For a certain process, the activation energy is greater

Define stability from both a kinetic and thermodynamic perspective. Give examples to show the differences in these concepts.

Describe at least two experiments you could perform to determine a rate law.

Make a graph of [A] versus time for zero-, first-, and secondorder reactions. From these graphs, compare successive half-lives.

How does temperature affect k, the rate constant? Explain.

Consider the following statements: In general, the rate of a chemical reaction increases a bit at first because it takes a while for the reaction to get warmed up. After that, however, the rate of the reaction decreases because its rate is dependent on the concentrations of the reactants, and these are decreasing. Indicate everything that is correct in these statements, and indicate everything that is incorrect. Correct the incorrect statements and explain.

For the reaction explain at least two ways in which the rate law could be zero order in chemical A.

A friend of yours states, A balanced equation tells us how chemicals interact. Therefore, we can determine the rate law directly from the balanced equation. What do you tell your friend?

Provide a conceptual rationale for the differences in the half-lives of zero-, first-, and second-order reactions.

Define what is meant by unimolecular and bimolecular steps. Why are termolecular steps infrequently seen in chemical reactions?

Hydrogen reacts explosively with oxygen. However, a mixture of H2 and O2 can exist indefinitely at room temperature. Explain why H2 and O2 do not react under these conditions.

For the reaction the observed rate law is Which of the changes listed below would affect the value of the rate constant k? a. increasing the partial pressure of hydrogen gas b. changing the temperature c. using an appropriate catalyst

The rate law for a reaction can be determined only from experiment and not from the balanced equation. Two experimental procedures were outlined in Chapter 12. What are these two procedures? Explain how each method is used to determine rate laws.

Table 12.2 illustrates how the average rate of a reaction decreases with time. Why does the average rate decrease with time? How does the instantaneous rate of a reaction depend on time? Why are initial rates used by convention?

The type of rate law for a reaction, either the differential rate law or the integrated rate, is usually determined by which data is easiest to collect. Explain.

The initial rate of a reaction doubles as the concentration of one of the reactants is quadrupled. What is the order of this reactant? If a reactant has a _1 order, what happens to the initial rate when the concentration of that reactant increases by a factor of two?

Reactions that require a metal catalyst are often zero order after a certain amount of reactant(s) are present. Explain.

The central idea of the collision model is that molecules must collide in order to react. Give two reasons why not all collisions of reactant molecules result in product formation.

Would the slope of a ln k versus 1/T (K) plot for a catalyzed reaction be more of less negative than the slope of the ln k versus 1/T (K) plot for the uncatalyzed reaction? Explain.

Consider the reaction If, in a certain experiment, over a specific time period, 0.0048 mol PH3 is consumed in a 2.0-L container each second of reaction, what are the rates of production of P4 and H2 in this experiment? 4PH31g2!P41g2 _ 6H21g2 Rate _ k3NO42 3H2 4 2H21g2 _ 2NO1g2!N21g2 _ 2H2O1g2

In the Haber process for the production of ammonia, what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?

At will decompose according to the following reaction: The following data were collected for the concentration of at various times. a. Calculate the average rate of decomposition of between 0 and s. Use this rate to calculate the average rate of production of over the same time period. b. What are these rates for the time period s to s?

Consider the general reaction and the following average rate data over some time period : Determine a set of possible coefficients to balance this general reaction.

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? a. rate of a chemical reaction b. rate constant for a zero-order rate law c. rate constant for a first-order rate law d. rate constant for a second-order rate law e. rate constant for a third-order rate law

The rate law for the reaction is What are the units for k, assuming time in seconds and concentration in mol/L?

The reaction 2NO1g2 _ Cl21g2!2NOCl1g2 was studied at . The following results were obtained where Rate _ _ 3Cl2 4 t a. What is the rate law? b. What is the value of the rate constant?

The reaction was studied at . The following results were obtained where Rate _ _ 3S2O8 2_4 t b. Calculate a value for the rate constant for each experiment and an average value for the rate constant.

The decomposition of nitrosyl chloride was studied: The following data were obtained where Rate _ _ 3NOCl4 t a. What is the rate law? b. Calculate the rate constant. c. Calculate the rate constant when concentrations are given in moles per liter.

The following data were obtained for the gas-phase decomposition of dinitrogen pentoxide, 2N2O51g2!4NO21g2 _ O21g2 Defining the rate as write the rate law and calculate the value of the rate constant.

The rate of the reaction between hemoglobin (Hb) and carbon monoxide (CO) was studied at . The following data were collected with all concentration units in _mol/L. (A hemoglobin concentration of 2.21 mmol/L is equal to 2.21 _ 10_6 mol/L.) a. Determine the orders of this reaction with respect to Hb and CO. b. Determine the rate law. c. Calculate the value of the rate constant. d. What would be the initial rate for an experiment with and ?

The following data were obtained for the reaction where Rate _ _ 3ClO2 4 t 2ClO21aq2 _ 2OH_1aq2!ClO3 _1aq2 _ ClO2 _1aq2 _ H2O1l2 a. Determine the rate law and the value of the rate constant. b. What would be the initial rate for an experiment with 0.175 mol/L and OH_0 _ 0.0844 mol/L?

The decomposition of hydrogen peroxide was studied, and the following data were obtained at a particular temperature: Assuming that determine the rate law, the integrated rate law, and the value of the rate constant. Calculate [H2O2] at 4000. s after the start of the reaction.

A certain reaction has the following general form: At a particular temperature and concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to ?

The rate of the reaction depends only on the concentration of nitrogen dioxide below . At a temperature below the following data were collected: Determine the rate law, the integrated law, and the value of the rate constant. Calculate after the start of the reaction.

A certain reaction has the following general form: At a particular temperature and concentration versus time data were collected for this reaction, and a plot of 1_[A] versus time resulted in a straight line with a slope value of a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to

The decomposition of ethanol (C2H5OH) on an alumina (Al2O3) surface was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope of a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. If the initial concentration of C2H5OH was calculate the half-life for this reaction. c. How much time is required for all the C2H5OH to decompose?

At 500 K in the presence of a copper surface, ethanol decomposes according to the equation The pressure of C2H5OH was measured as a function of time and the following data were obtained: Since the pressure of a gas is directly proportional to the concentration of gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the above data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C2H5OH after 900. s from the start of the reaction. (Hint: To determine the order of the reaction with respect to C2H5OH, compare how the pressure of C2H5OH decreases with each time listing.)

The dimerization of butadiene was studied at 500. K, and the following data were obtained: Assuming that determine the form of the rate law, the integrated rate law, and the rate constant for this reaction. (These are actual experimental data, so they may not give a perfectly straight line.)

The rate of the reaction was studied at a certain temperature. a. In the first set of experiments, NO2 was in large excess, at a concentration of molecules/cm3 with the following data collected: What is the order of the reaction with respect to oxygen atoms? b. The reaction is known to be first order with respect to NO2. Determine the overall rate law and the value of the rate constant.

Experimental data for the reaction have been plotted in the following three different ways (with concentration units in mol/L): What is the order of the reaction with respect to A and what is the initial concentration of A?

Consider the data plotted in Exercise 39 when answering the following questions. a. What is the concentration of A after 9 s? b. What are the first three half-lives for this experiment?

The reaction is known to be zero order in A and to have a rate constant of at An experiment was run at where a. Write the integrated rate law for this reaction. b. Calculate the half-life for the reaction. c. Calculate the concentration of B after s has elapsed.

The radioactive isotope 32P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a sample of 32P to decay?

A first-order reaction is 75.0% complete in 320. s. a. What are the first and second half-lives for this reaction? b. How long does it take for 90.0% completion?

The rate law for the decomposition of phosphine (PH3) is It takes 120. s for 1.00 M PH3 to decrease to 0.250 M. How much time is required for 2.00 M PH3 to decrease to a concentration of 0.350 M?

Consider the following initial rate data for the decomposition of compound AB to give A and B: Determine the half-life for the decomposition reaction initially having 1.00 M AB present.

The rate law for the reaction 2NOBr1g2!2NO1g2 _ Br21g2 at some temperature is a. If the half-life for this reaction is 2.00 s when [NOBr]0 _ 0.900 M, calculate the value of k for this reaction. b. How much time is required for the concentration of NOBr to decrease to 0.100 M?

For the reaction products, successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which Calculate the concentration of A at the following times. a. 80.0 min b. 30.0 min

Consider the hypothetical reaction where the rate law is An experiment is carried out where The reaction is started, and after 8.0 seconds, the concentration of A is a. Calculate k for this reaction. b. Calculate the half-life for this experiment. c. Calculate the concentration of A after 13.0 seconds. d. Calculate the concentration of C after 13.0 seconds.

Write the rate laws for the following elementary reactions. a. b. c. c.

The mechanisms shown below have been proposed to explain the kinetics of the reaction considered in Question 11. Which of the following are acceptable mechanisms? Explain. Mechanism I: Mechanism II: Slow Fast Fast Mechanism III: Slow Fast

A proposed mechanism for a reaction is Slow Fast C4H9OH2 Fast _ _ H2O!C4H9OH _ H3O_ C4H9 _ _ H2O!C4H9OH2 _ C4H9Br!C4H9 _ _ Br_ N2O1g2 _ H21g2!N21g2 _ H2O1g2 H21g2 _ 2NO1g2!N2O1g2 _ H2O1g2 H21g2 _ O1g2!H2O1g2 N1g2 _ NO1g2!N21g2 _ O1g2 H21g2 _ NO1g2!H2O1g2 _ N1g2 2H21g2 _ 2NO1g2!N21g2 _ 2H2O1g2 O31g2 _ O1g2 S2O21g2 O31g2 SO21g2 _ O1g2 O31g2 _ NO1g2 SO21g2 _ NO21g2 CH3NC1g2 SCH3CN1g2 3.8 _ 10_3 M. [B]0 _ 3.0 M, and [C]0 _ 2.0 M. [A]0 _ 1.0 _ 10_2 M, Rate _ _ 3A4 t _ k3A4 3B42 A _ B _ 2C!2D _ 3E [A]0 _ 0.10 M. A S Rate _ _ 3NOBr4 t _ k3NOBr42 Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?

The mechanism for the reaction of nitrogen dioxide with carbon monoxide to form nitric oxide and carbon dioxide is thought to be Slow Fast Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction?

For the following reaction profile, indicate a. the positions of reactants and products. b. the activation energy. c. for the reaction.

Draw a rough sketch of the energy profile for each of the following cases: a. b. c.

The activation energy for the reaction is 125 kJ/mol, and for the reaction is kJ/mol. What is the activation energy for the reverse reaction [ ]?

For a certain process, the activation energy is greater for the forward reaction than for the reverse reaction. Does this reaction have a positive or negative value for ?

The rate constant for the gas-phase decomposition of N2O5, has the following temperature dependence: Make the appropriate graph using these data, and determine the activation energy for this reaction.

The reaction in a certain solvent is first order with respect to and zero order with respect to In several experiments, the rate constant k was determined at different temperatures. A plot of ln(k) versus 1_T was constructed resulting in a straight line with a slope value of and y-intercept of 33.5. Assume k has units of a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor A. c. Calculate the value of k at

The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/mol. The rate constant at 555 K is L/mol s. What is the rate constant at 645 K?

A first-order reaction has rate constants of and at and , respectively. What is the value of the activation energy?

A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.

Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25 to ?

Which of the following reactions would you expect to proceed at a faster rate at room temperature? Why? (Hint: Think about which reaction would have the lower activation energy.)

One reason suggested for the instability of long chains of silicon atoms is that the decomposition involves the transition state shown below: The activation energy for such a process is 210 kJ/mol, which is less than either the SiOSi or the SiOH bond energy. Why would a similar mechanism not be expected to play a very important role in the decomposition of long chains of carbon atoms as seen in organic compounds? H3O_1aq2 _ OH_1aq2!2H2O1l2 2Ce4_1aq2 _ Hg2 2_1aq2!2Ce3_1aq2 _ 2Hg2_1aq2 35C 22C 8.1 _ 10_2 s_1 0C 20.C 4.6 _ 10_2 s_1 _ 3.52 _ 10_7 25C. s_1. _1.10 _ 104 K OH_. (CH3)3CBr 1CH323CBr _ OH_! 1CH323COH _ Br_

One mechanism for the destruction of ozone in the upper atmosphere is Slow Fast a. Which species is a catalyst? b. Which species is an intermediate? c. Ea for the uncatalyzed reaction is 14.0 kJ. Ea for the same reaction when catalyzed is 11.9 kJ. What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at ? Assume that the frequency factor A is the same for each reaction.

One of the concerns about the use of Freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the following reaction: Freon-12 Chlorine atoms can act as a catalyst for the destruction of ozone. The activation energy for the reaction is 2.1 kJ/mol. Which is the more effective catalyst for the destruction of ozone, Cl or NO? (See Exercise 65.)

Assuming that the mechanism for the hydrogenation of C2H4 given in Section 12.8 is correct, would you predict that the product of the reaction of C2H4 with D2 would be CH2DOCH2D or CHD2OCH3? How could the reaction of C2H4 with D2 be used to confirm the mechanism for the hydrogenation of C2H4 given in Section 12.8?

The decomposition of NH3 to N2 and H2 was studied on two surfaces: Cl _ O3!ClO _ O2 CCl2F2!hv CF2Cl _ Cl 25C O31g2 _ O1g2!2O2 Overall reaction O31g2 _ O1g2!2O21g2 NO21g2 _ O1g2!NO1g2 _ O21g2 O31g2 _ NO1g2!NO21g2 _ O21g2 Without a catalyst, the activation energy is 335 kJ/mol. a. Which surface is the better heterogeneous catalyst for the decomposition of NH3? Why? b. How many times faster is the reaction at 298 K on the W surface compared with the reaction with no catalyst present? Assume that the frequency factor A is the same for each reaction. c. The decomposition reaction on the two surfaces obeys a rate law of the form Rate _ k 3NH3 4 3H2 4 How can you explain the inverse dependence of the rate on the H2 concentration?

A famous chemical demonstration is the magic genie procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is 70.0 kJ/mol. When the catalyst is added, the activation energy (at ) is 42.0 kJ/mol. Theoretically, to what temperature ( ) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at ? Assume the frequency factor A is constant and assume the initial concentrations are the same.

The activation energy for a reaction is changed from 184 kJ/mol to 59.0 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2400 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant and assume the initial concentrations are the same.

The reaction was studied, and the following data were obtained where Rate _ _ 3O2 4 t What would be the initial rate for an experiment where [NO]0 _ molecules/cm3 and [O2]0 _ molecules/cm3?

Sulfuryl chloride (SO2Cl2) decomposes to sulfur dioxide (SO2) and chlorine (Cl2) by reaction in the gas phase. The following pressure data were obtained when a sample containing mol sulfuryl chloride was heated to 600. K in a - L container. Defining the rate as a. determine the value of the rate constant for the decomposition of sulfuryl chloride at 600. K. b. what is the half-life of the reaction? c. what fraction of the sulfuryl chloride remains after 20.0 h?

For the reaction the following data were collected, where Rate _ _ 3N2O5 4 t 2N2O51g2!4NO21g2 _ O21g2 Calculate Ea for this reaction.

Experimental values for the temperature dependence of the rate constant for the gas-phase reaction are as follows: NO _ O3!NO2 _ O2 Make the appropriate graph using these data, and determine the activation energy for this reaction.

For enzyme-catalyzed reactions that follow the mechanism a graph of the rate as a function of [S], the concentration of the substrate, has the following appearance: Note that at higher substrate concentrations the rate no longer changes with [S]. Suggest a reason for this.

The activation energy of a certain uncatalyzed biochemical reaction is 50.0 kJ/mol. In the presence of a catalyst at the rate constant for the reaction increases by a factor of as compared with the uncatalyzed reaction. Assuming the frequency factor A is the same for both the catalyzed and uncatalyzed reactions, calculate the activation energy for the catalyzed reaction.

Consider the reaction where the rate law is defined as An experiment is carried out where and a. If after 3.00 min, calculate the value of k. b. Calculate the half-life for this experiment. c. Calculate the concentration of B and the concentration of A after 10.0 min.

Consider a reaction of the type in which the rate law is found to be (termolecular reactions are improbable but possible). If the first half-life of the reaction is found to be 40. s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a termolecular reaction:

A study was made of the effect of the hydroxide concentration on the rate of the reaction The following data were obtained: Determine the rate law and the value of the rate constant for this reaction.

Two isomers (A and B) of a given compound dimerize as follows: 2B !k2 B2 Both processes are known to be second order in reactant, and k1 is known to be at . In a particular experiment A and B were placed in separate containers at , where and . It was found that after each reaction had progressed for 3.00 min, . In this case the rate laws are defined as a. Calculate the concentration of A2 after 3.00 min. b. Calculate the value of k2. c. Calculate the half-life for the experiment involving A.

The reaction was studied by performing two experiments. In the first experiment the rate of disappearance of NO was followed in the presence of a large excess of O3. The results were as follows ([O3] remains effectively constant at molecules/cm3): In the second experiment [NO] was held constant at molecules/cm3. The data for the disappearance of O3 are as follows: a. What is the order with respect to each reactant? b. What is the overall rate law? c. What is the value of the rate constant from each set of experiments? d. What is the value of the rate constant for the overall rate law? Rate _ k3NO4x 3O3 4y

Most reactions occur by a series of steps. The energy profile for a certain reaction that proceeds by a two-step mechanism is On the energy profile, indicate a. The positions of reactants and products. b. The activation energy for the overall reaction. c. for the reaction. d. Which point on the plot represents the energy of the intermediate in the two-step reaction? e. Which step in the mechanism for this reaction is rate determining, the first or the second step? Explain.

Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was 16.3 s at and 13.0 s at . a. What is the apparent activation energy of the reaction that controls the flashing? b. What would be the average interval between flashes of an individual firefly at ? c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.

The decomposition of NO2(g) occurs by the following bimolecular elementary reaction: The rate constant at 273 K is and the activation energy is 111 kJ/mol. How long will it take for the concentration of NO2(g) to decrease from an initial partial pressure of 2.5 atm to 1.5 atm at 500. K? Assume ideal gas behavior.

The following data were collected in two studies of the reaction 2A _ B!C _ D In experiment 1, In experiment 2, a. Why is [B] much greater than [A]? b. Give the rate law and value for k for this reaction.

The following data were collected in two studies of the reaction 2H21g2 _ 2NO1g2 !N21g2 _ 2H2O1g2 In experiment 1, In experiment 2, a. Use the concentration versus time data to determine the rate law for the reaction. b. Solve for the rate constant (k) for the reaction. Include units. c. Calculate the concentration of H2 in experiment 1 at

Consider the hypothetical reaction In a study of this reaction three experiments were run at the same temperature. The rate is defined as Experiment 1: 3A40 _ 2.0 M 3B40 _ 1.0 _ 10_3 M 3C40 _ 1.0 M Experiment 2: 3A40 _ 1.0 _ 10_2 M 3B40 _ 3.0 M 3C40 _ 1.0 M Experiment 3: 3A40 _ 10.0 M 3B40 _ 5.0 M 3C40 _ 5.0 _ 10_1 M Write the rate law for this reaction, and calculate the rate constant.

Hydrogen peroxide and the iodide ion react in acidic solution as follows: The kinetics of this reaction were studied by following the decay of the concentration of and constructing plots of versus time. All the plots were linear and all solutions had mol/L. The slopes of these straight lines depended on the initial concentrations of and The results follow: The rate law for this reaction has the form a. Specify the order of this reaction with respect to and[I_]. b. Calculate the values of the rate constants, k1 and k2. c. What reason could there be for the two-term dependence of the rate on ?

Sulfuryl chloride undergoes first-order decomposition at 320.C with a half-life of 8.75 h. What is the value of the rate constant, k, in s_1? If the initial pressure of SO2Cl2 is 791 torr and the decomposition occurs in a 1.25-L container, how many molecules of SO2Cl2 remain after 12.5 h?

Upon dissolving InCl(s) in HCl, In_(aq) undergoes a disproportionation reaction according to the following unbalanced equation: This disproportionation follows first-order kinetics with a half-life of 667 s. What is the concentration of In_(aq) after 1.25 h if the initial solution of In_(aq) was prepared by dissolving 2.38 g of InCl(s) in 5.00 _ 102 mL of dilute HCl? What mass of ln(s) is formed after 1.25 h?

The decomposition of iodoethane in the gas phase proceeds according to the following equation: At 660. K, k _ 7.2 _ 10_4 s_1; at 720. K, k _ 1.7 _ 10_2 s_1. What is the rate constant for this first-order decomposition at 325C? If the initial pressure of iodoethane is 894 torr at 245C, what is the pressure of iodoethane after three half-lives?

Consider the following reaction: At the following two experiments were run, yielding the following data: Experiment 1: [Y]0 _ 3.0 M Experiment 2: [Y]0 _ 4.5 M Experiments also were run at . The value of the rate constant at was found to be (with the time in units of hours), where [CH3X]0 _ 1.0 _ 10_2 M and [Y]0 _ 3.0 M. a. Determine the rate law and the value of k for this reaction at . b. Determine the half-life at . c. Determine Ea for the reaction. d. Given that the COX bond energy is known to be about 325 kJ/mol, suggest a mechanism that explains the results in parts a and c.