Atkins' Physical chemistry11th EditionATKINS, P. W. (peter William), 1940- (author.) Publisher: Oxford University Press,ISBN: 9780198814740
Atkins' Physical chemistry
Solutions for Atkins' Physical chemistry
Browse All Chapters of This Textbook
Chapter 1 - The Properties Of GasesChapter 2 - The First LawChapter 3 - The Second And Third LawsChapter 4 - Physical Transformations Of Pure SubstancesChapter 5 - Simple MixturesChapter 6 - Chemical EquilibriumChapter 7 - Quantum TheoryChapter 8 - Atomic Structure And SpectraChapter 9 - Molecular StructureChapter 10 - Molecular Symmetry
Sample Solutions for this Textbook
We offer sample solutions for Atkins' Physical chemistry homework problems. See examples below:
It is given that the sample of nitrogen gas has constant volume. The given initial pressure of the...The mass density of air at 0.987 bar and 27°C is given as 1.146 kg m−3. The mass of air is...The mass of neon given is equal to 225 mg . The number of moles of neon can be calculated using the...The perfect gas equation is given by the formula as, pV=nRT Where, Ø p is the total pressure. Ø V is...The expression for the distribution of molecular velocity in the x-direction is,...The expression for the velocity of the emerging beam is, vx=K∫0avxf(vx)dvx (1) Where, • K is the...The expression for the Maxwell-Boltzmann distribution is, f(v)=4π(M2πRT)32v2e−Mv22RT The proportion...(i) The expression for the gravitational force, F is given by Newton’s gravitational force law. F=...The molecular distribution of speeds is given by, f(v)=4π(M2πRT)32v2e−Mv22RT Where, • M is the molar...
The pressure of H2 is 1 atm. The temperature of H2 is 25° C. The conversion of given temperature...The pressure of N2 is 1 atm and temperature of N2 is 25° C . The conversion of given temperature...The virial equation of state is, pVm= RT (1+B/Vm+C/Vm2+...) (1) Where, Ø p is the pressure. Ø Vm is...The Virial equation of state in terms of B' is given by the formula as, pVm=RT(1+B'p+C'p2+...) (1)...It is given that the mass of water is 50 g. The temperature is 25 οC. Pressure is 1 atm. The...It is given that the constant-pressure heat capacity of a sample of a perfect gas varies with...It is given that the constant-pressure heat capacity of a sample of a perfect gas varies with...The given reactions are: H2(g)+ Cl2(g) → 2HCl(g) (1) 2H2(g) + O2(g) → 2H2O(g) (2) 4HCl(g) + O2(g) →...The given reactions are: H2(g) + I2(g) → 2HI(g) (1) 2H2(g) + O2(g)→ 2H2O(g) (2) 4HI(g) + O2(g) →...The given reaction is: C(graphite) + H2O(g) → CO(g) + H2(g) (1) The standard enthalpy for the...The given reaction is, C(graphite) + O2(g) → CO2(g) The standard enthalpy of the reaction is, ΔrH°...The given reaction is, N2(g) + 3H2(g) → 2NH3(g) The standard enthalpy of the reaction is, ΔrH° is...The reaction for the combustion of methane is, CH4(g)+2O2(g)→CO2(g)+2H2O(g) The standard enthalpy of...(i) The chemical equation for the combustion reaction of glucose is,...The given temperature of nitrogen gas is 298 K. The initial volume of nitrogen gas is 1.00 dm3. The...The given temperature of argon is 298 K. The initial volume of argon is 1.00 dm3. The initial molar...The expression for one mole of a van der Waals gas is, (p+aVm2)(Vm−b)=RT (1) The above expression is...The thermodynamic definition of entropy is expressed by formula, dS=dqrevT (1) Where, • dS is the...The relation between entropy change of the system, surroundings and the total entropy change is...The relation between entropy change of the system, surroundings and the total entropy change is...According to the first law of thermodynamics, ΔU=q+w For a reversible isothermal process, the...The pressure-volume diagram for the carnot cycle is represented as, Where Stage 1 represents...The work done for isochoric process is zero. Hence, the work done for (II) and (IV) process is zero....Given reaction is- CO2(g)+H2(g)→CO(g)+H2O(g) The values of standard enthalpy of formations are: •...Given reaction is- 12N2(g)+32H2(g)→NH3(g) The values of standard enthalpy of formations are: • The...The heat capacity at low temperature is calculated by the following formula. Cp,m(T)=aT3+bT Divide...The given reaction is, 2CH3CHO(g)+O2(g)→2CH3COOH(l) The standard reaction enthalpy of the reaction...The given reaction is, Zn(s)+Cu2+(aq)→Zn2+(aq)+Cu(s) (1) The standard enthalpy (ΔrHο) for a chemical...The pressure of perfect gas (p) is expressed as, p=nRTV (1) Where n is the number of moles of the...The expression for chemical potential is given as, ΔμΔp=Vm Or Δμ=Vm×Δp (1) Where • Δp is the change...The enthalpy of vaporization is calculated by the Clausius-Clapeyron’s formula....The change in entropy of hexane is calculated by the Trouton’s formula. ΔSvaporization=10.5×R (1)...The Clapeyron equation is shown below. dpdT=ΔvapHTΔVm (1) Where, dpdT is the change in pressure with...The slope of chemical potential against pressure is given by the following formula....The given data for the vapour pressure of nitric acid varies with temperature is written below as,...The Gibbs free energy is calculated by the formula, ΔG=ΔH−TΔS (1) Where, ΔG is the Gibbs free...The expression for the total volume in term of number of moles and partial molar volume of...The partial molar volumes of components of mixture vary with compositions. The nature of molecule...Carbon dioxide is dissolving in water, which is in small amount. Therefore, CO2 acts as a solute in...The entropy of mixing of perfect gases (ΔSmix) is calculated by the formula given below....The data for the mole fraction of methylbenzene (A) in the liquid phase, xA, vapour phase, yA and...The data of mass densities of aqueous solution of CuSO4 is given in the table shown below....The Propionic acid is assumed as component 1 and THP is assumed as component 2. The excess volume is...The equation used to determine the molar mass from osmotic pressure is, Πcmass, J=RTM+(BRTM2)cmass,...The given phase diagrams are shown below as, Figure 1 Figure 2 The region between the liquid phase...The ionic strength (I) of a solution is given by the equation, I=12∑izi2(bi/b°) (1) Where, zi is the...The ionic strength (I) of a solution is given by the equation, I=12∑izi2(bi/b°) (1) Where zi is the...The ionic strength (I) of a solution is given by the equation, I=12∑izi2(bi/b°) (1) The mean...The ionic strength (I) of a solution is given by the equation, I=12∑izi2(bi/b°) (1) The mean...The ionic strength (I) of a solution is given by the equation, I=12∑izi2(bi/bο) (1) The ionic...The data for the vapour pressure of mixture of iodoethane (I) and ethyl ethanoate (E) is given as,...The vapour pressure data for a mixture of benzene (B) and ethanoic acid (E) at 50 °C is given as,...The average number (ν) of small molecule A bound to macromolecule M is given by the expression...Cell I consists of pure solvent while cell II consists of concentrated solution and osmosis occurs...The standard reaction Gibbs energy of a reaction (ΔrGο) is given as, ΔrGο=nPΔfGPο+nRΔfGRο (1) Where,...The given reaction is shown below. N2+3H2→2NH3 The reaction quotient for the given reaction is...For the formation of H2O(s): The formation of H2O(s) at 190 K is shown by the following chemical...The standard Gibbs energy of reaction is expressed as, ΔrGο=ΔrHο−TΔrSο (1) Where, ΔrGο is the...The standard Gibbs energy of reaction is expressed as, ΔrGο=ΔrHο−TΔrSο (1) Where, ΔrGο is the...The decomposition of CH4(g) is represented by the reaction given below. CH4(g)→C(s)+2H2(g) The...The given reaction is shown below. CO2(g)⇌CO(g)+12O2(g) Initially total number of moles is...In the first experiment, the mass of the acetic acid present in the container was 0.0519 g. The...The given cell representation is, Ag(s)|AgBr(s)|KBr(aq, 0.050 mol kg−1)||Cd(NO3)2(aq,0.010 mol...The ionic strength of a salt is expressed as, I=12∑i=1nmizi2 (1) Where, I is the ionic strength of...The given cell is shown below. Zn(s)|ZnCl2(0.0050 mol kg−1)|Hg2Cl2|Hg(l) The cell reaction for this...The cell is given below. Pt|H2(g,pΘ)|NaOH(aq, 0.0100 mol kg−1),NaCl(aq, 0.01125 mol...The number of photons is calculated by using the formula, N=λEhc (1) Where, N is the number of...The energy of quantum is directly proportional to the frequency of radiation Therefore, E=hν (1)...The energy of quantum is directly proportional to the frequency of radiation Therefore, E=hν (1)...The energy of photon is inversely proportional to the wavelength of radiation Therefore, E=hcλ (1)...The energy of photon is inversely proportional to the wavelength of radiation. Therefore, E=hcλ (1)...The formula for Planck’s distribution is, ρ(λ,T)=8πhcλ5(ehc/λkT−1) (1) Where, λ is the wavelength. h...The value of Einstein temperature (θE) is expressed as, θE=hvk (1) Where, h is the Planck’s...The probability that the particle is in between x=4.95 nm and x=5.05 nm, is calculated by the...The probability of finding the particle between x=0 and x=L/2, y=0 and y=L/2 is calculated by the...The value of ψ is given below. ψ(x)=(2aπ)1/4e−ax2 (1) Where, a is a constant. The expectation value...The commutator of the operators is given by the formula shown below. [H^,p^x]=(H^⋅p^x−p^x⋅H^) (1)...The separation between the adjacent energy levels with quantum numbers n and n+1 is given by the...The separation between the adjacent energy levels with quantum numbers n and n+1 is given by the...The expression for translational kinetic energy is given below. Ek=3kT2 (1) Where, k is the...The Schrodinger equation for a particle of mass m in a three dimensional box is shown below....The transmission probability is given by the expression shown below. T=|A'|2|A|2 (1) Where, A and A'...For a diatomic molecule A-B, the vibrational frequency is expressed as, wA−B=(KfμA−B)12 (1) Where,...The formula to calculate vibrational frequency (ν) is given below. ν=12πkfμ (1) Where, kf is force...The energy of the photons is given by the relation given below. E=ℏω (1) Where, ℏ is a constant. ω...The Data table for the wavenumber number of the molecules is shown below....The wavefunction given is as follows. ψ=c1Yl, ml+c2Yl, ml' Apply Λ2 on the wavefunction as shown...The value of l^xl^yf is shown below. l^xl^yf=−ℏ2(y∂∂z−z∂∂y)(z∂f∂x−x∂f∂z) Multiply the parentheses as...The operator l^z in cartesian co-ordinates is expressed as shown below. l^z=ℏi(x∂∂y−y∂∂x) (1) The...The value of Δx is calculated by the following formula. Δx=(〈x2〉−〈x〉2)1/2 (1) The normalized ground...The value of Δx is calculated by the following formula. Δx=(〈x2〉−〈x〉2)1/2 (1) The normalized nth...The given data is shown below. n=3→n=215238 cm−1n=4→n=220571 cm−1n=5→n=223039 cm−1n=6→n=224380 cm−1...The radial distribution function of 3s orbital is shown below. R3,0=12431/2(Zaο)3/2(6−6ρ+ρ2)e−ρ/2...For the p electrons the value of orbital angular momentum l is 1. For p1 electron configuration, the...The wavefunction of 1s orbital is given by the expression shown below. ψ1s=2(14π)1/2(Za0)3/2e−Zr/a0...The normalized wavefunction for hydrogenic 1s (ψ1s) orbital is given below. ψ1s=1πa03/2e−r/a0 The...The number of electrons in He is 2. The electronic configuration of excited state is 1s12s1....The number of electrons in He is 2. The electronic configuration of excited state is 1s13s1....The mass of 4He+ nucleus is 4.00260 u. The mass of 4He+ nucleus in kg is converted as shown below....The term symbol for the He+ is written as shown below. 2S+1LJ..............(1) Where, L is the...The energy level for an atom is given by the expression shown below. En=−hcRHn2 (1) Where, h is...The molecular orbital ψ− is shown below. ψ−=N−(ψA−ψB) (1) Where, ψA is the wavefunction of atom A....The normalized molecular orbital is shown below. ψ1=N(0.88025A−0.356B) (1) Where, N is the...The normalized molecular orbital is shown below. ψ1=N(0.727A+0.144B) (1) Where, N is the...It is given that a small-electron probe having volume 1.00 pm3 is inserted in H2+ molecule-ion in...The elements present in the second period of periodic table are Li, Be, B, C, N, O, F, Ne. Except...The diatomic molecules of elements that belong to period 2 are Li2, Be2, B2, C2, N2, O2, F2 and Ne2....The structure of anthracene is shown below. Figure 1 The total number of carbon atoms in anthracene...The structure of azulene is shown below. Figure 1 The total number of carbon atoms in anthracene is...In CO32− ion 4 atoms are involved in delocalization. Therefore, the secular determinant for the...The expression for the energies Ek of the π molecular orbitals is shown below. Ek=α+2βcos2kπN (1)...The combination of wavefunction given is shown below. ψ=ψA−ψB+ψC−ψD The sign of the wavefunction (ψ)...The staggered form of ethane (CH3CH3) is shown below. Figure 1 The staggered CH3CH3 has a principal...The condition for orthonormality of irreducible representation is given below....The water (H2O) molecule taking two H1s orbital and the four valence orbitals of the O atom are...The character table for the C2v point group is shown below....The character table for D4h point group is given below. E2C4C22C2'2C2"i2S4σh2σv2σd A1g1111111111x2+...The character table of the Oh point group is given below....The structure of anthracene is shown below. Figure 1 The anthracene molecule belongs to the D2h...The give function is 3x2−1. The point group of the cube is Oh. The integration of the given function...The relationship between transmittance and absorption is given as shown below. A=−logT (1)Where, A...The molecule 12C1H335Cl is shown below. Figure 1 The moment of inertia is given by the formula as...The formula to calculate the ratio A/B for transition is given below. AB=8πhv3c3 (1) Where, A is the...The integrated absorption coefficient is calculated by the formula given below. A=12εmaxΔν˜...The inertia of a triatomic linear molecule (ABC) is given by the equation as follows....From the wavenumbers at various transitions, the separation is calculated as follows. 2B˜1(in...The given data for absorption in the microwave spectrum of 16O12CS in GHz is mentioned in the table...The energy of a rigid rotor (EJ) is calculated by the expression given below. EJ=hcB˜J(J+1) (1)...Rotation about any axis perpendicular to C6 may be represented by the rotation of a pseudo-linear...The wavenumber of a molecule is given by the equation shown below. ν˜=12πc(kfmeff)12 (1) Where, kf...The wavenumber of a molecule is given by the equation shown below. ν˜=12πc(kfmeff)12 (1) Where, kf...The expression for vibrational energy levels is shown below. ν˜=(ν+12)ν˜0−(ν+12)2xeν˜0 Where, ν is...The formula to calculate dissociation energy is shown below. D˜0=D˜e−ν˜' (1) Where, D˜0 is the...It is given that in the study of 85Rb1H, the value of wave number is v˜=936.8 cm−1 and xev˜=14.15...The fundamental vibrational wavenumber is given by the expression as shown below. v˜=D˜o Where, v˜...The CC and CH bond length is approximately same in the molecule 12C21H2 (which is C2H2) and 12C22H2...The rotational constant for a diatomic molecule in vibrational state with quantum number v is given...The vibrational wavenumber is given by the position of band centre. In case of carbon monoxide, a...The expression for the calculation of ν˜R(J) is given below....The symmetry elements in CH3Cl are shown below. Figure 1 The structure of CH3Cl is tetrahedral with...The Franck-Condon factor is given by the expression as shown below. |S(υf,υi)|2=(∫ψυ,f*ψυ,idτn)2 (1)...The normalized wavefunction for a one-dimensional box is given below. ψn=2Lsin(nπxL) Where, n is the...The Placzek-Teller relation is shown below. δ=(32B˜kThc)1/2 (1) Where, B˜ is the rotational...Ethanal (CH3CHO) has two types of protons. Therefore, it shows two lines in the NMR spectra, one at...The energies of the nuclear spin in a magnetic field is calculated by the formula shown below....The relative population difference of the nuclei is calculated by the formula shown below....The relative population difference of the nuclei is calculated by the formula shown below....The natural abundance of 13C is 1.108%. The value of γN for 13C is 6.73×107 T−1 s−1. The value of γN...The Karplus equation given is shown below. J3HH=Acos2ϕ+B (1) Where, J is the coupling constant. ϕ is...The Karplus equation for 3JHH is a linear equation in cosϕ and cos2ϕ. The experimentally determined...The Lorentzian function is given by the equation. IL(ω)=SoT21+T22(ω−ωo)2 (1) Where, So is a...The coupling constants of the ESR spectrum of a radical that has two inequivalent protons are 2.11...The given hyperfine interaction of 2s orbital of N atom with nucleus is 55.2 mT. The given isotropic...The two lines collapse into one when the lifetime (τ) is given by the expression below....If the plot of [I]0 against (δν)−1 is a straight line with the slope [E]0Δν and y-intercept −K1,...The expression for the energy of the state with quantum number J is shown below. εJ=hcB˜J(J+1) (1)...The total energy of the sample is 9ε. The total number of molecules in the sample is 9. A table for...The equation for a translational partition function for one-dimensional box is shown below....The electronic partition function is calculated by using the formula shown below. qE=∑jgje−εj/kT (1)...The important quantity in the thermodynamic is partition function that is represented as shown...The mean vibrational energy per mode is given by the expression as shown below. 〈εV〉=hcν˜ehcν˜/kT−1...The mean vibrational energy per mode is given by the expression as shown below. 〈εV〉=hcν˜ehcν˜/kT−1...The partition function in terms of wavenumber is given by the expression as shown below....The molar heat capacity is calculated by using the formula shown below. CV,m/R=f2 (1) The value of f...The molar entropy of a collection of oscillations is expressed by the formula shown below....The given value of fundamental vibrational wavenumber for the ground state of F2−, 2∑u∗, is 450...The given rotational constants for Cl2O2 are B=13109.4, 2409.8 and 2139.7 MHz. The given rotational...The given moment of inertia for C3 are I=39.340muA2∗, 39.032muA2∗ and 0.3082muA2∗ The value of mu is...The given illustration of methanal or formaldehyde is shown below. Figure 1 The positions of the...The molar mass of chlorobenzene is 112.56 g/mol. The constant density, ρ of chlorobenzene is 1.11...The molar polarizations of fluorobenzene vapour are shown below. (1) 70.62 cm3 mol−1=70.62×10−6 m3...The molar mass of trichloromethane is 119.38 g/mol. The value of εο is 8.854×10−12 J−1 C2 m−1. The...The molar mass of methanol is 32.04 g/mol. The value of εο is 8.854×10−12 J−1 C2 m−1. The value of...The two collinear linear quadrupoles which are separated by a distance r are shown below. Figure 1...The two parallel linear quadrupoles which are separated by a distance r are shown below. Figure 1...The positive end of the dipole will lie closer to the negative anion when the H2O molecule...The arrangement of a system containing an O−H group and O group is shown below. Figure 1 The...The probability function for a three dimension flexible chain with radius r is given by the equation...The structure of disk is shown below. Figure 1 The total mass of the disk is given by the expression...The Lennard-Jones potential energy (V) is given by the expression as shown below....The expression for the osmotic pressure (Π) in terms of osmotic virial coefficient B is given below....Given data: a=0.82 nmb= 0.94 nmc= 0.75 nmh= 1, k= 3 and l= 3 The separation of planes in an...First we have to derive the volume of a triclinic unit cell. Then we can take it as the reference to...First we have to derive the volume of a triclinic unit cell. Then we can take it as the reference to...First we have to derive the volume of a triclinic unit cell. Then we can take it as the reference to...As known the trigonometric function as follows, Figure 1 Consider an orthorhombic crystal with edges...Given data: θ=19.076∘,22.171∘,32.256∘λ=154.18 pm Expected reflections: Bravis latticeReflections...The location of the atoms in a bcc unit cell can be depicted as follows Figure 1 Calculation of...Required data to calculate the lattice enthalpy of CaCl(s): rCa+=138 pmrCl−=181 pmd*=34.5...Consider (ΔLL)z is the uniaxial strain, and (ΔLL)x, (ΔLL)y are the transverse strain. (ΔLL)x=(ΔLL)y....Consider (ΔLL)z is the uniaxial strain, and (ΔLL)x, (ΔLL)y are the transverse strain. (ΔLL)x=(ΔLL)y....Inter planar distances corresponds to the shift in reflections can be calculated using Bragg’s...The formula to calculate the rate of effusion is shown below. Rate of effusion=pA°NA2πMRT (1) Where,...The diffusion coefficient of a gas is given by the expression as shown below. D=13(kTσp)(8RTπM)1/2...The diffusion coefficient of a gas is given by the expression as shown below. D=13(kTσp)(8RTπM)1/2...The viscosity of air is calculated by the formula shown below. η=(m3σ)(4RTπM)1/2 (1) Where, R is the...The viscosity of benzene vapour is calculated by the formula shown below. η=(m3σ)(4RTπM)1/2 (1)...The equation for the Kohlrausch’s law is shown below. Λm=Λmo−kc12 (1) Where, Λm is the molar...The drift speed is calculated by the formula shown below. s=uE (1) Where, u is the mobility of ion....The diffusion coefficient is calculated by the formula shown below D=uRTzF (1) Where, u is the...Given equation is: 2NOBr(g) → 2NO(g) + Br2(g) NOBr is decomposed so its partial pressure falls from...The given reaction involves multiple mechanism steps, by adding the entire individual steps gives...Effective rate constant (Lindemann-Hinshelwood mechanism): 1kr = 1ka[A] −−−−−−−(1). Given data is as...The number of photochemical events is the number of decomposed molecules and is given as follows:...For experiments (I): ν = k[complex] ν2ν1 = k[complex1]k[complex]144125 = k(9.22 ×...A + B → Products Integrated rate law for this reaction is: ln([A]o[B][B]o[A]) = ([B]o-[A]o)ktk=rate...A + B → Products Integrated rate law for this reaction is: ln([A]o[B][B]o[A]) = ([B]o-[A]o)ktk=rate...For the first order reaction: ln([A][A]0) = -kt Plot a graph between ln([A][A]0) against t to see if...The stoichiometry of the reaction relates product and reaction concentration as follows: [A] = [A]0...Rate law for the nth order is given below, d[A]dt = −kr[A]n Here, Initial concentration of reactant...Given, 2A+3B→P Rate equation is shown below, Rate = -12d[A]dt = -13d[B]dt = +d[P]dt Rate of change...Given, 2A+B→P Rate equation is shown below, Rate = -12d[A]dt = d[B]dtrate= k[A]2[B]-d[A]dt =...Rate-determining step is the slow step of the reaction. The rate law for the slow reaction is υ = kb...Electron affinity (Eea) for chlorine is given as 230 kJmol-1. Ionization energy (I) of sodium is 496...Given information: Ionization energy values of alkali metals is given as, Na K Rb Cs5.1 eV 4.3 eV...Given information: M = 65 g/molT = 300 Kσ = 0.35 nm2 Entropy of collisions between two particles can...Given information: M = 92 g/molT = 450 Kσ = 0.45 nm2 Entropy of collisions between two particles can...Given information: A = 4.6 x 1012 dm3mol-1s-1T = 298 KEa = 10.0 kJmol-1 Entropy of activation: In...Given information: A = 2.3 x 1013 dm3mol-1s-1T = 298 KEa = 30.0 kJmol-1 Entropy of activation: In...Given information: Frequency factor (A)is given as 4.07 × 105 dm3mol-1s-1. Activation energy (Ea) is...Given information: θ/°C -24.82 -20.73 -17.02 -13.00 -8.95104 × kr/s−1 1.22 2.31 4.39 8.50 14.3 Gibbs...In terms of the LEED pattern, the farther apart the aton1s responsible for the pattern, the closer...Given: T = 300Kp = 100 kPa First using the collision frequency formula the Zw value at 100 kPa is...A(g)⇌A(ads)B(g)⇌B(ads)A(ads)+B(ads) slow→ AB(ads) fast→ AB(g) The rate of the reaction or the rate...A surface-catalyzed unimolecular reaction is one in which an adsorbed molecule undergoes...The zero-current potential of the Fe2+/Fe cathode and overpotential are calculated as, Fe2+ + 2e- →...The zero-current potential of fuel cell operating on hydrogen and oxygen is calculated as, E0 = -Δr...
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8th Edition
ISBN: 9780716774334
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