- In some catalytic reactions the products adsorb more strongly than the reacting gas. This is the case, for instance, in the catalytic decomposition of ammonia on platinum at 1000 °C. As a first step
- Account for the dependence of catalytic activity of a surface on the strength of chemisorption, as shown in Fig. 22B.8.Data in Fig. 22B.8 Sticking probability,
- A monolayer of N2 molecules is adsorbed on the surface of 1.00 g of an Fe/Al2O3 catalyst at 77K, the boiling point of liquid nitrogen. Upon warming, the nitrogen occupies 3.86 cm3 at 0 °C and
- Distinguish between the following adsorption isotherms: Langmuir, BET, Temkin, and Freundlich. Indicate when and why each is likely to be appropriate.
- The volume of oxygen gas at 0 °C and 104 kPa adsorbed on the surface of 1.00 g of a sample of silica at 0 °C was 0.286 cm3 at 145.4Torr and 1.443 cm3 at 760Torr. What is the value of Vmon?
- The following data are for the chemisorption of hydrogen on copper powder at 25 °C. Confirm that they fit the Langmuir isotherm at low coverages. Then find the value of α for the adsorption
- Drawing from knowledge you have acquired through the text, describe the advantages and limitations of each of the microscopy, diffraction, and ionizations techniques designated by the acronyms AFM,
- What approximations underlie the formulation of the Langmuir and BET isotherms?
- The following data have been obtained for the adsorption of H2 on the surface of 1.00 g of copper at 0 °C. The volume of H2 below is the volume that the gas would occupy at STP (0 °C and 1
- The LEED pattern from a clean unreconstructed (110) face of a metal is shown below. Sketch the LEED pattern for a surface that was reconstructed by tripling the horizontal separation between the
- A certain solid sample adsorbs 0.44mg of CO when the pressure of the gas is 26.0 kPa and the temperature is 300K. The mass of gas adsorbed when the pressure is 3.0 kPa and the temperature is 300K is
- To appreciate the distance dependence of the tunnelling current in scanning tunnelling microscopy, suppose that the electron in the gap between sample and needle has an energy 2.0 eV smaller than the
- C. Huang and W.P. Cheng (J. Colloid Interface Sci. 188, 270 (1997)) examined the adsorption of the hexacyanoferrate(III) ion, [Fe(CN)6]3−, on γ-Al2O3 from aqueous solution. They modelled the
- A solid in contact with a gas at 12 kPa and 25 °C adsorbs 2.5mg of the gas and obeys the Langmuir isotherm. The enthalpy change when 1.00mmol of the adsorbed gas is desorbed is +10.2 J. What is the
- The following data were obtained for the extent of adsorption, s, of acetone on charcoal from an aqueous solution of molar concentration, c, at 18°C: Which isotherm fits this data best,
- In a study relevant to automobile catalytic converters, C.E. Wartnaby et al. (J. Phys. Chem. 100, 12483 (1996)) measured the enthalpy of adsorption of CO, NO, and O2 on initially clean platinum (110)
- Discuss how the collision theory of gases builds on the kinetic– molecular theory.
- Calculate the collision frequency, z, and the collision density, Z, in ammonia, R=190pm, at 30 °C and 120 kPa. What is the percentage increase when the temperature is raised by 10K at constant
- Distinguish between a diffusion-controlled reaction and an activationcontrolled reaction. Do both have activation energies?
- Describe in outline the formulation of the Eyring equation.
- The interaction between two diatomic molecules is described by an attractive potential energy surface. What distribution of vibrational and translational energies among reactants and products is most
- Show that the intensities of a molecular beam before and after passing through a chamber of length L containing inert scattering atoms are related by I=I0e−NσL, where σ is the collision
- For a pair of electron donor and acceptor at 298K, Het(d)=0.04 cm−1, ΔrG⦵ =−0.185 eV and ket=37.5 s−1. Estimate the value of the reorganization energy.
- Describe the various models of the electrode–electrolyte interface.
- How might collision theory change for real gases?
- If the cumulative reaction probability were independent of energy, what is the temperature dependence of the rate constant predicted by the numerator of eqn 21D.6? Data in eqn 21D.6
- Describe the role of the encounter pair in the cage effect.
- Calculate the magnitude of the diffusion-controlled rate constant at 298K for a species in (i) water, (ii) pentane. The viscosities are 1.00×10−3 kgm−1 s−1, and 2.2×10−4 kgm−1 s−1,
- How is femtosecond spectroscopy used to examine the structures of activated complexes?
- When the reaction in Exercise 21C.1(a) occurs in a dioxane/ water mixture which is 30 per cent dioxane by mass, the rate constant fits kr=(7.78×1014)e−(9134K)/T dm3 mol−1 s−1 near 30 °C.
- In a molecular beam experiment to measure collision cross-sections it was found that the intensity of a CsCl beam was reduced to 60 per cent of its intensity on passage through CH2F2 at 10µTorr, but
- What role does tunnelling play in electron transfer?
- For a pair of electron donor and acceptor, ket=2.02×105 s−1 when d=1.11nm and ket=4.51×104 s−1 when r=1.23nm. Assuming that ΔrG⦵ and ΔER are the same in both experiments, estimate the
- Discuss the relationship between the saddle-point energy and the activation energy of a reaction.
- In what sense is electron transfer at an electrode an activated process?
- A useful strategy for the study of electron transfer in proteins consists of attaching an electroactive species to the protein’s surface and then measuring ket between the attached species and an
- Explain the physical origin of the kinetic salt effect. What might be the effect of the relative permittivity of the medium?
- The gas phase association reaction between F2 and IF5 is first order in each of the reactants. The energy of activation for the reaction is 58.6kJ mol−1. At 65 °C the rate constant is
- Explain why the rate constant decreases as the reaction becomes more exergonic in the inverted region.
- Determine the effect that increasing the overpotential from 0.50V to 0.60V has on the current density in the electrolysis of 1.0m NaOH(aq), which is 1.22mAcm−2 at 0.50V and 25 °C. Take α=0.50.
- Discuss the significance of the steric P-factor in the RRK model.
- How do kinetic isotope effects provide insight into the mechanism of a reaction?
- Calculate the entropy of activation for a collision between two structureless particles at 300K, taking M=65 gmol−1 and σ=0.35nm2.
- Consider a reaction with an attractive potential energy surface. Discuss how the initial distribution of reactant energy affects how efficiently the reaction proceeds. Repeat for a repulsive
- For the gas phase reaction A+A→A2, the experimental rate constant, kr , has been fitted to the Arrhenius equation with the pre-exponential factor A=4.07×105 dm3 mol−1 s−1 at 300K and
- Consider the unimolecular decomposition of a nonlinear molecule containing five atoms according to RRK theory. If P=3.0×10−5, what is the value of E*/E?
- Use the Debye–Hückel limiting law to show that changes in ionic strength can affect the rate of reaction catalysed by H+ from the deprotonation of a weak acid. Consider the mechanism: H+ + B→P,
- Suppose that an energy of 250 kJmol−1 is available in a collision but 200 kJmol−1 is needed to break a particular bond in a molecule with s=10. Use the RRK model to calculate the steric P-factor.
- What is the effective resistance at 25 °C of an electrode interface when the overpotential is small? Evaluate it for 1.0 cm2 (i) Pt,H2|H+, (ii) Hg,H2|H+ electrodes.
- Distinguish between the four levels of structure of a macromolecule: primary, secondary, tertiary, and quaternary.
- Refer to Fig. 14B.14 and use mathematical software, a spreadsheet, or the Living graphs on the web site of this book to draw a family of curves showing the variation of 3JHH with ϕ for which
- Use the equipartition theorem to estimate the constant-volume molar heat capacity of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.
- What is the significance and importance of the principle of equal a priori probabilities?
- Evaluate, by explicit summation, the mean vibrational energy of CCl4 and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate
- The refractive index of CH2I2 is 1.732 for 656nm light. Its density at 20 °C is 3.32 g cm−3. Calculate the polarizability of the molecule at this wavelength.
- A one-dimensional polymer chain consists of 700 segments, each 0.90nm long. If the chain were ideally flexible, what would be the r.m.s. separation of the ends of the chain?
- Distinguish between stress and strain.
- Calculate the change in molar entropy when the ends of a one dimensional polyethene chain of molar mass 65 kgmol−1 are moved apart by 1.0nm.
- Use mathematical software to reproduce the features in Fig. 17C.6.Data in Fig. 17C.6. Fraction present as micelles 0.4 0.3 0.2 0.1 0 N = 3 N=30 (magnified x 10) 2 4 6 Total number of surfactant
- Distinguish between a sol, an emulsion, and a foam. Provide examples of each.
- Consider the thermodynamic description of stretching rubber. The observables are the tension, t, and length, l (the analogues of p and V for gases). Because dw=tdl, the basic equation is dU=TdS+tdl.
- Develop an expression for the fundamental vibrational frequency of a one-dimensional random coil that has been slightly stretched and then released. Evaluate this frequency for a sample of polyethene
- The following table lists the glass transition temperatures, Tg, of several polymers. Discuss the reasons why the structure of the monomer unit has an effect on the value of Tg. Polymer
- Distinguish between elastic and plastic deformation.
- Calculate the restoring force when the ends of a one-dimensional polyethene chain of molar mass 65 kgmol−1 are moved apart by 1.0nm at 20 °C.
- Suggest reasons why different techniques produce different molar mass averages.
- What are the consequences of there being partial rigidity in an otherwise random coil?
- Deduce the relation 〈ri2〉 = Nl2 for the mean square distance of a monomer from the origin in a freely jointed chain of N units each of length l.
- Distinguish between the melting temperature and the glass transition temperature of a polymer.
- Deduce an expression for the radius of gyration of a three-dimensional freely-jointed chain (eqn 17A.6).Data in eqn 17A.6 1/2 R₂-(N), Rg = 1 6 Three-dimensional random coil Radius
- What effect is the inclusion of cholesterol likely to have on the transition temperatures of a lipid bilayer?
- Define the terms in, and identify the limits of the generality of, the following expressions:(a) Rc=Nl,(b) Rrms=N1/2l,(c) Rrms=(2N)1/2l,(d) Rrms=N1/2lF,(e) Rg=N1/2l,(f) Rg=(N/6)1/2l,(g) Rg=(N/3)1/2l.
- In an ultracentrifugation experiment at 20 °C on bovine serum albumin the following data were obtained: ρ =1.001 g cm−3, vs=1.112 cm3 g−1, ω/2π=322Hz,Evaluate the molar mass of the sample.
- What is the probability that the ends of a polyethene chain of molar mass 65 kgmol−1 are 10nm apart when the polymer is treated as a one dimensional freely jointed chain?
- Describe the mechanism of electrical conductivity in conducting polymers.
- Summarize the Core–Pauling rules and explain how they explain the helical and sheet-like structures of polypeptides.
- What is the probability that the ends of a polyethene chain of molar mass 65 kgmol−1 are between 10.0nm and 10.1nm apart when the polymer is treated as a three-dimensional freely jointed chain?
- Derive expressions for the moments of inertia and hence the radii of gyration of(a) A uniform thin disk,(b) A long uniform rod,(c) A uniform sphere.
- Use the following information and the expression for Rg of a solid sphere quoted in the text (following eqn 17A.6), to classify the given species as globular or rod-like.Data in eqn 17A.6 Serum
- By what percentage does the radius of gyration of a one-dimensional polymer chain increase (+) or decrease (−) when the bond angle between units is limited to 109°? What is the percentage change
- The viscosities of solutions of polyisobutylene in benzene were measured at 23 °C with the following results: Use the information in Table 17D.3 to deduce the molar mass of the polymer.Data in
- By what percentage does the radius of gyration of a one-dimensional polymer chain increase (+) or decrease (−) when the persistence length changes from l (the bond length) to 5.0 per cent of the
- Calculate the packing fraction for equilateral triangular rods stacked as shown in 3. 3
- The radius of gyration of a three-dimensional partially rigid polymer of 1000 units each of length 150pm was measured as 2.1nm. What is the persistence length of the polymer?
- In what respects is the hard-sphere model of metallic solids deficient?
- Rods of elliptical cross-section with semi-minor and major axes a and b are close-packed as shown in 4. What is the packing fraction? Draw a graph of the packing fraction against the eccentricity ε
- Calculate the atomic packing factor for diamond.
- Explain the origin of Davydov splitting in the exciton bands of a crystal.
- Describe the relationship between the space lattice and unit cell.
- Although the crystallization of large biological molecules may not be as readily accomplished as that of small molecules, their crystal lattices are no different. Tobacco seed globulin forms
- Calculate the packing fractions of (i) a primitive cubic unit cell, (ii) a bcc unit cell, (iii) an fcc unit cell composed of identical hard spheres.
- From the data in Table 18B.2 determine the radius of the smallest cation that can have (i) sixfold and (ii) eightfold coordination with the Cl− ion.Data in Table 18B.2
- In this and the following problem we explore further some of the properties of the Fermi–Dirac distribution, eqn 18C.6. For a threedimensional solid of volume V, it turns out that ρ(E)=CE1/2,
- Is arsenic-doped germanium a p-type or n-type semiconductor?
- Distinguish between light-emitting diodes and diode lasers.
- Calculate the scattering factor for a hydrogenic atom of atomic number Z in which the single electron occupies (a) the 1s orbital, (b) the 2s orbital. Plot f as a function of (sin θ)/λ.
- Show that the volume of a monoclinic unit cell is V=abc sin β.
- Calculate the separations of the planes {112}, {110}, and {224} in a crystal in which the cubic unit cell has side 562pm.
- Explore how the scattering factor of Problem 18.2 changes when the actual 1s wavefunction of a hydrogenic atom is replaced by a Gaussian function.Data in Problem 18.2Show that if a substance responds
- Derive an expression for the volume of a hexagonal unit cell.