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All Textbook Solutions for Physical Chemistry

16.1E 16.2E 16.3E 16.4E 16.5E 16.6E 16.7E 16.8E 16.9E 16.10E 16.11E 16.12E 16.13E 16.14E 16.15E 16.16E 16.17E 16.18E 16.19E 16.20E 16.21E 16.22E 16.23E 16.24E 16.25E 16.26E 16.27E 16.28E 16.29E 16.30E 16.31E 16.32E 16.33E 16.34E 16.35E 16.36E 16.37E 16.38E 16.39E 16.40E 16.41E 16.42E 16.43E 16.44E 16.45E a The structure of 2 chloroethanol is usually staggered, as shown in this Newman projection: How many distinct 1HNMR signals would you expect from this molecule? Assume that the OH bond is pointing away from the CC bond. b In some circumstances, 2 chloroethanol can be frozen in an eclipsed structure, whose Newman projection looks like this: How many distinct 1HNMR signals would you expect from this molecule?16.47E 16.48E 16.49E 16.50E 16.51E 16.52E 16.53E 16.54E 16.55E 16.56E A microwave oven emits radiation having a frequency of 2.45GHz. What magnetic field is necessary to see NMR transitions of 119Sn, which has a spin of 12 and a gN value of 2.0823?17.1E 17.2E 17.3E 17.4E 17.5E 17.6E 17.7E 17.8E 17.9E 17.10E 17.11E If the ni values are all the same, a shorthand way of indicating a combination is C(x,y), which is read, How many combinations are there of x distinguishable objects separated into systems, each of which have y things? Evaluate a C(10,2) b C(3,1) c C(6,3) d C(6,2). Hint:You should determine the number of systems you need for each case first.17.13E 17.14E 17.15E 17.16E 17.17E 17.18E 17.19E 17.20E 17.21E 17.22E Explain why q is a constant for a given system at a specified temperature.What is the ratio of ground-state nickel atoms in which E is defined as zero to nickel atoms that are in the first excited state of 201cm1 at 298K? The spectrum of Ni atoms is complicated by the existence of such an excited state. Does your answer explain why? Assume the two states have the same degeneracies.Ti3+ has the following electronic energy levels: idegeneracyE(cm1)04016384.32280378.6 Calculate q by summing the three terms, assuming a temperature of 2000K. Are additional terms needed to get a good value for q?Using the fact that =1/kT, show that equations 17.29 and 17.30 are equivalent.A one-dimensional particle-in-a-box has a length of 1.500108m. Assume that the box is filled with electrons and the temperature is 300.0K. Calculate q for the system.17.28E 17.29E 17.30E 17.31E What is the value of q at absolute zero? Is it the same for all systems?17.33E 17.34E 17.35E 17.36E 17.37E 17.38E 17.39E 17.40E 17.41E 17.42E What change is there in the Sackur-Tetrode equation if N=NA?17.44E 17.45E 17.46E Calculate the thermal de Broglie wavelength of He at 25K and 500K. Are the different values to be expected?17.48E 17.49E 17.50E 17.51E 17.52E 17.53E Use equation 17.56 to determine the change in energy, E, when 1mole of Ar is heated from 298K to 348K at constant volume. Compare this result with the change in energy calculated using massspecific heatchange in temperature. The specific heat of argon is 20.79J/(molK).For an electron that has a velocity of 0.01c where c is the speed of light, at what temperature will its thermal de Broglie wavelength equal its quantum-mechanical de Broglie wavelength? Note that the original de Broglie wavelength is not directly dependent on temperature.Use the Sackur-Tetrode equation to derive the relationship S=Rln(V2/V1) for an isothermal change and S=Cvln(T2/T1) for an isochoric change.17.57E 17.58E 18.1E 18.2E 18.3E 18.4E The following are the first four electronic energy levels of Ti atoms. Energy,cm-1Degeneracy00.00051170.13272386.873936556.863 What is qelect at 3560K, the boiling point of titanium?18.6E 18.7E 18.8E 18.9E 18.10E 18.11E 18.12E 18.13E 18.14E 18.15E 18.16E 18.17E 18.18E 18.19E 18.20E 18.21E 18.22E 18.23E 18.24E 18.25E 18.26E 18.27E 18.28E 18.29E 18.30E 18.31E 18.32E 18.33E What are qnuc and qrot for N2(I=1)? See Table 18.3 for r.The rovibrational spectrum of acetylene, HCCH, shows intensity variations consistent with expected nuclear degeneracies. Would you expect DCCH to show similar intensity variations? Why or why not?18.36E 18.37E 18.38E 18.39E 18.40E 18.41E 18.42E Use equation 18.44 to show that pV=NkT.18.44E Determine E,H,G, and S for CH4 at standard pressure and 25C. equals 12 for methane and the atomization energy of CH4 is 1163kJ/mol. Compare your calculated value of S with the tabulated that is, experimentally determined value in Appendix 2.18.48E 18.49E Calculate the heat capacity of NO2 at 298K and 400K? Data can be found in Table 18.2.18.51E In Chapters 17 and 18 we have derived expressions for the absolute amounts of the energies H and G. However, in tables of thermodynamic data, we always tabulate H and G that is, changes in enthalpy and Gibbs energy. How do you explain this apparent discrepancy?18.55E 18.56E 18.57E 18.58E 18.59E 18.60E 19.1E What is the kinetic energy of a single atom of mercury that has a speed of 200m/s? This is a good speed for Hg atoms at room temperature. What is the kinetic energy of a mole of Hg atoms having that speed?19.3E One mole of Ne atoms confined to a volume of 10.0L has an average velocity of 756m/s. What pressure is exerted by this gas?19.5E 19.6E 19.7E 19.8E 19.9E 19.10E 19.11E Interstellar space can be considered as having 10atoms of hydrogen per cubic centimeter and an average temperature far away from stars of 2.7K. Determine a the pressure of hydrogen in interstellar space and b the average speed of the hydrogen atoms. Compare these answers with values under normal Earth conditions.19.13E SF6 is a gas at room temperature, 295K. What is its root-mean-square speed at that temperature?19.15E 19.16E If relativistic effects were ignored, what temperature is required for hydrogen atoms to have an rms-average speed of 3.00108m/s? What do you think is the potential for actually achieving this temperature?19.18E 19.19E 19.20E 19.21E 19.22E 19.23E 19.24E What is the ratio of vrms/vmostprob for any gas at a given temperature?19.26E 19.27E 19.28E 19.29E 19.30E 19.31E The previous exercise gives an expression for sound, the speed of sound in a gas. Determine the ratios sound/rms, sound/mostprob, and sound/. Which, if any, of these ratios is less than one? What are the physical interpretations of these ratios?19.33E 19.34E 19.35E What must the pressure be if the mean free path of Kr is 1.00cm? Assume d=185pm and T=25.0C.19.37E 19.38E 19.39E Explain why the molecular diameter for argon, at 2.6A, is about the same as that for molecular hydrogen, at 2.4A, even though hydrogen is a much smaller atom than argon.19.41E 19.42E 19.43E A 1.00-mol sample of Xe gas is kept at a temperature of 298K.What volume must it have in order to have an average collision frequency of 1 per second? Assume that the collision diameter is 4.00A.19.45E 19.46E 19.47E 19.48E 19.49E Consider a gas mixture containing equal concentrations of argon and helium. Without performing any calculations, determine which is higher: the number of collisions between helium and helium, the number of collisions between argon and argon, or the number of collisions between helium and argon?The inverse of the collision rate, 1/z, is the average time between collisions of gas particles. Calculate the average time between collisions of an Xe atom in 1.00mol of Xe at STP.19.52E 19.53E 19.54E 19.55E Estimate the rate at which Hg effuses out a hole of area 0.10mm2 at 295K. The vapor pressure of Hg at this temperature is 0.0014mmHg.19.57E Knudsen effusion cells are used to determine vapor pressures of high-temperature materials. For example, a Knudsen cell is filled with tungsten and heated to 4500K in a vacuum. Measurements show that the cell loses mass assumed to be W vapor at the rate of 2.113gramsperhour out of a hole that is 1.00mm2 in area. Calculate the vapor pressure of W at 4500K.19.59E 19.60E 19.61E 19.62E 19.63E 19.64E 19.65E 19.66E 19.67E 19.68E 19.69E 19.70E 19.71E 19.72E 19.73E 20.1E The oxidation-reduction reaction between iron metal and aqueous permanganate ions in acidic solution is 16H+(aq)+5Fe(s)+2MnO4(aq)2Mn2+(aq)+5Fe2++8H2O(l) At some temperature, the reaction proceeds at such a rate that 1.00 millimole of H+ is consumed in 2 minutes 33.8 seconds. What is the invariant rate of this reaction in units of moles per second?The oxidation-reduction reaction between iron metal and aqueous permanganate ions in acidic solution is 16H+(aq)+5Fe(s)+2MnO4(aq)2Mn2+(aq)+5Fe2++8H2O(l) At some temperature, the reaction proceeds at such a rate that 1.00 millimole of H+ is consumed in 2 minutes 33.8 seconds. What is the rate of this reaction in units of moles of each reactant per second and moles of each product per second? How do these answers differ from the answer in the previous problem?The rate of the reaction HOCH2CH2NO2+2HNO2NO2CH2CH2NO2+2H2O is 0.045molHNO2/s. What are the rates of appearance and disappearance with respect to the other three substances?For a certain reaction between NO and O2, the rate law is rate=k[NO]2[O2] What is the order with respect to NO? With respect to O2? What is the overall order?For a reaction between SO2 and Cl2, the rate law is rate=k[Cl2] What is the order with respect to SO2? With respect to Cl2? What is the overall order?Consider the chemical reaction A+B+Cproducts Determine the order with respect to A,B,andC, and construct the complete rate law including the value of the rate law constant from the following experimental data. Initial rate (M/s) [A],M [B],M [C],M 6.76106 0.550 0.200 1.15 9.82107 0.210 0.200 1.15 1.68106 0.210 0.333 1.15 9.84107 0.210 0.200 1.77 For the chemical reaction Mn2+(aq)+H2O2(aq)products The following data are collected: [Mn2+],M [H2O2],M Initial rate (M/s) 0.740 0.556 3.43102 0.219 0.556 3.01103 0.740 0.662 4.86102 Determine the order with respect to Mn2+ and H2O2, and construct the complete rate law, including the value of the rate law constant.Explain how a species might be part of a rate law but not part of a balanced chemical reaction.Refer to Example 20.2 and explain whether any useful information can be obtained by comparing the second and the third set of data.Rate law experiments dont always give data in the form of a rate in moles per second. Some of them give an amount of time necessary for a reaction to proceed to a given point. The faster the rate, the less time necessary. For the following data, assume that the time given is to react 0.10M of A. Determining the complete rate law for the reaction A+Bproducts. Time taken (s) [A] [B] 36.8 0.20 0.40 25.0 0.20 0.60 10.0 0.50 0.60 A classic chemical reaction/demonstration called the iodine clock reaction is usually measured this way.20.12E What must the units on k be for the following rate law? rate=k[A]2[B]2 What must the units on k be for the following rate law? rate=k[A]1 The reaction 2O33O2 has first-order kinetics and a rate law constant of 7.66103s1. If the initial concentration of ozone is 3.4103M, what is the concentration of ozone after 100s? After 1000s?Digestive processes are first-order processes. The absorption of Fe2+ by the small intestine has a rate law constant of 3.09102s1. If the initial concentration of Fe2+ in food is 5.5M, how long before the concentration drops to 1.0M?20.18E Derive equation 20.15.20.20E To a very good approximation, the cooling of a hot body to room temperature (298K) follows first-order kinetics. In this case, however, the unit that is changing is kelvins, not molarity. This idea is known as Newtons law of cooling. If the rate constant for a body is 0.0344s1, how long would it take for a piece of matter to go from 1000K to 298K?Assume that thermal decomposition of mercuric oxide, HgO, follows first-order kinetics. It can be followed by the production of oxygen gas as a product: 2HgO(s)2Hg(l)+O2(g) At a particular temperature, k=6.02104s1. If 1.00gram of HgO were present initially, how long would it take to produce a1.00mL of O2(g) at STP; b10.0mL of O2(g) at STP? STP = standard temperature and pressure for a gas.20.23E 20.24E Derive equation 20.22.a Write a rate law and an integrated rate law for a chemical reaction that follows third-order kinetics in one of the reactants. b What would you have to plot on a graph in order to get a straight line for a reaction that follows third-order kinetics?Derive an expression for the half-life of a a third order reaction;b a reaction whose order is =1; c a reaction whose order is 12. In these last two cases, examples are rare but known.20.28E Rewrite equation 20.27 so that it has the form of a straight-line equation, and identify the expected slopes and intercepts of two possible plots.One can also define a third-life, t1/3, which is the amount of time necessary for one-third of an original amount of reactant to react. a For which order of kinetics is the third-life a constant? b Derive an expression for the t1/3 of a zeroth-order reaction. For how many third-lives will the reaction proceed before completion?The decomposition of NH3: 2NH3N2+3H2 is a zeroth-order reaction that, at elevated temperatures, has a rate constant of 1.04101M/s. If the initial concentration of NH3 is 1.00M, how long will it take for the concentration to drop to a 0.75M; b 0.50M; c 0.00M?20.32E 20.33E When ionic compounds crystallize from a supersaturated solution, the crystallization front that is, the barrier between the crystalline solid and the supersaturated solution typically travels at a constant speed through the solution until it reaches the boundaries of the system, then stops. What order of rate law is described by this behavior?An aqueous reaction that uses the solvent H2O as a reactant has a given rate law of rate=k[H2O][A] Where A is the other reactant species. Explain why, in most circumstances, this reaction can be defined in terms of pseudo first-order kinetics. What are the units on the rate constant?The rate law for the reaction C6H5OH+HNO2[OHcatalyst]C6H5NO2+H2O is rate=k[C6H5OH][HNO2] At 35.0C, k=7.04103M1s1. If [C6H5OH]=0.0433M and [HNO2]=6.05M, what is the pseudo first-order rate law and what is the value of k?If a reaction has the same rate constant, what time does it take for a reactant to decrease by 5 that is, still near the beginning of the reaction process if the kinetics are zeroth-order, first-order, and second-order with respect to that reactant?List at least four experimentally determined parameters that you, an experimenter, can define when exploring the hydrolysis of ethyl benzoate by aqueous sodium hydroxide.20.39E 20.40E 20.41E 20.42E What is the value of the equilibrium constant of a reaction if the forward rate constant was 2.8102M1s1 and the reverse rate constant was 3.6104M1s1?20.44E 20.45E Show how equation 20.33 reduces to a simpler form of an integrated first-order rate law when the reverse reaction of an equilibrium is negligible.Write expressions like equation 20.37 for a set of three parallel reactions from the same reactant. Use k1, k2, and k3 for the three rate constants.20.48E 20.49E 20.50E 20.51E 20.52E 20.53E 20.54E For what values of time, t, will 210Bi and 206Pb be at a maximum? See exercise 20.54.20.56E An interesting pair of consecutive reactions involve the absorption of ethyl alcohol by the body, which is a first-order process, and the consequent oxidation of alcohol to acetaldehyde by liver alcohol dehydrogenase LADH, which is a zeroth order process. The differential changes in the three states of ethanol can therefore be described as d[A]dt=k1[A]td[B]dt=k1[A]tk2d[C]dt=k2 which are slightly modified from equations 20.46. The integrated form of the first equation is the same as for two consecutive first-order reactions, but for the second and third reactions, they will not be. a What do A, B and C stand for in this example? b Determine an integrated form for [B] over time. Do this by finding an integrated expression for [A]t Hint: Refer to the chapter, substitute for [A]t in the second expression, rearrange the infinitesimals, and integrate one side over [B] as the variable and the other side over time, t, as the variable. The integrations are actually simpler than for the consecutive first-order reaction example in the chapter itself. c Determine an integrated form for [C] over time. d Rough values of k1 and k2 for people are 3.00103s1 and 4.44105mol/s, respectively. Use your expressions for the amounts over time to plot a graph of [A]t, [B]t, and [C]t versus time. A graphing calculator or a computer with a graphing program would be useful. Use 1.00mol of C2H5OH as [A]0. Vary this value and see how it affects the graphs of [A]t, [B]t, and [C]t.

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