Collection of Problems in Physical Chemistry (eBook)

Front Cover 1
Collection of Problems in Physical Chemistry 4
Copyright Page 5
Table of Contents 6
FOREWORD TO THE CZECH EDITION 18
FOREWORD TO THE ENGLISH EDITION 19
CHAPTER I. ATOMIC STRUCTURE AND THE FUNDAMENTALS OF QUANTUM MECHANICS 20
Chapter A. ATOMIC STRUCTURE 20
Illustration 1. Determination of specific charge of electron from deflection in magnetic field 20
Illustration 2. Determination of electronic charge 24
Illustration 3. Determination of neutron mass from nuclear photoeffect in heavy hydrogen 27
Illustration 4. Determination of wave-length of electron from diffraction on grating 29
Illustration 5. Determination of positron mass 32
Illustration 6. Photoelectric effect—calculation of characteristic frequency and Planck constant 33
Illustration 7. Compton effect—shift in wave-length of X-rays 35
Illustration 8. Spectral distribution of black-body radiation 38
Illustration 9. Determination of atomic number by means of X-ray spectra 40
Illustration 10. Calculation of wave-length of lines of Balmer series of hydrogen 43
Illustration 11. Determination of isotopes by means of electronic spectra 45
Illustration 12. Calculation of electronic mass from Rydberg constants of hydrogen and helium 47
Illustration 13. Calculation of critical potentials of helium from spectroscopic data 48
Illustration 14. Rate of radioactive disintegration and radioactive equilibrium 50
Illustration 15. Estimation of radioactive constant by Geiger-Nuttall rule 53
B. THE FUNDAMENTALS OF QUANTUM MECHANICS 55
Illustration 1. Calculation of translational partition function of ideal gas 55
Illustration 2. Rotational partition function of carbon monoxide 58
Illustration 3. Vibrational partition function of hydrogen chloride 62
RESULTS 72
CHAPTER 2. II. KINETIC THEORY OF IDEAL GAS 75
Illustration 1. Calculation of molecular velocities 75
Illustration 2. Calculation of molar heat capacity 76
Illustration 3. Mean free path 77
Illustration 4. Collision diameter of molecules 79
Illustration 5. Collision diameter and diffusion coefficient 82
Illustration 6. Determination of molecular weight from effusion of gas 83
Illustration 7. Determination of vapour pressure by effusion method 86
PROBLEMS 88
RESULTS 90
CHAPTER 3. III. IDEAL GAS 92
Illustration 1. Boyle's law 92
Illustration 2. Gay-Lussac's law and the absolute temperature scale 93
Illustration 3. Ideal gas equation—calculation of volume 96
Illustration 4. Ideal gas equation—calculation of molecular weight 97
Illustration 5. Determination of molecular weight by method of limiting densities 98
Illustration 6. Ideal gas equation—degree of dissociation 100
Illustration 7. Calculation of degree of association from molecular weights 102
Illustration 8. Expression of concentration of gas mixtures 104
Illustration 9. Calculation of total pressure of gas mixture from Dalton's law 106
Illustration 10. Calculation of partial pressure from Dalton's law 108
PROBLEMS 110
REESULTS 113
CHAPTER IV. FUNDAMENTALS OF THERMODYNAMICS 115
A. FIRST LAW OF THERMODYNAMICS 115
Illustration 1. Calculation of units 115
Illustration 2. Calculation of change in internal energy during evaporation 116
Illustration 3. Calculation of specific and atomic heat capacities from calorimetric data 117
Illustration 4. Dependence of molar heat capacity on temperature 119
Illustration 5. Calculation of heat of reaction from heats of formation of constituents 120
Illustration 6. Calculation of standard heat of formation from known heats of reaction 121
Illustration 7. Calculation of heat of reaction from heats of combustion 122
Illustration 8. Calculation of standard heats of formation from bond energies 123
Illustration 9. Dependence of standard heat of reaction on temperature 125
Illustration 10. Enthalpie balance 127
Illustration 11. Theoretical flame temperature 129
Illustration 12,. Work during isothermal process 131
Illustration 13. Heat, work and change in internal energy during expansion of ideal gas 132
Illustration 14. Adiabatic process 134
Illustration 15. Work done during adiabatic process 135
Illustration 16. Thermal engine 138
Illustration 17. Cooling engine 139
PROBLEMS 140
RESULTS 150
B. SECOND LAW OF THERMODYNAMICS 152
Illustration 1. Dependence of entropy on pressure 152
Illustration 2. Dependence of entropy on temperature 154
Illustration 3. Graphical calculation of entropy change with temperature 155
Illustration 4. Entropy of mixing 158
Illustration 5. Entropy change during irreversible adiabatic process 159
Illustration 6. Isothermal change in free energy and free enthalpy of ideal gas 161
Illustration 7. Dependence of free enthalpy on pressure 162
Illustration 8. Change in free enthalpy during isomorphous transformations 163
Illustration 9. Change in free enthalpy in irreversible phase transformations 163
Illustration 10. Thermodynamic functions of ideal gas 164
PROBLEMS 166
RESULTS 168
CHAPTER V. STATES OF MATTER 170
A. EEAL GASES 170
Illustration 1. Calculation of volume from Berthelot equation 170
Illustration 2. Calculation of volume from Beattie-Bridgeman equation 171
Illustration 3. Calculation of density from generalized compressibility diagram 173
Illustration 4. Comparison of van der Waals equation with generalized compressibility factor 175
Illustration 5. Calculation of temperature from generalized compressibility diagram 177
Illustration 6. Determination of second virial coefficient by method of limiting densities 179
Illustration 7. Beattie-Bridgeman equation for mixture of gases 181
Illustration 8. Calculation of pressure of gas mixture using generalized compressibility diagram 182
Illustration 9. Joule-Thomson coefficient 184
Illustration 10. Dependence of molar heat capacity eP on pressure 187
Illustration 11. Difference in molar heat capacities eP—eF for real gas 189
Illustration 12. Calculation of fugacity by analytical method 191
Illustration 13. Calculation of fugacity of constituent in mixture 193
PROBLEMS 195
RESULTS 201
B. LIQUIDS 202
Illustration 1. Calculation of density using generalized expansion factor 202
Illustration 2. Calculation of surface tension from capillary rise 204
Illustration 3. Eötvös equation 205
Illustration 4. Calculation of viscosity from Poiseuille equation 207
Illustration 5. Stokes' law 208
PROBLEMS 210
RESULTS 211
C. SOLIDS 211
Illustration 1. Determination of constants of ionic lattice from diffraction of X-rays 211
Illustration 2. Estimation of molar heat capacity of solid by means of Kopp's law 213
Illustration 3. Determination of temperature dependence of molar heat capacities of solids from known characteristic temperature 215
Illustration 4. Calculation of molar heat capacities of solids on basis of Born-Karmén theory 217
Illustration 5. Calculation of characteristic temperature from compressibility 220
Illustration 6. Calculation of characteristic temperature from melting point 221
PROBLEMS 222
RESULTS 224
CHAPTER VI. PHASE EQUILIBRIUM 225
A. SYSTEMS WITH ONE COMPONENT 225
Illustration 1. Clapeyron equation—calculation of change in melting point with pressure 225
Illustration 2. Clapeyron equation—graphical calculation of heat of fusion 226
Illustration 3. Clausius-Clapeyron equation—calculation of change in boiling point with pressure 227
Illustration 4. Clausius-Clapeyron equation—calculation of triple point 228
Illustration 5. Calculation of heat of vaporization from empirical equation for temperature dependence of vapour pressure 229
Illustration 6. Ramsay-Young rule 231
Illustration 7. Cox-Othmer diagram 233
Illustration 8. Adjustment of measured values of vapour pressure by method of least squares 235
Illustration 9. Cailletet-Mathias law—determination of critical volume 237
B. SYSTEMS WITH SEVERAL COMPONENTS 240
Illustration 1. Units of concentration 240
Blustration 2. Partial molar volumes—analytical calculation from apparent molar volumes 241
Illustration 3. Partial molar volume—graphical calculation from apparent molar volumes 243
Illustration 4. Calculation of partial molar enthalpy from heats of mixing 245
Illustration 5. Calculation of solubility of gases by means of Henry's law 248
Illustration 6. Bunsen and Ostwald absorption coefficients 249
Illustration 7. Temperature dependence of solubility of gases in liquids 250
Illustration 8. Vapour-liquid equilibrium in ideal solution at constant temperature 252
Illustration 9. Vapour-liquid equilibrium in ideal system at constant pressure 254
Illustration 10. Vapour-liquid equilibrium in real systems 256
Illustration 11. Dependence of composition of azeotropic mixture on pressure 259
Illustration 12. Determination of number of theoretical plates of distillation column 262
Illustration 13. Calculation of activity of constituents in solutions of non-electrolytes 263
Illustration 14. Steam distillation 265
Illustration 15. Solubility in ideal solution 266
Illustration 16. Nernst distribution law 267
Illustration 17. Phase diagrams 269
C. COLLIGATIVE PROPERTIES 271
Illustration 1. Lowering of vapour pressure above solution 271
Illustration 2. Calculation of degree of association from cryoscopic measurements 272
Illustration 3. Determination of molecular weight by ebullioscopic method 274
Illustration 4. Osmotic pressure 276
PROBLEMS 277
RESULTS 288
CHAPTER VII. CHEMICAL EQUILIBRIUM AND THIRD LAW OF THERMODYNAMICS 290
A. CHEMICAL EQUILIBRIUM 290
Illustration 1. Calculation of equilibrium constant from equilibrium composition of gas mixture 290
Illustration 2. Calculation of equilibrium composition of gas mixture from equilibrium constant 292
Illustration 3. Calculation of degree of dissociation 294
Illustration 4. Calculation of equilibrium constant from equilibrium conversion data 295
Illustration 5. Dependence of equilibrium constant on stoichiometric form of equation 296
Illustration 6. Calculation of equilibrium constant of homogeneous gas reaction from high-pressure equilibrium data 297
Illustration 7. Calculation of equilibrium constant of reaction in solution 300
Illustration 8. Calculation of equilibrium constant from change in standard free enthalpy 302
Illustration 9. Calculation of free enthalpy of reaction from tabulated data 304
Illustration 10. Calculation of standard free enthalpies of formation from tabulated data 305
Illustration 11. Graphical computation of temperature dependence of equilibrium constant 306
Illustration 12. Temperature dependence of free enthalpy of reaction 309
Illustration 13. Determination of heat of reaction from temperature dependence of equilibrium constant 311
Illustration 14. Calculation of decomposition temperature from temperature dependence of equilibrium pressure 315
Illustration 15. Influence of temperature and pressure on equilibrium conversion 318
Illustration 16. Calculation of equilibrium yield of reaction from thermal data of partial processes 321
Illustration 17. Calculation of equilibrium composition for simultaneous reaction 322
B. THIRD LAW OF THERMODYNAMICS 326
Illustration 1. Calculation of equilibrium conversion from tabulated data of G° 9£o/T and .9.2 effect of inert gas on equilibrium conversion
Illustration 2. Calculation of absolute entropy from calorimetric data 331
Illustration 3. Statistical calculation of thermodynamic functions of monatomic gas 336
Illustration 4. Calculation of thermodynamic functions of polyatomic molecule from spectroscopic data 339
PROBLEMS 345
RESULTS 357
CHAPTER VIII. ELECTROCHEMISTRY 359
A. TRANSPORT PHENOMENA 359
Illustration 1. Calculation of current intensity from Faraday's law 359
Illustration 2. Transference numbers 360
Illustration 3. Calculation of cell constant and specific conductivity of solution 364
Illustration 4. Calculation of equivalent conductivity from specific conductivity of solution 365
Illustration 5. Kohlrausch law of independent migration of ions 366
Illustration 6. Determination of purity of water from conductivity measurements 368
Illustration 7. Calculation of solubility of slightly soluble salt from conductivity measurements 370
Illustration 8. Calculation of dissociation constant from conductance measurements 371
B. IONIC EQUILIBRIA 374
Illustration 1. Calculation of activity coefficient from Debye-Hiickel law 374
Illustration 2. Calculation of activity coefficients from cryoscopic data 376
Illustration 3. Solubility product of sparingly soluble salt 380
Illustration 4. Calculation of activity coefficient from solubility data 383
Illustration 5. Calculation of second dissociation constant 386
Illustration 6. Calculation of degree of hydrolysis of salt of strong acid and weak base 389
Illustration 7. Calculation of degree of hydrolysis of salt of weak acid and weak base 392
C. GALVANIC CELLS 394
Illustration 1. Calculation of pH of solution from e. m. f.'s 394
Illustration 2. Calculation of standard potential of electrode from dependence of e. m. f. of cell on concentration of electrolyte 396
Illustration 3. Calculation of transference number and liquid-junction potential from e. m. f. of concentration cell 399
Illustration 4. Calculation of solubility product from e. m. f. 403
Illustration 5. Calculation of dissociation constant of weak acid from e. m. f. 405
Illustration 6. Calculation of standard reduction-oxidation potential of system Re07/Re03 408
Illustration 7. Calculation of equilibrium constant by means of Luther's relation 411
Illustration 8. Gibbs-Helmholtz equation in electrochemistry 413
PROBLEMS 415
RESULTS 422
CHAPTER IX. REACTION KINETICS 424
A. CHEMICAL KINETICS 424
Illustration 1. Determination of order of reaction by numerical method 424
Illustration 2. Determination of order of reaction from the time of halfchange 426
Illustration 3. Determination of order of reaction by differential method 430
Illustration 4. Kinetics of pseudo-unimolecular reaction 432
Illustration 5. Kinetics of side reactions 435
Illustration 6. Kinetics of consecutive processes 439
Illustration 7. Opposing reactions 445
Illustration 8. Time dependence of composition in complicated reaction system 447
Illustration 9. Calculation of activation energy of reaction from temperature dependence of rate constant 451
Illustration 10. Determination of activation energy and frequency factor of homogeneous gas reaction by graphical method 452
Illustration 11. Calculation of rate constant by means of collision theory 455
Illustration 12. Rate constant of reaction expressed in different units 457
Illustration 13. Enthalpy of activation, entropy of activation and correlation of kinetic data 459
Illustration 14. Calculation of temperature dependence of equilibrium constant from enthalpies and entropies of activation of opposing reactions 462
Illustration 15. Calculation of volume of flow reactor 464
Illustration 16. Determination of mechanism of chain reaction 467
Illustration 17. Kinetics of complex chain reaction 470
Illustration 18. Order of homogeneous catalyzed reaction 473
Illustration 19. Dependence of rate of ionic reaction on ionic strength 476
Illustration 20. Kinetics of heterogeneous catalyzed reaction 480
Illustration 21. Quantum yield of photochemical reaction 482
B. KINETICS OF PHYSICAL PROCESSES 485
Illustration 1. Fick's law and relative determination of diffusion coefficient 485
Illustration 2. Rate of dissolution of solid in liquid 490
Illustration 3. Kinetics of flow of liquids through porous medium 494
PROBLEMS 496
RESULTS 506
CHAPTER X. SURFACE PHENOMENA AND COLLOIDAL SYSTEMS 509
A. SURFACE PHENOMENA 509
Illustration 1. Graphical determination of constants of Langmuir adsorption isotherm 509
Illustration 2. Determination of surface area of solids by Brunauer, Emmett and Teller method 511
Illustration 3. Determination of heat of adsorption from isosteres 514
Illustration 4. Calculation of amount adsorbed according to Gibbs equation 518
Illustration 5. Determination of molecular weight of high-molecular substance from pressure measurement of surface monolayer 521
B. COLLOIDAL SYSTEMS 523
Illustration 1. Determination of Avogadro number from measuring sedimentation equilibrium in gravitational field 523
Illustration 2. Determination of molecular weight of high-molecular compounds by measuring sedimentation equilibrium in ultracentrifuge 526
Illustration 3. Determination of molecular weight of high-molecular compounds from sedimentation velocity in ultracentrifuge 528
Illustration 4. Sedimentation analysis 531
Illustration 5. Determination of molecular weight of high-molecular substance from viscosity measurements 538
Illustration 6. Determination of molecular weight of high-molecular substanceby light scattering 541
PROBLEMS 544
RESULTS 549
CHAPTER XI. MOLECULAR STRUCTURE AND PHYSICAL PROPERTIES 550
Illustration 1. Neumann-Kopp law 550
Illustration 2. Parachor 551
Illustration 3. Molar refraction 553
Illustration 4. Molar refraction—optical anomaly 555
Illustration 5. Dipole moment of gas 556
Illustration 6. Calculation of dipole moment from dielectric constants of solutions 558
Illustration 7. Polarimetry 561
Illustration 8. Beer's law 563
Illustration 9. Determination of internuclear distances from micro-wave spectrum 564
PROBLEMS 566
RESULTS 569
TABLES 570
SUBJECT INDEX 620