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All Textbook Solutions for Physical Chemistry

Find limiting forms of equation 20.47 for a k1>>k2 and b k1<<k2.20.59E 20.60E 20.61E 20.62E At room temperature (22C), the rate constant for proton transfer between water molecules in solution is about 11011s1, which is one of the fastest known reactions in a condensed phase. If the activation energy for this process equals one-half of the OH bond strength of 498kJ/mol, what is the pre-exponential factor A for this reaction?Recently, researchers studying the kinetics of metal atom reactions with small gas molecules measured a rate constant for the gas-phase reaction of Co+NOproducts as 9.91012cm3/s at 1153K. If the activation energy of this reaction is 1.9kJ/mol, what is the value of the pre-exponential factor?A reaction has k=1.771061/(Ms) at 25.0C and an activation energy of 2.00kJ/mol. a What order is the reaction? b What is the value of the rate constant at 100C?20.66E 20.67E 20.68E Nitric oxide, NO, is known to break down ozone, O3, by the following bimolecular reaction: NO(g)+O3(g)NO2(g)+O2(g) If the activation energy of this reaction is 10.5kJ/mol and the pre-exponential factor is 7.91011cm3/(mols), a what is the rate constant of this reaction at 298K? b If the ozone concentration were 5.41012mol/cm3 and the NO concentration were 2.01012mol/cm3 conditions that might exist in a high-pollution area, what is the rate of this reaction?a Suggest a mechanism for the bromination of ethane: Br2+CH3CH3CH3CH2Br+HBr b Would you expect that this reaction might go faster or slower than the chlorination of methane? Hint: Consider the strengths of the bonds involved in the initial steps of the mechanism.20.71E 20.72E Determine a rate law for the chlorination of methane assuming that the first step is the rate-determining step.Determine a rate law for the chlorination of methane assuming that the second step is the rate-determining step and that the first step can be approximated by the steady-state approximation. What is the difference between the answer here and the answer for the previous exercise?A proposed mechanism for the gas-phase chlorination of methane is Cl2+CH4CH4Cl+ClCH4ClCH3+HClCH3+Cl2CH3Cl+ClCl+CH4CH3+HCl Suppose the first step is the RDS. What is the expected rate law in terms of the original reactants, Cl2 and CH4? How would you determine if this mechanism might be a potentially correct or, for that matter, a potentially incorrect one?20.76E The nitration of methanol, CH3OH, by nitrous acid is thought to proceed via the following mechanism: CH3OH+H+CH3OH2+CH3OH2+CH3++H2OCH3++NO2CH3NO2 Suppose the first step is the RDS. What is the expected rate law in terms of the original reactants?20.78E Many gas-phase reactions require some inert body, usually represented as M, to absorb or supply energy in a collision in order to proceed. In the spontaneous decomposition of ozone, O3, we can suggest the mechanism O3+MO3*+MO3RDSO2+OO+O32O2 for the overall reaction 2O33O2 In the mechanism, O3* refers to an ozone molecule in some energetically excited state that can react spontaneously to form O2 and O atoms. Determine the rate law of the proposed mechanism in terms of O3 and M, where the second step is the rate-determining step. Will adding an inert gas like Ar to a sample of ozone increase or decrease the rate of the reaction?20.80E Carbonic anhydrase, an enzyme whose substrate is CO2, has a K of 12mM. When the concentration of CO2 is 1.4104M, the rate of reaction between carbonic anhydrase and CO2 is 2.72107mol/s, and when the concentration of CO2 is 2.2104M, the rate is 4.03107mol/s. If the reaction follows Michaelis-Menten kinetics, what is V for this reaction?Show that another form of the Michaelis-Menten equation is rate=V[S]K+[S]20.83E 20.84E 20.85E 20.86E Pyrolysis involves heating compounds to break them into smaller molecules, and typically involves free-radical chain reactions. Pyrolysis of crude oil fractions is a common method of making smaller hydrocarbons from large-chain hydrocarbons. Pyrolysis of ethane, C2H6, forms ethylene and hydrogen gases C2H4 and H2 as the primary products. Suggest a mechanism for this pyrolysis reaction, labeling your reactions as initiation, propagation, and termination steps.20.88E Label the elementary processes for the reaction between H2 and O2 see section 20.7 as initiation, propagation, branching, or termination reactions.20.90E What are the rate laws of mechanisms 1 and 2 for oscillating reactions if the second reactions were the rate-determining steps?Estimate G for an elementary process whose rate constant k is 8.5101M1s1 at 450K.20.93E 20.94E 20.95E For the following two reactions H+Cl2HCl+Cl H+Br2HBr+Br the first reaction has a lower value of A than the second reaction. What can one say about the relative properties of the intermediates HCl2 and HBr2, just from the relative values of A?20.97E 20.98E 20.99E Consider a reaction that has two parallel pathways both first-order to products. Pathway 1, leading to product B, has a rate constant of 1.34105s1. Product C- producing pathway 2 has a rate constant of 6.55104s1. Plot the concentrations of A, B, and C versus time, and determine the time necessary to produce the maximum amount of the kinetically favored product.Consider a set of first-order consecutive reactions ABC. The rate constants are 8.4104s1 and 3.02105s1, respectively. Plot the concentrations of A, B, and C versus time, and determine the time necessary to produce the maximum amount of the intermediate product B.20.102E 21.1E Boron nitride, BN, is a very hard material, harder than diamond if prepared properly. Explain why it has diamond-like properties.21.3E 21.4E Figure 21.35 shows a unit cell of diamond. Identify the atoms that define the unit cell and determine the Bravais lattice of this structure of diamond. How many atoms are in the unit cell? Figure 21.35 The unit cell of diamond. See exercise 21.5.21.6E How many different unit cells can a crystal have if the unit cell a has all 90 angles between its crystal axes; b has all of its unit cell dimensions the same length; c has at least one 90 angle between axes; d has no perpendicular axes or equivalent unit cell dimensions?21.8E 21.9E 21.10E 21.11E 21.12E 21.13E 21.14E 21.15E 21.16E 21.17E 21.18E 21.19E 21.20E 21.21E 21.22E 21.23E 21.24E 21.25E 21.26E 21.27E 21.28E For a simple cubic lattice, what is the ratio of the d spacings for the (100), (110), and (111) planes?21.30E 21.31E Consider Figure 21.21. If the lower rightmost corner of the unit cell were selected arbitrarily as the origin, what would be the Miller indices of the indicated plane? Compare your answer to the solution of Example 21.7.21.33E The aluminum-nickel alloy AlNi has a simple cubic lattice with a unit cell parameter of 2.88A. If X rays having a wavelength of 1.544A were used, at what angles would the X rays be diffracted by a the (100) plane of atoms; b the (110) plane of atoms; c the (210) plane of atoms?21.35E The first two signals from a powdered sample has X rays (=1.47742A) diffracted at angles of 13.48 and 15.62. What type of cubic crystal is it, and what is the unit-cell parameter?21.37E 21.38E 21.39E 21.40E 21.41E 21.42E 21.43E 21.44E 21.45E What is the coordination number in the cesium chloride cubic structure?21.47E Which solid phase that is, which allotrope of carbon is more stable, graphite or diamond? You should consult some of the tables in the thermodynamics section of this text.. Both solid phases exist under normal conditions of pressure and temperature. Explain why this is so, given that one solid phase is more thermodynamically stable than the other. Do their unit cells provide any suggestion for their relative stabilities?21.49E 21.50E Write Born-Haber cycles showing the relationship between the formation reaction and lattice energy definitions of each of the ionic compounds in exercise 21.49. You may need to review the definition of formation reaction from earlier in the text.21.52E 21.53E 21.54E The lattice energy for potassium iodide, KI, is 627.2kJ/mol. If the ionic separation is 3.533A, what is the repulsive range parameter for KI? You will have to determine which Madelung constant to use.21.56E 21.57E 21.58E 21.59E 21.60E 21.61E 21.62E 21.63E 21.64E Using the explanation of unbalanced forces as the source of surface tension, justify why it requires energy to increase the surface area of a liquid. Is there any circumstance in which energy is given off when increasing a liquids surface area?Show that the right side of equation 22.1 has units of work.The text claims that surface tension varies with temperature, but does not say how. Use the data in Table 22.1 to propose a trend in versus T.22.4E 22.5E 22.6E 22.7E Equation 22.6 defines surface tension in terms of Gibbs energy. Borrowing an analogy from chemical potential, we submit that surface tension can also be defined in terms of enthalpy, internal energy, or Helmholtz energy. Write partial derivatives for those definitions.22.9E 22.10E 22.11E 22.12E 22.13E 22.14E 22.15E 22.16E 22.17E 22.18E 22.19E Determine the pressure difference on a droplet of mercury with a surface tension of 480dyn/cm if its radius is a 1.00mm or b 0.001mm.22.21E 22.22E 22.23E 22.24E 22.25E 22.26E 22.27E The Young-Dupr equation, equation 22.16, is difficult to use directly because of the near-impossibility of measuring the surface tension of the liquid-gas interface, /v. However, the form of the Young-Dupr equation in equation 22.17 is useful to help determine what needs to be done to the solid-liquid interface to increase or decrease the wettability of a solid by a liquid. a What would you do to a liquid if you wanted to increase the wettability that is, make cos q as small as possible? b What would you do to a solid if you wanted to decrease the wettability that is, make cos as large as possible?Why are capillary rises and depressions not seen for cylinders with large radii?22.30E 22.31E 22.32E 22.33E 22.34E 22.35E 22.36E 22.37E 22.38E A china cup breaks when the ionic or covalent bonds are broken due to shock, stress, or some other influence. Even if such a cup were broken into two simple pieces, just putting the pieces back together will not make the bonds re-form. Why? We need things like glue because of this phenomenon.Satellites in space often suffer from vacuum welding, in which two metal parts in contact tend to stick together more than expected over a period of time. Why does this phenomenon occur in space and not on Earth?22.41E 22.42E 22.43E Are the following processes examples of homogeneous or heterogeneous catalysis? a Hydrolysis of immiscible ethyl acetate (l) in an aqueous basic solution. b Conversion of NOX gases to N2 and O2 by platinum metal. c Decomposition of atmospheric ozone by NO gas. d Oxidation of ethyl alcohol, C2H5OH, by the enzyme alcohol dehydrogenase, ADH, to acetaldehyde in the body. e Solid-state conversion of C graphite to C diamond by transition metal additives at high pressure.22.45E Early attempts to coat metals with Teflon, poly tetrafluoroethylene, resulted in a polymer layer that peeled off the surface easily. Later attempts gave coatings that were much more durable. What type of adsorption processes are being manifested in either situation? What technical problem had to be solved in order to develop durable coatings?22.47E 22.48E 22.49E

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