Solutions Manual for Principles of Physical Chemistry, 3rd Edition, Solutions Manual E-Book
Hans Kuhn
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This is a Solutions Manual to Accompany with solutions to the exercises in the main volume of Principles of Physical Chemistry, Third Edition.
This book provides a unique approach to introduce undergraduate students to the concepts and methods of physical chemistry, which are the foundational principles of Chemistry. The book introduces the student to the principles underlying the essential sub-fields of quantum mechanics, atomic and molecular structure, atomic and molecular spectroscopy, statistical thermodynamics, classical thermodynamics, solutions and equilibria, electrochemistry, kinetics and reaction dynamics, macromolecules, and organized molecular assemblies. Importantly, the book develops and applies these principles to supramolecular assemblies and supramolecular machines, with many examples from biology and nanoscience. In this way, the book helps the student to see the frontier of modern physical chemistry developments.
The book begins with a discussion of wave-particle duality and proceeds systematically to more complex chemical systems in order to relate the story of physical chemistry in an intellectually coherent manner. The topics are organized to correspond with those typically given in each of a two course semester sequence. The first 13 chapters present quantum mechanics and spectroscopy to describe and predict the structure of matter: atoms, molecules, and solids. Chapters 14 to 29 present statistical thermodynamics and kinetics and applies their principles to understanding equilibria, chemical transformations, macromolecular properties and supramolecular machines. Each chapter of the book begins with a simplified view of a topic and evolves to more rigorous description, in order to provide the student (and instructor) flexibility to choose the level of rigor and detail that suits them best. The textbook treats important new directions in physical chemistry research, including chapters on macromolecules, principles of interfaces and films for organizing matter, and supramolecular machines -- as well as including discussions of modern nanoscience, spectroscopy, and reaction dynamics throughout the text.
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface Third Edition
Acknowledgment
1 Wave–Particle Duality
1.1 Exercises
1.2 Problems
2 Essential Aspects of Structure and Bonding
2.1 Exercises
2.2 Problems
3 Schrödinger Equation
3.1 Exercises
3.2 Problems
4 Hydrogen Atom
4.1 Exercises
4.2 Problems
5 Atoms and Variational Principle
5.1 Exercises
5.2 Problems
6 A Quantitative View of Chemical Bonding
6.1 Exercises
6.2 Problems
7 Bonding Described by Electron Pairs and Molecular Orbitals
7.1 Exercises
7.2 Problems
Notes
8 Molecules with PI-Electron Systems
8.1 Exercises
8.2 Problems
Notes
9 Absorption of Light
9.1 Exercises
9.2 Problems
Notes
10 Emission of Light
10.1 Exercises
10.2 Problems
Note
11 Nuclei: Particle and Wave Properties
11.1 Exercises
11.2 Problems
Notes
12 Nuclear Spin
12.1 Exercises
12.2 Problems
Note
13 Solids and Intermolecular Forces
13.1 Exercises
13.2 Problems
14 Thermal Motion of Molecules
14.1 Exercises
14.2 Problems
15 Energy Distribution in Molecular Assemblies
15.1 Exercises
15.2 Problems
Note
16 Work
w
, Heat
q
, and Internal Energy
U
16.1 Exercises
16.2 Problems
17 Reversible Work , Reversible Heat , and Entropy
17.1 Exercises
17.2 Problems
Note
18 General Conditions for Spontaneity and its Application to Equilibria of Ideal Gases and Dilute Solutions
18.1 Exercises
18.2 Problems
Note
19 Formal Thermodynamics and Its Application to Phase Equilibria
19.1 Exercises
19.2 Problems
Notes
20 Real Gases
20.1 Exercises
20.2 Problems
Notes
21 Real Solutions
21.1 Exercises
21.2 Problems
Note
22 Reaction Equilibria in Aqueous Solutions and Biosystems
22.1 Exercises
22.2 Problems
Note
23 Chemical Reactions in Electrochemical Cells
23.1 Exercises
23.2 Problems
Notes
24 Chemical Kinetics
24.1 Exercises
24.2 Problems
Notes
25 Transition States and Chemical Reactions
25.1 Exercises
25.2 Problems
Notes
26 Macromolecules
26.1 Exercises
26.2 Problems
Notes
27 Organized Molecular Assemblies
27.1 Exercises
27.2 Problems
Notes
28 Supramolecular Machines
28.1 Exercises
28.2 Problems
Notes
29 Origin of Life. Matter Carrying Information
29.1 Exercises
29.2 Problems
End User License Agreement
List of Tables
Chapter 4
Table P4.8 Calculating the Zeros of .
Chapter 5
Table E5.15 Periodic Table. Electron Configuration of the Highest Occupied O...
Table P5.3 Parameters , , and , and Calculated Energies .
Table P5.10a Result of the Calculation of with the Parameters pm, J, a...
Table P5.10b Result of the Calculation of According to Equation (5P10.5) w...
Chapter 8
Table E8.11 List of Eigenvalues, which results from an HMO Calculation for...
Chapter 9
Table 9.1 Absorption of the Diethylthiacarbocyanine Dyes with Different Val...
Chapter 11
Table 11.1 Evaluation of the Absorption Lines in the Rotational Spectrum of...
Chapter 12
Table E12.2 Evaluation of Equation (12E2.1).
Chapter 14
Table P14.3 Displacement in a One-Dimensional Random Walk for 10 Steps.
Table 14.9 Output file of (, , ) coordinates from simulation runs.
Chapter 15
Tablle E15.29 Vibrational Parameters and Population Probabilities and fo...
Chapter 18
Table E18.8 List of Chemical Reactions.
Chapter 21
Table P21.3 Relative Change of Vapor Pressure for Solutions of Sucrose in ...
Chapter 22
Table P22.8 Change pH of buffer solutions versus concentration of added a...
Chapter 25
Table E25.3 Rate constants for Reaction (25.4).
Table E25.7 Calculation of Rate Constant Ratios and Comparison to Experiment...
Table E5.10a Evaluation of Obtained from the Arrhenius Plots for Different...
Table E25.10b Comparison of and .
Chapter 26
Table E26.14 Molar Mass Calculated from the Osmotic Pressure.
Table P26.10a , , and Calculated for , , and nm.
Table P26.10b , , and Calculated for , m , and nm.
Table P26.10c Flow Speed and Fractional Extension for m.
Chapter 27
Table E27.6 Comparison of Calculated and Measured Rise Height for Differen...
Chapter 28
Table 28.11 Number of Cases When the Particle Is Found at Position
List of Illustrations
Chapter 1
Figure E1.9 Diffraction of light on a double slit.
Figure P1.1 Photoelectric effect. Kinetic energy of the ejected electrons ve...
Figure P1.4a Diffraction on a slit.
Figure P1.4b Diffraction on a slit: intensity distributions are plotted for ...
Figure P1.5 Equation (1P5.1) is plotted in two figures. The left panel shows...
Chapter 2
Figure E2.5 Each panel shows a sketch of a plausible wavefunction versus a...
Figure E2.7a Wavefunctions for a particle in a one-dimensional box for , ,...
Figure E2.7b Wavefunctions for a particle in a one-dimensional box for , ...
Figure E2.10 A plot of the variational energy for the H-atom, in which the e...
Figure E2.12a Plots of the wavefunction of a particle in a one-dimensional b...
Figure E2.12b Plots of the probability density of a particle in a one-dimens...
Figure P2.1a Emission lines of the Balmer series. The image is taken from G....
Figure P2.1b Plot of the H-atom energy levels. Note that the levels converge...
Figure P2.2 Plots of the current–voltage profiles observed in a Franck–Hertz...
Figure P2.6 The natural logarithm of the ionization energy (IE) is plotted v...
Figure P2.7 Kinetic energy versus the box length for each of the cases: ,...
Figure P2.9a Variational energy of a particle in a three-dimensional box v...
Figure P2.9b Variational energy of an electron in the field of two protons (
Chapter 3
Figure E3.10a Sketch of a wavefunction for a particle confined in a well (ki...
Figure E3.10b Sketch of a wavefunction for a particle that is not confined t...
Figure P3.2a as a function of for pm and J.
Figure P3.2b Electric current versus the kinetic energy of the photon (left)...
Figure P3.2c Apparatus for measuring the kinetic energy of an electron emitt...
Figure P3.3a Plot of ground-state wavefunction (dashed curve) and its square...
Figure P3.3b Normalization factor for one-dimensional box function. Full cir...
Figure P3.6a Normalized particle-in-a-box wavefunctions for , , and (lef...
Figure P3.6b Plot of the superposition function (curve 3) of the functions w...
Figure P3.6c The left panel shows an amplitude plot for equally weighted sup...
Figure P3.7a Plot of the wavefunction (left) and the probability density
Figure P3.7b Plot of the wavefunction (left) and the probability density
Figure P3.8a A matter wave traveling from left to right is partly reflected ...
Figure P3.8b Outcomes of the MathCAD worksheet for tunneling through a poten...
Figure P3.8c Outcomes of the MathCAD worksheet for tunneling through a poten...
Figure P3.8d Outcomes of the MathCAD worksheet for tunneling through a poten...
Figure P3.10 Gaussian distribution function d/d for the momentum (left) ...
Chapter 4
Figure E4.1 Radial (a) and angular (b and c) part of the -wavefunction.
Figure E4.2 Radial (a) and angular (b and c) part of the -wavefunction.
Figure E4.3 Radial (a) and angular (b and c) part of the -wavefunction.
Figure E4.4 E4.4 Radial (a) and angular (b) part of the -wavefunction.
Figure E4.6 Probability function for the radial part of the -wavefunction...
Figure E4.7 Density for the radial part of the 2s-wavefunction. (a) Total ...
Figure E4.9 Radial and angular parts of the 2-wavefunction. (a) Radial part...
Figure E4.12 (a) Radial part of the 1s, 2s, and 3s-wavefunctions, the probab...
Figure E4.13 Probability function (radial distribution function) of the wa...
Figure E4.14 (a) Spherical coordinates , , and of point P. From geometry...
Figure P4.1 Bohr atom model; the electron circles at a distance with the s...
Figure P4.2 This diagram indicates the geometry for the center of mass.
Figure P4.3a H-atom in the , and 3-state. Left: wavefunction , right: squ...
Figure P4.3b The figure shows a plot of the squares of the first three s-orb...
Figure P4.3c The radial distribution functions are plotted for the first t...
Figure P4.3d,e Contour plots are shown for the H-atom orbital (top) and ...
Figure P4.3f The figure shows plots of the radial distribution function for...
Figure P4.3g This image shows contour plots for the probability density of t...
Figure P4.3h The image shows angular plots for three of the five d orbitals....
Figure P4.3i The image on the left shows a contour plot for the orbital’s ...
Figure P4.7 Probability of the radial part of the 2s orbital of the H atom...
Figure P4.12a Square of wavefunction versus the coordinate inside a sphe...
Figure P4.12b Energy in the spherical box model for the H atom as a functi...
Chapter 5
Figure E5.21a The spin angular momentum vector is drawn with its three possi...
Figure 5.21b Nine possible combinations of the total angular momentum vector...
Figure P5.3a Plots of the exact wavefunction and the trial function
Figure P5.3b Radial dependence of the wavefunctions for the H-atom. Upper cu...
Figure P5.7 The curve starting at shows a plot of the H-atom 2
s
wavefuncti...
Figure P5.8 The 2s radial distribution function.
Figure P5.9 The ionization energies for the atoms and ions reported in the t...
Figure P5.10a Bottom: Box of length with infinite high walls; a potential ...
Figure P5.10b Bottom: Box of length with infinite high walls; a sinus pote...
Chapter 6
Figure E6.1 Energy cycle for calculating the bond energy of .
Figure E6.8 The molecule consists of two negatively charged electrons in t...
Figure P6.3 This plot compares the Morse function approximation to the numer...
Figure P6.5 Plot of the function . (a) according to Equation (6P5.1) and ...
Figure P6.6 Plot of the function . (a) according to Equation (6P6.1) and ...
Figure P6.10a Energy versus the bond distance for the cases , , and ....
Figure P6.10b Energy versus the bond distance for the cases , , and ....
Chapter 7
Figure E7.2 Three connectivities for the binding of three H atoms to a N ato...
Figure E7.3 Connectivities for the binding in the FCN molecule.
Figure E7.12 LCAO scheme of the molecule in which hybrids are used as ba...
Figure E7.13 LCAO molecular orbital energy scheme for C, NO, and Ne.
Figure E7.14 LCAO scheme for N.
Figure E7.15 The renderings correspond to the orbital (lower image) and th...
Figure E7.18 LCAO molecular orbital energy scheme for the formaldehyde molec...
Figure E7.21a Torsion energy versus the torsion angle for the methyl group...
Figure E7.21b Geometry of the methyl group in ethane.
Figure P7.1a Slater functions, , . Note the different ordinate scaling an...
Figure P7.1b The overlap for the function is plotted versus with .
Figure P7.4 Orbital picture of a 2 (top) and a 2 (bottom) function of the ...
Figure P7.5 LCAO orbital scheme for the molecule. A qualitative molecular ...
Figure P7.6 LCAO orbital scheme for the methanol molecule.
Figure P7.7 Geometry of the O molecule.
Figure P7.8 Restoring force versus the elongation of the bond for , , ...
Figure P7.9 Photoelectron spectrum of S.
Figure P7.10 Energy of the HF molecule. Full circles: quantum chemical cal...
Figure P7.11 Evaluation of the force constant of the H ion (exact calcula...
Figure P7.12 Panel (a) shows the geometry for the Li-H-Li ionic compound, an...
Figure 7P.13 Energy states of HF in comparison with those of the H atom and ...
Chapter 8
Figure E8.5a The LCAO energy levels and orbitals of benzene.
Figure E8.5b Energies (panel a) and wavefunctions (panel b) of benzene accor...
Figure E8.8 Degenerate wavefunctions for the guanidinium ion.
Figure E8.11a HMO eigenvalues for naphthalene.
Figure E8.11b The first four ionization energies for naphthalene versus th...
Figure E8.13 HMO orbital diagrams of H, , and H.
Figure E8.20a. The diagram shows the anthracene carbon framework and numbers...
Figure E8.20b Bond length (HMO) versus (exp). The dashed line indicates ...
Figure E8.21 Energy level plot, the wavefunctions, and the probability densi...
Figure P8.1 HMO energy scheme for fulvene. The numbers denote the eigenvalue...
Figure P8.3 HMO energy scheme for the square and rectangular forms of cyclob...
Figure P8.4 Energy scheme for cyclobutadiene using the FEMO model. Panel (a)...
Figure P8.5 HMO energy scheme for cyclopropene with the eigenvalues .
Figure P8.8a Molecular skeleton of naphthalene.
Figure P8.8b Determination of the roots of the characteristic polynomial for...
Figure P8.9a. FEMO wavefunctions of benzene for as a function of the coord...
Figure P8.9b Wavefunctions for quantum states with (a, b) and (c, d) .
Figure P8.9c Energy levels of benzene according to the FEMO model (schematic...
Figure P8.10. Estimating . The electron is considered to be in points and...
Chapter 9
Figure E9.1 Contribution of nitrogen atoms to the -electron system.
Figure E9.3 Absorption maxima of different sets of dyes.
Figure E9.4 Two different dye molecules A and B.
Figure E9.7 Polyenes. versus , where is the number of -electrons.
Figure E9.8 Molecular skeleton of phthalocyanine and porphyrin.
Figure E9.9 Optical rotation versus the concentration of propylene oxide...
Figure E9.13 Vector sum versus of the two components of an elliptically ...
Figure E9.14a Right polarized light. Angle between the electric field vector...
Figure E9.14b Left polarized light. Angle between the electric field vector
Figure E9.18 Absorbance of anthranthrene versus its concentration. The inset...
Figure E9.21 Integrand in Equation (9E21.1) along the circle approximating t...
Figure E9.22 Comparison of phthalocyanine and porphyrin.
Figure P9.4 Evaluation of and for the cyanines in Table 9.2.
Figure P9.7 Integrand in Equation for along the circle approximating the r...
Figure P9.9a Phase shift of a damped oscillator versus the frequency . Da...
Figure P9.9b Displacement of the damped oscillator. Same parameters as i...
Figure P9.22a Absorption spectrum of -Carotene. Solid line: trans-form, das...
Figure P9.22b Structural formulae of -carotene. (a) all-Trans-form, (b) -c...
Chapter 10
Figure E10.9 Energy scheme and box wavefunctions for systems consisting of t...
Figure P10.5 Absorption, spontaneous and stimulated emission in a two-level ...
Chapter 11
Figure E11.1 Calculation of center of mass.
Figure E11.9 Potential energy curves. Energy versus bond length .
Figure E11.11 The plot shown here ( versus ) allows the rotational constan...
Figure E11.15 Potential (dark gray) and kinetic (light gray) energies of the...
Figure E11.18a Morse functions with the parameters N , J (dark gray sol...
Figure E11.18b–d Squares of the wavefunctions of the harmonic (dark gray) an...
Figure E11.18e Squares of the wavefunctions of the anharmonic (Morse) oscill...
Figure E11.19a Plots of the Franck Condon (FCF) factors as a function of the...
Figure E11.20a The plot shows the Franck–Condon factors (FCF) versus the tra...
Figure E11.20b The plot shows the Franck–Condon factors (FCF) versus the tra...
Figure E11.22 Evaluation of frequency and the constant . is plotted ver...
Figure E11.24 Rotation axes in the water molecule. (a) A-axis, (b) B-axis, (...
Figure E11.25 Rotation of the molecule. (a) Molecular skeleton, (b) constr...
Figure P11.1 Intensity pattern of the absorption spectrum of HCl in the 10 t...
Figure P11.4 Energy scheme for the vibrational/rotational spectrum of LiF. D...
Figure P11.7a Fundamental vibration and the first four overtones of OH (blac...
Figure P11.7b Transition energies for OH (black lines) and OD (dark gray lin...
Figure P11.8 Potential energy curves for CO.
Figure P11.9a Potential energy curves of CaH. This image is redrawn from th...
Figure P11.9b Transitions for the case that the minima of the potential ener...
Figure P11.9c Rovibrational spectrum for CaH near its vibrational fundament...
Figure P11.10a CO molecule. Excitation energy versus .
Figure P11.11a Potential energy curves of the first two electronic states of...
Figure P11.11b Rovibratonal spectrum for N (X-state) at its vibrational fun...
Figure P11.11c Rovibrational spectrum of N (A-state) near its vibrational f...
Figure P11.12 Plot of as a function of , according to Equation (11P12.1)....
Chapter 12
Figure E12.4 Rotational Raman spectrum of .
Figure E12.8 NMR spectrum of ethanol.
Figure P12.2 The sketch shows an energy level diagram for the case of two eq...
Chapter 13
Figure E13.2 Energy of an ion pair versus the distance .
Figure E13.18 Dimer of two ammonia molecules.
Figure E13.22 Two dipoles arranged in line.
Figure E13.24 Orientation of the two dipoles at an angle .
Figure E13.26a The diagram aims to illustrate that a beam of electrons impin...
Figure E13.26b Collector current (detector current) versus bombarding potent...
Figure E13.26c The scattered intensity pattern (75 eV electrons). (a,b): fro...
Figure P13.2 Energy versus /
Figure P13.4 Energy gap versus
Figure P13.5 versus distance for -wavefunction. pm (light gray) and
Figure P13.6 Evaluation of bandgap energy. cm versus .
Figure P13.7a Orientation of two collinear dipoles by an angle
Figure P13.7b Dependence of energy of two dipoles in collinear geometry on...
Figure P13.8 Energies of the dipole–dipole (dark gray), induction (light gra...
Figure P13.9 Determination of the polarizability of an electrically conducti...
Figure P13.13 Energy of a NaCl ion pair calculated for pm and , (dark g...
Figure P13.14a Two-dimensional lattice.
Figure P13.14b Diffraction: traveling distance.
Figure P13.15 Diffraction: Traveling distance.
Chapter 14
Figure P14.1 of a gas as a function of the pressure .
Figure P14.6 Root mean square displacement versus the square root of time....
Figure P14.7 Enzyme interlocking with a substrate: (a) shows the substrate S...
Figure P14.9 Diffusion path. - and -displacements of the particles after a...
Chapter 15
Figure E15.3 Fraction as a function of the quantum number .
Figure E15.15
Left panel
: Most probable speed versus temperature .
Right
...
Figure E15.17 Distribution of speed s for the He atom at K and K. The fu...
Figure E15.18 Distribution of speeds at K for Ar atoms (light gray curve) ...
Figure E15.21a Change of the Gaussian distribution with the number of partic...
Figure E15.21b The Gaussian distributions shown here approach the mean value...
Figure E15.22 Black solid line:; Black dashed line: with J; Light gray ...
Figure E15.29 Population probability of molecules in a vibrational state
Figure E15.31 Population probability of molecules in a rotational state ...
Figure P15.1 Plot of as a function of for the values in column I of the ...
Figure P15.7 Distribution of speeds for the molecule at K, K, and K....
Figure P15.8a Distribution of speeds at K for Ar (light gray), Ne (dark gr...
Figure P15.8b Distribution of speeds at K for Ar (light gray), Ne (dark gr...
Figure P15.10 Iodine spectrum. Predicted wavenumbers versus experimental wav...
Figure P15.11 of versus the temperature .
Figure P15.13 Internal energy of a two-level system (NO molecules) versus ...
Figure P15.15 Planck’s radiation law: spectral energy density versus the w...
Chapter 16
Figure E16.8 Temperature dependence of the molar heat capacity for HF and ...
Figure E16.14 Cycle for determining reaction enthalpies.
Figure E16.21 diagram.
Figure P16.1a Energy for a particle in a one-dimensional box with length ....
Figure P16.1b Population probability exp for particles in a one-dimensiona...
Figure P16.1c Numerically calculated energies for particles in a one-dimensi...
Figure P16.2 Isothermal expansion of an ideal gas.
Figure P16.3 Adiabatic expansion of an ideal gas.
Figure P16.5 Molar heat capacity of versus temperature. Filled circles: ex...
Figure P16.7 Temperature dependence of for molecules (solid line) and ma...
Figure P16.8 Otto cycle.
Chapter 17
Figure E17.8 Two solids in temperature contact.
Figure E17.23 Separation of two gases using semipermeable pistons.
Figure P17.4 Heat capacity for Ne, HF, and O versus temperature .
Figure P17.7 Heat capacity of versus temperature . The dashed lines mark ...
Chapter 18
Figure E18.9 for the CaO CO
2
reaction versus temperature .
Figure E18.23 Vapor pressure of water as a function of temperature calcula...
Figure P18.4 for the reaction () ()+ () versus the fraction of...
Figure P18.9 Osmotic pressure of -chymotrypsin versus for (filled squ...
Figure P18.12 Depression () of vapor pressure, elevation of boiling point...
Chapter 19
Figure E19.8 Phase diagram. Black filled circle: triple point, light gray fi...
Figure E19.9 Phase diagram of acetic acid.
Figure E19.10 versus for a gas and a liquid at a particular pressure (...
Figure E19.13 (a) Vapor pressure above liquid water versus temperature. (b) ...
Figure E19.20 Vapor pressure of water versus temperature . Experimental dat...
Figure P19.1 Vapor pressure of versus temperature . Experiment (filled ci...
Figure P19.2a Sketch of phase diagram of .
Figure P19.2b Phase diagram of .
Figure P19.2c Triple point curves of .
Figure P19.2d Gibbs energy versus temperature for
Figure P19.3a Phase diagram of . Vapor pressure of versus temperature
Figure P19.3b ln() (where is the vapor pressure) versus / for the subli...
Figure P19.3c ln( (where is the vapor pressure) versus for the vaporiza...
Figure P19.3d versus temperature for .
Figure P19.5 versus .
Figure P19.8 Top: Gibbs energy for the liquid and the gas versus temperatu...
Figure P19.11 Vapor pressure of water in the range 300–500 K. Dark gray soli...
Chapter 20
Figure E20.9 Determination of the roots of the van der Waals equation for ...
Figure E20.17a versus pressure for at K.
Figure E20.17b Step-by-step calculation of the area under a curve.
Figure E20.18 versus pressure for at K.
Figure E20.19 Compression factor for at K. Solid lines with filled cir...
Figure E20.21a The molar Gibbs energy for Mg. and are plotted as a funct...
Figure E20.21b The pressure versus temperature curve for Ar gas/solid co...
Figure E20.21c The pressure versus temperature curve for Mg gas/solid co...
Figure P20.4a Compression factor versus the pressure for a hard sphere g...
Figure P20.4b Fugacity for a hard sphere gas versus the pressure at diff...
Chapter 21
Figure E21.1 Chemical potential in a solution of HCl in water versus the m...
Figure E21.7 Volume of a KCl solution as a function of the amount of subst...
Figure E21.8 Activity coefficient versus molality for an aqueous solutio...
Figure E21.9 Activity coefficient versus molality for an aqueous solutio...
Figure E21.18 versus for a solution of oxygen in water.
Figure P21.1 Volume of a NaCl solution in water versus the amount of subst...
Figure P21.2a Vapor pressure versus the mole fraction of acetone. Dark g...
Figure P21.2b for a mixture of water and acetone versus the mole fraction ...
Figure P21.3 Panel (a) Activity coefficient for solutions of sucrose in wa...
Chapter 22
Figure E22.3 pH of acetic acid as a function of its concentration .
Figure E22.14 The figure shows the species involved in the chemical equilibr...
Figure P22.3 Fraction of S and versus pH.
Figure P22.5 Cycle for a gas-phase reaction. electron affinity, ionizati...
Figure P22.6 Different forms of glycine versus pH. Black solid line: glycina...
Figure P22.7 Titration of mol of glycine with HCl. pH versus of added HC...
Figure P22.8 pH of a buffer solution as a function of the concentration of...
Chapter 23
Figure E23.10 Calomel electrode. (a) Calomel electrode measured against a st...
Figure E23.15a Conductance versus for solutions of KCl in water at 298 K...
Figure E23.15b Conductance versus concentration .
Figure P23.4 Standard potential of a silver/silver chloride cell versus te...
Figure P23.5a versus for a /AgCl cell for different HCl concentrations....
Figure P23.5b Activity coefficient versus for a /AgCl cell for differen...
Figure P23.6a in Equation (23.1) versus the ionic strength
Figure P23.6b ln versus .
Figure P23.9a Electron affinity versus reduction potential for the molec...
Figure P23.9b Thermodynamic cycle to show the relationship between the elect...
Figure P23.10 Molar conductivity for KCl and NaCl versus the square root o...
Figure P23.11 versus where is the distance between two adjacent ions....
Figure P23.12 Conductivity as a function of at different temperatures ....
Chapter 24
Figure E24.6 versus for (dark gray) and NO (light gray).
Figure E24.12 versus for the decomposition of .
Figure E24.13 versus / for the gas-phase decomposition of the cyclobuten...
Figure P24.2 Plot of the quantity in Equation (24P2.1) versus time .
Figure P24.3 Temperature dependence of reaction 24.2. versus at Torr....
Figure P24.5 Dependence of the first-order rate constant for the thermal dec...
Figure P24.9 versus time plot according to Equation (24.58) with L a...
Chapter 25
Figure E25.3 versus .
Figure E25.4 Energy versus reaction coordinate diagram showing the transitio...
Figure E25.7 Plot of versus for the reaction (25.5) with different isoto...
Figure E25.11 Potential energy surface for the reaction of O with .
Figure E25.12 Potential energy surface for the reaction of O with .
Figure E25.20 Activated complex DHH, calculation of center of mass. The op...
Figure P25.1 Potential energy curves for the ground state and the first exci...
Figure P25.5a This surface is sketched from that given by H. F. Schaeffer II...
Figure P25.5b Experimental setup for a molecular beam apparatus.
Figure P25.6 Gibbs energy versus reaction coordinate for reaction 25.6.
Figure P25.11 Cross section versus (.
Chapter 26
Figure E26.7 ( versus angle . Dark gray solid circles: experiment; light ...
Figure E26.8 Diffusion coefficient versus , where is the number of mono...
Figure E26.9 versus the number of monomer units for polybutylene in chlo...
Figure E26.10 versus the number of monomer units for polybutylene in cyc...
Figure E26.11 Diffusion coefficient versus , where is the number of mon...
Figure E26.12 Sedimentation constant versus where is the number of mon...
Figure E26.16 Speed versus applied field strength for the movement of DN...
Figure P26.5 versus the number of monomer units for polybutylene in chlo...
Figure P26.6 Radius of gyration versus the number of monomers for denatu...
Figure P26.9 Coil radius versus the number of monomer units for proteins...
Figure P26.10a versus for m, m , N , and K. Dark gray filled c...
Figure P26.10b The fractional extension as a function of flow speed for
Figure P26.12 Rubber idealized by molecular chains, oriented in the dire...
Chapter 27
Figure E27.5 Quantity in Equation (27.1) versus the height .
Figure E27.16 Drop of liquid A on a surface of liquid B.
Figure E27.17 Quantity in Equation (E27E17.1) versus .
Figure E27.18a Monolayer assembly with monolayers deposited on a glass pla...
Figure E27.18b Integer versus the number of monolayers.
Figure P27.2 The quantity for a capacitor made of alkanethiol self-assembl...
Figure P27.4 Diagram of a spherical micelle whose hydrophobic core has the r...
Figure P27.5a Side-view and front-view of a plate (black) immersed in a liqu...
Figure P27.5b The sketch illustrates the shape for the liquid volume which a...
Figure P27.6 The dark light gray area represents a surface element for a sma...
Figure P27.8 dd versus the concentration
Chapter 28
Figure E28.3 Chromophore in the electric field of two negative charges.
Figure E28.4 Model for the circular dichroism of chlorosomes.
Figure E28.5 Exciton; for a dye molecule (pseudocyanine bromide) in an eth...
Figure E28.7 versus the distance . Dark gray solid line: black solid li...
Figure E28.11 Monolayer film with hydrocarbon chains perpendicular (a) and i...
Figure E28.12 Two types of thiol contacts.
Figure E28.13a Pseudorotaxane system.
Figure E28.13b The rate constant is plotted versus the barrier height
Figure P28.11a The position of the particle is plotted versus the number of ...
Figure P28.11b The number of steps necessary to reach the position in the ...
Chapter 29
Figure E29.1 Plot of versus .
Figure P29.1 Diffusion of two folded strands to form an aggregate. Panel (a)...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface Third Edition
Acknowledgment
Begin Reading
End User License Agreement
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SI Base Units
SI Derived or Related Units
Prefixes
Solutions Manual for Principles of Physical Chemistry
Third Edition
Edited by Hans Kuhn, David H. Waldeck, and Horst-Dieter Försterling
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Preface Third Edition
This book poses many exercises and problems for the students to use as tools to gain mastery over the methods and concepts introduced in the textbook. The exercises are intended to be activities for you to perform that will reinforce the concepts and important equations introduced in the textbook, whereas the problems are intended to be more challenging questions that often ask you to integrate concepts or to analyze data. The problems use data from published works and in the later chapters you are asked to read research articles and answer questions on them. The goal of this approach is to enhance your appreciation for science as a community activity.
Learning physical chemistry includes both the mastering of skills and the integration of new concepts into knowledge and understanding. Like other endeavors, for example, sports or music, daily practice is important for developing your skills. By applying effort on skills and knowledge accumulation on a daily basis, you will find that you develop a mastery and deeper understanding of physical chemistry over a period of time.
August 2023
David H. Waldeck and Horst-Dieter Försterling
Acknowledgment
Here we acknowledge those who have been important to the preparation of this third edition of Solutions Manual for Principles of Physical Chemistry. We are greatly indebted to Michael Leventhal and his colleagues at John Wiley & Sons, Ltd for their encouragement and support during all stages of this third edition. We are indebted to Professor Jeffry Madura (who died in 2017) who collaborated on the original version of the solutions manual. David Waldeck thanks his wife, Janet, and children, Aaron and Anna, for their support and understanding during this endeavor. Horst-Dieter Försterling is thankful for the great support by his family during the time of developing this book and its precursors, first of all to his wife Inge (who died in 2019) for their encouragement.
1Wave–Particle Duality
1.1 Exercises
E1.1
Consider a microwave source that is generating 2.0 GHz electromagnetic radiation. Compute the wavelength of the microwaves. If this microwave source was used in an oven of width 30 cm, how many wavelengths of the microwave can be included across the oven’s width?
Compute the energy per photon for the 2.0 GHz frequency. If a cup containing 250 mL of water is irradiated by this source, how many photons must be absorbed to raise the temperature of the water from 25 °C to 80 °C (a nice temperature for a cup of tea). For simplicity, assume that the water density is 1.0 g/mL, that the heat capacity is 4.184 J/(g °C), and that they do not change over the temperature range.
Solution
First we calculate the wavelength of a 2.0 GHz microwave and then compare it to the oven’s width. The wavelength and frequency are related by with being the speed of light cm , so
Hence, the oven is about wide.
Here we calculate the energy in a 2.0 GHz photon and compare it to the energy needed to warm the water (assuming no extraneous losses). The energy and frequency are related by , so that the energy per photon is
The amount of energy the water must absorb is , where is the mass of water (250 mL or 250 g), is the heat capacity, and is the change in temperature °C. Thus
so that the number of 2.0 GHz photons will be
Because we have ignored any extraneous losses (e.g., heat conduction to the container and convective cooling), this value is a lower bound.
E1.2
Consider an ultraviolet light source that generates 300 nm electromagnetic radiation. Compute the frequency of the ultraviolet light. If one photon of this light is absorbed by an organic molecule, how much energy does the molecule gain? Is this energy enough to break a carbon–carbon bond in the molecule? Use a “typical” carbon–carbon bond energy of J for your comparison. Perform the same calculations for a photon of wavelength 600 nm and a photon of wavelength 1200 nm. Perform your comparisons using the energy units of J and of eV.
Solution
The wavelength and frequency are related by with being the speed of light ( m ), so m m.
The energy and frequency are related by , so the energy per photon J s) () J.
This amount of energy is “just” sufficient to break a bond of J.
The corresponding energies for 600 and 1200 nm photons are J and J, neither of which is sufficient to break the typical carbon-carbon double bond.
The corresponding energies in eV ( J eV) are 4.12 eV (300 nm light), 2.06 eV (600 nm light), and 1.03 eV (1200 nm light).
E1.3
Consider an electron with a kinetic energy of 1.0 eV (i.e., it has been accelerated across a 1 V potential difference).
Compute the momentum of this electron. Compare this momentum to that of a “typical” gas molecule at room temperature (consider the gas molecule to have a speed of 500 m/s).
Compute this electron’s speed. At what fraction of light speed ( m/s) is the electron moving?
Compute this electron’s wavelength. Compare this wavelength to the diameter of a hydrogen atom (ca. 128 pm). Perform this same calculation for a 10 eV electron and a 100 eV electron. Comment on the trends in your values. How many electron wavelengths can fit into a hydrogen atom at these different energies?
Solution
The momentum is related to the kinetic energy by , so we find the momentum by
The momentum of a “typical” gas-phase nitrogen molecule () is
which is about 43 times greater than the momentum of the electron.
The electron’s speed is
This value is 0.002, or 0.2%, of the speed of light! While this speed is significant, it is still small enough to neglect relativistic effects.
The electron’s wavelength can be calculated using the de Broglie relationship, so that
where we have used kg m for the momentum of the electron. This wavelength is 9 to 10 times larger than the characteristic size of an H atom.
For 10 eV electrons nm, and for 100 eV electrons pm. The electron wavelength decreases as the square root of its kinetic energy and a 100 eV electron has a wavelength that is similar to the diameter of an H-atom.
E1.4
A typical value for a particle’s kinetic energy at 25 °C is J. Use this value of the kinetic energy to estimate the speed of spheres with different masses; i.e.,
ping pong ball (2.60 g)
a 10.0 diameter polystyrene bead (0.300 g/ kg/)
a 50.0 nm radius colloidal particle of Ag (10.5 g/)
Buckminster fullerene () (0.720 kg/mol)
He atom (4.0 g/mol kg/mol).
Use these speeds and masses to estimate the de Broglie wavelength of these spheres. Comment on the trend in your wavelengths. For which, if any, of these particles would you expect their wave properties to be important? If the kinetic energy was decreased by 100 times, how would your wavelengths change? Do you think that wave properties would be important under these circumstances?
Solution
The speed and kinetic energy are related by
Hence we find
for the ping pong ball
for the polystyrene bead we first compute its mass by and then find its speed by
for the silver colloid particle we first compute its mass by and then find its speed by
for the Buckminsterfullerene we first compute its mass by and then find its speed by
for the He atom we first compute its mass by and then find its speed by To find the de Broglie wavelengths , we use the fundamental relation By way of example, we consider the Ag colloid particle and calculate
Proceeding in a like manner for each of the cases above we find
particle
/m
ping-pong ball
polystyrene bead
Ag particle
fullerene,
He atom
These numbers suggest that it is not necessary to consider the wave nature of these particles under these conditions; i.e., the wavelength is small compared to the size of structures from which it might collide so that diffraction is not important.
E1.5
Describe the photoelectric effect experiment.
Provide a sketch of the apparatus.
State the implications of the experiment.
Describe what is observed in the experiment and how it relates to the experiment’s implications.
Solution
Fig. 1.2a of the textbook gives a schematic of the photoelectric effect apparatus.
The principal implication is that light can behave has a particle.
The two observations are that the stopping potential depends on the light frequency and not on intensity, while the number of photoelectrons depends on light intensity and not frequency. These results are exactly the opposite of the behavior that one expects for a classical wave and are exactly what would be expected if the light behaved as a particle.
E1.6
Consider the diffraction of photons, electrons, and neutrons from an aperture with diameter . Consider the case where is 1 cm and the case where it is cm.
If you direct a light beam onto the aperture, how large must the wavelength be so that diffraction can be observed? What is the frequency of the light you found?
If you direct an electron beam onto the aperture, how large must the speed of the electrons be so that diffraction can be observed?
We assume that the de Broglie relationship holds not only for electrons, but also for any particle. How large must the speed of the neutrons be for the aperture to diffract a neutron beam?
Do not be disturbed if the answers to these exercises are not experimentally feasible. The goal is to clarify the content of Equations (1.7) and (1.9)
Solution
Diffraction occurs when the wavelength of the wave is approximately the same as the size of the aperture. Considering the size of the aperture as 1 cm and cm,
For an aperture of 1 cm, the wavelength is 1 cm, and the corresponding frequency is cm / 1 cm . For a cm aperture, the wavelength is cm, and the corresponding frequency is cm cm .
We need to find the electron’s wavelength through the de Broglie relationship, . For a 1 cm wavelength J s) kg0.01 m) cm . For a cm wavelength J s) kg) ( m) cm .
We need to find the neutron’s wavelength through the de Broglie relationship, For a 1 cm wavelength J s) kg0.01 m) cm . For a cm wavelength J s) kg m) cm .
E1.7
If photons are particles they have momentum. Compute the momentum of a 590 nm photon. Compare this momentum to that of a Na atom moving at a speed of 900 m/s, which is a typical value at 1200 °C. Assume that 590 nm photons collide head on with the sodium atom so that the momentum exchange is twice the photon momentum, how many photons are needed to ’stop’ the sodium atom?
Solution
Again we employ the de Broglie relationship,
and find that the momentum of a photon is
Thus for a wavelength of nm we obtain
This photon momentum should be compared with the sodium atom’s momentum, which is
Thus interactions with about 30,600 photons would be required to slow a sodium atom to a stop. Processes of this sort are used in the cooling and trapping of atoms (see Laser Trapping of Neutral Particles, by S. Chu, Scientific American, February 1992, p. 71).
E1.8
Imagine you build an experimental apparatus in which you can use a photon to eject an electron from an H-atom; i.e., absorb a photon and generate a proton and a free electron. This is called a photoelectron experiment. Imagine that you perform this experiment on single hydrogen atoms, in a chamber where the atoms are surrounded by a thousand electron detectors (numbered ed1 through ed1000), so that all sides (all steradians) are sensed and the detected electron’s position can be reported. In more technical language, imagine measuring the full angular distribution of photoejected electrons. In addition, assume that the hydrogen atoms are in their ground electronic state, and that the photons irradiate the sample isotropically with photons of energy much higher than that which is needed to eject an electron from the hydrogen atom.
If the experiment is performed on a single hydrogen atom, what is the probability that
ed375
detects the photoejected electron? If the experiment is performed on one-hundred hydrogen atoms in succession, what is the probability that
ed375
detects the first photoejected electron? What is the probability that
ed375
detects any photoelectron?
Imagine a related experiment in which hydrogen atoms that are initially excited are injected into a chamber and they emit light. Perform experiments of the same type as in part (a) but detecting photons instead of electrons. Does your analysis change? Explain!
Solution
The photoelectrons should be emitted with equal probability into all steradians. The probability of
ed375
detecting the photoejected electron or the first electron is thus 1/1000. If done 100 times in succession, the probability is now 100 (1/1000) = 0.010 for
ed375
to detect any electron.
Assuming that photoelectrons and photons are both emitted isotropically (independently of direction) there is no change in the analysis.
E1.9
Using Fig. 1.6, calculate the distance between the intensity maxima, and , in terms of the wavelength of the incident light and the parameters and . If your apparatus has m and m, and you illuminate the slit with monochromatic light of nm (red light of a laser pointer), what is the distance in the figure?
Solutions
Using Fig. E1.9 we can calculate the distance between the intensity maxima, and . The point is the location where a light ray from each slit traverses the same distance to the screen. For this reason the phases of the light waves arriving at point are the same, and we obtain an intensity maximum at point . The point is the position where the light ray from the lower slit travels an extra distance of one wavelength and constructively interferes with a light ray from the upper slit. Thus, at point we find the next intensity maximum: the distances and differ by ; thus, the phases of the two waves arriving at point are the same.
Figure E1.9 Diffraction of light on a double slit.
We restrict our consideration to the case that the distance between the slits is much smaller than the distance between the points and . In this case the angle ABC is approximately , and we can set (the triangle ABC is approximately a right triangle). Then we obtain
In addition, we can use trigonometry to relate the tangent of the angle to its sine, so that
Now we can combine these results to relate the separation between the intensity maxima to the wavelength and the parameters and
We can rearrange this expression to solve for and obtain
Because the distance is much larger than , we can simplify this expression as
As an example, we illuminate a double slit of width m with the light of a red laser pointer ( nm). For a screen at a distance of m we calculate
We can solve this equation for the wavelength .
Note that the remaining term with is a correction term, and we can approximate it by setting in Equation (1E9.1) leading to
and
With the data m, m, and cm from our example for we obtain
This is less than the expected 640 nm by 1.4%.
We can improve the calculation by using Equation (1E9.2) instead of Equation (1E9.3)
or
leading to the improved equation
With the data m, m, and cm for we obtain the correct value:
Note that optical measurements are very precise and it is a good choice to use equally precise equations to describe the experiments.
1.2 Problems
P1.1
Consider the following data, taken from O. W. Richardson and K. T. Compton, Phil. Mag. 24 (1913) 575, for the photoemission of electrons from a metal substrate. is the kinetic energy of the photoelectrons and is the wavelength of the light. Analyze these data using a least squares analysis. Find the workfunction of the metal and determine a value for Planck’s constant. The workfunction is the minimum energy that is needed to remove an electron from the metal and place it at the detector some macroscopic distance away.
Sodium
Copper
/eV
nm
/eV
nm
0.60
436
0.35
260
1.00
366
0.48
254
1.50
313
0.73
230
2.30
254
1.02
210
3.00
210
1.25
200
Solutions
In analogy to the discussion in Section 1.2.2.5, we plot the kinetic energy versus the photon frequency
