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Chapter: 6 -Problem: 5 >> Under what conditions is dA ? 0 a condition that defines the spontaneity of a process?
Answer Preview: This is the ca…

, Chapter: 22 -Problem: 19 >> In this problem you will supply the missing steps in the derivation of the formula Esinglet= E1s+ E2s+ J + K for the singlet level of the 1s12s1configuration of He.a. Expand Equation (22.17) to obtain b. Starting from the equations 1 2 Hˆ i1s(i) = E s1s(i) and Hˆ i 2s(i) = E s 2s(i), show that c. Expand the previous equation using the definitionsto obtain the desired result, Esinglet = E1s + E2s
Answer Preview: a The integral can be expressed as the sum of three integrals each containing one of the three o…

, Chapter: 30 -Problem: 40 >> The lowest two electronic energy levels of the molecule NO are illustrated in the text. Determine the probability of occupying one of the higher-energy states at 100, 500, and 2000. K.
Answer Preview: Both the lower and higher energy states are two fold degenerate with an energy spacing of 121 …

, Chapter: 26 -Problem: 35 >> A surface for which the electrostatic potential is negative delineates regions in a molecule that are subject to electrophilic attack. It can help you to rationalize the widely different chemistry of molecules that are structurally similar.Optimize the geometries of benzene and pyridine using the HF/3-21G model and examine electrostatic potential surfaces corresponding to 100 kJ/mol. Describe the
Answer Preview: benzene pyridine The surfaces correspond to regions in benzene and pyridine for which the electrosta…

, Chapter: 23 -Problem: 23 >> If there is a node in ?u, is the electron in this wave function really delocalized? How does it get from one side of the node to the other?
Answer Preview: This same problem arose in discussing the particle in the box and is only a probl…

, Chapter: 11 -Problem: 6 >> The temperature dependence of the potential of a cell is vanishingly small. What does this tell you about the thermodynamics of the cell reaction?
Answer Preview: Because …

, Chapter: 9 -Problem: 7 >> Using the differential form of G, dG = V dP – S dT, show that if ?G mixing = nRT ?i xi ln xi, then ?H mixing = ?V mixing = 0.
Answer Preview: AG mixing nRT x lnx x i aG mixin…

, Chapter: 22 -Problem: 12 >> Show that t1/2 ? 1/[A]n?1 for a reaction that is nth-order in A.
Answer Preview: Solution Here A is the reactant concentration n is the nu…

, Chapter: 36 -Problem: 2 >> For a reaction mechanism to be considered correct, what property must it demonstrate?
Answer Preview: In order to be valid …

, Chapter: 33 -Problem: 47 >> Consider the diagram of a molecular beam apparatus provided in the text.In the design of the apparatus, it is important to ensure that the molecular beam effusing from the oven does not collide with other particles until the beam is well past the skimmer, a device that selects molecules that are traveling in the appropriate direction, resulting in the creation of a molecular beam. The skimmer is l
Answer Preview: P 6 0 10 7 atm P 4 6 10 4 torr …

, Chapter: 17 -Problem: 10 >> Calculate and plot as a function of temperature, in the range 300 K to 1000 K, the equilibrium constant for the reaction CD4(g) + HCl(g) ? CHD3(g) + DCl(g) using the following data (numbers in parentheses are degeneracies): ?(CHD3)/cm?1 = 2993(1), 2142(1), 1003(3), 1291(2), 1036(2); ?(CD4)/cm?1 = 2109(1), 1092(2), 2259(3), 996(3); ?(HCl)/cm?1 = 2991; ?(DCl)/cm?1 = 2145; B(HCl)/cm?1 = 10.59; B(DCl)
Answer Preview: Solution The general equilibrium expression is y z 0 where y and z are the concentrations …

, Chapter: 6 -Problem: 42 >> Consider the equilibrium CO(g) + H2O(g) ???? CO2(g) + H2(g). At 1150. K, the composition of the reaction mixture isa. Calculate KP and ΔGoR at 1150. K.b. Given the answer to part (a), use the ΔHof of the reaction species to calculate ΔGoR at 298.15 K. Assume that ΔHR° is independent of temperature. Transcribed Image Te
Answer Preview: a CO g H 2 O g CO 2 g H 2 g For each co…

, Chapter: 21 -Problem: 19 >> How can you tell if one basis set is better than another in calculating the total energy of an atom?
Answer Preview: The best basi…

, Chapter: 31 -Problem: 17 >> Why is it possible to set the energy of the ground vibrational and electronic energy level to zero?
Answer Preview: The energy of the ground state can …

, Chapter: 27 -Problem: 22 >> XeF4belongs to the D4hpoint group with the following symmetry elements: E, C4, C24, C2, C€²2, C€²€²2, i, S4, S24, σ, 2σ€², and 2σ€²€². Make a drawing similar to Figure 27.1 showing these elements. Transcribed Image Text: ??, SA C2 ?4 ?? ?? C'2 C2 H1 C1 ?2 ?? Sg ?y C1 C2 C13 ?? C15 - C2 C14 C12
Answer Preview: The four fold axis is perpendicular to the plane of t…

, Chapter: 23 -Problem: 26 >> Why do we neglect the bond length in He2when discussing the trends shown in Figure 23.20?Figure 23.20 Transcribed Image Text: O, ?? ??, Liz Be, B2 C2 N, F2 Nez N, ?? ??* 300 200 100 10 15 20 Number of electrons Force constant (N/m) Bond length (pm) Bond energy (eV) Bond order 2. 2. ??
Answer Preview: Because the bond in He is not a chemical bond …

, Chapter: 11 -Problem: 18 >> What is the function of a salt bridge in an electrochemical cell?
Answer Preview: The salt bridge allows curr…

, Chapter: 9 -Problem: 48 >> The dissolution of 7.75g of a substance in 825 g of benzene at 298 K raises the boiling point by 0.575°C. Note that K f = 5.12 K kg mol–1, Kb = 2.53 K kg mol–1, and the density of benzene is 876.6 kg m–3. Calculate the freezing point depression, the ratio of the vapor pressure above the solution to that of the pure solvent, the osmotic pressure, and the molecular weight of the solute.  P= benzene
Answer Preview: AT 0 575 K K 2 53 K kg mol AT Komsolute msolute 7 75 g 0 227 mol kg x 0 …

, Chapter: 22 -Problem: 5 >> A first-order decomposition reaction is observed to have the following rate constants at the indicated temperatures. Estimate the activation energy.  Transcribed Image Text: k/(10-s-) ?/°C 2.46 0 45.1 20.0 576 40.0
Answer Preview: we have K A e Ea RT so ln K2 K1 Ea …

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, Chapter: 35 -Problem: 54 >> Calculate the ratio of rate constants for two thermal reactions that have the same Arrhenius preexponential term, but with activation energies that differ by 1, 10, and 30 kJ/mol.
Answer Preview: a E a E a 1 kJ mol 1 b E a …

, Chapter: 35 -Problem: 13 >> In a parallel reaction in which two products can be formed from the same reactant, what determines the extent to which one product will be formed over another?
Answer Preview: The extent to which a product will be formed or …

, Chapter: 20 -Problem: 19 >> In a Patterson synthesis, the spots correspond to the lengths and directions of the vectors joining the atoms in a unit cell. Sketch the pattern that would be obtained for a planar, triangular isolated BF3 molecule.
Answer Preview: Answer The pattern that would be obtained for a pl…

, Chapter: 6 -Problem: 52 >> You place 3.00 mol of NOCl(g) in a reaction vessel. Equilibrium is established with respect to the decomposition reaction NOCl(g) ? NO(g) + 1/2Cl2 (g).a. Derive an expression for KP in terms of the extent of reaction ? .b. Simplify your expression for part (a) in the limit that ? is very small.c. Calculate ? and the degree of dissociation of NOCl in the limit that ? is very small at 375 K and a pr
Answer Preview: a We next express K P in terms of and P b We now derive an e…

, Chapter: 23 -Problem: 2 >> Consider the molecular electrostatic potential map for the NH3molecule shown here. Is the hydrogen atom (shown as a white sphere) an electron acceptor or an electron donor in this molecule?
Answer Preview: It is an electron donor because t…

, Chapter: 31 -Problem: 15 >> Why is the electronic partition function generally equal to the degeneracy of the ground electronic state?
Answer Preview: For electronic energy levels the spacings between the ground and …

, Chapter: 24 -Problem: 10 >> Why can’t localized orbitals be represented in an MO energy diagram?
Answer Preview: Localized orbitals are not eigenfunct…

, Chapter: 11 -Problem: 47 >> The data in the following table have been obtained for the potential of the cell Pt(s) |H2(g, f = 1atm) HCl(aq, m)|AgCl(s) Ag(s) as a function of m at 25°C.a. Determine E° using a graphical method.b. Calculate γ ± for HCl at m = 0.00100, 0.0100, and 0.100 mol kg–1. Transcribed Image Text: m (m
Answer Preview: Cell reaction 2AgCl s H 2 g 2Ag s 2H aq 2Cl aq In the …

, Chapter: 8 -Problem: 29 >> It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this hypothesis. At 1 atm pressure, ice melts at 273.15 K, 6010. Jmol-1, ?H fusion = the density of ice is 920. kgm?3, and the density of liquid water is 997 kgm?3.a. What pressure is required to lower the melting temperature by 4.0°C
Answer Preview: a The pressure must be increased by 582 bar to lower the melti…

, Chapter: 16 -Problem: 5 >> Calculate the electronic contribution to the molar internal energy at 1900 K for a sample composed of the atoms specified in Exercise 16.4a. Data in  Exercise 16.4a.A certain atom has a threefold degenerate ground level, a non degenerate electronically excited level at 3500 cm?1, and a threefold degenerate level at 4700 cm?1. Calculate the partition function of these electronic states at 1900 K.
Answer Preview: Solution Let the partition function of a threefold degenerate electronic state at 1900K be give…

, Chapter: 36 -Problem: 49 >> Given the limitations of the Langmuir model, many other empirical adsorption isotherms have been proposed to better reproduce observed adsorption behavior. One of these empirical isotherms is the Temkin isotherm: V adsorbed = r ln (sP), where V is the volume of gas adsorbed, P is pressure, and r and s are empirical constants.a. Given the Temkin isotherm provided, what type of plot is expected to g
Answer Preview: a The Temkin isotherm can be manipulated to the form V ads r ln P r ln s Therefore a plot of V ad…

, Chapter: 34 -Problem: 47 >> Boundary centrifugation is performed at an angular velocity of 40,000. rpm to determine the sedimentation coefficient of cytochrome c (M = 13,400 g mol?1) in water at 20°C (? = 0.998 g cm?3,? = 1.002 cP). The following data are obtained on the position of the boundary layer as a function of time:Time (h)…………………xb(cm)0…………………………….4.002.5………………………… 4.115.2………………………….4.2312.3………………………..4.5719.1………………
Answer Preview: a Using the data from the table a plot of in x b x b t 0 versus t can be constructed th…

, Chapter: 6 -Problem: 9 >> Is the equation (?U/?V )T = (?T ? ?P)/? valid for liquids, solids, and gases?
Answer Preview: Yes No assumpti…

, Chapter: 22 -Problem: 22 >> The Doppler broadening in a gas can be expressed aswhere M is the molar mass. For the sodiumtransition, ν0 5.0933 Ã— 1014 s-1. Calculate Δν and Δν /ν0 at 500.K. Transcribed Image Text: Av = (2vo/c)/2 In2(RT/M)) Bp P3/2 ? 3s S1/2
Answer Preview: 2v 2kgI ln 2 m Av C 2x 5 0933 x 1…

, Chapter: 30 -Problem: 31 >> 14N is a spin 1 particle such that the energy levels are at 0 and ±? B?, where ? is the magnetogyric ratio and B is the strength of the magnetic field. In a 4.8-T field, the energy splitting between any two spin states expressed as the resonance frequency is 14.45 MHz. Determine the occupation numbers for the three spin states at 298 K.
Answer Preview: The resonance frequency can be converted to en…

, Chapter: 23 -Problem: 38 >> Calculate the value for the coefficients of the AOs in Example Problem 23.4 for S12 = 0.45. How are they different from the values calculated in that problem for S12 = 0.3? Can you offer an explanation for the changes?
Answer Preview: We first obtain the result Solving for the energies of 1 and 2 bonding and anti bonding MOs respecti…

, Chapter: 10 -Problem: 31 >> Express a± in terms of a+ and a? for (a) Li2CO3(b) CaCl2(c) Na3PO4(d) K4Fe(CN)6. Assume complete dissociation.
Answer Preview: a b c…

, Chapter: 9 -Problem: 9 >> You boil an ethanol–benzene mixture with x ethanol = 0.35. What is the composition of the vapor phase that first appears? What is the composition of the last liquid left in the vessel?
Answer Preview: From Table 9 1 we see that an ethanolbenzene mixture forms a minimum boiling po…

, Chapter: 4 -Problem: 5 >> When benzene freezes at 5.5°C its density changes from 0.879 g cm?3 to 0.891 g cm?3. Its enthalpy of fusion is 10.59 kJ mol?1. Estimate the freezing point of benzene at 1000 atm.
Answer Preview: Using Clapeyron equation deltaP deltaT deltaH fus Tm delltaV fus deltaV fus 78 11 g …

, Chapter: 24 -Problem: 5 >> A typical diffusion coefficient for small molecules in aqueous solution at 25°C is 5 × 10?9 m2 s?1. If the critical reaction distance is 0.4 nm, what value is expected for the second-order rate constant for a diffusion-controlled reaction?
Answer Preview: Solution Critical distance is given as a 2 where diffusion coefficient of the i…

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, Chapter: 36 -Problem: 9 >> How is the standard enzyme kinetic scheme modified to incorporate competitive inhibition? What plot is used to establish competitive inhibition and to determine the kinetic parameters associated with inhibition?
Answer Preview: A competitive inhibitor is a molecule that structurally resembles the substrate of interest but …

, Chapter: 34 -Problem: 7 >> Why is the thermal conductivity for an ideal gas expected to be independent of pressure? Why does the thermal conductivity for an ideal gas increase as T1/2?
Answer Preview: With reference to the equation provided in Question Q34 …

, Chapter: 8 -Problem: 40 >> Use the following vapor pressures of propane given here to calculate the enthalpy of vaporization using a graphical method or a least squares fitting routine. Transcribed Image Text: P (Torr) T (K) 0.01114 100. 120 2.317 140. 73.91 160. 838.0 5054 180. 2.016 x 104 200. 6.046 x 10* 220.
Answer Preview: A least squares fit of ln P …

, Chapter: 22 -Problem: 13 >> Why does one need to put a sample in a vacuum chamber to study it with XPS or AES?
Answer Preview: The electrons will contain the informat…

, Chapter: 30 -Problem: 38 >> A two-level system is characterized by an energy separation of 1.30 × 10?18 J. At what temperature will the population of the ground state be five times greater than that of the excited state?
Answer Preview: a1 1 ao 5 …

, Chapter: 23 -Problem: 22 >> For the case of two H1s AOs, the value of the overlap integral Sab is never exactly zero even at very large separation of the H atoms. Explain this statement.
Answer Preview: This is the case because the amplitude of the …

, Chapter: 11 -Problem: 43 >> Consider the half-cell reaction O2(g) + 4H+ (aq) + 4e– ? 2H2O(l). By what factor are n, Q, E, and Eo changed if all the stoichiometric coefficients are multiplied by the factor two? Justify your answers.
Answer Preview: n is proportional to the number of electrons transferred and increases by …

, Chapter: 8 -Problem: 59 >> Use the vapor pressures of n-butane given in the following table to calculate the enthalpy of vaporization using a graphical method or a least squares fitting routine. Transcribed Image Text: P (Pa) 1000 x 104 1000 x 105 T (°C) -134.3 P (Pa) T (°C) 49.10 1.00 -0.800 -121.9 10.00 -103.9 100.0 -81.10
Answer Preview: A least squares fit of l…

, Chapter: 24 -Problem: 4 >> Discuss the physical origin of the kinetic salt effect.
Answer Preview: The kinetic salt effect in physical chemistry is th…

, Chapter: 25 -Problem: 31 >> Calculate the maximum (zero-current) potential difference of a nickel–cadmium cell, and the maximum possible power output when 100 mA is drawn at 25°C.
Answer Preview: Solution Here we know E d ln A dt d ln 110 3 25 dt 0 693 dt dA …

, Chapter: 35 -Problem: 42 >> For the sequential reactionthe rate constants are kA = 5 × 106 s-1 and kB = 3 × 106 s-1 . Determine the time at which [B] is at a maximum. Transcribed Image Text: ?B- ?C. A-
Answer Preview: For a sequential reaction The maximum occurs …

, Chapter: 35 -Problem: 8 >> What is the difference between a first-order reaction and a second-order reaction?
Answer Preview: In a first order reaction the reaction rate depends linearly on the co…

, Chapter: 8 -Problem: 45 >> The vapor pressure of an unknown solid is approximately given by ln(P/Torr) = 22.413 ? 2211 (K/T), and the vapor pressure of the liquid phase of the same substance is approximately given by ln(P/Torr) = 18.352 ? 1736 (K/T).a. Calculate ?H vaporization and ?H sublimation.b. Calculate ?H fusion.c. Calculate the triple point temperature and pressure.
Answer Preview: a From Equation 8 19 For this specific case H sublimation R 2211 H sublimation 18 4 10 …

, Chapter: 21 -Problem: 28 >> Show that the functions [? (1) ?(2) + ? (1) ? (2)] / ?2 and [? (1)?(2) ? ? (1)? (2)] 2 are eigenfunctions of S?2total What is the eigenvalue in each case?
Answer Preview: Solve this problem by acting on 1 2 and 1 2 separately and combining the resul…

, Chapter: 30 -Problem: 20 >> Consider the energy-level diagrams depicted in the text.a. At what temperature will the probability of occupying the second-energy level be 0.15 for the states depicted in part (a) of the figure?b. Perform the corresponding calculation for the states depicted in part (b) of the figure. Before beginning the calculation, do you expect the temperature to be higher or lower than that determined in par
Answer Preview: a According to the energy level diagram there is one state at 0 and one state at 300 …

, Chapter: 23 -Problem: 8 >> Distinguish between the following concepts used to describe chemical bond formation: basis set, minimal basis set, atomic orbital, molecular orbital, and molecular wave function.
Answer Preview: Basis set The set of AOs used to construct the MOs Min…

, Chapter: 11 -Problem: 25 >> The standard half-cell potential for the reaction O2(g) + 4H+ (aq) + 4e? ? 2H2O(l) is + 1.229 V and 298.15 K. Calculate E for a 0.300-molal solution of H2SO4 for  aO2 = 1.00a. Assuming that the aH+ is equal to the molalityb. Using the measured mean ionic activity coefficient for this concentration from the Data Tables. How large is the relative error if the concentrations, rather than the activiti
Answer Preview: Because Ka for HSO 4 is 0 012 we assume tha…

, Chapter: 9 -Problem: 51 >> Describe the changes you would observe as the temperature of a mixture of phenol and water at point a in Figure 9.21 is increased until the system is at point a€². How does the relative amount of separate phases of phenol and water change along this path?Figure 9.21 Transcribed Image Text: a' L1 L2
Answer Preview: As T increases the number of moles in separate phases decreases u…

, Chapter: 22 -Problem: 2 >> The data below apply to the reaction, (CH3)3CBr + H2O ? (CH3)3COH + HBr. Determine the order of the reaction, the rate constant, and the molar concentration of (CH3)3CBr after 43.8 h. Transcribed Image Text: t/h 0 3.15 6.20 10.00 18.30 30.80 [(CH3)3CBr]/(10-2 mol dm-³) 10.39 8.96 7.76 6.39 3.53 2.07
Answer Preview: FIRST ORDER REACTIONs follow a DIFFERENTIAL EQUATION as thefo…

, Chapter: 21 -Problem: 6 >> The nuclide 244Bk (berkelium) decays by producing ? particles, which capture electrons and form He atoms. Its half-life is 4.4 h. A sample of mass 1.0 mg was placed in a container of volume 1.0 cm3 that was impermeable to ? radiation, but there was also a hole of radius 2.0 µm in the wall. What is the pressure of helium at 298 K, inside the container after(a) 1.0 h,(b) 10 h?
Answer Preview: Solution a The decay of a radioactive nuclide Rh in an O2 molecule can be represented by Here is the …

, Chapter: 35 -Problem: 23 >> Consider the following reaction involving bromophenol blue (BPB) and OH: HBPB(aq) + OH– (aq) ? BPB–(aq) H2O(l)The concentration of HBPB can be monitored by following the absorption of this species and using theBeer–Lambert Law. In this law, absorption, A, and concentration are linearly related.a. Express the reaction rate in terms of the change in absorbance as a function of time.b. Let A0 be the
Answer Preview: a Beers Law states that A b HBPB where is the molar absorptivity of BPB and b is the cell path leng…

, Chapter: 34 -Problem: 25 >> An advertisement for a thermopane window company touts its Kr-filled windows, and states that these windows provide ten times better insulation than conventional windows filled with Ar. Do you agree with this statement? What should the ratio of thermal conductivities be for Kr (? = 0.52 nm2) versus Ar (? = 0.36 nm2)?
Answer Preview: Using the expression for thermal conductivity the ratio of thermal conductiv…

, Chapter: 4 -Problem: 31 >> At 295 k, ?HoR = 131.28 kJ mol-1 for the reaction C (graphite) + H2O(g) ? CO(g), with CP,m = 8.53, 33.58, 29.12, and 28.82 J K-1 mol-1 for graphite. H2O(g), CO(g), and H2(g) respectively. Calculate ?HoR at 240 oC form this information. Assume that the heat capacities are independent of temperature.
Answer Preview: For this problem it …

, Chapter: 6 -Problem: 2 >> The reaction A + B ? C + D is at equilibrium for ? = 0.1. What does this tell you about the variation of G pure with ? ?
Answer Preview: It tells you that G o f for A B is less than t…

, Chapter: 30 -Problem: 35 >> Determine the partition function for the vibrational degrees of freedom of 1 Cl2 (v = 525 cm-1) and calculate the probability of occupying the first excited vibrational level at 300 and 1000 k. Determine the temperature at which identical probabilities will be observed for 1 F2 (v = 917 cm-1).
Answer Preview: For Cl 2 at 300 K For Cl 2 at 1000 K To determine the …

, Chapter: 24 -Problem: 19 >> Are the localized bonding orbitals in Equation (24.13) defined byAndorthogonal? Answer this question by evaluating the integral ˆ« (σ€²)*σ€²€²dÏ„. Transcribed Image Text: GC4. + C2Be2s lo = 201:4 C3 o = 2g1:B +| CzB02= C3
Answer Preview: Because of the symmetry of the molecule Because of the orthogonality of the atomic orbitals on Be Be…

, Chapter: 11 -Problem: 21 >> You are given the following half-cell reactions:Pd2+ (aq) + 2e– ? Pd(s)………………………Eo= = 0.83 VPdCl2–4 (aq) + 2e– ? Pd (s) + 4Cl– (aq)……Eo = 0.64 Va. Calculate the equilibrium constant for the reactionPd2+ (aq) + 4Cl– (aq) ? PdCl2–4(aq)b. Calculate ?Go for this reaction.
Answer Preview: a b G o nFE o 2 96 485 C mol 1 0 19 V 36 7 kJ …

, Chapter: 8 -Problem: 32 >> Use the vapor pressures for hexane given in the following table to estimate the temperature and pressure of the triple point and also the enthalpies of fusion, vaporization, and sublimation. Transcribed Image Text: Phase T (K) 168 P (Pa) 0.1296 Solid Solid Liquid Liquid 178 1.111 1.400 x 104 4.822 x
Answer Preview: To calculate the triple point temperature take subli…

, Chapter: 2 -Problem: 33 >> Given that µ = 0.25 K atm?1 for nitrogen, calculate the value of its isothermal Joule–Thomson coefficient. Calculate the energy that must be supplied as heat to maintain constant temperature when 15.0 mol N2 flows through a throttle in an isothermal Joule–Thomson experiment and the pressure drop is 75 atm.
Answer Preview: T Cp For a diatomic gas C…

, Chapter: 22 -Problem: 28 >> Consider the dimerization A ? A2 with forward rate constant ka and backward rate constant kb. Show that the relaxation time is: Transcribed Image Text: T= 1 kb + 4k? [A]eq
Answer Preview: Solution The forward rate constant for dimerization A A2 is give…

, Chapter: 25 -Problem: 2 >> In a study of the catalytic properties of a titanium surface it was necessary to maintain the surface free from contamination. Calculate the collision frequency per square centimetre of surface made by O2 molecules at(a) 100 kPa,(b) 1.00 Pa and 300 K.Estimate the number of collisions made with a single surface atom in each second. The conclusions underline the importance of working at very low pre
Answer Preview: Solution a The collision frequency per square centimetre of surface made by O2 molecules at 100 kPa …

, Chapter: 36 -Problem: 30 >> Using the preequilibrium approximation, derive the predicted rate law expression for the following mechanism: Transcribed Image Text: ?? A+B- ?P
Answer Preview: The rate expression for the formati…

, Chapter: 33 -Problem: 33 >> Using the distribution of particle translational kinetic energy provided in Problem P33.19, derive expressions for the average and most-probable translational kinetic energies for a collection of gaseous particles. Distribution The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or indi
Answer Preview: The average energy is given by The most probable energy is determined …

, Chapter: 6 -Problem: 61 >> Calculate the degree of dissociation of N2O4 in the reaction N2O4(g) ? 2NO2(g) at 300. K and a total pressure of 1.50 bar. Do you expect the degree of dissociation to increase or decrease as the temperature is increased to 550. K? Assume that ?HoR is independent of temperature.
Answer Preview: We set up the following table We next express K P in terms of n 0 and P We convert t…

, Chapter: 8 -Problem: 44 >> Calculate the vapor pressure of water droplets of radius 1.00 × 10?8 m at 360. K in equilibrium with water vapor. Use the tabulated value of the density and the surface tension at 298 K from Appendix B for this problem.
Answer Preview: We first calculate the vapor pressure of water at 298 K usi…

, Chapter: 30 -Problem: 41 >> Molecular oxygen populating the excited singlet state (1?g) can relax to the ground triplet state (3?), which is the lowest energy state by emitting a 1270-nm photon.a. Construct the partition function involving the ground and excited-singlet state of molecular oxygen.b. What temperature is required to have 10.0% population in the excited-singlet state?
Answer Preview: a The photon energy can be used to determine the energy separation be…

, Chapter: 24 -Problem: 32 >> Predict whether the ground state or the first excited state of CH2should have the larger bond angle on the basis of the Walsh correlation diagram shown in Figure 24.11. Explain your answer. Transcribed Image Text: 1b, 17u 2a, 1b2 1a, tog 180 160 140 120 100 Bond angle 20/degrees Orbit al energy
Answer Preview: CH 2 has six valence electrons In the ground state the HOMO is the 2a …

, Chapter: 10 -Problem: 6 >> Tabulated values of standard entropies of some aqueous ionic species are negative. Why is this statement not inconsistent with the third law of thermodynamics?
Answer Preview: This is possible due to the choice of standard state as S f H aq 0 Although absolut…

, Chapter: 8 -Problem: 62 >> Calculate the vapor pressure of a droplet of benzene of radius 1.25 × 10?8 m at 38.0°C in equilibrium with its vapor. Use the tabulated value of the density and the surface tension at 298 K from Appendix B for this problem.
Answer Preview: Using Equation 8 29 For a very large droplet P0 …

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, Chapter: 16 -Problem: 3 >> Enumerate the ways by which the parameter ? may be identified with 1/kT.
Answer Preview: is the ratio of translational kinetic energy to volume of the mol…

, Chapter: 21 -Problem: 5 >> How many collisions does a single Ar atom make in 1.0 s when the temperature is 25°C and the pressure is(a) 10 atm,(b) 1.0 atm,(c) 1.0 µatm?
Answer Preview: By using the mean freepath 3 Pd cofficient of viscosity …

, Chapter: 35 -Problem: 53 >> A standard “rule of thumb” for thermally activated reactions is that the reaction rate doubles for every 10 K increase in temperature. Is this statement true independent of the activation energy (assuming that the activation energy is positive and independent of temperature)?
Answer Preview: The analysis is best performed numerically …

, Chapter: 34 -Problem: 36 >> The viscosity of H2 at 273 K at 1 atm is 84.0 ? P. Determine the viscosities of D2 and HD.
Answer Preview: The expression for viscosity is Taking the ratio of viscosities for t…

, Chapter: 6 -Problem: 62 >> Oxygen reacts with solid glycylglycine C4H8N2O3 to form urea CH4N2O, carbon dioxide, and water: 3O2(g) + C4H8N2O3(s) ? CH4N2O(s) + 3CO2(g) + 2H2O(l)At T = 298 K and 1.00 atm, solid glycylglycine has the following thermodynamic properties:?Gof = ?491.5 kJ mol?1, ?Hof = ?746.0 kJ mol?1, S° = 190.0 J K?1 mol?1Calculate ?GoR at T = 298.15 K and at T = 310.0 K. State any assumptions that you make.
Answer Preview: We have assumed that the enthalpy of reaction is independent of temperature wh…

, Chapter: 6 -Problem: 51 >> Calculate ?G for the isothermal expansion of 2.25 mol of an ideal gas at 325 K from an initial pressure of 12.0 bar to a final pressure of 2.5 bar.
Answer Preview: Soluiton dG SdT VdP At constant T we consider the re…

, Chapter: 30 -Problem: 6 >> What does a partition function represent? Can you describe this term using concepts from probability theory?
Answer Preview: The partition function is the normalization factor for th…

, Chapter: 23 -Problem: 4 >> Why is it reasonable to approximate H11 and H22 by the appropriate ionization energy of the corresponding neutral atom?
Answer Preview: If the AOs were eigenfunctions of the HartreeFock total ene…

, Chapter: 11 -Problem: 36 >> The cell potential E for the cell Pt(s)|H2(g, aH2 = 1) H+(aq, aH+ = 1)NaCl(aq, m = 0.300) AgCl(s) Ag(s) is +0.260 V. Determine ? Cl? assuming that ? ± = ? Na+ = ?Cl–.
Answer Preview: The half cell and overall reactions are AgCl s e Ag s Cl …

, Chapter: 10 -Problem: 48 >> Calculate ?HR and ?GR for the reaction AgNO3(aq) + KCl(aq) ? AgCl(s) + KNO3(aq).
Answer Preview: AG AG AgC1 s AG K aq AG NOaq AG Ag aq AG NO3 aq …

, Chapter: 3 -Problem: 20 >> Prove that two reversible adiabatic paths can never cross. Assume that the energy of the system under consideration is a function of temperature only.
Answer Preview: Answer Two reversible adiabatic paths can never intersect If they did then there would be heat dissi…

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, Chapter: 25 -Problem: 1 >> Calculate the frequency of molecular collisions per square centimetre of surface in a vessel containing(a) Hydrogen,(b) Propane at 25°C when the pressure is (i) 100 Pa, (ii) 0.10 µTorr.
Answer Preview: The given data shows that H2 molecules are monatomic Hence the collision cross section of the molecu…

, Chapter: 35 -Problem: 59 >> At 552.3 K, the rate constant for the thermal decomposition of SO2Cl2 is 1.02 × 10–6 s–1. If the activation energy is 210. kJ mol–1, calculate the Arrhenius preexponential factor and determine the rate constant at 600. K.
Answer Preview: k552 3 K 1 02 x 10 6s E 210 kJ mol 1 02 x 10 6s Ae 2 1010 Jmol 8 314 Jmol K 552 3 K S A 1 02 x 10 6 …

, Chapter: 34 -Problem: 5 >> How does the root-mean-square diffusion distance vary with the diffusion coefficient? How does this quantity vary with time?
Answer Preview: The root mean square d…

, Chapter: 1 -Problem: 29 >> An athlete at high performance inhales ~3.75 L of air at 1.00 atm and 298 K. The inhaled and exhaled air contain 0.50 and 6.2% by volume of water, respectively. For a respiration rate of 32 breaths per minute, how many moles of water per minute are expelled from the body through the lungs?
Answer Preview: VH 2 O number breaths V air frac…

, Chapter: 6 -Problem: 7 >> Under what conditions is dG ? 0 a condition that defines the spontaneity of a process?
Answer Preview: This is the ca…

, Chapter: 30 -Problem: 13 >> In example problem 30.1, the weights associated with observing 40 heads and 50 heads after flipping a coin 100 times were determined. Perform a similar calculation to determine the weights associated with observing 400 and 500 heads after tossing a coin 1000 times. (Stirling’s approximation will be useful in performing these calculations)
Answer Preview: The outcome that 50 heads and 50 tails are observed is approximately e 21 …

, Chapter: 23 -Problem: 47 >> A surface displaying a contour of the total charge density in LiH is shown here. The molecular orientation is the same as in Problem P23.13. What is the relationship between this surface and the MOs displayed in Problem P23.13? Why does this surface closely resemble one of the MOs?In problem 23.13Images of molecular orbitals for LiH calculated using the minimal basis set are shown here. In these i
Answer Preview: The surface of electron density will be determined by all filled MOs but the unfil…

, Chapter: 11 -Problem: 35 >> By finding appropriate half-cell reactions, calculate the equilibrium constant at 298.15 K for the following reactions:a. 4NiOOH(s) + 2?2O(l) ? 4Ni(OH)2(s) + O2(g)b. 4NO3– (aq)+  4H+ (aq)  ?4NO(g) + 2H2O(l) + 3O2(g)
Answer Preview: a The half cell reactions are The overa…

, Chapter: 8 -Problem: 2 >> Why do the temperature versus heat curves in the solid, liquid, and gas regions of Figure 8.7 have different slopes?Figure 8.7 Transcribed Image Text: ?? AHusion AHaporization Solid Liquid + Solid Liquid Liquid + Gas Gas ?? Temperature
Answer Preview: The slope of these curves are equal to the inv…

, Chapter: 23 -Problem: 7 >> In a photochemical reaction A ? 2 B + C, the quantum efficiency with 500 nm light is 2.1 × 102 mol einstein?1 (1 Einstein = 1 mol photons). After exposure of 300 mmol of A to the light, 2.28 mmol of B is formed. How many photons were absorbed by A?
Answer Preview: A 2B C quantum yield no of moles that react einsteins of radiation adsorbed According to stotiome…

, Chapter: 32 -Problem: 3 >> List the energetic degrees of freedom expected to contribute to the internal energy at 298 K for a diatomic molecule. Given this list, what spectroscopic information do you need to numerically determine the internal energy?
Answer Preview: Translational rotational and vibrational energetic degrees of …

, Chapter: 36 -Problem: 16 >> What is photochemistry? How does one calculate the energy of a photon?
Answer Preview: Photochemistry is the initiation of a chemical …

, Chapter: 35 -Problem: 11 >> What is meant by the rate-determining step in a sequential reaction?
Answer Preview: The rate determining step in a sequential chemical reaction …

, Chapter: 3 -Problem: 34 >> Use the result of Problem P3.10 to derive a formula for (ˆ‚CV /ˆ‚V )Tfor a gas that obeys the Redlich€“Kwong equation of state, Transcribed Image Text: RT 1 a Vm - b VT VVm + b)' T VVm P:
Answer Preview: We use the relationship …

, Chapter: 6 -Problem: 27 >> Is the partial pressure of H2 (g) dependent on T? If so, how will it change as T decreases?H2(g) + Cl2(g) ? 2HCl(g) at equilibrium. Assume ideal gas behavior.
Answer Preview: The reaction is exothermic Th…

, Chapter: 31 -Problem: 13 >> How does the presence of degeneracy affect the form of the total vibrational partition function?
Answer Preview: Degeneracy can be thought of as the case where two or …

, Chapter: 24 -Problem: 14 >> What is the rational for setting Hij = 0 for nonadjacent atoms in the Huckel model?
Answer Preview: The primary ratio…

, Chapter: 10 -Problem: 33 >> Calculate the ionic strength in a solution that is 0.0750 m in K2SO4, 0.0085 m in Na3PO4, and 0.0150 m in MgCl2.
Answer Preview: Total ionic strength L 0 225 0 0510 0 0…

, Chapter: 9 -Problem: 46 >> DNA is capable of forming complex helical structures. An unusual triple-helix structure of poly(dA).2poly(dT) DNA was studied by P. V. Scaria and R. H. Shafer [Journal of Biological Chemistry 266 (1991): 5417] where the intercalation of ethidium bromide was studied using UV absorption and circular dichroism spectroscopy. The following representative data were obtained using the results of this stu
Answer Preview: The Scatchard plot of the data is Best fit to the data by a str…

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, Chapter: 17 -Problem: 2 >> 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: The heat capacity of a molecule is the amount of heat required to raise the temperature of the molecule by one unit The molar heat capacity is the heat capacity per mole of the molecule The specific h…

, Chapter: 32 -Problem: 56 >> Consider the molecule NNO, which has a rotational constant nearly identical to CO2. Would you expect the standard molar entropy for NNO to be greater or less than CO2? If greater, can you provide a rough estimation of how much greater?
Answer Preview: Since NNO has almost exactly the same mass as CO 2 we would expect the t…

, Chapter: 35 -Problem: 62 >> In the limit where the diffusion coefficients and radii of two reactants are equivalent, demonstrate that the rate constant for a diffusion-controlled reaction can be written as: Transcribed Image Text: 8RT ka 37 %3D
Answer Preview: ka 4NA A B …

, Chapter: 34 -Problem: 49 >> A current of 2.00 A is applied to a metal wire for 30.0 s. How many electrons pass through a given point in the wire during this time?
Answer Preview: Current I is equal to the amount of charge Q …

, Chapter: 8 -Problem: 13 >> You get a P–T phase diagram by projecting a P–V–T phase diagram on the P–T plane.
Answer Preview: You get a PT ph…

, Chapter: 6 -Problem: 33 >> Calculate KP at 298 and 490. K for the reaction NO(g) + 1/2O2(g) ? NO2(g) assuming that ?HoR is constant over the interval 298?600. K. Do you expect Kp to increase or decrease as the temperature is increased to 600. K?
Answer Preview: Using equation 6 66 Because H o R 0 K P decreases as …

, Chapter: 31 -Problem: 22 >> At what temperature are there Avogadro’s number of translational states available for O2 confined to a volume of 1000. cm3?
Answer Preview: Since the number of translational states is …

, Chapter: 23 -Problem: 49 >> The bond dissociation energies of the species NO, CF–, and CF+ follow the trend CF+ > NO > CF–. Explain this trend using MO theory.
Answer Preview: The configurations for the molecules are …

, Chapter: 11 -Problem: 41 >> Harnet and Hamer [J. American Chemical Society 57 (1935): 33] report values for the potential of the cell Pt(s) PbSO4(s) H2SO4(aq, a) PbSO4(s) PbO2(s) Pt(s) over a wide range of temperature and H2SO4 concentrations. In 1m H2SO4, their results were described by E(V) = 1.91737 + 56.1 × 10?6 t + 108 × 10?8 t2,where t is the temperature on the Celsius scale. Calculate ?GR, ?HR, and ?SR for the cell re
Answer Preview: a 11C b 35C E V 1 9…

, Chapter: 10 -Problem: 44 >> Calculate I, ? ±, and a± for a 0.0215 m solution of K2SO4 at 298 K. How confident are you that your calculated results will agree with experimental results?
Answer Preview: Not very confident Figures 10 6 and 10 7 show significant deviatio…

, Chapter: 23 -Problem: 4 >> Distinguish between competitive, non-competitive, and uncompetitive inhibition of enzymes. Discuss how these modes of inhibition may be detected experimentally.
Answer Preview: Competitive inhibition is when a molecule binds to an enzyme and competes with the su…

, Chapter: 33 -Problem: 6 >> How does the average speed of a collection of gas particles vary with particle mass and temperature?
Answer Preview: The average speed of a particle in a gas is directly proportion…

, Chapter: 35 -Problem: 65 >> Catalase is an enzyme that promotes the conversion of hydrogen peroxide (H2O2) into water and oxygen. The diffusion constant and radius for catalase are 6.0 × 10–7 cm2 s–1 and 51.2 Å, respectively. For hydrogen peroxide the corresponding values are 1.5 × 10–5 cm2 s–1 and r ? 2.0 Å. The experimentally determined rate constant for the conversion of hydrogen peroxide by catalase is 5.0 × 106 M–1 s–1.
Answer Preview: Using the information provided the diffusion controlled rate constant can be …

, Chapter: 33 -Problem: 42 >> a. The stratosphere begins at 11 km above the Earth’s surface. At this altitude P = 22.6 kPa and T = –56.5oC. What is the mean free path of N2 at this altitude?b. The stratosphere extends to 50 km, where P = 0.085 kPa and T = 18.3oC. What is the mean free path of N2 at this altitude?
Answer Preview: a The collisional cross section of N 2 is 0 43 10 18 m …

, Chapter: 2 -Problem: 18 >> An ideal gas is expanded reversibly and adiabatically. Decide which of q, w, ?U, and ?H is positive, negative, or zero.
Answer Preview: Because the process is …

, Chapter: 8 -Problem: 35 >> You have collected a tissue specimen that you would like to preserve by freeze drying. To ensure the integrity of the specimen, the temperature should not exceed ?5.00°C. The vapor pressure of ice at 273.16 K is 624 Pa. What is the maximum pressure at which the freeze drying can be carried out?
Answer Preview: In Pf P Pf In P Pf P sublima…

, Chapter: 31 -Problem: 55 >> a. In this chapter, the assumption was made that the harmonic oscillator model is valid such that anharmonicity can be neglected. However, anharmonicity can be included in the expression for vibrational energies. The energy levels for an anharmonic oscillator are given byNeglecting zero-point energy, the energy levels become En = hcν̅n €“ hcχ̅ ν̅n2 +... Using the preceding expression, demons
Answer Preview: a Performing a series expansion for the second exponential term and keeping …

, Chapter: 23 -Problem: 33 >> Explain the difference in the appearance of the MOs in Problem P23.13 with those for HF. Based on the MO energies, do you expect LiH+to be stable? Do you expect LiH€“to be stable? Transcribed Image Text: ??* Li2s H1s 20 Lils lo
Answer Preview: The MOs on LiH are more delocalized than on HF so that …

, Chapter: 11 -Problem: 40 >> Determine E° for the reaction Cr2+ (aq) + 2e– ? Cr(s) from the one-electron reduction potential for Cr3+ (aq) and the three-electron reduction potential for Cr3+ (aq) given in Table 11.1.
Answer Preview: Cr aq 3e Cr s Cr aq Cr ag e Cr aq 2e Cr s EC …

, Chapter: 8 -Problem: 58 >> The variation of the vapor pressure of the liquid and solid forms of a pure substance near the triple point are given by ln P solid/Pa = -8750K/T + 34.143 and In P liquid /Pa = -4053K/T + 21.10. Calculate the temperature and pressure at the triple point.
Answer Preview: At the triple point P solid P …

, Chapter: 21 -Problem: 2 >> Provide a molecular interpretation for each of the following processes: diffusion, thermal conduction, electric conduction, and viscosity.
Answer Preview: The process of diffusion can be explained by the random thermal motion of molecules In a gas this is …

, Chapter: 32 -Problem: 20 >> Assume you have an equilibrium expression that involves monatomic species only. What difference in energy between reactants and products would you use in the expression for KP?
Answer Preview: The difference in energy would be z…

, Chapter: 35 -Problem: 55 >> The conversion of NO2 to NO and O2 can occur through the following reaction:NO2(g) ? 2NO(g) + O2(g)The activation energy for this reaction is 111 kJ mol?1 and the preexponential factor is 2.0 × 10?9 M?1 s?1; assume that these quantities are temperature independent.a. What is the rate constant for this reaction at 298 K?b. What is the rate constant for this reaction at the tropopause where T = 225
Answer Preview: a b Assuming that k and E a are temperature i…

, Chapter: 33 -Problem: 37 >> The vapor pressure of various substances can be determined using effusion. In this process, the material of interest is placed in an oven (referred to as a Knudsen cell) and the mass of material lost through effusion is determined. The mass loss (Δm) is given by Δm = ZcAm Δt, where Zcis the collisional flux, A is the area of the aperture through which effusion occurs, m is the particle mass, an
Answer Preview: a b m Z c Am t 1 10 10 26 m 2 s 1 3 14 10 …

, Chapter: 2 -Problem: 16 >> Discuss the following statement: If the temperature of the system increased, heat must have been added to it.
Answer Preview: The statement is incorrect The temperature of th…

, Chapter: 8 -Problem: 39 >> The vapor pressure of a liquid can be written in the empirical form known as the Antoine equation, where A(1), A(2), and A(3) are constants determined from measurements:Starting with this equation, derive an equation giving ΔH Vaporization m as a function of temperature. Transcribed Image Text: A(2
Answer Preview: For a liquidgas equilibriu…

, Chapter: 31 -Problem: 33 >> Calculate the rotational partition function for SO2 at 298 K, where BA = 2.03 cm?1, BB = 0.344 cm–1, and BC = 0.293 cm–1.
Answer Preview: qR r 1 o BB 1 2 1 2 1 BB…

, Chapter: 27 -Problem: 17 >> Use the 3 × 3 matrices for the C2v group in Equation (27.3) to verify the group multiplication table for the following successive operations:a. ??v ???vb. ??v C?2c. C?2 C?2
Answer Preview: a b c Ov 100 0 …

, Chapter: 21 -Problem: 15 >> The angular functions, Θ (θ)Φ(ˆ…), for the one-electron Hartree€“Fock orbitals are the same as for the hydrogen atom, and the radial functions and radial probability functions are similar to those for the hydrogen atom. The contour coloring is explained in the caption to Figure 20.7. The following figure shows:(a) A contour plot in the xy plane with the y axis being the vertical axis,(b) The ra
Answer Preview: a b c This orbita…

, Chapter: 10 -Problem: 38 >> Calculate the probability of finding an ion at a distance greater than 1/? from the central ion.
Answer Preview: u dv uv v du 1 Let u qxr dv …

, Chapter: 9 -Problem: 39 >> An ideal solution is formed by mixing liquids A and B at 298 K. The vapor pressure of pure A is 151 Torr and that of pure B is 84.3 Torr. If the mole fraction of A in the vapor is 0.610, what is the mole fraction of A in the solution?
Answer Preview: Using Equation 9 1…

, Chapter: 22 -Problem: 16 >> The effective rate constant for a gaseous reaction that has a Lindemann–Hinshelwood mechanism is 2.50 × 10?4 s?1 at 1.30 kPa and 2.10 × 10?5 s?1 at 12 Pa. Calculate the rate constant for the activation step in the mechanism.
Answer Preview: The rate of the reaction is Rate k reciprocal h 2 50 104 s 1 exp 3MPa 1 3 kPa …

, Chapter: 32 -Problem: 71 >> In “Direct Measurement of the Size of the Helium Dimer” by F. Luo, C. F. Geise, and W. R. Gentry [J. Chemical Physics 104 (1996): 1151], evidence for the helium dimer is presented. As one can imagine, the chemical bond in the dimer is extremely weak, with an estimated value of only 8.3mJ/mol.a. An estimate for the bond length of 65 Å is presented in the paper. Using this information, determine the
Answer Preview: a Since the helium is 4 He only even J states are allowed therefore the …

, Chapter: 36 -Problem: 15 >> What is an oscillating reaction?
Answer Preview: Oscillating reactions a…

, Chapter: 35 -Problem: 3 >> What is an elementary chemical step, and how is one used in kinetics?
Answer Preview: An elementary reaction step is …

, Chapter: 6 -Problem: 64 >> A sample containing 2.50 mol of an ideal gas at 325 K is expanded from an initial volume of 10.5 L to a final volume of 60.0 L. Calculate ?G and ?A for this process for a. An isothermal reversible pathb. An isothermal expansion against a constant external pressure equal to the final pressure. Explain why ?G and ?A do or do not differ from one another.
Answer Preview: a For the isothermal reversible path b Because A and G are state functions the answ…

, Chapter: 6 -Problem: 44 >> Ca(HCO3)2(s) decomposes at elevated temperatures according to the stoichiometric equation Ca(HCO3)2(s) ???? CaCO3(s) + H2O(g) + CO2(g).a. If pure Ca(HCO3)2(s) is put into a sealed vessel, the air is pumped out, and the vessel and its contents are heated, the total pressure is 0.290 bar. Determine KP under these conditions.b. If the vessel also contains 0.120 bar H2O(g) at the final temperature, wh
Answer Preview: a Ca HCO 3 2 s CaCO 3 s H 2 O g CO 2 g Partial pressure at equilib…

, Chapter: 30 -Problem: 30 >> The 13C nucleus is a spin 1/2 particle as is a proton. However, the energy splitting for a given field strength is roughly 1/4 of that for a proton. Using a 1.45-T magnet as in Example Problem 30.6, what is the ratio of populations in the excited and ground spin states for 13C at 298 K?
Answer Preview: Using the information provided in the exampl…

, Chapter: 27 -Problem: 20 >> Benzene, C6H6, belongs to the D6hgroup. The reducible representation for the vibrational modes isa. How many vibrational modes does benzene have?b. How many of these modes are infrared active and to which representation do they belong?c. Which of the infrared active modes are degenerate in energy and what is the degeneracy for each?d. How many of these modes are Raman active and to which represent
Answer Preview: a Benzene has 3n 6 30 normal modes b The requirement that a normal mode is inf…

, Chapter: 22 -Problem: 40 >> The spectrum of the hydrogen atom reflects the splitting of the 1s2S and 2p2P terms into levels. The energy difference between the levels in each term is much smaller than the difference in energy between the terms. Given this information, how many spectral lines are observed in the 1s2S ? 2p2P transition? Are the frequencies of these transitions very similar or quite different?
Answer Preview: The 2 S term has a single level 2 S 1 2 The 2 P term splits into …

, Chapter: 10 -Problem: 41 >> The equilibrium constant for the hydrolysis of dimethylamine,(CH3)2NH(aq) + H2O(aq) ? CH3NH3+ (aq) + OH?(aq)Is 5.12 × 10?4. Calculate the extent of hydrolysis for a. A 0.210 m solution of (CH3)2NH in water using an iterative calculation until the answer is constant in the second decimal place. b. Repeat the calculation for a solution that is also 0.500 m in NaNO3. Do you need to use an iterative c
Answer Preview: a CH 3 2 NH aq H 2 O l CH 3 NH 3 aq OH aq If y L m 1 01 10 2 mol kg 1 When m 1 …

, Chapter: 8 -Problem: 30 >> Answer the following questions using the P–T phase diagram for carbon sketched below. a. Which substance is denser, graphite or diamond? Explain your answer.b. Which phase is more dense, graphite or liquid carbon? Explain your answer.c. Why does the phase diagram have two triple points? Explain your answer.
Answer Preview: a According to Le Chateliers principle for a given temperature the phase with …

, Chapter: 24 -Problem: 8 >> Discuss how the following factors determine the rate of electron transfer in homogeneous systems: the distance between electron donor and acceptor, and the reorganization energy of redox active species and the surrounding medium.
Answer Preview: The rate of electron transfer in hom ogeneous systems is determined by the distance between the elec…

, Chapter: 25 -Problem: 20 >> Estimate the limiting current density at an electrode in which the concentration of Mg2+ ions is 1.5 mmol dm?3 at 25°C. The thickness of the Nernst diffusion layer is 0.32 mm. The ionic conductivity of Mg2+ at infinite dilution and 25°C is 10.60 mS m2 mol?1.
Answer Preview: Ionic conductance at infinite dilution of Al3 and SO42 io…

, Chapter: 35 -Problem: 44 >> (Challenging) For the sequential reaction in Problem P35.19, plot the concentration of each species for the case where kB = kA. Can you use the analytical expression for [B] in this case?
Answer Preview: When k B k A the analytical expression for B cannot be used since k B k A …

, Chapter: 4 -Problem: 4 >> Does the enthalpy of formation of H2O(l) change if the absolute enthalpies of H2(g) and O2(g) are set equal to 100. kJ mol?1 rather than to zero? Answer the same question for CO2(g). Will ?HoR for the reaction H2O(l) + CO2(g) ? H2CO3(l) change as a result of this change in the enthalpy of formation of the elements?
Answer Preview: The enthalpy of formation for a compound is defined as the change in enthalpy in the reaction in whi…

, Chapter: 3 -Problem: 35 >> The function f (x, y) is given by f (x, y) = xy sin 5x + x2ˆšy in y +3e-2x2cos y. DetermineandObtain an expression for the total differential df. Transcribed Image Text: 2² f af a (af ay ax of ay? ax ? ay ? a (af ?? ?? a (af ?? ?? .Is ay ??( ?? ?
Answer Preview: IS BIS a ay af alaf ax aj ax 5xy cos 5x y sin 5x 12xe 2x xsin 5x xxy y 2…

, Chapter: 8 -Problem: 38 >> Calculate the vapor pressure for a mist of spherical water droplets of radius a. 1.95 × 10?8 m b. 2.25 × 10?6 m at 298 K. The vapor pressure of water at this temperature is 25.2 Torr.
Answer Preview: a Using Equation 8 25 b Using …

, Chapter: 31 -Problem: 54 >> You have in your possession the first vibrational spectrum of a new diatomic molecule, X2, obtained at 1000. K. From the spectrum you determine that the fraction of molecules occupying a given vibrational energy state n is as follows:What are the vibrational energy spacings for X2? Transcribed Image Text:
Answer Preview: To answer this question it is helpful to consider the ratio of pop…

, Chapter: 26 -Problem: 28 >> Molecular orbitals are most commonly delocalized throughout the molecule and exhibit distinct bonding or anti-bonding character. Loss of an electron from a specific molecular orbital from excitation by light or by ionization would, therefore, be expected to lead to distinct changes in bonding and changes in molecular geometry.a. Obtain equilibrium geometries for ethene, formaldimine, and formaldeh
Answer Preview: a Ethene formaldimine formaldehyde Based on the shape and nodal structure of the HOMO the geometry o…

, Chapter: 24 -Problem: 33 >> The occupied MOs of ethene are shown next along with the MO energies. Indicate which AOs are most important in each MO and indicate the relative phases of the AOs. Classify the MOs as localized or delocalized, σ or π bonds, and bonding, nonbonding, or antibonding. Transcribed Image Text: +. -305.5
Answer Preview: The MOs corresponding to the energies 303 56 eV and 303 51eV are the in phase and out of phase combi…

, Chapter: 11 -Problem: 24 >> Determine the half-cell reactions and the overall cell reaction, calculate the cell potential, and determine the equilibrium constant at 298.15K for the cellIs the cell reaction spontaneous as written? Transcribed Image Text: Cd(s) Ca²*(aq. aca: = 0.150)|CT (ag. acr = 0.0100)|Ag(5)|A£C1(s)
Answer Preview: The reaction is spontaneous as written because Q 0 150 0 …

, Chapter: 8 -Problem: 28 >> A cell is roughly spherical with a radius of 20.0 × 10?6 m. Calculate the work required to expand the cell surface if the radius increases by a factor of three. Assume the cell is surrounded by pure water and that T = 298.15 K.
Answer Preview: The surface tension of water is listed i…

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, Chapter: 36 -Problem: 27 >> The hydrogen€“bromine reaction corresponds to the production of HBr(g) from H2(g) and Br2(g) as follows: H2(g) + Br2(g) †’ 2HBr(g). This reaction is famous for its complex rate law, determined by Bodenstein and Lind in 1906:where k and m are constants. It took 13 years for the correct mechanism of this reaction to be proposed, and this feat was accomplished simultaneously by Christiansen, Herzfeld
Answer Preview: a b c Applying the steady sta…

, Chapter: 4 -Problem: 3 >> Is the following statement correct? If not rewrite it so that it is correct. The standard state of water is H2O(g).
Answer Preview: The statement sho…

, Chapter: 3 -Problem: 40 >> Because U is a state function, (?/?V (?U/?T)V)T = (?/?T (

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