Collection of Problems in Physical Chemistry

Collection of Problems in Physical Chemistry provides illustrations and problems covering the field of physical chemistry. The material has been arranged into illustrations that are solved and supplemented by problems, thus enabling readers to determine the extent to which they have mastered each subject. Most of the illustrations and problems were taken from original papers, to which reference is made. The English edition of this book has been translated from the manuscript of the 2nd Czech edition. It has been changed slightly in some places and enlarged on in others on the basis of further experience gained in teaching physical chemistry at the Institute of Chemical Technology in Prague. The book begins with illustrations and problems on the atomic structure and the fundamentals of quantum mechanics. Subsequent chapters cover the kinetic theory of ideal gas; fundamentals of thermodynamics; states of matter; phase equilibrium; chemical equilibrium and third law of thermodynamics; electrochemistry; reaction kinetics; surface phenomena and colloidal systems; and molecular structure and physical properties.

Foreword to the Czech Edition

Foreword to the English Edition

I. Atomic Structure and the Fundamentals of Quantum Mechanics

A. Atomic Structure

1. Determination of Specific Charge of Electron from Deflection in Magnetic Field

2. Determination of Electronic Charge

3. Determination of Neutron Mass from Nuclear Photoeffect in Heavy Hydrogen

4. Determination of Wave-Length of Electron from Diffraction on Grating

5. Determination of Positron Mass

6. Photoelectric Effect—Calculation of Characteristic Frequency and Planck Constant

7. Compton Effect—Shift in Wave-Length of Xrays

8. Spectral Distribution of Black-Body Radiation

9. Determination of Atomic Number by Means of X-Ray Spectra

10. Calculation of Wave-Length of Lines of Balmer Series of Hydrogen

11. Determination of Isotopes by Means of Electronic Spectra

12. Calculation of Electronic Mass from Eydberg Constants Oi Hydrogen and Helium

13. Calculation of Critical Potentials of Helium from Spectroscopic Data

14. Eate of Radioactive Disintegration and Radioactive Equilibrium

15. Estimation of Radioactive Constant by Geiger-Nuttall Rule

B. The Fundamentals of Quantum Mechanics

1. Calculation of Translational Partition Function of Ideal Gas

2. Eotational Partition Function of Carbon Monoxide

3. Vibrational Partition Function of Hydrogen Chloride

Problems

Results

II. Kinetic Theory of Ideal Gas

1. Calculation of Molecular Velocities

2. Calculation of Molar Heat Capacity

3. Mean Free Path

4. Collision Diameter of Molecules

5. Collusion Diameter and Diffusion Coefficient

6. Determination of Molecular Weight from Effusion of Gas

7. Determination of Vapour Pressure by Effusion Method

Problems

Results

ΙII. Ideal Gas

1. Boyle's Law

2. Gay-Lussac's Law and the Absolute Temperature Scale

3. Ideal Gas Equation—Calculation of Volume

4. Ideal Gas Equation—Calculation of Molecular Weight

5. Determination of Molecular Weight by Method of Limiting Densities

6. Ideal Gas Equation—Degree of Dissociation

7. Calculation of Degree of association from Molecular Weights

8. Expression of Concentration of Gas Mixtures

9. Calculation of Total Pressure of Gas Mixture from Dalton's Law

10. Calculation of Partial Pressure from Dalton's Law

Problems

Results

IV. Fundamentals of thermodynamics

A. First Law of thermodynamics

1. Calculation of Units

2. Calculation of Change in Internal Energy during Evaporation

3. Calculation of Specific and Atomic Heat Capacities from Calorimetric Data

4. Dependence of Molar Heat Capacity on Temperature

5. Calculation of Heat of Reaction from Heats of Formation

6. Calculation of Standard Heat of Formation from Known Heats of Reaction

7. Calculation of Heat of Reaction from Heats of Combustion

8. Calculation of Standard Heats of Formation from Bond Energies

9. Dependence of Standard Heat of Reaction on Temperature

10. Enthalpie Balance

11. Theoretical Flame Temperature

12. Work during Isothermal Process

13. Heat, Work and Change in Internal Energy during Expansion of Ideal Gas

14. Adiabatic Process

15. Work Done during Adiabatic Process

16. Thermal Engine

17. Cooling Engine

Problems

Results

B. Second Law of thermodynamics

1. Dependence of Entropy on Pressure

2. Dependence of Entropy on Temperature

3. Graphical Calculation of Entropy Change with Temperature

4. Entropy of Mixing

5. Entropy Change during Irreversible Adiabatic Process

6. Isothermal Change in Free Energy and Free Enthalpy of Ideal Gas

7. Dependence of Free Enthalpy on Pressure

8. Change in Free Enthalpy during Isomorphous Transformations

9. Change in Free Enthalpy in Irreversible Phase Transformations

10. Thermodynamic Functions of Ideal Gas

Problems

Results

V. States of Matter

A. Keal Gases

1. Calculation of Volume from Berhelot Equation

2. Calculation of Volume from Beattie-Bridgeman Equation

3. Calculation of Density from Generalized Compressibility Diagram

4. Comparison of Van Der Waals Equation with Generalized Compressibility Factor

5. Calculation of Temperature from Generalized Compressibility Diagram

6. Determination of Second Virial Coefficient by Method of Limiting Densities

7. Beattie-Bridgeman Equation for Mixture of Gases

8. Calculation of Pressure of Gas Mixture Using Generalized Compressibility Diagram

9. Joule-Thomson Coefficient

10. Dependence of Molar Heat Capacity on Pressure

11. Difference in Molar Heat Capacities EP—EV for Real Gas

12. Calculation of Fugacity by Analytical Method

13. Calculation of Fugacity of Constituent in Mixture

Problems

Results

B. Liquids

1. Calculation of Density Using Generalized Expansion Factor

2. Calculation of Surface Tension from Capillary Rise

3. Eötvös Equation

4. Calculation of Viscosity from Poiseuille Equation

5. Stokes' Law

Problems

Results

C. Solids

1. Determination of Constants of Ionic Lattice from Diffraction of X-Rays

2. Estimation of Molar Heat Capacity of Solid Means of Kopp's Law

3. Determination of Temperature Dependence of Molar Heat Capacities of Solids from Known Characteristic Temperature

4. Calculation of Molar Heat Capacities of Solids on Basis of Born-Kârmân Theory

5. Calculation of Characteristic Temperature from Compressibility

6. Calculation of Characteristic Temperature from Melting Point

Problems

Results

VI. Phase Equilibrium

A. Systems with One Component

1. Clapeyron Equation—Calculation of Change in Melting Point with Pressure

2. Clapeyron Equation—Graphical Calculation of Heat of Fusion

3. Clausius-Clapeyron Equation—Calculation of Change in Boiling Point with Pressure

4. Clausius-Clapeyron Equation—Calculation of Triple Point

5. Calculation of Heat of Vaporization from Empirical Equation for Temperature Dependence of Vapour Pressure

6. Eamsay- Young Rule

7. Cox-Othmer Diagram

8. Adjustment of Measured Values of Vapour Pressure by Method of Least Squares

9. Cailletet-Mathias Law—Determination of Critical Volume

B. Systems with Several Components

1. Units of Concentration

2. Partial Molar Volumes—Analytical Calculation from Apparent Molar Volumes

3. Partial Molar Volume—Graphical Calculation from Apparent Molar Volumes

4. Calculation of Partial Molar Enthalpy from Heats of Mixing

5. Calculation of Solubility of Gases by Means of Henry's Law

6. Bunsen and Ostwald Absorption Coefficients

7. Temperature Dependence of Solubility of Gases in Liquids

8. Vapour-Liquid Equilibrium in Ideal Solution at Constant Temperature

9. Vapour-Liquid Equilibrium in Ideal System at Constant Pressure

10. Vapour-Liquid Equilibrium in Real Systems

11. Dependence of Composition of Azeotropic Mixture on Pressure

12. Determination of Number of theoretical Plates of Distillation Column

13. Calculation of Activity of Constituents in Solutions of Non-Electrolytes

14. Steam Distillation

15. Solubility in Ideal Solution

16. Nernst Distribution Law

17. Phase Diagrams

C. Colligative Properties

1. Lowering of Vapour Pressure above Solution

2. Calculation of Degree of association from Cryoscopic Measurements

3. Determination of Molecular Weight by Ebullioscopic Method

4. Osmotic Pressure

Problems

Results

VII. Chemical Equilibrium and Third Law of thermodynamics

A. Chemical Equilibrium

1. Calculation of Equilibrium Constant from Equilibrium Composition of Gas Mixture

2. Calculation of Equilibrium Composition of Gas Mixture from Equilibrium Constant

3. Calculation of Degree of Dissociation

4. Calculation of Equilibrium Constant from Equilibrium Conversion Data

5. Dependence of Equilibrium Constant on Stoichiometric Form of Equation

6. Calculation of Equilibrium Constant of Homogeneous Gas Reaction from High-Pressure Equilibrium Data

7. Calculation of Equilibrium Constant of Reaction in Solution

8. Calculation of Equilibrium Constant from Change in Standard Free Enthalpy

9. Calculation of Free Enthalpy of Reaction from Tabulated Data

10. Calculation of Standard Free Enthalpies of Formation from Tabulated Data

11. Graphical Computation of Temperature Dependence of Equilibrium Constant

12. Temperature Dependence of Free Enthalpy of Reaction

13. Determination of Heat of Reaction from Temperature Dependence of Equilibrium Constant

14. Calculation of Decomposition Temperature from Temperature Dependence of Equilibrium Pressure

15. Influence of Temperature and Pressure on Equilibrium Conversion

16. Calculation of Equilibrium Yield of Reaction from thermal Data of Partial Processes

17. Calculation of Equilibrium Composition for Simultaneous Reaction

B. Third Law of thermodynamics

1. Calculation of Equilibrium Conversion from Tabulated Data of (G°—H°°)/T and ΔH°°; Effect of Inert Gas on Equilibrium Conversion

2. Calculation of Absolute Entropy from Calorimetric Data

3. Statistical Calculation of thermodynamic Functions of Monatomic Gas

4. Calculation of thermodynamic Functions of Polyatomic Molecule from Spectroscopic Data

Problems

Results

VIII. Electrochemistry

A. Transport Phenomena

1. Calculation of Current Intensity from Faraday's Law

2. Transference Numbers

3. Calculation of Cell Constant and Specific Conductivity of Solution

4. Calculation of Equivalent Conductivity from Specific Conductivity of Solution

5. Kohlrausch Law of Independent Migration of Ions

6. Determination of Purity of Water from Conductivity Measurements

7. Calculation of Solubility of Slightly Soluble Salt from Conductivity Measurements

8. Calculation of Dissociation Constant from Conductivity Measurements

B. Ionic Equilibria

1. Calculation of Activity Coefficient from Debye-Hückel Law

2. Calculation of Activity Coefficients from Cryoscopic Data

3. Solubility Product of Sparingly Soluble Salt

4. Calculation of Activity Coefficient from Solubility Data

5. Calculation of Second Dissociation Constant

6. Calculation of Degree of Hydrolysis of Salt of Strong Acid and Weak Base

7. Calculation of Degree of Hydrolysis of Salt of Weak Acid and Weak Base

C. Galvanic Cells

1. (Calculation of Ph of Solution from E.M.F.'S

2. Calculation of Standard Potential of Electrode from Dependence of E. M. F. of Cell on Concentration of Electrolyte

3. Calculation of Transference Number and Liquid, Junction Potential from E. M. F. of Concentration Cell

4. Calculation of Solubility Product from E.M.F.

5. Calculation of Dissociation Constant of Weak Acid from E.M.F.

6. Calculation of Standard Reduction-Oxidation Potential of System Ee07/Ee08

7. Calculation of Equilibrium Constant by Means of Luther's Relation

8. Gibbs-Helmholtz Equation in Electrochemistry

Problems

Results

IX. Reaction Kinetics

A. Chemical Kinetics

1. Determination of Order of Reaction by Numerical Method

2. Determination of Order of Reaction from the Time of Half-Change

3. Determination of Order of Reaction by Differential Method

4. Kinetics of Pseudo-Unimolecular Reaction

5. Kinetics of Side Reactions

6. Kinetics of Consecutive Processes

7. Opposing Reactions

8. Time Dependence of Composition in Complicated Reaction System

9. Calculation of Activation Energy of Reaction from Temperature Dependence of Rate Constant

10. Determination of Activation Energy and Frequency Factor of Homogeneous Gas Reaction by Graphical Method

11. Calculation of Rate Constant by Means of Collision Theory

12. Eate Constant of Reaction Expressed in Different Units

13. Enthalpy of Activation, Entropy of Activation and Correlation of Kinetic Data

14. Calculation of Temperature Dependence of Equilibrium Constant from Enthalpies and Entropies of Activation of Opposing Reactions

15. Calculation of Volume of Flow Reactor

16. Determination of Mechanism of Chain Reaction

17. Kinetics of Complex Chain Reaction

18. Order of Homogeneous Catalyzed Reaction

19. Dependence of Rate of Ionic Reaction on Ionic Strength

20. Kinetics of Heterogeneous Catalyzed Reaction

21. Quantum Yield of Photochemical Reaction

B. Kinetics of Physical Processes

1. Fick's Law and Relative Determination of Diffusion Coefficient

2. Eate of Dissolution of Solid in Liquid

3. Kinetics of Flow of Liquids through Porous Medium

Problems

Results

X. Surface Phenomena and Colloidal Systems

A. Surface Phenomena

1. Graphical Determination of Constants of Langmuir Adsorption Isotherm

2. Determination of Surface Area of Solids by Brunauer, Emmett and Teller Method

3. Determination of Heat of Adsorption from Isosteres

4. Calculation of Amount Adsorbed According to Gibbs Equation

5. Determination. of Molecular Weight of Highmolecular Substance from Pressure Measurement of Surface Monolayer

B. Colloidal Systems

1. Determination of Avogadro Number from Measuring Sedimentation Equilibrium in Gravitational Field

2. Determination of Molecular Weight of Highmolecular Compounds by Measuring Sedimentation Equilibrium in Ultracentrifuge

3. Determination of Molecular Weight of Highmolecular Compounds from Sedimentation Velocity in Ultracentrifuge

4. Sedimentation Analysis

5. Determination of Molecular Weight of Highmolecular Substance from Measurements of Viscosity

6. Determination of Molecular Weight of Highmolecular Substance by Light Scattering

Problems

Results

XI Molecular Structure and Physical Properties

1. Neumann-Kopp Law

2. Parachor

3. Molar Refraction

4. Molar Refraction—Optical Anomaly

5. Dipole Moment of Gas

6. Calculation of Dipole Moment from Dielectric Constants of Solution

7. Polarimetry

8. Beer's Law

9. Determination of Internuclear Distances from Micro-Wave Spectrum

Problems

Results

XI Molecular Structure and Physical Properties

1. Neumann-Kopp Law

2. Parachor

3. Molar Refraction

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Collection of Problems in Physical Chemistry

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