Bundle: Physical Chemistry, 2nd + Stude...2nd EditionDavid W. Ball Publisher: Cengage LearningISBN: 9781285257594
Bundle: Physical Chemistry, 2nd + Stude...
Solutions for Bundle: Physical Chemistry, 2nd + Student Solutions Manual
Problem 10.1E:
State the postulates of quantum mechanics introduced throughout the chapter in your own words.Problem 10.3E:
State whether the following functions are acceptable wavefunctions over the range given. If they are...Problem 10.4E:
State whether the following functions are acceptable wavefunctions over the range given. If they are...Problem 10.8E:
The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3...Problem 10.10E:
Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue. a...Problem 10.11E:
Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue....Problem 10.14E:
Using the original definition of the momentum operator and the classical form of kinetic energy,...Problem 10.15E:
Under what conditions would the operator described as multiplication by i the square root of 1 be...Problem 10.16E:
A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate...Problem 10.17E:
Calculate the uncertainty in position, x, of a baseball having mass 250g moving at 160km/hr with an...Problem 10.18E:
For an atom of mercury, an electron in the 1s shell has a velocity of about 58(0.58) of the speed of...Problem 10.19E:
Classically, a hydrogen atom behaves as if it were 74pm across. What is the uncertainty in momentum,...Problem 10.20E:
The largest known atom, francium, has an atomic diameter of 540pm. What is the uncertainty in...Problem 10.21E:
How is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it...Problem 10.22E:
Though not strictly equivalent, there is a similar uncertainty relationship between the observables...Problem 10.23E:
The uncertainty principle is related to the order of the two operators operating on a wavefunction....Problem 10.26E:
For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the...Problem 10.28E:
A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the...Problem 10.32E:
Normalize the following wavefunctions over the range indicated. You may have to use the integral...Problem 10.35E:
For an unbound or free particle having mass m in the complete absence of any potential energy that...Problem 10.39E:
Evaluate the expression for the total energies for a particle having mass m and a wavefunction...Problem 10.41E:
Verify that the following wavefunctions are indeed eigenfunctions of the Schrdinger equation, and...Problem 10.42E:
In exercise 10.41a, the wavefunction is not normalized. Normalize the wavefunction and verify that...Problem 10.45E:
Explain why n=0 is not allowed for a particle-in-a-box.Problem 10.49E:
Carotenes are molecules with alternating CC and C=C bonds in which the electrons are delocalized...Problem 10.50E:
The electronic spectrum of the molecule butadiene, CH2=CHCH=CH2, can be approximated using the one...Problem 10.53E:
Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the...Problem 10.56E:
An official baseball has a mass of 145g. a Assuming that a baseball in New Orleans Superdome width...Problem 10.57E:
Is the uncertainty principle consistent with our description of the wavefunctions of the 1D...Problem 10.60E:
Instead of x=0 to a, assume that the limits on the 1-D box were x=+(a/2) to (a/2). Derive acceptable...Problem 10.61E:
In a plot of ||2, the maximum maxima in the plot is/are called the most probable positions. What...Problem 10.64E:
The average value of radius in a circular system, r, is determined by the expression r=0r4r2dr. a...Problem 10.70E:
Assume that for a particle on a ring the operator for the angular momentum, p, is i(/). What is the...Problem 10.71E:
Mathematically, the uncertainty A in some observable A is given by A=A2A2. Use this formula to...Problem 10.74E:
Verify that the wavefunctions in equation 10.20 satisfy the three-dimensional Schrdinger equation.Problem 10.75E:
An electron is confined to a box of dimensions 2A3A5A. Determine the wavefunctions for the five...Problem 10.76E:
a What is the ratio of energy levels having the same quantum numbers in a box that is 1nm1nm1nm and...Problem 10.77E:
Consider a one-dimensional particle-in-a-box and a three-dimensional particle-in-a-box that have the...Problem 10.82E:
What are x,y, and z for 111 of a 3-D particle-in-a-box? The operators for y and z are similar to the...Problem 10.89E:
Substitute (x,t)=eiEt/(x) into the time-dependent Schrdinger equation and show that it does solve...Browse All Chapters of This Textbook
Chapter 1 - Gases And The Zeroth Law Of ThermodynamicsChapter 2 - The First Law Of ThermodynamicsChapter 3 - The Second And Third Laws Of ThermodynamicsChapter 4 - Gibbs Energy And Chemical PotentialChapter 5 - Introduction To Chemical EquilibriumChapter 6 - Equilibria In Single-component SystemsChapter 7 - Equilibria In Multiple-component SystemsChapter 8 - Electrochemistry And Ionic SolutionsChapter 9 - Pre-quantum MechanicsChapter 10 - Introduction To Quantum Mechanics
Chapter 11 - Quantum Mechanics: Model Systems And The Hydrogen AtomChapter 12 - Atoms And MoleculesChapter 13 - Introduction To Symmetry In Quantum MechanicsChapter 14 - Rotational And Vibrational SpectroscopyChapter 15 - Introduction To Electronic Spectroscopy And StructureChapter 16 - Introduction To Magnetic SpectroscopyChapter 17 - Statistical Thermodynamics: IntroductionChapter 18 - More Statistical ThermodynamicsChapter 19 - The Kinetic Theory Of GasesChapter 20 - KineticsChapter 21 - The Solid State: CrystalsChapter 22 - Surfaces
Sample Solutions for this Textbook
We offer sample solutions for Bundle: Physical Chemistry, 2nd + Student Solutions Manual homework problems. See examples below:
Chapter 1, Problem 1.1EChapter 1, Problem 1.21EThe various properties of gases which can be observed with our oral senses, include pressure,...In many circumstances such as at low temperature and high pressures the gases deviate from the ideal...Chapter 1, Problem 1.38EThe ideal gas law considered the gas molecules a point particles which interact only with their...An ideal gas is denoted as the one in which there are no intermolecular attractive forces or...Chapter 1, Problem 1.51EThe non-ideal gas equation represented as; [p+an2/V2][V–nb]=nRT …(1) In the above equation, [p+...
Chapter 2, Problem 2.1EChapter 2, Problem 2.6EChapter 2, Problem 2.35EIn an adiabatic process, the change in work can be expressed in relationship with change in...Generally, the molar heat capacity of gaseous system is determined at constant volume and can be...Chapter 2, Problem 2.91EGiven, The vibrational partition function is given by Cv (vib) = 11- e-hϑkT Single vibrational...Chapter 3, Problem 3.1EChapter 3, Problem 3.24EChapter 3, Problem 3.32EChapter 3, Problem 3.34EChapter 3, Problem 3.35EChapter 3, Problem 3.56EFor the Carnot cycle, the first and the third step are reversible isothermal processes. On the other...Chapter 4, Problem 4.1EChapter 4, Problem 4.14EChapter 4, Problem 4.16EThe equation 4.18 is shown below. (∂U∂S)V=T Where, • U is the internal energy. • T is the...Chapter 4, Problem 4.36EThe number of moles of water is 1.00 mol. The molar volume is 18.02 cm3 which means that the volume...The Gibbs free energy of mixing of gases is shown below. ΔmixG=RT∑i=1no of gasesnilnxi …(1) Where, •...The formula to calculate Gibb’s free energy of mixing is shown below.- ΔmixG=nRT(xAlnxA+xBlnxB)…(1)...Chapter 5, Problem 5.1EThe given reaction is, 2NO(g)+O2(g)⇌2NO2(g) The expression for K for the given equilibrium is,...Chapter 5, Problem 5.27EThe equilibrium constant for the given reaction can be expressed as the product of the concentration...Chapter 5, Problem 5.35EChapter 5, Problem 5.51EThe equilibrium constant of the reaction is 4.33×10−2. The given balanced chemical reaction is,...Systems which contain only one component are known as one component systems. In an iceberg of pure...Chapter 6, Problem 6.11EChapter 6, Problem 6.25ESublimation is a process in which the substance in a solid state is directly converted into a vapor...Chapter 6, Problem 6.33EAt constant pressure and temperature, the equation is represented as shown below....The phase diagram of water shown in Figure 6.6 is shown below. Figure 1 In the given diagram, the...Chapter 6, Problem 6.70EThe example 7.1 has a system of two components that is ethanol and water. On addition of olive,...The mole fraction of the two components in vapor phase can be calculated by using variables y1 and...The 25.0 g of pentane (C5H12), 45.0 g of hexane (C6H14), and 55.0 g of cyclohexane (C6H12) are mixed...The mole fraction of CCl2F2 was found to be 4.17×10−5 at normal pressure. The mass of CCl2F2 is...Chapter 7, Problem 7.55EThe pressure at high altitudes is low and the water starts boiling below its normal boiling point....Chapter 7, Problem 7.72EThe equation 7.41 can be represented for the vaporization process as shown below....Given temperature 30.0°C and the composition of solution is 0.100 mol of NaCl and 0.900 mol of H2O....Chapter 7, Problem 7.86EChapter 8, Problem 8.1EChapter 8, Problem 8.10EThe given reaction is represented as, MnO2+O2→OH−+MnO4− From Table 8.2, the reduction half reaction...Reason for correct answer: (b) The given chemical equation (b) is represented as, Ca(s)+H+→Ca2++H2...Reason for correct answer: (b) The given chemical equation (b) is represented as, Fe+Ag+→Fe3++Ag...The given reaction is represented as, I2+I−→I3− From Table 8.2, the reduction half reaction of I3−...The given concentration cell is, Fe2+[react]→Fe2+[prod] For a concentration cell, standard electrode...Chapter 8, Problem 8.77EThe expression of force between unit charges of opposite sign in vacuum can be written as follows....Chapter 9, Problem 9.1EChapter 9, Problem 9.13EIt is given that temperature and wavelength is 1000 K and 500 nm respectively. To calculate slope of...Chapter 9, Problem 9.32EChapter 9, Problem 9.35EThe energy of single photon in joules is calculated by the formula, E=hν The formula can be written...The wavenumber in the hydrogen atom spectrum is calculated by the formula, υ¯=RH(1n22−1n12) Where, •...Chapter 10, Problem 10.1EChapter 10, Problem 10.26EFor the probability of the wavefunction the expression is as follows. ∫0∞(NΨ)(NΨ*)=P Where, • N is...The given wavefunction is Ψ=x2. Assume the normalization constant of the wavefunction as N. The...The given wavefunction is Ψ=x. The normalization constant of the given wavefunction is assumed to be...Chapter 10, Problem 10.71EThe formula to calculate energy for an electron confined to a three dimensional box is given below....The formula to calculate energy for 2-D box can be written as given below. E=h28m(nx2a2+ny2b2)...For particle in 3-D box, Ψ111 wavefunction is written as follows. Ψ111=8abcsinπxasinπybsinπzc The...The combined expression for orthogonality and normality of wave functions is given by the equation...Chapter 11, Problem 11.1EThe general wavefunction of harmonic oscillator is expressed as,...The wavefunction Ψ1 of a harmonic oscillator is expressed as, Ψ1=(απ)14⋅(12)12H1(α1/2x)⋅e−αx2/2 The...Chapter 11, Problem 11.40EExplanation: The general equation for the wavefunction in the 3-dimensional rotation is, Ψl,ml=12π...The moment of inertia for the electron in the spherical C60 molecule is 1.12×10−49 kg⋅m2 The energy...Chapter 11, Problem 11.58EChapter 11, Problem 11.67EChapter 11, Problem 11.73EFrom Table 11.4, the equations used to determine five 3d wavefunctions are given below....Chapter 12, Problem 12.1EChapter 12, Problem 12.15EChapter 12, Problem 12.24EChapter 12, Problem 12.44EThe expression for trial function can be written as given below. 〈Etrial〉=∫ϕ*H^ϕdτ∫ϕ*ϕdτ Substitute...The value of S12 is calculated as follows: S12=e−R/a0(1+Ra0+R23a02) …(1) Where, • a0 is a Bohr’s...The diatomic molecules shown in Figure 12.23 are Li2, Be2, B2, C2, N2, O2, F2 and Ne2. The number of...Chapter 13, Problem 13.1EThe structure of ammonia molecule is, Figure 1 The total coordinates in the given system is 3N,...The symmetry elements present in octahedral symmetry are, E, C3, C2, C4, C2', i, S4, S6, σh and σd....Chapter 13, Problem 13.59EThe formula to calculate the value of χC3 is, χC3=1+2cosθ …(1) Substitute the value of θ=120° in...The formula to calculate the value of χC2 is, χC2=1+2cosθ+2cos2θ+2cos3θ …(1) Substitute the value of...Chapter 13, Problem 13.71EThe structure of H2S is shown below. Figure 1 The geometry of hydrogen selenide is bent due to...The symmetry elements present in octahedral symmetry are, E, C3, C2, C4, C2', i, S4, S6, σh and σd....The rotational spectrum for a molecule is observed when the rotation of molecule changes the...Chapter 14, Problem 14.2EWater is an asymmetric top molecule. For asymmetric top molecule, Ia<Ib<Ic. The higher of the...The most populated rotational level is calculated by the formula as shown below. Jmax=(kT2B)12…(1)...Chapter 14, Problem 14.45EChapter 14, Problem 14.46EThe energy of a Morse oscillator is calculated by the formula shown below. E=hve(v+12)−hvexe(v+12)2...The structure of cubane is shown below. Figure 1 The point group of cubane is Oh. It is non-linear....The symmetry of CH4 molecule is tetrahedral. The character table for point group Td is shown below....It is assumed that the shape of xenon tetrafluoride is tetrahedral. The character table for point...The formula to energy of rotation (Erot) is given by the formula below. Erot=BJ(J+1)+(C−B)K2 …(1)...Chapter 15, Problem 15.1EChapter 15, Problem 15.4EThe selection rules are shown below. Δl=±1Δml=0,±1 Where, • l represents the azimuthal quantum...Chapter 15, Problem 15.9EThe value of orbital angular momentum (l) for a d electron is 2. The total number of z components of...The value of an azimuthal quantum number, l, for each d electron is 2. The possible term symbols for...Chapter 15, Problem 15.48EThe quantities that are expressed in terms of both magnitude, as well as direction, are known as...In case of 1S→1P transition, the splitting of 1S state does not take place because for this state,...The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are calculated by the...The give ESR spectrum is shown below. Figure 1 The number of spins in the ESR spectrum is shown...The spin value of I(D) or I(2H) is 1. The number of H atom is 2. The spin value of I(N) is 1. The...The z component of nuclear spin is given by the formula shown below. Lz=mIℏ…(1) Where, • mI is the...Combination formula is the possible way of grouping of distinguishable objects into various...The given function ϕ can be expressed as, Φ=∑i=13Ciξi …(1) Where, • ξi represents the ith variable •...The given value of temperature is 1000 K. The standard temperature is 298 K. The given pressure is 1...Chapter 17, Problem 17.56EThe Stirling’s approximation for large value of N is, lnN!≈NlnN−N …(1) NlnN!NlnN−N...The given values of temperatures are 50 K, 100 K, 200 K, 300 K, 500 K and 1000 K. It is given that a...From Appendix 5, The nuclear spin of 12C atoms is 0. The degeneracy for nuclear state is given as,...The term symbol of a diatomic compound is represented as, 2S+1ΛΩ Where, • S represents the total...It is given that the diatomic oxygen has an antisymmetric ground electronic state. The oxygen nuclei...The expression for E is given below as,...Chapter 18, Problem 18.45EThe heat capacity at constant volume for nonlinear polyatomic molecule is given by the formula,...According to science, a postulate is a logical statement. It is assumed to be true without a proof....The root-mean-square speed is calculated by the formula, vrms=3RTM…(1) Where, • R is the universal...The distribution function gx is given by, gx=(m2πkT)1/2e−mvx2/2kT It is given that the value of...It is given that the O2 molecules at 300 K move between 10 m/s and 20 m/s. The average velocity is...The mean free path of collisions between gaseous atoms is given by the formula given below....The mean free path of collisions between gaseous atoms is given by the formula given below....It is given that the helium is at 1.00 atm, that is, standard pressure and 273 K. The molar mass of...The given temperature is 298 K. The molar mass of the helium gas is 4×10−3 kg/mol. The graph of G(v)...The given chemical reaction is represented as, aA+bB→cC+dD The rate of reaction is represented in...Chapter 20, Problem 20.22EIt is given that the thermal decomposition of mercuric oxide follows second order kinetics and the...Chapter 20, Problem 20.27EChapter 20, Problem 20.29EThe given reaction is shown below. A+B⇌C+D The given concentrations and rate are shown below....The given reaction is shown below. ethyl acetate+water→ethyl alcohol+acetic acid The given...The [B]t expression in equation 20.47 is given as follows: [B]t=k1⋅[A]0k2−k1⋅(e−k1t−e−k2t) Where, •...The reaction in Example 20.7 is shown below. 83210Bi→k1t1/2,1 84210Po→k2t1/2,2 82206Pb The...Chapter 20, Problem 20.57EThe given isomerization reaction is, hv+cis-retinal→trans-retinal It is given that the wavelength of...Ionic crystals are composed of cations and anions. The negatively and positively charged ions in the...Chapter 21, Problem 21.34EThe d spacing is calculated by formula as shown below. d=ah2+k2+l2 …(1) Where, • h, k, lare the...Consider a cube having a side of 1 unit. It contains three axis x, y and z that corresponds to...According to Coulomb’s law the potential energy of two oppositely charged particles that are r...The volume of a unit cell is given as, V=a×b×c×(1−cos2α−cos2β−cos2γ+2cosαcosβcosγ) …(1) Where, • a...The wavelength of the given X-ray is 1.5418 A∘. The given lattice parameter is 6.46 A∘. The value of...Chapter 22, Problem 22.1EThe work done to increase the surface area is calculated by the formula shown below. w=γ⋅ΔA …(1)...The Kelvin equation is given by an expression shown below. lnpvaporp°vapor=2γ⋅V¯r⋅RT Where, • pvapor...The structure of a face-centered cubic lattice is shown below. Figure 1 The plane of face-centered...The given temperature is 450 K. The given data of carbon monoxide coverage and pressure in torr is...
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Physical Chemistry
2nd Edition
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PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
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Physical Chemistry
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Student Solutions Manual for Ball's Physical Chemistry, 2nd
2nd Edition
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EBK PHYSICAL CHEMISTRY
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Physical Chemistry
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Essential Math For Physical Chemistry
19th Edition
ISBN: 9781793172747
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ISBN: 9789706863287
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