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Chapter: 5 -Problem: 2 >> Consider the plot of log ?± against I1/2 with B=1.50 and C=0 in the Davies equation as a representation of experimental data for a certain MX electrolyte. Over what range of ionic strengths does the application of the limiting law lead to an error in the value of the activity coefficient of less than 10 per cent of the value predicted by the extended law?
Answer Preview: The Debye Huckel limiting law is given as Where is the activity coefficient A is …

, Chapter: 14 -Problem: 3 >> To gain some appreciation for the numerical work done by computers interfaced to NMR spectrometers, perform the following calculations.(a) The total FID F(t) of a signal containing many frequencies, each corresponding to a different nucleus, is given by where, for each nucleus j, S0j is the maximum intensity of the signal, ?Lj is the Larmor frequency, and T2j is the spin–spin relaxation time. Plot
Answer Preview: a The total FID F t for a signal containing many frequencies can be calculated using the formula F t …

, Chapter: 4 -Problem: 2 >> What is the physical reason for the fact that the chemical potential of a pure substance increases as the pressure is raised?
Answer Preview: Usually the molar volume of a liquid is greater …

, Chapter: 18 -Problem: 1 >> Describe the relationship between the space lattice and unit cell.
Answer Preview: Each point in a space lattice represents an atom o…

, Chapter: 13 -Problem: 2 >> Use mathematical software or an electronic spreadsheet to simulate the output of a mode-locked laser (that is, plots such as that shown in Fig. 13C.8) for L=30 cm and N=100 and 1000. Data in Fig. 13C.8 Transcribed Image Text: Intensity, I m 1 hud Time, ct/2L 2 3 m m 5
Answer Preview: To simulate the output of a mode locked laser using mathematical software or an electronic spreadshe…

, Chapter: 6 -Problem: 2 >> When the reaction A?2 B advances by 0.10mol (that is, ?? =+0.10mol) the Gibbs energy of the system changes by –6.4 kJmol?1. What is the Gibbs energy of reaction at this stage of the reaction?
Answer Preview: Calculation The Gibbs energy of the reaction is given by …

, Chapter: 14 -Problem: 3 >> Explain why groups of equivalent protons do not exhibit the spin–spin coupling that exists between them.
Answer Preview: G roups of equivalent prot ons do not exhibit the spin spin coupl…

, Chapter: 18 -Problem: 1 >> Calculate the atomic packing factor for diamond.
Answer Preview: The atomic packing factor (APF) is a measure of the …

, Chapter: 10 -Problem: 5 >> To what extent can orbital overlap be related to bond strength?
Answer Preview: Doing so forms the basis for a description of chemical …

, Chapter: 8 -Problem: 1 >> The rotation of a molecule can be represented by the motion of a point mass moving over the surface of a sphere. Calculate the magnitude of its angular momentum when l=1 and the possible components of the angular momentum on an arbitrary axis. Express your results as multiples of h.
Answer Preview: The magnitude of the angular momentum is L l l 1 h where l is the angular momentum …

, Chapter: 14 -Problem: 4 >> Sketch the form of the 19F-NMR spectra of a natural sample of 10BF4? and 11BF4?.
Answer Preview: Answer The 19F NMR spectra of a natural sample of 10BF4 and 11BF4 will …

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, Chapter: 17 -Problem: 5 >> Derive expressions for the moments of inertia and hence the radii of gyration of(a) A uniform thin disk,(b) A long uniform rod,(c) A uniform sphere.
Answer Preview: (a) A uniform thin disk: The moment of inertia of a uniform thin disk is g…

, Chapter: 13 -Problem: 2 >> A certain laser can generate radiation in pulses, each of which delivers an energy of 0.10mJ, with peak power of 5.0MW and average power of 7.0 kW. What are the pulse duration and repetition frequency?
Answer Preview: Thorough calculation The pulse duration can be calculated using the equation P …

, Chapter: 7 -Problem: 3 >> Describe the constraints that the Born interpretation puts on acceptable wavefunctions.
Answer Preview: The Born interpretation implies that such solutions are unac…

, Chapter: 15 -Problem: 2 >> Evaluate 8! by using (i) the exact formula, (ii) Stirling’s approximation, eqn 15A.2b; (iii) the more accurate version of Stirling’s approximation, eqn 15A.2a. Data in eqn 15A.2a Transcribed Image Text: Inx!=(x+1)Inx-x+In 2 X>1 Stirling's approxi- mation (15A.2a)
Answer Preview: Answer i Exact Formula 8 40320 ii Stir…

, Chapter: 22 -Problem: 3 >> A certain solid sample adsorbs 0.44mg of CO when the pressure of the gas is 26.0 kPa and the temperature is 300K. The mass of gas adsorbed when the pressure is 3.0 kPa and the temperature is 300K is 0.19mg. The Langmuir isotherm is known to describe the adsorption. Find the fractional coverage of the surface at the two pressures.
Answer Preview: Calculations. The fractional coverage of the surface at 26 0kPa is give…

, Chapter: 12 -Problem: 8 >> Which of the normal modes of CH2Cl2 (Exercise 12E.7(a)) are infrared active? Which are Raman active? Data in Exercise 12E.7(a)The molecule CH2Cl2 belongs to the point group C2v. The displacements of the atoms span 5A1+2A2+4B1+4B2. What are the symmetry species of the normal modes of vibration?
Answer Preview: The normal modes of vibration of CH2Cl2 are A1 symmetric st…

, Chapter: 6 -Problem: 6 >> Estimate the temperature at which CaCO3(calcite) decomposes.
Answer Preview: The decomposition reaction of Ca…

, Chapter: 15 -Problem: 3 >> How does a statistical analysis of the equilibrium constant account for the latter’s temperature dependence?
Answer Preview: A statistical analysis of the equilibrium constant accounts for the latters temperature d…

, Chapter: 17 -Problem: 8 >> The radius of gyration of a three-dimensional partially rigid polymer of 1000 units each of length 150pm was measured as 2.1nm. What is the persistence length of the polymer?
Answer Preview: The persistence length of the polymer is 3 4nm. The radius of gy…

, Chapter: 5 -Problem: 1 >> Francesconi, Lunelli, and Comelli studied the liquid–vapour equilibria of trichloromethane and 1,2-epoxybutane at several temperatures (Francesconi et al., J. Chem. Eng. Data 41, 310 (1996)). Among their data are the following measurements of the mole fractions of trichloromethane in the liquid phase (xT) and the vapour phase (yT) at 298.15K as a function of pressure.Compute the activity coefficie
Answer Preview: Raoult s Law states that the activity coefficient of a component in an ideal solution is equal to it…

, Chapter: 7 -Problem: 2 >> Discuss the relation between probability amplitude, probability density, and probability.
Answer Preview: In quantum mechanics a probability …

, Chapter: 14 -Problem: 9 >> A proton jumps between two sites with ?=2.7 and ?=4.8. At what rate of interconversion will the two signals collapse to a single line in a spectrometer operating at 550MHz?
Answer Preview: The proton will jump between the two sites at a rate of approximately 2 7 MHz The prot…

, Chapter: 18 -Problem: 2 >> Distinguish between light-emitting diodes and diode lasers.
Answer Preview: Light-emitting diodes (LEDs), like laser diodes, generate r…

, Chapter: 5 -Problem: 1 >> The mean activity coefficients for aqueous solutions of NaCl at 25 °C are given opposite. Confirm that they support the Debye–Hückel limiting law and that an improved fit is obtained with the Davies equation. Transcribed Image Text: b/(mmol kg ¹) V+ 1.0 2.0 0.9649 0.9519 0.9275 5.0 10.0 0.9024 20.0
Answer Preview: The DebyeHckel limiting law is given by ln z2A 1 Bz2 wh…

, Chapter: 6 -Problem: 2 >> Explain the role of a salt bridge.
Answer Preview: Salt bridge prevents the diffusion or mechanical flow of sol…

, Chapter: 15 -Problem: 4 >> Evaluate, by explicit summation, the mean rotational energy of CH3Cl and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate value? ?A=5.097cm-1. and ?B =0.443cm?1.
Answer Preview: Thorough explanation The mean rotational energy of CH3Cl is 5 097 cm 1 Th…

, Chapter: 17 -Problem: 3 >> What effect is the inclusion of cholesterol likely to have on the transition temperatures of a lipid bilayer?
Answer Preview: Cholesterol gradually increases the temperature …

, Chapter: 12 -Problem: 11 >> Absorptions in the v=1?0 vibration–rotation spectrum of 1H35Cl were observed at the following wavenumbers (in cm?1):Assign the rotational quantum numbers and use the method of combination differences to determine the rotational constants of the two vibrational levels. Transcribed Image Text: 2998.05
Answer Preview: The wavenumbers observed correspond to the v 10 vibrationrotation spectrum of 1H35Cl which means tha…

, Chapter: 8 -Problem: 2 >> Explain why the particle in a box and the harmonic oscillator are useful models for quantum mechanical systems: what chemically significant systems can they be used to represent?
Answer Preview: Because of its mathematical simplicity the particle in a box model is used to find approximate solut…

, Chapter: 15 -Problem: 1 >> Discuss the relationship between ‘population’, ‘configuration’, and ‘weight’. What is the significance of the most probable configuration?
Answer Preview: Discuss the relationship between population configuration and weight The statistical weight …

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, Chapter: 5 -Problem: 1 >> Why do the activity coefficients of ions in solution differ from 1? Why are they less than 1 in dilute solutions?
Answer Preview: yes activity coefficient can be …

, Chapter: 7 -Problem: 5 >> Which of the functions in Problem 7C.3 are(a) Also eigenfunctions of d2/dx2 (b) Only eigenfunctions of d2/dx2 Give the eigenvalues where appropriate. Data in Problem 7C.3Identify which of the following functions are eigenfunctions of the operator d/dx:(a) Eikx,(b) K,(c) Kx,(d) E?ax2Give the corresponding eigenvalue where appropriate.
Answer Preview: Thorough explanation The functions which are also eigenfunctions …

, Chapter: 15 -Problem: 1 >> Compute the mean energy at 298K of a two-level system of energy separation equivalent to 500 cm?1.
Answer Preview: The mean energy at 298K of a two level system of energy separation equivalent to 500 cm 1 is …

, Chapter: 21 -Problem: 1 >> Describe the various models of the electrode–electrolyte interface.
Answer Preview: The various models of the electrodeelectrolyte interface are the: 1. Planar model. 2. Diffuse double …

, Chapter: 12 -Problem: 16 >> The analysis of combination differences summarized in the text considered the R and P branches. Extend the analysis to the O and S branches of a Raman spectrum.
Answer Preview: In a Raman spectrum the R and P branches correspond to transitions between different vibrational …

, Chapter: 5 -Problem: 3 >> Prove that a straight line from the apex A of a ternary phase diagram to the opposite edge BC represents mixtures of constant ratio of B and C, however much A is present.
Answer Preview: The vertices of a ternary phase diagram to the opposite edge represent the components of the mixture …

, Chapter: 14 -Problem: 1 >> Given that g is a dimensionless number, what are the units of ?N expressed in tesla and hertz?
Answer Preview: The units of …

, Chapter: 22 -Problem: 7 >> C. Huang and W.P. Cheng (J. Colloid Interface Sci. 188, 270 (1997)) examined the adsorption of the hexacyanoferrate(III) ion, [Fe(CN)6]3?, on ?-Al2O3 from aqueous solution. They modelled the adsorption with a modified Langmuir isotherm, obtaining the following values of ? at pH=6.5:Determine the isosteric enthalpy of adsorption, ?adsH?, at this pH. The researchers also reported ?adsS? =+146 Jmol?1
Answer Preview: Calculation. The enthalpy of adsorption, adsH, is given by; ad…

, Chapter: 14 -Problem: 1 >> A scientist investigates the possibility of neutron spin resonance, and has available a commercial NMR spectrometer operating at 300MHz. What field is required for resonance? What is the relative population difference at room temperature? Which is the lower energy spin state of the neutron?
Answer Preview: What field is required for resonance The field required for resonance is 30…

, Chapter: 17 -Problem: 9 >> Use the following information and the expression for Rg of a solid sphere quoted in the text (following eqn 17A.6), to classify the given species as globular or rod-like. Data in eqn 17A.6 Transcribed Image Text: Serum albumin Bushy stunt virus DNA M/(g mol-¹) 66x10³ 10.6x106 4x106 v/(cm³g-¹) 0.752
Answer Preview: To classify a species as globular or rod-like based o…

, Chapter: 14 -Problem: 4 >> Explain the difference between magnetically equivalent and chemically equivalent nuclei, and give two examples of each.
Answer Preview: Magnetically equivalent nuclei have the same number of protons but different numb…

, Chapter: 21 -Problem: 4 >> How do kinetic isotope effects provide insight into the mechanism of a reaction?
Answer Preview: Vibrational changes from isotopic substitution at atoms awa…

, Chapter: 15 -Problem: 12 >> Calculate the vibrational partition function of CCl4 at 500K given the wavenumbers 459 cm?1 (symmetric stretch, A), 217 cm?1 (deformation, E), 776 cm?1 (deformation, T), 314 cm?1 (deformation, T).
Answer Preview: The vibrational partition function of CCl4 is Qvib …

, Chapter: 15 -Problem: 1 >> Use mathematical software, a spreadsheet, or the Living graphs on the web site for this book to:(a) Consider a three-level system with levels 0, ?, and 2?. Plot the partition function against kT/?.(b) Plot the function dS/dT for a twolevel system, the temperature coefficient of its entropy, against kT/?. Is there a temperature at which this coefficient passes through a maximum? If you find a maxi
Answer Preview: The partition function of a three level system can be represented as Z 1 e kT e 2 kT where Z is the …

, Chapter: 15 -Problem: 1 >> Describe the molecular features that determine the magnitudes of the constant-volume molar heat capacity of a molecular substance.
Answer Preview: The constant volume m olar heat capacity is determined by the number of degrees of freedom of th…

, Chapter: 15 -Problem: 7 >> Calculate the rotational partition function of H2O at 298K from its rotational constants 27.878 cm?1, 14.509 cm?1, and 9.287 cm?1 and use your result to calculate the rotational contribution to the molar entropy of gaseous water at 25 °C.
Answer Preview: The rotational partition function of H2O is Qrot 1 Z eE kBTdE where Z …

, Chapter: 22 -Problem: 1 >> A monolayer of N2 molecules is adsorbed on the surface of 1.00 g of an Fe/Al2O3 catalyst at 77K, the boiling point of liquid nitrogen. Upon warming, the nitrogen occupies 3.86 cm3 at 0 °C and 760Torr. What is the surface area of the catalyst?
Answer Preview: Calculation. The surface area of the catalyst, S, is given by; …

, Chapter: 14 -Problem: 2 >> Explain how the EPR spectrum of an organic radical can be used to identify and map the molecular orbital occupied by the unpaired electron.
Answer Preview: The E PR spectrum of an organic radical can be used to identify and map the molecular orbital occupi…

, Chapter: 17 -Problem: 2 >> Calculate the restoring force when the ends of a one-dimensional polyethene chain of molar mass 65 kgmol?1 are moved apart by 1.0nm at 20 °C.
Answer Preview: The restoring force when the ends of a one-dimensional polyethene chain of molar mass 65 kgmol1 …

, Chapter: 15 -Problem: 20 >> It is possible to write an approximate expression for the partition function of a protein molecule by including contributions from only two states: the native and denatured forms of the polymer. Proceeding with this crude model gives us insight into the contribution of denaturation to the heat capacity of a protein. According to this model, the total energy of a system of N protein molecules is wh
Answer Preview: a The partition function for a system of N protein molecules is given by Q QN QD N exp kT N 1 exp kT …

, Chapter: 17 -Problem: 1 >> Develop an expression for the fundamental vibrational frequency of a one-dimensional random coil that has been slightly stretched and then released. Evaluate this frequency for a sample of polyethene of molar mass 65 kgmol?1 at 20 °C. Account physically for the dependence of frequency on temperature and molar mass.
Answer Preview: The fundamental vibrational frequency of a one-dimensi…

, Chapter: 15 -Problem: 4 >> Deduce an expression for the root mean square energy, ??2?1/2, in terms of the partition function and hence an expression for the root mean square deviation from the mean, ??=(??2? – ???2)1/2. Evaluate the resulting expression for a harmonic oscillator.
Answer Preview: Thorough explanation The root mean square energy 21 2 is the square root of the mean square energy T…

, Chapter: 15 -Problem: 2 >> What is the significance and importance of the principle of equal a priori probabilities?
Answer Preview: A priori probability stipulates that the outcome of the next …

, Chapter: 15 -Problem: 1 >> Calculate the weight of the configuration in which 16 objects are distributed in the arrangement 0, 1, 2, 3, 8, 0, 0, 0, 0, 2.
Answer Preview: Assuming that each object has a mass of 1 unit the weight of …

, Chapter: 17 -Problem: 11 >> The viscosities of solutions of polyisobutylene in benzene were measured at 23 °C with the following results: Use the information in Table 17D.3 to deduce the molar mass of the polymer. Data in Table 17D.3 Transcribed Image Text: c/(g/10² cm³) n/(10³ kg m-¹s-¹) 0 0.647 0.4 0.6 0.8 0.690 0.733 0.777
Answer Preview: The Mark-Houwink equation relates the intrinsic viscosity [] of a polymer to its molecular weight (M…

, Chapter: 15 -Problem: 7 >> The variation of the atmospheric pressure p with altitude h is predicted by the barometric formula to be p=p0e?h/H where p0 is the pressure at sea level and H=RT/Mg with M the average molar mass of air and T the average temperature. Obtain the barometric formula from the Boltzmann distribution. Recall that the potential energy of a particle at height h above the surface of the Earth is mgh. Conver
Answer Preview: The barometric formula is p p0emgh kBT where p0 is the pressure at sea level m …

, Chapter: 1 -Problem: 1 >> Specify and analyse critically the assumptions that underlie the kinetic model of gases.
Answer Preview: The simplest kinetic model is based on the assumption…

, Chapter: 18 -Problem: 1 >> In what respects is the hard-sphere model of metallic solids deficient?
Answer Preview: The hard sp here model of metallic sol ids is def…

, Chapter: 20 -Problem: 8 >> The first step in plant photosynthesis is absorption of light by chlorophyll molecules bound to proteins known as ‘light-harvesting complexes’, where the fluorescence of a chlorophyll molecule is quenched by nearby chlorophyll molecules. Given that for a pair of chlorophyll a molecules R0=5.6nm, by what distance should two chlorophyll a molecules be separated to shorten the fluorescence lifetime f
Answer Preview: Calculations The distance at which t…

, Chapter: 1 -Problem: 6 >> A vessel of volume 22.4dm3 contains 2.0mol H2 and 1.0mol N2 at 273.15K initially. All the H2 reacted with sufficient N2 to form NH3. Calculate the partial pressures and the total pressure of the final mixture.
Answer Preview: Calculations and Explanations The final volume of the …

, Chapter: 21 -Problem: 3 >> The gas phase association reaction between F2 and IF5 is first order in each of the reactants. The energy of activation for the reaction is 58.6kJ mol?1. At 65 °C the rate constant is 7.84×10?3 kPa?1 s?1. Calculate the entropy of activation at 65 °C.
Answer Preview: Calculation. The entropy of activation, S*, is given by; S* = (R/2) * lo…

, Chapter: 14 -Problem: 1 >> It is possible to produce very high magnetic fields over small volumes by special techniques. What would be the resonance frequency of an electron spin in an organic radical in a field of 1.0kT? How does this frequency compare to typical molecular rotational, vibrational, and electronic energy-level separations?
Answer Preview: What would be the resonance frequency of an electron spin in an organic radical in a field of 1 …

, Chapter: 17 -Problem: 4 >> Summarize the Core–Pauling rules and explain how they explain the helical and sheet-like structures of polypeptides.
Answer Preview: The CorePauling rules are a set of guidelines for predicting the three-dimensional structure of prot…

, Chapter: 15 -Problem: 8 >> Give the symmetry number for each of the following molecules: (i) CO, (ii) O2, (iii) H2S, (iv) SiH4, and (v) CHCl3.
Answer Preview: i CO The symmetry number is 2 ii O2 The symmetry number is 4 iii H2S The symmetry numbe…

, Chapter: 17 -Problem: 6 >> By what percentage does the radius of gyration of a one-dimensional polymer chain increase (+) or decrease (?) when the bond angle between units is limited to 109°? What is the percentage change in volume of the coil?
Answer Preview: The radius of gy ration of a one dimensional polymer chain incr…

, Chapter: 14 -Problem: 4 >> The proton chemical shifts for the NH, C?H, and C?H groups of alanine are 8.25ppm, 4.35ppm, and 1.39ppm, respectively. Sketch the COSY spectrum of alanine between 1.00 and 8.50ppm.
Answer Preview: Answer The COSY spectrum of alanine between 1 00 and 8 5…

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, Chapter: 21 -Problem: 1 >> Discuss how the collision theory of gases builds on the kinetic– molecular theory.
Answer Preview: The collision theory of gases is based on the kineticmolecular theory, which states that gases are c…

, Chapter: 14 -Problem: 3 >> What is the Larmor frequency? What is its role in magnetic resonance?
Answer Preview: Magnetic fields used in MRI are typically in the …

, Chapter: 22 -Problem: 8 >> In a study relevant to automobile catalytic converters, C.E. Wartnaby et al. (J. Phys. Chem. 100, 12483 (1996)) measured the enthalpy of adsorption of CO, NO, and O2 on initially clean platinum (110) surfaces. They report ?adsH? for NO to be ?160 kJmol?1. How much more strongly adsorbed is NO at 500 °C than at 400 °C?
Answer Preview: Calculation. The enthalpy of adsorption, adsH, is given by; adsH = adsH - RT where adsH is the s…

, Chapter: 14 -Problem: 2 >> Use mathematical software to construct the FID curve for a set of three nuclei with resonances at ? =3.2, 4.1, and 5.0 in a spectrometer operating at 800MHz. Suppose that T1=1.0s. Go on to plot FID curves that show how they vary as the magnetic field of the spectrometer is changed.
Answer Preview: To construct the FID curve for a set of three nuclei with resonances at 3 2 4 1 and 5 0 in a spectro…

, Chapter: 3 -Problem: 1 >> Consider a perfect gas contained in a cylinder and separated by a frictionless adiabatic piston into two sections A and B. All changes in B are isothermal; that is, a thermostat surrounds B to keep its temperature constant. There is 2.00mol of the gas molecules in each section. Initially TA =TB =300K, VA =VB =2.00dm3. Energy is supplied as heat to Section A and the piston moves to the right revers
Answer Preview: Section A Initial V T p Ti 300 K V i 2 L p i 24 6 atm from ideal gas equationof state pV nRT Section …

, Chapter: 18 -Problem: 1 >> Explain the origin of Davydov splitting in the exciton bands of a crystal.
Answer Preview: The Davydov splitting is a result of the interaction between t…

, Chapter: 15 -Problem: 4 >> The H2O molecule is an asymmetric rotor with rotational constants 27.877 cm?1, 14.512 cm?1, and 9.285 cm?1. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.
Answer Preview: The rot ational partition function of a molecule is a measu…

, Chapter: 9 -Problem: 2 >> Highly excited atoms have electrons with large principal quantum numbers. Such Rydberg atoms have unique properties and are of interest to astrophysicists.(a) For hydrogen atoms with large n, derive a relation for the separation of energy levels.(b) Calculate this separation for n?=?100; also calculate the average radius, the geometric cross section, and the ionization energy.(c) Could a thermal c
Answer Preview: a For hydrogen atoms with large n derive a relation for the separation of energy levels The separati…

, Chapter: 17 -Problem: 2 >> Suggest reasons why different techniques produce different molar mass averages.
Answer Preview: Different techniques produce different m olar mass averages because of the differen…

, Chapter: 15 -Problem: 5 >> The rotational constant of CO is 1.931 cm?1. Evaluate the rotational partition function explicitly (without approximation) and plot its value as a function of temperature. At what temperature is the value within 5 per cent of the value calculated from the approximate formula?
Answer Preview: Thorough explanation The rotational partition function of CO is 1 931 cm 1 Th…

, Chapter: 1 -Problem: 5 >> Assume that air consists of N2 molecules with a collision diameter of 395 pm. Calculate(i) The mean speed of the molecules,(ii) The mean free path,(iii) The collision frequency in air at 1.0 atm and 25 °C.
Answer Preview: i The mean speed of the molecules At 25C the most probable sp…

, Chapter: 8 -Problem: 10 >> What is the value of n of a particle in a one-dimensional box such that the separation between neighbouring levels is equal to the mean energy of thermal motion (1/2 kT).
Answer Preview: n 2 n 2 is the value of n for a particle in a one dimensional box …

, Chapter: 21 -Problem: 3 >> Explain the physical origin of the kinetic salt effect. What might be the effect of the relative permittivity of the medium?
Answer Preview: The kinetic salt effect is the increased rate of a chemical reaction in the presence of a salt. The …

, Chapter: 14 -Problem: 4 >> 14N has a nuclear spin of 1 and a nuclear g-factor of 0.404. Calculate the energies of the nuclear spin states in a magnetic field of 10.50T.
Answer Preview: The energies of the nuclear spin states are E gNB I where …

, Chapter: 3 -Problem: 1 >> Calculate ?rG? (375K) for the reaction 2 CO(g)+O2(g)?2 CO2(g) from the value of ?rG? (298K), ?rH? (298K), and the Gibbs–Helmholtz equation.
Answer Preview: rH 298K sum of fH 298K of products sum of fH 298K of reactants 2 3…

, Chapter: 17 -Problem: 1 >> Distinguish between a sol, an emulsion, and a foam. Provide examples of each.
Answer Preview: Solution (a). Sol: Solid particles are dispersed in a liquid medium. Ex- ink, …

, Chapter: 15 -Problem: 5 >> Explore the consequences of using the full version of Stirling’s approximation, x!?(2?)1/2xx+1/2e?x, in the development of the expression for the configuration of greatest weight. Does the more accurate approximation have a significant effect on the form of the Boltzmann distribution?
Answer Preview: Thorough explanation The full version of Stirling s approximation has a sig…

, Chapter: 2 -Problem: 3 >> Use mathematical software, a spreadsheet, or the Living graphs on the web site for this book to:(a) Calculate the work of isothermal reversible expansion of 1.0mol CO2(g) at 298K from 1.0m3 to 3.0m3 on the basis that it obeys the van der Waals equation of state.(b) Explore how the parameter ? affects the dependence of the pressure on the volume. Does the pressure–volume dependence become stronger
Answer Preview: a First calculate the work of isothermal reversible expansion of the CO2 molecule Second calculate t…

, Chapter: 17 -Problem: 6 >> In an ultracentrifugation experiment at 20 °C on bovine serum albumin the following data were obtained: ? =1.001 g cm?3, vs=1.112 cm3 g?1, ?/2?=322Hz,Evaluate the molar mass of the sample. Transcribed Image Text: r/cm c/(mg cm-³) 5.0 0.536 5.1 0.284 5.2 0.148 5.3 0.077 5.4 0.039
Answer Preview: Calculations. The molar m…

, Chapter: 15 -Problem: 4 >> Why and when is it necessary to include a symmetry number in the calculation of a partition function?
Answer Preview: The symmetry number is generally used in the calculation of partition functions to account for the f…

, Chapter: 2 -Problem: 4 >> The isothermal compressibility of water at 293K is 4.96×10?5 atm?1. Calculate the pressure that must be applied in order to increase its density by 0.10 per cent.
Answer Preview: Isothernal compressibility 1 v dV …

, Chapter: 21 -Problem: 2 >> If the cumulative reaction probability were independent of energy, what is the temperature dependence of the rate constant predicted by the numerator of eqn 21D.6?  Data in eqn 21D.6 Transcribed Image Text: k?(T)= 00 0 P(E)e-E/kT dE hQR (T) Rate constant (21D.6)
Answer Preview: Calculations. The temperature dependence of the rate constan…

, Chapter: 15 -Problem: 3 >> Evaluate, by explicit summation, the mean rotational energy of CH4 and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate value? ?B(CH4)=0.0527 cm-1.
Answer Preview: The mean rotational energy of CH4 is given by Erot 1 2 B CH4 T where B C…

, Chapter: 2 -Problem: 10 >> In biological cells that have a plentiful supply of oxygen, glucose is oxidized completely to CO2 and H2O by a process called aerobic oxidation. Muscle cells may be deprived of O2 during vigorous exercise and, in that case, one molecule of glucose is converted to two molecules of lactic acid (CH3CH(OH)COOH) by a process called anaerobic glycolysis.(a) When 0.3212 g of glucose was burned in a bomb
Answer Preview: i Standard enthalpy of combustion mass X Hc calculated 0 3212g 43 5kJmol1 16 95 kJmol1 ii Standard i…

, Chapter: 21 -Problem: 1 >> Calculate the collision frequency, z, and the collision density, Z, in ammonia, R=190pm, at 30 °C and 120 kPa. What is the percentage increase when the temperature is raised by 10K at constant volume?
Answer Preview: Calculation. The percentage increase is give…

, Chapter: 16 -Problem: 1 >> Which of the following molecules may be polar: CIF3, O3, H2O2?
Answer Preview: CIF 3 and O 3 are molecules that have polar bon…

, Chapter: 4 -Problem: 16 >> Figure 4B.1 gives a schematic representation of how the chemical potentials of the solid, liquid, and gaseous phases of a substance vary with temperature. All have a negative slope, but it is unlikely that they are truly straight lines as indicated in the illustration. Derive an expression for the curvatures (specifically, the second derivatives with respect to temperature) of these lines. Is ther
Answer Preview: The curvature of a line is determined by the second derivative of the line with respect to temperatu…

, Chapter: 8 -Problem: 11 >> For a particle in a rectangular box with sides of length L1=L and L2=2L, find a state that is degenerate with the state n1=n2=2. Degeneracy is normally associated with symmetry; why, then, are these two states degenerate?
Answer Preview: The two states are degener ate because they have the same e…

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, Chapter: 15 -Problem: 10 >> The vibrational wavenumber of Br2 is 323.2 cm?1. Evaluate the vibrational partition function explicitly (without approximation) and plot its value as a function of temperature. At what temperature is the value within 5 per cent of the value calculated from the approximate formula?
Answer Preview: The vibrational partition function of Br2 is Qvib i eEi kBT where Ei is …

, Chapter: 3 -Problem: 3 >> Calculate the change in entropy when 100 kJ of energy is transferred reversibly and isothermally as heat to a large block of copper at (i) 0 °C, (ii) 50 °C.
Answer Preview: Entropy change kJ U Entropy Change J K TR TM TR TM 1 564 Entropy ch…

, Chapter: 21 -Problem: 4 >> Calculate the entropy of activation for a collision between two structureless particles at 300K, taking M=65 gmol?1 and ?=0.35nm2.
Answer Preview: Calculation. The entropy of activation is given by; S* = R ln(P/P_0) where R is the …

, Chapter: 15 -Problem: 2 >> Suggest a physical interpretation of the relation between equilibrium constant and the partition functions of the reactants and products in a reaction.
Answer Preview: In a chemical reaction the equilibrium constant is related to the partition functions of …

, Chapter: 2 -Problem: 2 >> Why is the heat capacity at constant pressure of a substance normally greater than its heat capacity at constant volume?
Answer Preview: The heat capacity at constant press…

, Chapter: 21 -Problem: 2 >> For a pair of electron donor and acceptor, ket=2.02×105 s?1 when d=1.11nm and ket=4.51×104 s?1 when r=1.23nm. Assuming that ?rG? and ?ER are the same in both experiments, estimate the value of ?.
Answer Preview: Calculation. The rate constant, k, is given by; k = …

, Chapter: 16 -Problem: 1 >> Calculate the molar energy required to reverse the direction of an H2O molecule located 100pm from a Li+ ion. Take the magnitude of the dipole moment of water as 1.85 D.
Answer Preview: The molar energy required to reverse the direction of the water molecule is …

, Chapter: 2 -Problem: 1 >> Describe two calorimetric methods for the determination of enthalpy changes that accompany chemical processes.
Answer Preview: Solution 1 The two calorimetric methods which are used to measure the enthalpy changes are A Con…

, Chapter: 21 -Problem: 2 >> In what sense is electron transfer at an electrode an activated process?
Answer Preview: In order for electron transfer to occur at an electrode, t…

, Chapter: 16 -Problem: 3 >> Phenylalanine (Phe, 4) is a naturally occurring amino acid. What is the energy of interaction between its phenyl group and the electric dipole moment of a neighbouring peptide group? Take the distance between the groups as 4.0nm and treat the phenyl group as a benzene molecule. The dipole moment of the peptide group is ? =2.7 D and the polarizability volume of benzene is ??=1.04×10?29m3.
Answer Preview: The energy of interaction between the phenyl group and the electric dipole moment of the p…

, Chapter: 1 -Problem: 8 >> Derive an expression for ?vn?1/n from the Maxwell–Boltzmann distribution of speeds. You will need standard integrals given in the Resource section.
Answer Preview: Solution Some data about gas molecules in a box The probability density …

, Chapter: 3 -Problem: 7 >> The molar heat capacity of chloroform (trichloromethane, CHCl3) in the range 240K to 330K is given by Cp,m/(JK?1mol?1)=91.47+7.5×10?2 (T/K).
Answer Preview: Thorough calculation and explanation The molar heat capacity of chloro…

, Chapter: 22 -Problem: 4 >> The LEED pattern from a clean unreconstructed (110) face of a metal is shown below. Sketch the LEED pattern for a surface that was reconstructed by tripling the horizontal separation between the atoms.
Answer Preview: LEED is an low energy electron diffraction pattern which is very much surface sensitive. Surface rec…

, Chapter: 14 -Problem: 5 >> Show that the coupling constant as expressed by the Karplus equation passes through a minimum when cos ?=B/4C.
Answer Preview: The Karplus equation is a mathematical expression used to describe the strength of nuclear magn…

, Chapter: 8 -Problem: 6 >> What is the magnitude of the angular momentum of a CH4 molecule when it is rotating with its minimum energy?
Answer Preview: The magnitude of the angular momentum of a CH 4 molecule when it is …

, Chapter: 21 -Problem: 2 >> Calculate the magnitude of the diffusion-controlled rate constant at 298K for a species in (i) water, (ii) pentane. The viscosities are 1.00×10?3 kgm?1 s?1, and 2.2×10?4 kgm?1 s?1, respectively.
Answer Preview: (i) The standard free energy change for the reaction between water and pentane is 8 5775 kJ/…

, Chapter: 14 -Problem: 2 >> For a proton, what are the magnitude of the spin angular momentum and its allowed components along the z-axis? What are the possible orientations of the angular momentum in terms of the angle it makes with the z-axis?
Answer Preview: For a proton what are the magnitude of the spin angular momentum and its allowed components along th…

, Chapter: 4 -Problem: 3 >> How may differential scanning calorimetry (DSC) be used to identify phase transitions?
Answer Preview: Differential scanning calorimetry DSC is a powerful an…

, Chapter: 3 -Problem: 3 >> Estimate the change in the Gibbs energy and molar Gibbs energy of 1.0dm3 of octane when the pressure acting on it is increased from 1.0 atm to 100 atm. The mass density of octane is 0.703 g cm?3.
Answer Preview: The moles of octane at a given pressure can be obtained from its molecul…

, Chapter: 16 -Problem: 6 >> The refractive index of CH2I2 is 1.732 for 656nm light. Its density at 20 °C is 3.32 g cm?3. Calculate the polarizability of the molecule at this wavelength.
Answer Preview: The distortion polarizability ( 0 ) can be calculated as …

, Chapter: 15 -Problem: 16 >> Derive the Sackur–Tetrode equation for a monatomic gas confined to a two-dimensional surface, and hence derive an expression for the standard molar entropy of condensation to form a mobile surface film.
Answer Preview: The SackurTetrode equation for a monatomic gas conf…

, Chapter: 4 -Problem: 2 >> Water is heated from 25 °C to 100 °C. By how much does its chemical potential change?
Answer Preview: The chemical potential of water increases by 75 J mol The chemical pote…

, Chapter: 2 -Problem: 1 >> Use the equipartition principle to estimate the values of ? =Cp/CV for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the expected experimental value at 25 °C?
Answer Preview: Answer and thorough explanation The equipartition principle stat…

, Chapter: 22 -Problem: 4 >> The following data have been obtained for the adsorption of H2 on the surface of 1.00 g of copper at 0 °C. The volume of H2 below is the volume that the gas would occupy at STP (0 °C and 1 atm).Determine the volume of H2 necessary to form a monolayer and estimate the surface area of the copper sample. The density of liquid hydrogen is 0.708g cm?3.  
Answer Preview: To determine the volume of H2 necessary to form a monolayer, we can use the following equation: V …

, Chapter: 14 -Problem: 3 >> Predict the maximum enhancement (as the value of ?) that could be obtained in a NOE observation in which 31P is coupled to protons.
Answer Preview: The answer is 31 The maximum enhancement that can be achieved in an NOE experiment is …

, Chapter: 1 -Problem: 4 >> Explain how the van der Waals equation accounts for critical behaviour.
Answer Preview: A state of matter is critical when there is no temperature difference between the two phase…

, Chapter: 8 -Problem: 4 >> The vibrational frequency of H2 is 131.9THz. What is the vibrational frequency of D2 (D=2H)?
Answer Preview: Thorough Calculation The vibrational frequency of D2 is …

, Chapter: 18 -Problem: 3 >> In this and the following problem we explore further some of the properties of the Fermi–Dirac distribution, eqn 18C.6. For a threedimensional solid of volume V, it turns out that ?(E)=CE1/2, with C=4?V(2me/h2)3/2. Show that at T=0,and deduce that ?(0)=(3N/8?)2/3(h2/2me), where N=N/V, the number density of electrons in the solid. Evaluate ?(0) for sodium (where each atom contributes one electron)
Answer Preview: The Fermi-Dirac distribution is a probability distribution that describes the distribution of electr…

, Chapter: 15 -Problem: 6 >> Evaluate, by explicit summation, the mean vibrational energy of CS2 and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate value? Use the wavenumbers 658 cm?1 (symmetric stretch), 397 cm?1 (bend; two modes), 1535 cm?1 (asymmetric stretch). The A modes are non-degenerate, E modes are doubly degenerate, and T modes are triply
Answer Preview: Evaluation The mean vibrational energy of CS2 is given by E hnu 1 ehnu kT 1 where nu wavenumber h P…

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, Chapter: 17 -Problem: 1 >> A one-dimensional polymer chain consists of 700 segments, each 0.90nm long. If the chain were ideally flexible, what would be the r.m.s. separation of the ends of the chain?
Answer Preview: The r m s. separation of the ends of the chain is given by; d = sqrt((…

, Chapter: 15 -Problem: 2 >> Use the information in Exercise 15E.3(a) to calculate the electronic contribution to the molar Gibbs energy of Cl atoms at (i) 500K and (ii) 900K. Data in Exercise 15E.3(a)The ground level of Cl is 2P3/2 and a 2P1/2 level lies 881 cm?1 above it. Calculate the electronic contribution to the heat capacity of Cl atoms at (i) 500K and (ii) 900K.
Answer Preview: Calculation The ground level of Cl is 2P3 2 and a 2P1 2 level …

, Chapter: 8 -Problem: 4 >> Determine the values of ?x=(?x2???x?2)1/2 and ?p=(?p2???p?2)1/2 for the ground state of(a) A particle in a box of length L(b) An harmonic oscillator. Discuss these quantities with reference to the uncertainty principle.
Answer Preview: Thorough calculation and explanation For a particle in a box of length L we have …

, Chapter: 18 -Problem: 3 >> From the data in Table 18B.2 determine the radius of the smallest cation that can have (i) sixfold and (ii) eightfold coordination with the Cl? ion. Data in Table 18B.2 Transcribed Image Text: Li+(4) 59 Na+(6) 102 K+(6) 138 Rb+(6) 149 Cs+(6) 167 Be²+(4) 27 Mg²+ (6) 72 Ca²+ (6) 100 Sr²+(6) 116 Ba²+(6
Answer Preview: To determine the radius of the smallest cation that can have sixfold and eightfold coordination with …

, Chapter: 16 -Problem: 3 >> Acetic acid vapour contains a proportion of planar, hydrogen bonded dimers (2). The apparent dipole moment of molecules in pure gaseous acetic acid has a magnitude that increases with increasing temperature. Suggest an interpretation of this observation.  Transcribed Image Text: H 2
Answer Preview: Explanation The dipole moment of a molecule is a measure of the electric charge distribution …

, Chapter: 3 -Problem: 7 >> Derive an expression for the molar entropy of a monatomic solid on the basis of the Einstein and Debye models and plot the molar entropy against the temperature (use T/? in each case, with ? the Einstein or Debye temperature). Use the following expressions for the temperature-dependence of the heat capacities: Use mathematical software to evaluate the appropriate expressions.
Answer Preview: First let s derive the expression for the molar entropy based on the Einstein model The Einstein mod…

, Chapter: 21 -Problem: 5 >> For the gas phase reaction A+A?A2, the experimental rate constant, kr , has been fitted to the Arrhenius equation with the pre-exponential factor A=4.07×105 dm3 mol?1 s?1 at 300K and an activation energy of 65.43 kJmol?1. Calculate ?‡S, ?‡H, ?‡U, and ?‡G for the reaction.
Answer Preview: Calculation. The rate constant, kr , is given by; kr = A exp(Ea/RT) where A is the pre-exponential …

, Chapter: 15 -Problem: 2 >> Describe how the mean energy of a system composed of two levels varies with temperature.
Answer Preview: The mean energy of a system composed of two levels …

, Chapter: 21 -Problem: 2 >> Discuss the relationship between the saddle-point energy and the activation energy of a reaction.
Answer Preview: The saddle point energy is the highest energy that the reactants can achieve while sti…

, Chapter: 14 -Problem: 1 >> Consider the following series of molecules: benzene, methylbenzene, trifluoromethylbenzene, benzonitrile, and nitrobenzene in which the substituents para to the C atom of interest are H, CH3, CF3, CN, and NO2, respectively.(a) Use the computational method of your choice to calculate the net charge at the C atom para to these substituents in this series of organic molecules.(b) It is found empirica
Answer Preview: a The net charge at the C atom para to these substituents in this series of organic molecules can be calculated using various computational methods su…

, Chapter: 4 -Problem: 15 >> Combine the ‘barometric formula’, p=?p0e?a/H, where H=?8 km, for the dependence of the pressure on altitude, a, with the Clausius–Clapeyron equation, and predict how the boiling temperature of a liquid depends on the altitude and the ambient temperature. Take the mean ambient temperature as 20 °C and predict the boiling temperature of water at 3000m.
Answer Preview: Answer and thorough explanation The barometric formula is p p0ea H where p i…

, Chapter: 3 -Problem: 2 >> Discuss the relationship between the thermodynamic and statistical definitions of entropy.
Answer Preview: Entropy is a thermodynamic property that measures the amount of disorder in a system The higher the …

, Chapter: 22 -Problem: 1 >> In some catalytic reactions the products adsorb more strongly than the reacting gas. This is the case, for instance, in the catalytic decomposition of ammonia on platinum at 1000 °C. As a first step in examining the kinetics of this type of process, show that the rate of ammonia decomposition should follow in the limit of very strong adsorption of hydrogen. Start by showing that when a gas J adsor
Answer Preview: To start, we need to derive an expression for the fraction of uncovered sites when a gas J adsorbs very strongly. Let be the fraction of sites covered …

, Chapter: 14 -Problem: 6 >> In a liquid, the dipolar magnetic field averages to zero: show this result by evaluating the average of the field given in eqn 14B.15.  Data in eqn 14B.15. Transcribed Image Text: Bu nuc Y???? 4ntR -(1-3cos²0)m (14B.15)
Answer Preview: Eqn 14B 15 gives the dipolar magnetic field caused by a nuclear magnetic moment in a liquid …

, Chapter: 8 -Problem: 13 >> Suppose that the junction between two semiconductors can be represented by a barrier of height 2.0 eV and length 100pm. Calculate the transmission probability of an electron with energy 1.5 eV.
Answer Preview: The transmission probability of an electron with energy 1 5 eV is 0 0357 This can …

, Chapter: 17 -Problem: 3 >> Define the terms in, and identify the limits of the generality of, the following expressions:(a) Rc=Nl,(b) Rrms=N1/2l,(c) Rrms=(2N)1/2l,(d) Rrms=N1/2lF,(e) Rg=N1/2l,(f) Rg=(N/6)1/2l,(g) Rg=(N/3)1/2l.
Answer Preview: (a) Rc=Nl, where N is the number of poles in the machine. Rc=2N1/2lF. Rrms=N1/2l, where N is the number of poles in the machine. (b) Rrms=N1/2lF. Rrms…

, Chapter: 15 -Problem: 3 >> The bond length of O2 is 120.75pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300K.
Answer Preview: Calculations The rotational partition function of a diato…

, Chapter: 2 -Problem: 3 >> Identify varieties of additional work.
Answer Preview: You can find additional work or freelancing opportunities in many places These includ…

, Chapter: 21 -Problem: 2 >> Describe the role of the encounter pair in the cage effect.
Answer Preview: A pair of reactants end up in the same solvent cage, where …

, Chapter: 14 -Problem: 3 >> The hyperfine coupling constant in ·CH3 is 2.3mT. Use the information in Table 14D.1 to predict the splitting between the hyperfine lines of the spectrum of ·CD3. What are the overall widths of the hyperfine spectra in each case? Data in Table 14D.1  Transcribed Image Text: Nuclide 1? 2H 14N 19F Iso
Answer Preview: To predict the splitting between the hyperfine lines of the spectrum of CD3 we can us…

, Chapter: 8 -Problem: 6 >> Calculate the values of ?x3? and ?x4? for a harmonic oscillator by using the relations in Table 8B.1. Data in Table 8B.1. Transcribed Image Text: V 0 1 2 3 4 5 6 H?(y) 1 2y 4y²-2 8y³-12y 16y¹-48y²+12 32y5-160y³+120y 64y6-480y¹+720y² - 120
Answer Preview: Answer The values of x3 and …

, Chapter: 18 -Problem: 2 >> Calculate the scattering factor for a hydrogenic atom of atomic number Z in which the single electron occupies (a) the 1s orbital, (b) the 2s orbital. Plot f as a function of (sin ?)/?.
Answer Preview: Calculations. The scattering factor for a hydrogenic atom o…

, Chapter: 16 -Problem: 2 >> Draw examples of the arrangements of electrical charges that correspond to monopoles, dipoles, quadrupoles, and octupoles. Suggest a reason for the different distance dependencies of their electric fields.
Answer Preview: Monopoles have a single charge dipoles have two charges that are equal and …

, Chapter: 8 -Problem: 8 >> What are the most probable displacements of a harmonic oscillator with v=1?
Answer Preview: The most probable displacements of a harmonic oscillator …

, Chapter: 17 -Problem: 2 >> Distinguish between elastic and plastic deformation.
Answer Preview: When energy goes into changing the shap…

, Chapter: 14 -Problem: 8 >> What are the relative population differences of 19F spin states in spectrometers operating at 60MHz and 450MHz at 25 °C?
Answer Preview: Question Description What are the relative population differences of 19F spin states in spe…

, Chapter: 1 -Problem: 10 >> Given that the density of air at 0.987bar and 27°C is 1.146 kg m?3,calculate the mole fraction and partial pressure of nitrogen and oxygen assuming that(i) Air consists only of these two gases,(ii) Air also contains 1.0 mole percent Ar.
Answer Preview: The mole fraction of a gas is the number of m oles of that gas divided by the total number …

, Chapter: 2 -Problem: 1 >> In 2006, the Intergovernmental Panel on Climate Change (IPCC) considered a global average temperature rise of 1.0–3.5 °C likely by the year 2100, with 2.0 °C its best estimate. Predict the average rise in sea level due to thermal expansion of sea water based on temperature rises of 1.0 °C, 2.0 °C, and 3.5 °C given that the volume of the Earth’s oceans is 1.37×109 km3 and their surface area is 361×
Answer Preview: Answer and thorough explanation The approximate rise in sea level due to thermal expansion of sea …

, Chapter: 21 -Problem: 4 >> Consider a reaction with an attractive potential energy surface. Discuss how the initial distribution of reactant energy affects how efficiently the reaction proceeds. Repeat for a repulsive potential energy surface.
Answer Preview: Answer. If the potential energy surface is attractive, the re…

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, Chapter: 4 -Problem: 3 >> What is the maximum number of phases that can be in mutual equilibrium in a two-component system?
Answer Preview: answer There are a maximum of three phases that can be in mutual equilibrium in a two component syst…

, Chapter: 9 -Problem: 2 >> Compute the wavelength, frequency, and wavenumber of the n?=?2???n=?1 transition in He+.
Answer Preview: Thorough calculation and explanation The wavelength …

, Chapter: 17 -Problem: 3 >> The following table lists the glass transition temperatures, Tg, of several polymers. Discuss the reasons why the structure of the monomer unit has an effect on the value of Tg. Transcribed Image Text: Polymer Poly (oxymethylene) Structure -(OCH?),- T/K 198 Polyethene Poly(vinyl chloride) -(CH?CH?)-
Answer Preview: The structure of the monomer unit has a significant effect on the glass transition temperature (Tg) …

, Chapter: 14 -Problem: 1 >> Suppose that the FID in Fig. 14C.5 was recorded in a 400MHz spectrometer, and that the interval between maxima in the oscillations in the FID is 0.12s. What is the Larmor frequency of the nuclei and the spin–spin relaxation time? Data in Fig. 14C.5 Transcribed Image Text: Signal AAA Time, t
Answer Preview: The Larmor frequency is f B 2 where is the gyromagnetic rat…

, Chapter: 3 -Problem: 4 >> Two empirical equations of state of a real gas are as follows:Evaluate (?S/?V)T for each gas. For an isothermal expansion, for which kind of gas (also consider a perfect gas) will ?S be greatest? Explain your conclusion.   Transcribed Image Text: RT a van der Waals: p=V-b V m m RTe-a/RTVm Dieterici:
Answer Preview: For the van der Waals gas we have S V p V T p T V S V RT Vm b Vm 2 bVm a RT Vm 2 …

, Chapter: 21 -Problem: 4 >> Discuss the significance of the steric P-factor in the RRK model.
Answer Preview: The RR K model is a model used in physical chemistry to predict the rate of a ch…

, Chapter: 14 -Problem: 1 >> What are the relative values of the chemical shifts observed for nuclei in the spectrometers mentioned in Exercise 14A.9a in terms of (i) ? values, (ii) frequencies? Data in Exercise 14A.9aWhat magnetic field would be required in order to use an EPR X-band spectrometer (9GHz) to observe 1H-NMR and a 300MHz spectrometer to observe EPR?
Answer Preview: Calculation The relative values of the chemical shif…

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, Chapter: 21 -Problem: 1 >> Describe in outline the formulation of the Eyring equation.
Answer Preview: The Eyring equation is a statistical mechanics equation that describes th…

, Chapter: 15 -Problem: 11 >> Calculate the vibrational partition function of CS2 at 500K given the wavenumbers 658 cm?1 (symmetric stretch), 397 cm?1 (bend; two modes), 1535 cm?1 (asymmetric stretch).
Answer Preview: The vibrational partition function of CS2 is Qv…

, Chapter: 9 -Problem: 1 >> An electron in the ground-state He+ ion undergoes a transition to a state described by the wavefunction R4,1(r)Y1,1(?,?).(a) Describe the transition using term symbols.(b) Compute the wavelength, frequency, and wavenumber of the transition.(c) By how much does the mean radius of the electron change due to the transition?
Answer Preview: a The transition is from the 1s state to the 4p state b The wavelength is given …

, Chapter: 22 -Problem: 2 >> What approximations underlie the formulation of the Langmuir and BET isotherms?
Answer Preview: The Lang mu ir is other m assumes that each ads or ption site on the surface of …

, Chapter: 16 -Problem: 2 >> Plot the magnitude of the electric dipole moment of hydrogen peroxide as the HeOeOeH (azimuthal) angle ? changes from 0 to 2?. Use the dimensions shown in 1. Transcribed Image Text: H 97 pm O 149 pm 1
Answer Preview: To plot the magnitude of the electric dipole moment of hydrogen peroxide as the HeOeOeH angle change…

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, Chapter: 9 -Problem: 10 >> Locate the radial nodes and nodal planes of each of the 3p orbitals of a hydrogenic atom of atomic number Z. To locate the angular nodes, give the angle that the plane makes with the z-axis.
Answer Preview: The radial nodes are located at the points where the radial wave …

, Chapter: 17 -Problem: 7 >> By what percentage does the radius of gyration of a one-dimensional polymer chain increase (+) or decrease (?) when the persistence length changes from l (the bond length) to 5.0 per cent of the contour length? What is the percentage change in volume of the coil?
Answer Preview: Answer and explanation. The radius of gyration of …

, Chapter: 16 -Problem: 1 >> Describe the process of condensation.
Answer Preview: Condensation is the process of water vapor turning ba…

, Chapter: 4 -Problem: 1 >> What is the physical reason for the fact that the chemical potential of a pure substance decreases as the temperatures is raised?
Answer Preview: The physical reason for this is that the entropy of the substance increases as the temperature is r…

, Chapter: 2 -Problem: 3 >> When 3.0mol O2 is heated at a constant pressure of 3.25 atm, its temperature increases from 260K to 285K. Given that the molar heat capacity of O2 at constant pressure is 29.4 J K?1 mol?1, calculate q, ?H, and ?U.
Answer Preview: Answer 467 J Q U q W Q H W H is the internal energy change of O2 Given that the internal energy of O…

, Chapter: 21 -Problem: 7 >> What is the effective resistance at 25 °C of an electrode interface when the overpotential is small? Evaluate it for 1.0 cm2 (i) Pt,H2|H+, (ii) Hg,H2|H+ electrodes.
Answer Preview: The effective resistance at 25 C of an electrode interface when the overpotential is small i…

, Chapter: 15 -Problem: 5 >> Account for the temperature and volume dependence of the entropy of a perfect gas in terms of the Boltzmann distribution.
Answer Preview: The entropy of a perfect gas can be explained in terms of the Bolt z mann distribution …

, Chapter: 1 -Problem: 12 >> Evaluate numerically the fraction of molecules with speeds in the range 100ms?1 to 200ms?1 at 300K and 1000K.
Answer Preview: So

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