalent protons, 509 Ostwald’s dilution law, 909 Molar Normality, 533 Output devices, 1105 Nuclear Overpotential, 1026 concentration, 869 heat capacities, 254, 255 binding energy, 126 Overvoltage, 1026 refraction, 436, 490 chain reaction, 131 Oxidation-reduction reaction, 996 viscosity, 485 chemistry, 103 Oxidation-reduction titrations, 1024 Molarity, 530 energy, 131 Mole fraction, 530 equations, 123, 122 Molecular fission process, 130 Oxygen, 162 Ozone, 166 collision theory, 626 fission reactions, 120 crystals, 464 fusion process, 136 energy levels, 498 fusion reactions, 121 ion, 515 isomerism, 125 orbital theory, 213 sieve theory, 600 magnetic resonance (NMR) spectroscopy, 508 spectra, 496 power plant, 135 Partial differentiation, 1083 velocities, 374, 377 reactions, 120 Partition chromatography, 687, 688 weight, 515, 831 reactor, 135 Partition law, 673 system, 1114 Parts of a computer, 1101 Molecularity of reaction, 735 Monoisotopic, 94 Paramagnetic substances, 494 Parameters of a gas, 356 Parke’s process, 688 Pauli’s exclusion principle, 58 Molecularity, 737 Monitor, 1106 Parachors, 483 Octahedral hybridization, 203 Peak area, 511 Peak splitting, 512 Monoprotic acids, 937 Octal number system, 1117 Pen drive, 1110 Monoprotic bases, 937 Octet rule, 153, 174 Peptization, 811 Monotropy, 704 Ohm, 862 Peptizing agent, 811 Mouse, 1103 One-component system, 702 Periodic table, 68 Moving boundary method, 892 Open system, 239 MRI, 513 Opposing reactions, 760 Permutations and combinations, 1088 Multiple extraction, 681 Optical activity, 438, 492 Nanotube membranes, 603 mouse, 1103 properties of sols, 815 Pfeffer’s method, 597 pH of solutions, 944 pH range of indicators, 963 pH scale, 946, 948 1142 PHYSICAL CHEMISTRY Relative pH values, 948 Protons, Phase diagrams, 702 Pseudo-first order, 738 speed of ions, 886 Phase rule, 697 Purification of sols, 813 strength of acids, 940 Phenol-water system, 537 Pyramidal molecules, 182 strength of bases, 943 viscosity, 432 Phosphorescence, 1054 Phosphorus trichloride, 183 Photochemical reactions, 1043, 1044 Quantum efficiency, 1048 Relaxation effect, 912, 913 Reverse osmosis, 602 Reversible Photochemistry, 1043 numbers, 53 cells, 1003 Photoelectric cell, 1046 theory 12 expansion, 247 Photoelectric effect, 20 theory, 19 process, 242, 243 Photoelectrons, 20 yield, 1048 reactions, 621, 760 Photo-ionisation, 70 Quinhydrone electrode, 1016 Rheochor, 485 Photons, 19 Racemate, 492 Ring-detachment method, 429 Photophysical processes, 1053 Racemic mixture, 492 Role of emulsifier, 827 Photosenitized reactions, 1053 Radioactive ROM, 1108 Physical adsorption, 845, 846 dating, 118 Root mean square velocity, 375 Pi(π) bond, 197 decay series, 111 Rotating crystal method, 458 Pioseulle’s equation, 432 disintegration series, 111 Rotational energy, 498 Plane of symmetry, 449 equilibrium, 118 Rotational spectra, 500, 501 Plasma, 137 series, 111 Rutherford’s model, Polar covalent bonds, 167 Radioactivity, 103 Rydberg constant, 29 Polarimeter, 439 Radix, 1114 Rydberg’s constant, 29 Polymorphism, 704 RAM, 1108 Polynomial, 1073 Raman Polyprotic acids, 937 effect, 516 Salt bridge, 997 Polyprotic bases, 937 frequency, 517 Salt hydrolysis, 976 Positive rays, lines, 516 Scanners, 1104 Potentiometric titrations, 1023 scattering, 516 Schrodinger’s wave equation, 50 Powder method, 459 spectra, 516 Scintillation counter, 108 Preparation of emulsions, 827 spectrum, 516 Scroll mouse, 1103 Preparation of sols, 811 Random access memory, 1108 Primary memory, 1107 Raoult’s law, 560 Second law of thermodynamics, 303, 307 Principal quantum number, 24, 54 Rast’s Camphor method, 577 Second order reactions, 743 Printers, 1105 Rate laws, 734 Secondary memory, 1108 Probability, 1090, 1091 Rate of radioactive decay, 113 Selective precipitation, 922 Programming languages, 1113 Rayleigh line, 516 Semiconductors, 471 Promoters, 786 Rayleigh scattering, 516 Semipermeable membranes, 595 Properties of Reaction rate, 732 Separation of isotopes, 89 emulsions, 827 Read only memory, 1108 Shape of gels, 828 Recrystallisation, 547 ammonia molecule, 208 sols, 815 Redox reaction, 996 Proton number, 11 Refractive index, 435 phosophorus pentachloride molecule, 211 INDEX sulphur hexafluoride molecules, 212 sp3 hybridization of carbon, 206 sp3 hybridization, 202 Surface tension, 423, 483 water molecule, 210 sp3d2 hybrid orbitals, 203 Symmetry of crystals, 449 molecules, 184 Specific Syneresis, 828 SHE, 1006 conductance, 865 SI units, 1063 heat ratio, 384 SI unit of heat, 384 1143 Svedberg’s method, 834 Synthesis of ammonia, 656 temperature, 1065 refraction, 436 Tau scales, 509 length, 1064 resistance, 865 Tetrahedral hybridization, 202 rotation, 439 Tetramethylsilane, 509 volume, 1064 Sigma (σ) bond, 197 Spectroscope, 18 Theories of catalysis, 790 Sign convention of Spin quantum number, 57 Theories of osmosis, 600 heat, 244 Spin-spin coupling, 512 Theory of work, 244 Spontaneous processes, 303 dilute solutions, 559 Significance of entropy, 318 Spontaneous reactions, 731 electrolytic dissociation, 883 Silica garden, 594 Square planar hybridization, 203 strong electrolytes, 911 Silver-silver electrode, 1014 Stabilisation energy, 195 valence, 153 Simultaneous reactions, 760 Stability of sols, 824 Thermal equilibrium, 241 Single electrode potential, 1005 Stalagmometer, 428 Thermochemical equations, 277 Slope of a line, 1078 Standard emf of a cell, 1005 Thermochemical reactions, 1044 Smectic liquid crystals, 473 Standard entropy, 309 Thermochemistry, 271 Sodium chloride crystal, 460 Standard heat of Thermodynamic equilibrium, 240 Sodium chloride, 156 formation, 281 Thermonuclear reactions, 137 Solar cell, 472 reaction, 281 Thermopile, 1045 Solar energy, 137 Stark effect, 54 Solid state, 447 Stark-Einstein law, 1047 Third law of thermodynamics, 308, 318 Solubility State functions, 240 Third order reactions, 745 curves, 549 State method, 421 Thixotropic paints, 829 equilibria, 917 State variables, 240 Thixotropy, 828 product, 909, 917 Steam distillation, 543 Thorium series, 111 Solutions, 528 Strong electrolytes, 871 Time’s arrow, 344 Solvation, 810 Structural parachors, 483 Transition state theory, 765 Solvent extraction, 687 Structure of Transport number, 888 Trends in Sommerfeld orbits, 31 atom, 43 Sommerfeld’s modification, 30 benzene, 484 electronegativities, 75 sp hybrid orbitals, 201 diamond, 465 electron affinities, 74 sp hybridization, 201, 208 sp2 hybrid orbitals, 202 metal crystals, 467 nitro group, 484 Triethylamine-water system, 538 sp2 hybridization of carbon, 207 sp2 hybridization, 202 quinone, 484 Trigonal hybridization, 202 sp2d hybridization, 203 sp3d hybridization, 203 sp3 hybrid orbitals, 202 ionisation energies, 71 Subatomic particles, Trigonal planar molecules, 180 Sulphate ion, 165 Trigonometric functions, 1079 Sulphur dioxide, 165, 184 Triple point, 703 Sulphur trioxide, 181 Two-component systems, 710 1144 PHYSICAL CHEMISTRY Tyndall effect, 815 surface tension, 424 Weak electrolytes, 871 Types of third order rate constant, 746 Web camera, 1104 adsorption, 845 viscosity, 432 Weston standard cell, 1002 catalysis, 782 work and heat energy, 1067 Wheatstone bridge, 871 colloidal systems, 809 work, 244 Windows, 1111 zero order rate constant, 746 Work function, 336 computers, 1100 gels, 828 Uranium series, 111 hybridization, 201 hydrogen-bonding, 171 X-ray crystallography, 456 molecular spectra, 500 Vacancy defect, 469 radiations, 104 Valence bond theory, 195 radioactive decay, 108 Valence electrons, 152 Zeeman effect, 34 solutions, 529 Valence, 151 Zeeman effect, 54 thermodynamic systems, 238 van der Walls equation, 388, 390 Zeotropic mixtures, 540 van der Walls forces, 415 Zero order reaction, 735, 739 van’t Hoff equation, 604 Zeroth law of thermodynamics, 344 Ultrafiltration, 815 factor, 581 Zeta potential, 819 Ultramicroscope, 816 isochore, 338 Zinc electrode, 1007 Ultraviolet-visible spectroscopy, 506 isotherm, 336 Zip disk, 1109 Unit of dipole moment, 486 reaction, 646 Unit of equivalent conductance, 867 theory of dilute solutions, 605 Ultracentrifuge, 90 reaction isotherm, 643 Unit cells, 452 Vapour pressure, 420 Units of Variable valence, 175 density, 1068 Velocity-time graphs, 1075 energy changes, 272 Vibrational energy, 498 entropy, 309 Vibrational spectra, 500, 502 equilibrium constant, 642 Virial theorem, 194 first order rate constant, 746 Viscosity method, 834 force, 1067 Viscosity, 431, 485 heat capacity, 254 Volt, 862 heat, 244 Voltaic cells, 998 internal energy, 249 Volumetric titrations, 901 mass and weight, 1066 VSEPR theory, 179 pressure, 1068 radioactivity, 113 rate constant, 745 Water calorimeter, 292 rate, 732 Water softening, 852 second order rate constant, 746 Water, 161, 170 specific conductance, 866 Wave number, 14 Wavelength, 13 ... 1450-1600 1 620 -1680 1630-1690 1690-1750 1700-1 725 1770-1 820 21 00 -22 00 22 10 -22 60 25 00 27 00 -28 00 25 00-3000 3000-3100 3330 3 020 -3080 28 00-3000 3300-3500 320 0-3600 3600-3650 C–O C–N C–H NO2 C=C C=C... 69.5 × 12. 5 = 12. 5 × 20 .0 = 40.0 × 23 .2 = 46.4 Total = 98.9 Structure III 1N 2O (=) (→) × 12. 5 = × 20 .0 = × 23 .2 = × (– 1.6) = 12. 5 40.0 23 .2 – 1.6 Total = 74.1 The experimental value of parachor... 3 .2 3.3 Ar–O–CH3 Ether 3.7–4.0 R–CO–CH3 Ketone 2. 1 2. 4 Ar–CO–CH3 Ketone 2. 4 2. 6 CH3–COOR Ester 1.9 2. 2 R–COOCH3 Ester 3.0–3.9 CH3–N< Amine 2. 2 2. 6 R–CH2–R Alkane 1.1–1.5 R–CH2–Ar Arene 2. 5 2. 9