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Chemistry

Chemistry | 12th Edition | ISBN: 9780078021510 | Authors: Raymond Chang; Kenneth Goldsby

Chemistry 12th Edition solutions

Author: Raymond Chang; Kenneth Goldsby
Publisher: McGraw-Hill Education
ISBN: 9780078021510
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Chapter 13 Problems

Chapter: 13 Problem: 13.1

Chemistry 12
What is meant by the rate of a chemical reaction? What are the units of the rate of a reaction?

Chapter: 13 Problem: 13.2

Chemistry 12
Distinguish between average rate and instantaneous rate. Which of the two rates gives us an unambiguous measurement of reaction rate? Why?

Chapter: 13 Problem: 13.3

Chemistry 12
What are the advantages of measuring the initial rate of a reaction?

Chapter: 13 Problem: 13.4

Chemistry 12
Can you suggest two reactions that are very slow (take days or longer to complete) and two reactions that are very fast (reactions that are over in minutes or seconds)?

Chapter: 13 Problem: 13.5

Chemistry 12
Write the reaction rate expressions for the following reactions in terms of the disappearance of the reactants and the appearance of products: (a) H2(g) 1 I2(g) 2HI(g) (b) 5Br2(aq) 1 BrO2 3 (aq) 1 6H1(aq) 3Br2(aq) 1 3H2O(l)

Chapter: 13 Problem: 13.6

Chemistry 12
Write the reaction rate expressions for the following reactions in terms of the disappearance of the reactants and the appearance of products: (a) 2H2(g) 1 O2(g) 2H2O(g) (b) 4NH3(g) 1 5O2(g) 4NO(g) 1 6H2O(g)

Chapter: 13 Problem: 13.7

Chemistry 12
Consider the reaction 2NO(g) 1 O2(g) 2NO2(g) Suppose that at a particular moment during the reaction nitric oxide (NO) is reacting at the rate of 0.066 M/s. (a) At what rate is NO2 being formed? (b) At what rate is molecular oxygen reacting?

Chapter: 13 Problem: 13.8

Chemistry 12
Consider the reaction N2(g) 1 3H2(g) 2NH3(g) Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the rate of 0.074 M/s. (a) At what rate is ammonia being formed? (b) At what rate is molecular nitrogen reacting?

Chapter: 13 Problem: 13.9

Chemistry 12
Explain what is meant by the rate law of a reaction

Chapter: 13 Problem: 13.1b

Chemistry 12
What are the units for the rate constants of zero-order, first-order, and second-order reactions?

Chapter: 13 Problem: 13.11

Chemistry 12
Consider the zero-order reaction: A product. (a) Write the rate law for the reaction. (b) What are the units for the rate constant? (c) Plot the rate of the reaction versus [A].

Chapter: 13 Problem: 13.12

Chemistry 12
On which of the following properties does the rate constant of a reaction depend? (a) reactant concentrations, (b) nature of reactants, (c) temperature.

Chapter: 13 Problem: 13.13

Chemistry 12
The rate law for the reaction NH4 1(aq) 1 NO2 2 (aq) N2(g) 1 2H2O(l) is given by rate 5 k[NH4 1][NO2 2]. At 258C, the rate constant is 3.0 3 1024 /M ? s. Calculate the rate of the reaction at this temperature if [NH4 1] 5 0.26 M and [NO2 2] 5 0.080 M.

Chapter: 13 Problem: 13.14

Chemistry 12
Use the data in Table 13.2 to calculate the rate of the reaction at the time when [F2] 5 0.010 M and [ClO2] 5 0.020 M.

Chapter: 13 Problem: 13.15

Chemistry 12
Consider the reaction A 1 B products From the following data obtained at a certain temperature, determine the order of the reaction and calculate the rate constant: [A] (M) [B] (M) Rate (M/s) 1.50 1.50 3.20 10 1 1.50 2.50 3.20 10 1 3.00 1.50 6.40 1

Chapter: 13 Problem: 13.16

Chemistry 12
Consider the reaction X 1 Y Z From the following data, obtained at 360 K, (a) determine the order of the reaction, and (b) determine the initial rate of disappearance of X when the concentration of X is 0.30 M and that of Y is 0.40 M. Initial Rate of Disappearance of X (M/s) [X] (M) [Y] (M) 0.053 0.

Chapter: 13 Problem: 13.17

Chemistry 12
Determine the overall orders of the reactions to which the following rate laws apply: (a) rate 5 k[NO2] 2 , (b) rate 5 k, (c) rate 5 k[H2][Br 2] 1 2, (d) rate 5 k[NO]2 [O2]

Chapter: 13 Problem: 13.18

Chemistry 12
Consider the reaction A B The rate of the reaction is 1.6 3 1022 M/s when the concentration of A is 0.35 M. Calculate the rate constant if the reaction is (a) first order in A and (b) second order in A.

Chapter: 13 Problem: 13.19

Chemistry 12
Cyclobutane decomposes to ethylene according to the equation C4H8(g) 2C2H4(g) Determine the order of the reaction and the rate constant based on the following pressures, which were recorded when the reaction was carried out at 4308C in a constant-volume vessel. Time (s) PC4H8 (mmHg) 0 400 2,000 316

Chapter: 13 Problem: 13.2b

Chemistry 12
The following gas-phase reaction was studied at 2908C by observing the change in pressure as a function of time in a constant-volume vessel: ClCO2CCl3(g) 2COCl2(g) Determine the order of the reaction and the rate constant based on the following data: Time (s) P (mmHg) 0 15.76 181 18.88 513 22.79

Chapter: 13 Problem: 13.21

Chemistry 12
Write an equation relating the concentration of a reactant A at t 5 0 to that at t 5 t for a first-order reaction. Define all the terms and give their units. Do the same for a second-order reaction.

Chapter: 13 Problem: 13.22

Chemistry 12
Define half-life. Write the equation relating the halflife of a first-order reaction to the rate constant.

Chapter: 13 Problem: 13.23

Chemistry 12
Write the equations relating the half-life of a secondorder reaction to the rate constant. How does it differ from the equation for a first-order reaction?

Chapter: 13 Problem: 13.24

Chemistry 12
For a first-order reaction, how long will it take for the concentration of reactant to fall to one-eighth its original value? Express your answer in terms of the half-life (t1 2 ) and in terms of the rate constant k.

Chapter: 13 Problem: 13.25

Chemistry 12
What is the half-life of a compound if 75 percent of a given sample of the compound decomposes in 60 min? Assume first-order kinetics.

Chapter: 13 Problem: 12.26

Chemistry 12
The thermal decomposition of phosphine \(PH_3)\ into phosphorus and molecular hydrogen is a first-order reaction: \4PH_3(g) + P_4(g) \rightarrow 6H_2(g)\ The half-life of the reaction is 35.0 s at \680^oC\. Calculate (a) the first-order rate constant for the reaction and (b) the time required for

Chapter: 13 Problem: 13.27

Chemistry 12
The rate constant for the second-order reaction 2NOBr(g) 2NO(g) 1 Br2(g) is 0.80/M ? s at 108C. (a) Starting with a concentration of 0.086 M, calculate the concentration of NOBr after 22 s. (b) Calculate the half-lives when [NOBr]0 5 0.072 M and [NOBr]0 5 0.054 M.

Chapter: 13 Problem: 13.28

Chemistry 12
The rate constant for the second-order reaction 2NO2(g) 2NO(g) 1 O2(g) is 0.54/M ? s at 3008C. How long (in seconds) would it take for the concentration of NO2 to decrease from 0.62 M to 0.28 M?

Chapter: 13 Problem: 13.29

Chemistry 12
Consider the first-order reaction A B shown here. (a) What is the rate constant of the reaction? (b) How many A (yellow) and B (blue) molecules are present at t 5 20 s and 30 s? t 0 s t 10 s

Chapter: 13 Problem: 13.3b

Chemistry 12
The reaction X Y shown here follows first- order kinetics. Initially different amounts of X molecules are placed in three equal-volume containers at the same temperature. (a) What are the relative rates of the reaction in these three containers? (b) How would the relative rates be affected if the vo

Chapter: 13 Problem: 13.31

Chemistry 12
Define activation energy. What role does activation energy play in chemical kinetics?

Chapter: 13 Problem: 13.32

Chemistry 12
Write the Arrhenius equation and define all terms

Chapter: 13 Problem: 13.33

Chemistry 12
Use the Arrhenius equation to show why the rate constant of a reaction (a) decreases with increasing activation energy and (b) increases with increasing temperature.

Chapter: 13 Problem: 13.34

Chemistry 12
The burning of methane in oxygen is a highly exothermic reaction. Yet a mixture of methane and oxygen gas can be kept indefinitely without any apparent change. Explain

Chapter: 13 Problem: 13.35

Chemistry 12
Sketch a potential energy versus reaction progress plot for the following reactions: (a) S(s) 1 O2(g) SO2(g) H 5 2296 kJ/mol (b) Cl2(g) Cl(g) 1 Cl(g) H 5 243 kJ/mol

Chapter: 13 Problem: 13.36

Chemistry 12
The reaction H 1 H2 H2 1 H has been studied for many years. Sketch a potential energy versus reaction progress diagram for this reaction.

Chapter: 13 Problem: 13.37

Chemistry 12
(1) The diagram in (a) shows the plots of ln k versus 1/T for two first-order reactions, where k is the rate constant and T is the absolute temperature. Which reactionhas a greater activation energy? (2) The diagramin (b) shows the plots for a first-order reaction at twodifferent temperatures. Which

Chapter: 13 Problem: 13.38

Chemistry 12
Given the same reactant concentrations, the reaction CO(g) 1 Cl2(g) COCl2(g) at 2508C is 1.50 3 103 times as fast as the same reaction at 1508C. Calculate the activation energy for this reaction. Assume that the frequency factor is constant

Chapter: 13 Problem: 13.39

Chemistry 12
Some reactions are described as parallel in that the reactant simultaneously forms different products with different rate constants. An example is A k1 B and A k2 C The activation energies are 45.3 kJ/mol for k1 and 69.8 kJ/mol for k2. If the rate constants are equal at 320 K, at what temperature wil

Chapter: 13 Problem: 13.4b

Chemistry 12
Variation of the rate constant with temperature for the first-order reaction 2N2O5(g) 2N2O4(g) 1 O2(g) is given in the following table. Determine graphically the activation energy for the reaction. T (K) k (s 1 ) 298 1.74 10 5 308 6.61 10 5 318 2.51 10 4 328 7.59 10 4 338 2.40 10 3

Chapter: 13 Problem: 13.41

Chemistry 12
For the reaction NO(g) 1 O3(g) NO2(g) 1 O2(g) the frequency factor A is 8.7 3 1012 s21 and the activation energy is 63 kJ/mol. What is the rate constant for the reaction at 758C?

Chapter: 13 Problem: 13.42

Chemistry 12
The rate constant of a first-order reaction is 4.60 3 1024 s21 at 3508C. If the activation energy is 104 kJ/mol, calculate the temperature at which its rate constant is 8.80 3 1024 s21 .

Chapter: 13 Problem: 13.43

Chemistry 12
The rate constants of some reactions double with every 10-degree rise in temperature. Assume that a reaction takes place at 295 K and 305 K. What must the activation energy be for the rate constant to double as described?

Chapter: 13 Problem: 13.44

Chemistry 12
Consider the first-order reaction CH3NC(g) CH3CN(g) Given that the frequency factor and activation energy for the reaction are 3.98 3 1013 s21 and 161 kJ/mol, respectively, calculate the rate constant at 6008C.

Chapter: 13 Problem: 13.45

Chemistry 12
Consider the second-order reaction NO(g) 1 Cl2(g) NOCl(g) 1 Cl(g) Given that the frequency factor and activation energy for the reaction are 4.0 3 109 /M ? s and 85 kJ/mol, respectively, calculate the rate constant at 5008C.

Chapter: 13 Problem: 13.46

Chemistry 12
The rate at which tree crickets chirp is 2.0 3 102 per minute at 278C but only 39.6 per minute at 58C. From these data, calculate the activation energy for the chirping process. (Hint: The ratio of rates is equal to the ratio of rate constants.)

Chapter: 13 Problem: 13.47

Chemistry 12
The diagram here describes the initial state of the reaction A2 1 B2 2AB. A2 B2 AB Suppose the reaction is carried out at two temperatures as shown below. Which picture represents the result at the higher temperature? (The reaction proceeds for the same amount of time at both temperatures.) (a) (b)

Chapter: 13 Problem: 13.48

Chemistry 12
What do we mean by the mechanism of a reaction? What is an elementary step? What is the molecularity of a reaction?

Chapter: 13 Problem: 13.49

Chemistry 12
Classify each of the following elementary steps as unimolecular, bimolecular, or termolecular. (a)   8n  (c)  8n  (b) 8n

Chapter: 13 Problem: 13.5b

Chemistry 12
Reactions can be classified as unimolecular, bimolecular, and so on. Why are there no zero-molecular reactions? Explain why termolecular reactions are rare.

Chapter: 13 Problem: 13.51

Chemistry 12
Determine the molecularity and write the rate law for each of the following elementary steps: (a) X products (b) X 1 Y products (c) X 1 Y 1 Z products (d) X 1 X products (e) X 1 2Y products

Chapter: 13 Problem: 13.52

Chemistry 12
What is the rate-determining step of a reaction? Give an everyday analogy to illustrate the meaning of rate determining.

Chapter: 13 Problem: 13.53

Chemistry 12
The equation for the combustion of ethane (C2H6) is 2C2H6(g) 1 7O2(g) 4CO2(g) 1 6H2O(l) Explain why it is unlikely that this equation also represents the elementary step for the reaction.

Chapter: 13 Problem: 13.54

Chemistry 12
Specify which of the following species cannot be isolated in a reaction: activated complex, product, intermediate.

Chapter: 13 Problem: 13.55

Chemistry 12
The rate law for the reaction 2NO(g) 1 Cl2(g) 2NOCl(g) is given by rate 5 k[NO][Cl2]. (a) What is the order of the reaction? (b) A mechanism involving the following steps has been proposed for the reaction: NO(g) 1 Cl2(g) NOCl2(g) NOCl2(g) 1 NO(g) 2NOCl(g) If this mechanism is correct, what does i

Chapter: 13 Problem: 13.56

Chemistry 12
For the reaction X2 1 Y 1 Z XY 1 XZ it is found that doubling the concentration of X2 doubles the reaction rate, tripling the concentration of Y triples the rate, and doubling the concentration of Z has no effect. (a) What is the rate law for this reaction? (b) Why is it that the change in the conce

Chapter: 13 Problem: 13.57

Chemistry 12
The rate law for the decomposition of ozone to molecular oxygen 2O3(g) 3O2(g) is rate 5 k [O3] 2 [O2] The mechanism proposed for this process is O O3 k2 2O2 O3 k1 k 1 O O  2  Derive the rate law from these elementary steps. Clearly state the assumptions you use in the derivation. Explain why the r

Chapter: 13 Problem: 13.58

Chemistry 12
The rate law for the reaction 2H2(g) 1 2NO(g) N2(g) 1 2H2O(g) is rate 5 k[H2][NO]2 . Which of the following mechanisms can be ruled out on the basis of the observed rate expression? Mechanism I H2 NO 88n H2O N (slow) N NO 88n N2 O (fast) O H2 88n H2O (fast) Mechanism II H2 2NO 88n N2O H2O (slow) N2O

Chapter: 13 Problem: 13.59

Chemistry 12
How does a catalyst increase the rate of a reaction?

Chapter: 13 Problem: 13.6b

Chemistry 12
What are the characteristics of a catalyst?

Chapter: 13 Problem: 13.61

Chemistry 12
A certain reaction is known to proceed slowly at room temperature. Is it possible to make the reaction proceed at a faster rate without changing the temperature?

Chapter: 13 Problem: 13.62

Chemistry 12
Distinguish between homogeneous catalysis and heterogeneous catalysis. Describe three important industrial processes that utilize heterogeneous catalysis.

Chapter: 13 Problem: 13.63

Chemistry 12
Are enzyme-catalyzed reactions examples of homogeneous or heterogeneous catalysis? Explain.

Chapter: 13 Problem: 13.64

Chemistry 12
The concentrations of enzymes in cells are usually quite small. What is the biological significance of this fact?

Chapter: 13 Problem: 13.65

Chemistry 12
The diagram shown here represents a two-step mechanism. (a) Write the equation for each step and the overall reaction. (b) Identify the intermediate and catalyst. The color codes are A 5 green and B 5 red. 8n 8n

Chapter: 13 Problem: 13.66

Chemistry 12
Consider the following mechanism for the enzymecatalyzed reaction: (fast equilibrium) ES (slow) k2 E P ESk1 k 1 1 ES 1 Derive an expression for the rate law of the reaction in terms of the concentrations of E and S. (Hint: To solve for [ES], make use of the fact that, at equilibrium, the rate of forw

Chapter: 13 Problem: 13.67

Chemistry 12
The following diagrams represent the progress of the reaction A B, where the red spheres represent A molecules and the green spheres represent B molecules. Calculate the rate constant of the reaction. t 0 s t 20 s t 40 s 1

Chapter: 13 Problem: 13.68

Chemistry 12
The following diagrams show the progress of the reaction 2A A2. Determine whether the reaction is first order or second order and calculate the rate constant. t 0 min t 15 min t 30 min 1

Chapter: 13 Problem: 13.69

Chemistry 12
Suggest experimental means by which the rates of the following reactions could be followed: (a) CaCO3(s) CaO(s) 1 CO2(g) (b) Cl2(g) 1 2Br2(aq) Br2(aq) 1 2Cl2(aq) (c) C2H6(g) C2H4(g) 1 H2(g) (d) C2H5I(g) 1 H2O(l) C2H5OH(aq) 1 H1(aq) 1 I 2(aq)

Chapter: 13 Problem: 13.7b

Chemistry 12
List four factors that influence the rate of a reaction

Chapter: 13 Problem: 13.71

Chemistry 12
The rate constant for the reaction NO2(g) 1 CO(g) NO(g) 1 CO2(g) is 1.64 3 1026 /M ? s. What is incomplete about this statement?

Chapter: 13 Problem: 13.72

Chemistry 12
In a certain industrial process involving a heterogeneous catalyst, the volume of the catalyst (in the shape of a sphere) is 10.0 cm3 . Calculate the surface area of the catalyst. If the sphere is broken down into eight spheres, each having a volume of 1.25 cm3 , what is the total surface area of the

Chapter: 13 Problem: 13.73

Chemistry 12
Use the data in Example 13.5 to determine graphically the half-life of the reaction.

Chapter: 13 Problem: 13.74

Chemistry 12
The following data were collected for the reaction between hydrogen and nitric oxide at 7008C: 2H2(g) 1 2NO(g) 2H2O(g) 1 N2(g) Experiment [H2] [NO] Initial Rate (M/s) 1 0.010 0.025 2.4 10 6 2 0.0050 0.025 1.2 10 6 3 0.010 0.0125 0.60 10 6    (a) Determine the order of the reaction. (b) Calculate

Chapter: 13 Problem: 13.75

Chemistry 12
When methyl phosphate is heated in acid solution, it reacts with water: CH3OPO3H2 1 H2O CH3OH 1 H3PO4 If the reaction is carried out in water enriched with 18O, the oxygen-18 isotope is found in the phosphoric acid product but not in the methanol. What does this tell us about the mechanism of the re

Chapter: 13 Problem: 13.76

Chemistry 12
The rate of the reaction CH3COOC2H5(aq) 1 H2O(l2 CH3COOH(aq) 1 C2H5OH(aq) shows first-order characteristicsthat is, rate 5 k[CH3COOC2H5]even though this is a second-order reaction (first order in CH3COOC2H5 and first order in H2O). Explain.

Chapter: 13 Problem: 13.77

Chemistry 12
Which of the following equations best describes the diagram shown above: (a) A B, (b) A 3B, (c) 3A B? Concentration t (s)

Chapter: 13 Problem: 13.78

Chemistry 12
The reaction 2A 1 3B C is first order with respect to A and B. When the initial concentrations are [A] 5 1.6 3 1022 M and [B] 5 2.4 3 1023 M, the rate is 4.1 3 1024 M/s. Calculate the rate constant of the reaction.

Chapter: 13 Problem: 13.79

Chemistry 12
The bromination of acetone is acid-catalyzed: CH3COCH3 Br2 88 catal H y Sst CH3COCH2Br H Br The rate of disappearance of bromine was measured for several different concentrations of acetone, bromine, and H1 ions at a certain temperature: Rate of Disappearance [CH3COCH3] [Br2] [H ] of Br2 (M/s) (1) 0.

Chapter: 13 Problem: 13.8b

Chemistry 12
The decomposition of N2O to N2 and O2 is a firstorder reaction. At 7308C the half-life of the reaction is 3.58 3 103 min. If the initial pressure of N2O is 2.10 atm at 7308C, calculate the total gas pressure after one half-life. Assume that the volume remains constant.

Chapter: 13 Problem: 13.81

Chemistry 12
The reaction S2O22 8 1 2I2 2SO4 22 1 I2 proceeds slowly in aqueous solution, but it can be catalyzed by the Fe31 ion. Given that Fe31 can oxidize I 2 and Fe21 can reduce S2O8 22, write a plausible two-step mechanism for this reaction. Explain why the uncatalyzed reaction is slow.

Chapter: 13 Problem: 13.82

Chemistry 12
What are the units of the rate constant for a thirdorder reaction?

Chapter: 13 Problem: 13.83

Chemistry 12
The integrated rate law for the zero-order reaction A B is [A]t 5 [A]0 2 kt. (a) Sketch the following plots: (i) rate versus [A]t and (ii) [A]t versus t. (b) Derive an expression for the half-life of the reaction. (c) Calculate the time in half-lives when the integrated rate law is no longer valid,

Chapter: 13 Problem: 13.84

Chemistry 12
A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for A and 18.0 min for B. If the concentrations of A and B are equal initially, how long will it take for the concentration of A to be four times that of B?

Chapter: 13 Problem: 13.85

Chemistry 12
Shown here are plots of concentration of reactant versus time for two first-order reactions at the same temperature. In each case, determine which reaction has a greater rate constant.ln [A]t [A]t t t (a) (b)

Chapter: 13 Problem: 13.86

Chemistry 12
The diagrams here represent the reaction A 1 B C carried out under different initial concentrations of A and B. Determine the rate law of the reaction. (The color codes are A 5 red, B 5 green, C 5 blue.) I t 5 0 s t 5 50 s II t 5 0 s t 5 50 s III t 5 0 s t 5 50 s

Chapter: 13 Problem: 13.87

Chemistry 12
Referring to Example 13.5, explain how you would measure the partial pressure of azomethane experimentally as a function of time.

Chapter: 13 Problem: 13.88

Chemistry 12
The rate law for the reaction 2NO2 (g) N2O4(g) is rate 5 k[NO2] 2 . Which of the following changes will change the value of k? (a) The pressure of NO2 is doubled. (b) The reaction is run in an organic solvent. (c) The volume of the container is doubled. (d) The temperature is decreased. (e) A cataly

Chapter: 13 Problem: 13.89

Chemistry 12
The reaction of G2 with E2 to form 2EG is exothermic, and the reaction of G2 with X2 to form 2XG is endothermic. The activation energy of the exothermic reaction is greater than that of the endothermic reaction. Sketch the potential energy profile diagrams for these two reactions on the same graph.

Chapter: 13 Problem: 13.9b

Chemistry 12
In the nuclear industry, workers use a rule of thumb that the radioactivity from any sample will be relatively harmless after 10 half-lives. Calculate the fraction of a radioactive sample that remains after this time period. (Hint: Radioactive decays obey first-order kinetics.)

Chapter: 13 Problem: 13.91

Chemistry 12
Briefly comment on the effect of a catalyst on each of the following: (a) activation energy, (b) reaction mechanism, (c) enthalpy of reaction, (d) rate of forward step, (e) rate of reverse step.

Chapter: 13 Problem: 13.92

Chemistry 12
When 6 g of granulated Zn is added to a solution of 2 M HCl in a beaker at room temperature, hydrogen gas is generated. For each of the following changes (at constant volume of the acid) state whether the rate of hydrogen gas evolution will be increased, decreased, or unchanged: (a) 6 g of powdered Z

Chapter: 13 Problem: 13.93

Chemistry 12
Strictly speaking, the rate law derived for the reaction in Problem 13.74 applies only to certain concentrations of H2. The general rate law for the reaction takes the form rate 5 k1[NO]2 [H2] 1 1 k2[H2] where k1 and k2 are constants. Derive rate law expressions under the conditions of very high and

Chapter: 13 Problem: 13.94

Chemistry 12
A certain first-order reaction is 35.5 percent complete in 4.90 min at 258C. What is its rate constant?

Chapter: 13 Problem: 13.95

Chemistry 12
The decomposition of dinitrogen pentoxide has been studied in carbon tetrachloride solvent (CCl4) at a certain temperature: 2N2O5 4NO2 1 O2 [N2O5] Initial Rate (M/s) 0.92 0.95 10 5 1.23 1.20 10 5 1.79 1.93 10 5 2.00 2.10 10 5 2.21 2.26 10 5 Determine graphically the rate law for the reaction and cal

Chapter: 13 Problem: 13.96

Chemistry 12
The thermal decomposition of N2O5 obeys first- order kinetics. At 458C, a plot of ln [N2O5] versus t gives a slope of 26.18 3 1024 min21 . What is the half-life of the reaction?

Chapter: 13 Problem: 13.97

Chemistry 12
When a mixture of methane and bromine is exposed to visible light, the following reaction occurs slowly: CH4(g) 1 Br2(g) CH3Br(g) 1 HBr(g) Suggest a reasonable mechanism for this reaction. (Hint: Bromine vapor is deep red; methane is colorless.)

Chapter: 13 Problem: 13.98

Chemistry 12
The rate of the reaction between H2 and I2 to form HI (discussed on p. 596) increases with the intensity of visible light. (a) Explain why this fact supports the two-step mechanism given. (The color of I2 vapor is shown on p. 502.) (b) Explain why the visible light has no effect on the formation of H

Chapter: 13 Problem: 13.99

Chemistry 12
The carbon-14 decay rate of a sample obtained from a young tree is 0.260 disintegration per second per gram of the sample. Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.186 disintegration per second per gram of the sample. What is the ag

Chapter: 13 Problem: 13.1c

Chemistry 12
Consider the following elementary step: X 1 2Y XY2 (a) Write a rate law for this reaction. (b) If the initial rate of formation of XY2 is 3.8 3 1023 M/s and the initial concentrations of X and Y are 0.26 M and 0.88 M, what is the rate constant of the reaction?

Chapter: 13 Problem: 13.101

Chemistry 12
In recent years ozone in the stratosphere has been depleted at an alarmingly fast rate by chlorofluorocarbons (CFCs). A CFC molecule such as CFCl3 is first decomposed by UV radiation: CFCl3 CFCl2 1 Cl The chlorine radical then reacts with ozone as follows: Cl 1 O3 ClO 1 O2 ClO 1 O Cl 1 O2 The

Chapter: 13 Problem: 13.102

Chemistry 12
Chlorine oxide (ClO), which plays an important role in the depletion of ozone (see Problem 13.101), decays rapidly at room temperature according to the equation 2ClO(g) Cl2(g) 1 O2(g) From the following data, determine the reaction order and calculate the rate constant of the reaction Time (s) [ClO]

Chapter: 13 Problem: 13.103

Chemistry 12
A compound X undergoes two simultaneous firstorder reactions as follows: X Y with rate constant k1 and X Z with rate constant k2. The ratio of k1/k2 at 408C is 8.0. What is the ratio at 3008C? Assume that the frequency factors of the two reactions are the same

Chapter: 13 Problem: 13.104

Chemistry 12
Consider a car fitted with a catalytic converter. The first 5 minutes or so after it is started are the most polluting. Why?

Chapter: 13 Problem: 13.105

Chemistry 12
The following scheme in which A is converted to B, which is then converted to C is known as a consecutive reaction. A B C Assuming that both steps are first order, sketch on the same graph the variations of [A], [B], and [C] with time.

Chapter: 13 Problem: 3.106

Chemistry 12
Hydrogen and iodine monochloride react as follows: H2(g) 1 2ICl(g) 2HCl(g) 1 I2(g) The rate law for the reaction is rate 5 k[H2][ICl]. Suggest a possible mechanism for the reaction.

Chapter: 13 Problem: 13.107

Chemistry 12
The rate law for the following reaction CO(g) 1 NO2(g) CO2(g) 1 NO(g) is rate 5 k[NO2] 2 . Suggest a plausible mechanism for the reaction, given that the unstable species NO3 is an intermediate.

Chapter: 13 Problem: 13.108

Chemistry 12
Radioactive plutonium-239 1t1 2 5 2.44 3 105 yr2 is used in nuclear reactors and atomic bombs. If there are 5.0 3 102 g of the isotope in a small atomic bomb, how long will it take for the substance to decay to 1.0 3 102 g, too small an amount for an effective bomb?

Chapter: 13 Problem: 13.109

Chemistry 12
Many reactions involving heterogeneous catalysts are zero order; that is, rate 5 k. An example is the decomposition of phosphine (PH3) over tungsten (W): 4PH3(g) P4(g) 1 6H2(g) It is found that the reaction is independent of [PH3] as long as phosphines pressure is sufficiently high ($ 1 atm). Explai

Chapter: 13 Problem: 13.11c

Chemistry 12
Thallium(I) is oxidized by cerium(IV) as follows: Tl1 1 2Ce41 Tl31 1 2Ce31 The elementary steps, in the presence of Mn(II), are as follows: Ce41 1 Mn21 Ce31 1 Mn31 Ce41 1 Mn31 Ce31 1 Mn41 Tl1 1 Mn41 Tl31 1 Mn21 (a) Identify the catalyst, intermediates, and the rate-determining step if the rate la

Chapter: 13 Problem: 13.111

Chemistry 12
Sucrose (C12H22O11), commonly called table sugar, undergoes hydrolysis (reaction with water) to produce fructose (C6H12O6) and glucose (C6H12O6): C12H22O11 1 H2O C6H12O6 1 C6H12O6 fructose glucose This reaction is of considerable importance in the candy industry. First, fructose is sweeter than sucr

Chapter: 13 Problem: 13.112

Chemistry 12
The first-order rate constant for the decomposition of dimethyl ether (CH3)2O(g) CH4(g) 1 H2(g) 1 CO(g) is 3.2 3 1024 s21 at 4508C. The reaction is carried out in a constant-volume flask. Initially only dimethyl ether is present and the pressure is 0.350 atm. What is the pressure of the system after

Chapter: 13 Problem: 13.113

Chemistry 12
At 258C, the rate constant for the ozone-depleting reaction O(g) 1 O3(g) 2O2(g) is 7.9 3 10215 cm3 /molecule ? s. Express the rate constant in units of 1/M ? s

Chapter: 13 Problem: 13.114

Chemistry 12
Consider the following elementary steps for a consecutive reaction: A k1 B k2 C (a) Write an expression for the rate of change of B. (b) Derive an expression for the concentration of B under steady-state conditions; that is, when B is decomposing to C at the same rate as it is formed from A.

Chapter: 13 Problem: 13.115

Chemistry 12
Ethanol is a toxic substance that, when consumed in excess, can impair respiratory and cardiac functions by interference with the neurotransmitters of the nervous system. In the human body, ethanol is metabolized by the enzyme alcohol dehydrogenase to acetaldehyde, which causes hangovers. (a) Based o

Chapter: 13 Problem: 13.116

Chemistry 12
Strontium-90, a radioactive isotope, is a major product of an atomic bomb explosion. It has a halflife of 28.1 yr. (a) Calculate the first-order rate constant for the nuclear decay. (b) Calculate the fraction of 90Sr that remains after 10 half-lives. (c) Calculate the number of years required for 99.

Chapter: 13 Problem: 13.117

Chemistry 12
Consider the potential energy profiles for the following three reactions (from left to right). (1) Rank the rates (slowest to fastest) of the reactions. (2) Calculate DH for each reaction and determine which reaction(s) are exothermic and which reaction(s) are endothermic. Assume the reactions have r

Chapter: 13 Problem: 13.118

Chemistry 12
Consider the following potential energy profile for the A D reaction. (a) How many elementary steps are there? (b) How many intermediates are formed? (c) Which step is rate determining? (d) Is the overall reaction exothermic or endothermic? Reaction progress A B C D Potential energy

Chapter: 13 Problem: 13.119

Chemistry 12
A factory that specializes in the refinement of transition metals such as titanium was on fire. The firefighters were advised not to douse the fire with water. Why?

Chapter: 13 Problem: 13.12c

Chemistry 12
The activation energy for the decomposition of hydrogen peroxide 2H2O2(aq) 2H2O2(l) 1 O2(g) is 42 kJ/mol, whereas when the reaction is catalyzed by the enzyme catalase, it is 7.0 kJ/mol. Calculate the temperature that would cause the uncatalyzed reaction to proceed as rapidly as the enzymecatalyzed

Chapter: 13 Problem: 13.121

Chemistry 12
The activity of a radioactive sample is the number of nuclear disintegrations per second, which is equal to the first-order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactivity is the curie (Ci), where 1 Ci corresponds to exactly 3.70 3 1010 disintegrati

Chapter: 13 Problem: 13.122

Chemistry 12
To carry out metabolism, oxygen is taken up by hemoglobin (Hb) to form oxyhemoglobin (HbO2) according to the simplified equation Hb(aq) 1 O2(aq) k HbO2(aq) where the second-order rate constant is 2.1 3 106 /M ? s at 378C. (The reaction is first order in Hb and O2.) For an average adult, the concentra

Chapter: 13 Problem: 13.123

Chemistry 12
At a certain elevated temperature, ammonia decomposes on the surface of tungsten metal as follows: 2NH3 N2 1 3H2 From the following plot of the rate of the reaction versus the pressure of NH3, describe the mechanism of the reaction. PNH3 Rate

Chapter: 13 Problem: 13.124

Chemistry 12
The following expression shows the dependence of the half-life of a reaction (t1 2 ) on the initial reactant concentration [A]0: t1 2 r 1 [A]n21 0 where n is the order of the reaction. Verify this dependence for zero-, first-, and second-order reactions.

Chapter: 13 Problem: 13.125

Chemistry 12
Polyethylene is used in many items, including water pipes, bottles, electrical insulation, toys, and mailer envelopes. It is a polymer, a molecule with a very high molar mass made by joining many ethylene molecules together. (Ethylene is the basic unit, or monomer for polyethylene.) The initiation st

Chapter: 13 Problem: 13.126

Chemistry 12
The rate constant for the gaseous reaction H2(g) 1 I2(g) 2HI(g) is 2.42 3 1022 /M ? s at 4008C. Initially an equimolar sample of H2 and I2 is placed in a vessel at 4008C and the total pressure is 1658 mmHg. (a) What is the initial rate (M/min) of formation of HI? (b) What are the rate of formation o

Chapter: 13 Problem: 13.127

Chemistry 12
A protein molecule, P, of molar mass m dimerizes when it is allowed to stand in solution at room temperature. A plausible mechanism is that the protein molecule is first denatured (that is, loses its activity due to a change in overall structure) before it dimerizes: P k P*(denatured) slow 2P* P2 fa

Chapter: 13 Problem: 13.128

Chemistry 12
When the concentration of A in the reaction A B was changed from 1.20 M to 0.60 M, the half-life increased from 2.0 min to 4.0 min at 258C. Calculate the order of the reaction and the rate constant. (Hint: Use the equation in Problem 13.124.)

Chapter: 13 Problem: 13.129

Chemistry 12
At a certain elevated temperature, ammonia decomposes on the surface of tungsten metal as follows: NH3 1 2N2 1 3 2H2 The kinetic data are expressed as the variation of the half-life with the initial pressure of NH3: P (mmHg) 264 130 59 16 t1 456 228 102 60 2 (s) (a) Determine the order of the reacti

Chapter: 13 Problem: 13.13c

Chemistry 12
The activation energy for the reaction N2O(g) N2(g) 1 O(g) is 2.4 3 102 kJ/mol at 600 K. Calculate the percentage of the increase in rate from 600 K to 606 K. Comment on your results.

Chapter: 13 Problem: 3.131

Chemistry 12
The rate of a reaction was followed by the absorption of light by the reactants and products as a function of wavelengths (l1, l2, l3) as time progresses. Which of the following mechanisms is consistent with the experimental data? (a) A B, A C (b) A B 1 C (c) A B, B C 1 D (d) A B, B C Time

Chapter: 13 Problem: 13.132

Chemistry 12
A gas mixture containing CH3 fragments, C2H6 molecules, and an inert gas (He) was prepared at 600 K with a total pressure of 5.42 atm. The elementary reaction CH3 1 C2H6 CH4 1 C2H5 has a second-order rate constant of 3.0 3 104 /M ? s. Given that the mole fractions of CH3 and C2H6 are 0.00093 and 0.0

Chapter: 13 Problem: 13.133

Chemistry 12
To prevent brain damage, a drastic medical procedure is to lower the body temperature of someone who has suffered cardiac arrest. What is the physiochemical basis for this treatment?

Chapter: 13 Problem: 13.134

Chemistry 12
The activation energy (Ea) for the reaction 2N2O(g) 2N2(g) 1 O2(g) H 5 2164 kJ/mol is 240 kJ/mol. What is Ea for the reverse reaction?

Chapter: 13 Problem: 13.135

Chemistry 12
The rate constants for the first-order decomposition of an organic compound in solution are measured at several temperatures: k (s21 ) 0.00492 0.0216 0.0950 0.326 1.15 T (K) 278 288 298 308 318 Determine graphically the activation energy and frequency factor for the reaction

Chapter: 13 Problem: 13.136

Chemistry 12
Assume that the formation of nitrogen dioxide: 2NO(g) 1 O2(g) 2NO2(g) is an elementary reaction. (a) Write the rate law for this reaction. (b) A sample of air at a certain temperature is contaminated with 2.0 ppm of NO by volume. Under these conditions, can the rate law be simplified? If so, write t

Chapter: 13 Problem: 13.137

Chemistry 12
An instructor performed a lecture demonstration of the thermite reaction (see p. 258). He mixed aluminum with iron(III) oxide in a metal bucket placed on a block of ice. After the extremely exothermic reaction started, there was an enormous bang, which was not characteristic of thermite reactions. Gi

Chapter: 13 Problem: 13.138

Chemistry 12
Account for the variation of the rate of an enzymecatalyzed reaction versus temperature shown here. What is the approximate temperature that corresponds to the maximum rate in the human body? Rate T

Chapter: 13 Problem: 13.139

Chemistry 12
Is the rate constant (k) of a reaction more sensitive to changes in temperature if Ea is small or large?

Chapter: 13 Problem: 13.14

Chemistry 12
Shown here is a plot of [A]t versus t for the reaction A product. (a) Determine the order and the rate constant of the reaction. (b) Estimate the initial rate and the rate at 30 s. 0 0.0 0.2 0.4 0.6 0.8 1.0 10 20 30 [A]t (M) t (s) 40 50 60

Chapter: 13 Problem: 13.141

Chemistry 12
What are the shortest and longest times (in years) that can be estimated by carbon-14 dating?

Chapter: 13 Problem: 13.142

Chemistry 12
In addition to chemical and biological systems, kinetic treatments can sometimes be applied to behavioral and social processes such as the evolution of technology. For example, in 1965, Gordon Moore, a co-founder of Intel, described a trend that the number of transistors on an integrated circuit (N)

Glossary

Key Chemistry Terms and definitions covered in this textbook

absolute temperature scale.
A temperature scale that uses the absolute zero of temperature as the lowest temperature. (5.3)
absolute zero.
Theoretically the lowest attainable temperature. (5.3)
acceptor impurities.
Impurities that can accept electrons from semiconductors. (21.3)
accuracy.
The closeness of a measurement to the true value of the quantity that is measured. (1.8)
acid ionization constant (Ka).
The equilibrium constant for the acid ionization. (15.5)
acid.
A substance that yields hydrogen ions (H1) when dissolved in water. (2.7)
actinide series.
Elements that have incompletely filled 5f subshells or readily give rise to cations that have incompletely filled 5f subshells. (7.9)
activated complex.
The species temporarily formed by the reactant molecules as a result of the collision before they form the product. (13.4)
activation energy (Ea).
The minimum amount of energy required to initiate a chemical reaction. (13.4)
activity series.
A summary of the results of many possible displacement reactions. (4.4)
actual yield.
The amount of product actually obtained in a reaction. (3.10)
addition reaction.
A reaction in which one molecule adds to another. (24.2)
adhesion.
Attraction between unlike molecules. (11.3)
alcohol.
An organic compound containing the hydroxyl group —OH. (24.4)
aldehydes.
Compounds with a carbonyl functional group and the general formula RCHO, where R is an H atom, an alkyl, or an aromatic group. (24.4)
aliphatic hydrocarbons.
Hydrocarbons that do not contain the benzene group or the benzene ring. (24.1)
alkali metals.
The Group 1A elements (Li, Na, K, Rb, Cs, and Fr). (2.4)
alkaline earth metals.
The Group 2A elements (Be, Mg, Ca, Sr, Ba, and Ra). (2.4)
alkanes.
Hydrocarbons having the general formula CnH2n12, where n 5 1,2, . . . . (24.2)
alkenes.
Hydrocarbons that contain one or more carbon-carbon double bonds. They have the general formula CnH2n, where n 5 2,3, . . . . (24.2)
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