Name____________________________________________ Kinetics

Block Info Homework

TEST REVIEW (Answer as you learn them? Wait till the end? This might get assigned….)

1. What are orders? What does it mean to have an order with respect to a reactant? How do you find overall orders? How could you use experimental data to calculate orders?

2. How will making changes to a system change the rate? Temperature? Concentrations?3. Be able to use experimental data to solve for rate laws and rate constants.4. What is activation energy? What other things affect whether a reaction will take place? What is a frequency factor?

Understand how to use the equation: ln (k )=−EaR ( 1

T )+ ln (A)

5. What factors affect rates specifically? (discuss in relation to energy / rxn coordinate graph)6. You are given initial rates and initial concentrations. What do you do? How do you do it? How do you solve for k?

How do you figure out the units of k?7. You are given time and concentration. What do you do? How do you do it? How do you solve for k? How do you

figure out the units of k?8. You are given temperatures and rate constants. What do you do? How do you get Kelvin? What equation will you

work with? What is A? What are its units? What is Ea? What are its units? What value of R should you use?9. What are reaction mechanisms? What is a rate-determining step? What is an elementary reaction? What is an

intermediate? How do you determine the rate law if you’re given a reaction mechanism? How do you select a reaction mechanism if you’re given an experimentally determined rate law?

10. Complete the following problem from an old AP test:For a hypothetical chemical reaction that has the stoichiometry 2 X + Y Z, the following initial rate data were obtained.

All measurements were made at the same temperature.

(a) Give the rate law for this reaction from the data above.(b) Calculate the specific rate constant for this reaction and specify its

units.(c) How long must the reaction proceed to produce a concentration of

Z equal to 0.20 molar, if the initial reaction concentrations are [X]o

= 0.80 molar, [Y]o = 0.60 molar and [Z]0 = 0 molar?(d) Select from the mechanisms below the one most consistent with the

observed data, and explain your choice. In these mechanisms M and N are reaction intermediates.

(1) X + Y M (slow)X + M Z (fast)

(2) X + X M (fast)Y + M Z (slow)

(3) Y M (slow)M + X N (fast)N + X Z (fast)

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Problems from the following texts:Chemistry by Brown, LeMay, BurstenChemistry by Moore, Stanitski, Jurs

Initial Rate of Formation of Z,

(mol.L-1.sec-1) Initial [X]o, (mol.L-1)

Initial [Y]o, (mol.L-1)

7.010-4 0.20 0.10

1.410-3 0.40 0.20

2.810-3 0.40 0.40

4.210-3 0.60 0.60

Reaction Mechanisms

1. (a) What is meant by the term elementary reaction? (b) What is the difference between a unimolecular and a bimolecular elementary reaction? (c) What is a reaction mechanism?

2. [3.] (a) What is meant by the term molecularity? (b)

Why are termolecular elementary reactions so rare? (c) What is an intermediate in a mechanism?

3.[4.] [5.] What is the molecularity of each of the following

elementary reactions? Write the rate law for each.a. Cl2(g) 2Cl(g)b. OCl-(aq) + H2O(l) HOCl(aq) + OH-(aq)c. NO(g) + Cl2(g) NOCl2(g)d. 2 NO(g) N2O2(g)e. SO3(g) SO2(g) + O2(g)

4.[6.] Based on the following reaction profile, how many intermediates are formed in the reaction A D? (b) How many transition sates are there? (c) Which step is the fastest? (d) Is the reaction A D exothermic or endothermic?

5.[7.] Consider the following energy profile.

(a) How many elementary reactions are in the reaction mechanism? (b) How many intermediates are formed in the reaction? (c) Which step is rate limiting? (d) Is the overall reaction exothermic of endothermic?

6.[8.] The following mechanism has been proposed for the gas-phase reaction of H2 with ICl:

H2(g) + ICl(g) HI(g) + HCl(g)

HI(g) + ICl(g) I2(g) + HCl(g)(a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) Write rate laws for each elementary reaction in the mechanism. (d) If the first step is slow and the second one is fast, what rate law do you expect to be observed for the overall reaction?

7.[9.] The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism:

H2O2(aq) + I-(aq) H2O(l) + IO-(aq) (slow)IO-(aq) + H2O2(aq) H2O(l) + O2(g) + I-(aq) (fast)

(a) Write rate laws for each elementary reaction in the mechanism. (b) Write the chemical equation for the overall process. (c) Identify the intermediates, if any, in the mechanism. (d) Assuming the first step of the mechanism is rate determining, predict the rate law for the overall process?

8.[10.] The reaction 2NO(g) + Cl2(g) 2NOCl(g) obeys the rate law, rate = k[NO]2[Cl2]. The following mechanism has been proposed for this reaction:

NO(g) + Cl2(g) NOCl2(g)NOCl2(g) + NO(g) 2NOCl(g)

(a) What would the rate law be if the first step were rate determining? (b) Based on the observed rate law, what can we conclude about the relative rates of the two steps?

9.[11.] You have studied the gas-phase oxidation of HBr by O2:

4HBr(g) + O2(g) 2H2O(g) + 2Br2(g)You find the reaction to be first order with respect to HBr and first order with respect to O2. You propose the following mechanism:

HBr(g) + O2(g) HOOBr(g)HOOBr(g) + HBr(g) 2 HOBr(g)

HOBr(g) + HBr(g) H2O(g) + Br2(g)(a) Indicate how the elementary reactions add to give the overall reaction. (Hint: You will need to multiply the coefficients of one of the equations by 2.) (b) Based on the rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or

2

HOOBr among the products, does this disprove your mechanism?

[12.] 13.70When the rate of the reaction 2NO(g) + O2(g) 2NO2(g) was studied, it was found that the rate doubled when the O2 concentration alone was doubled, but quadrupled when the NO concentration alone was doubled. Which of the following mechanisms accounts for these observations?

(a) Step 1. NO + O2 NO3, and its reverse (both fast) Step 2. NO + NO3 NO2 + NO2 (slow)

(b) Step 1. NO + NO N2O2 (slow) ) Step 2. O2 + N2O2 N2O4 (fast) ) Step 3. N2O4 NO2 + NO2 (fast)

Method of Initial Rates Practice Problems

10.[13.] Rate data were collected for the following reaction at a particular temperature.

[14.] A + B Products

Expt. Initial [A] (mol/L)

Initial [B] (mol/L)

Initial Rate of Rxn (M•S-1)

1 0.10 0.10 0.00902 0.20 0.10 0.0363 0.10 0.20 0.0184 0.10 0.30 0.027a. What is the rate-law expression for this reaction?

b. Describe the order of the reaction with respect to each reactant and to the overall order.

11.[15.] Rate data were collected for the following reaction at a particular temperature.

2ClO2 (aq) + 2OH- (aq)ClO3- (aq) +ClO2

- (aq) +H2O (l)

Expt. Initial [ClO2] (mol/L)

Initial [OH-] (mol/L)

Initial Rate of Rxn (M•S-1)

1 0.012 0.012 2.07 x 10-4

2 0.024 0.012 8.28 x 10-4

3 0.012 0.024 4.14 x 10-4

4 0.024 0.024 1.66 x 10-3

[a.] What is the rate-law expression for this reaction?a.[b.] Describe the order of the reaction with respect to

each reactant and to the overall order.

12.[16.] The reaction: [17.] (C2H5)2(NH)2 + I2 (C2H5)2N2 + HI

gives the following initial rates.I

Expt. [(C2H5)2(NH)2]0 (mol/L)

[I2]0 (mol/L)

Initial Rate of Formation of (C2H5)2N2

1 0.015 0.015 3.15 M • s-1

2 0.015 0.045 9.45 M • s-1

3 0.030 0.030 12.6 M • s-1

Write the rate-law expression and solve for the constant.

13.[18.] The reaction: [19.] 2NO(g) + Cl2(g) 2NOCl(g)[20.]

was studied at -10°C. The following results were obtained

[NO]0 (mol/L) [Cl2]0 (mol/L) Initial Rate(mol/L •s)

0.10 0.10 0.180.10 0.20 0.360.20 0.20 1.45a. What is the rate law?

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b. What is the value of the rate constant?

14.[21.] The reaction:[22.]

2I-(aq) + S2O82-(aq) I2(aq) + 2SO4

2-(aq)

[I-]0 (mol/L) [S2O8

2-]0 (mol/L) Initial Rate (mol/L • s)

0.080 0.040 12.5 × 10-6

0.040 0.040 6.25 × 10-6

0.080 0.020 6.25 × 10-6

0.032 0.040 5.00 × 10-6

0.060 0.030 7.00 × 10-6

a. Determine the rate law.b. Calculate a value for the rate constant for each

experiment and an average value for the rate constant.

15.[23.] Given these data for the reaction A + B C, write the rate-law expression and solve for the constant.

Expt. Initial [A] (M)

Initial [B] (M)

Initial Rate of Formation of C (M • s-1)

1 0.20 0.10 5.0 × 10-6

2 0.30 0.10 7.5 × 10-6

3 0.40 0.20 4.0 × 10-5

16. Given these data for the reaction A + B C, write

the rate-law expression and solve for the constant.

Expt. Initial [A] (M)

Initial [B] (M)

Initial Rate of Formation of C(M • s-1)

1 0.25 0.15 8.0 × 10-5

2 0.25 0.30 3.2 × 10-4

3 0.50 0.60 5.12 × 10-3

17. The rate of the reaction between hemoglobin (Hb) and carbon monoxide (CO) was studied at 20°C. The following data were collected with all concentration unites in µmol/L. (A hemoglobin concentration of 2.21 µmol/L is equal to 2.21 × 10-6 mol/L.)

[Hb]0 (µmol/L) [CO]0 (µmol/L) Initial Rate (µmol/L • s)

2.21 1.00 0.6192.21 2.00 1.244.42 4.00 4.95a. 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 [Hb]0 = 3.36 µmol/L and [CO]0 = 2.40 µmol/L?

18.[24.] The following data were obtained for the reaction

[25.]

2ClO2(aq) + 2OH-(aq)ClO3-(aq) + ClO2

-(aq) + H2O(l)

[ClO2]0 (mol/L) [OH-]0 (mol/L) Initial Rate (mol/L • s)

0.0033 0.0750 5.75 × 10-2

0.1000 0.1000 2.30 × 10-1

0.1000 0.0500 1.15 × 10-1

a. Determine the rate law and the value of the rate constant.

b. What would be the initial rate for an experiment with [ClO2]0 = 0.175 mol/L and [OH-]0 = 0.0844 mol/L?

19.[26.] The following data was collected for the rate of disappearance of NO in the reaction 2NO(g) + O2(g) 2NO2 (g):

Expt.

[NO] (M)

[O2] (M)

Initial Rate (M/s)

1 0.0126 0.0119 1.41 x10-2

2 0.0252 0.0250 1.13 x10-1

3 0.0252 0.0125 5.64 x10-2

a. What is the rate law for the reaction?b. What are the units of the rate constant?

c. What is the average value of the rate constant calculated from the three data sets?

20.[27.] Consider the gas-phase reaction between nitric oxide and bromine at 273°C: 2NO (g) + Br2 (g)

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2NOBr (g). The following data for the initial rate of appearance of NOBr were obtained:

Expt [NO] (M) [Br2] (M) Initial Rate (M/s)

1 0.10 0.20 242 0.25 0.20 1503 0.10 0.50 604 0.35 0.50 735

a. Determine the rate law.b. Calculate the average value of the rate constant for

the appearance of NOBr from the four data sets.c. How is the rate of appearance of NOBr related to

the rate of disappearance of BR2? d. What is the rate of disappearance of Br2 when [NO]

= .075M and [Br2] = .185M

21.[28.] The following kinetic data were obtained for the reaction 2ICl (g) + H2 (g) I2 (g) + 2 HCl (g):

Expt [ICl]0 (M) [H2]0 (M) Initial Rate (mmol/L•s)

1 1.5 1.5 0.372 3.0 1.5 0.743 3.0 4.5 2.24 4.7 2.7 ?

a. Write the rate law for the reaction.b. From the data, determine the value of the rate

constant.c. Use the data to predict the initial rate for

experiment 4.

Half-Life*For first-order reactions ONLY, half-life is independent of starting concentration. For all other reaction orders, the half-life will depend on the starting concentration. *Be able to estimate half-lives of first-order reactions from graphs

22.[29.] The half-life of a certain first-order reaction is 15 minutes. What fraction of the original reactant concentration will remain after 2.0 hours?

23.[30.] A certain first-order reaction has a rate constant k=1.6x10-3 s-1. What is the half-life for this reaction?

24.[31.] The decomposition of NOCl, the compound that gives a yellow-orange color to aqua regia (a mixture of concentrated HCl and HNO3 that’s able to dissolve gold and platinum) follows the reaction 2NOCl 2NO + Cl2. It is a second-order reaction with k=6.7x10-4 M-1 s-1 at 400K. What is the half-life of this reaction if the initial concentration of NOCl is 0.20 M?

[32.]

Rates of Chemical Reactions Lab: Iodination of Acetone A Summative LabThis lab involves a reaction where one of the hydrogens in acetone (commonly used as a paint remover) is replaced with an iodine atom.

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CH 3 COCH 3 (aq) + I 2 (aq) CH 3 COCH 2 I(aq) + H +

(aq) and I - (aq)

The rate of the reaction is dependent not only on acetone and iodine but also on hydrogen ions. Acid serves as a catalyst for this reaction. The rate law or rate law expression for this reaction is: Rate = k [acetone] m [I 2 ] n [H + ] p

Our goal will be determine the k, m, n,

and p from the rate expression above using the method of initial rates.

Procedure for Part A: Select five test tubes. They should be clean and have no coloration to them. Fill one with distilled water. This is your control. Label the others 1-4.Label three beakers “acetone”, “HCl” and “I 2 ”. Add a small amount (~15 mL) of the appropriate chemical to each beaker, and bring back to your lab bench.

6

In test tubes 1-4 add the following amounts of each chemical:

Test Tube

Acetone (mL)

Hydrochloric acid (mL)

Distilled water (mL)

1 2 2 4

2 2 2 2

3 4 2 2

4 2 4 2

In test tube 1, add 2mL of iodine solution, start timer, and stir. Holding

it in front of a white paper, mark the time when the solution just clears. In test tube 2, add 4mL of iodine solution, start timer, and stir. Holding it in front of a white paper, mark the time when the solution just clears. In test tube 3, add 2mL of iodine solution, start timer, and stir. Holding it in front of a white paper, mark the time when the solution just clears.In test tube 4, add 2mL of iodine solution, start timer, and stir. Holding

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it in front of a white paper, mark the time when the solution just clears.When the reaction is complete, pour the contents of the test tube into the beaker labeled “Waste” in the fume hood. Do not pour the contents of the test tube into the sink. Rinse the test tube with distilled water (placing the distilled water into the waste container and invert on your test tube rack to dry.

Calculations in Part B:

The initial concentration of the reactions in the mixture will be less than the initial concentration of the pure solutions because of dilution by the other components of the mixture (the water from the other solutions will dilute all your initial concentrations). Remember the dilution equation: M c V c = M d V d ? M c and V c represent the initial molarity and volume of the pure reactants, where as M d and V d

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represent the initial molarity and volume of the reactants in the mixture . The final volume will always be 5ml. Use this equation and data from part A to complete the first three columns in the data table for part B.

The rate of the reaction in Data Table B equals the initial concentration of I 2 in the reaction mixture divided by the elapsed time from part A (we assume that the final concentration of iodine is zero). Calculate the

rate. Finally, using the method of initial rates calculate the m, n, and p in the rate equation. Then find k for each mixture and the average k for the reaction.

Procedure for Part C Choose whatever volumes you wish for the reactants but keep the total volume of the mixture at 5ml. Reduce the amount of water accordingly. Find the initial concentrations, and using the equation you

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found from Part B to predict the rate and reaction time. Then perform the experiment and determine the actual time.

Procedure for Part DWe will investigate the effect of temperature on the iodination of acetone. Select one of the reaction mixtures you have already used that gave a convenient time, and use that mixture to measure the rate at two different temperatures (~10°C and ~ 40°C). A

beaker with cold water and a hot plate with the warm water will be set up at the back of the room. Initiate the reaction as you did in Part A, note your initial time, and move the tube to the cold water. Record the time required for the color of the iodine to disappear. Repeat with the warm water bath. From these two rates plus the rate at room temperature, calculate the activation energy of the reaction by graphical analysis. You may use your

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graphing calculator to perform a linear regression of your data. However, sketch a graph of your data using the provided grid.

Finally, write a conclusion paragraph with the following (approximate number of sentences in parentheses): purpose (2), basics of procedure (3), k and the orders (2), short explanation of how you found k/orders (3), and two sources of error (at least one of

them should be systematic) and how those would have affected k and the orders (4).

Help with data tables

(put these in the appropriate locations; I would leave space to reference what pages your work is on)

A. Reaction Rate Data

Mixtur

Volume

Volum

Volum

Volum

Total V

Total tim

Temperatur

11

e of 4.0M acetone (mL)

e of 1.0 M HCl (mL)

e of 0.005 M I2

(mL)

e of H2

O (mL)

olume added (mL)

e elapsed (seconds)

e (°C)

1

2

3

4

B. Determination of Reaction Orders with Respect to Acetone, H + , and I 2 . *M 1 V 1 = M 2 V 2

Mixture

*[acetone]

*[H+

]

*[I2 ]

Rate = *[I2 ]/time

1

2

12

3

4

C. Determination of the Rate Constant k

Mixture

1 2 3 4 Average

k

D. Determination of Activation Energy Reaction mixture used (you picked):________

DATA Time(seconds)

Temperature (°C)

Temperature (K)

Cold:

Room:

Hot:

CALCULATIONS Temperature (Kelvin)

Rate

k 1/T

ln(k)

Cold:

Room:

Hot:

13

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Integrated Rate Law

25.[33.] [34.] 43For the reaction Aproducts. Successive half-

lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A]0 = 0.10 M. Calculate the concentration of A at the following times given the orders.

a. 80.0 min if the reaction is first orderb. 30.0 min if the reaction is second order

[35.] 73The reactionNO(g) + O3(g) NO2(g) + O2(g)

was studied by performing two experiments. In the first experiment the rate of disappearance of NO was followed by the presence of a large excess of O3. The results were as follows ([O3] remains effectively constant at 1.0 x 1010 molecules/cm3):

Time (ms) [NO] (molecules/cm3)0 6.0 x 108

100 ± 1 5.0 x 108

500 ± 1 2.4 x 108

700 ± 1 1.7 x 108

1000 ± 1 9.9 x 107

If the reaction is known to be second order with respect to ozone, write the rate law expression for the reaction.

26.[36.] [37.] [38.] The thermal decomposition of ammonia at high

temperatures was studied in the presence of inert gases. Data at 2000 K are given for a single experiment.

NH3 NH2 + Ht (hours) [NH3] (mol/L)0 8.000 x 10-7

25 6.75 x 10-7

50 5.84 x 10-7

75 5.15 x 10-7

Plot the appropriate concentration expressions against time to find the order of the reaction. Find the rate constant of the reaction from the slope of the line. Use the given data and the appropriate integrated rate equation to check your answer.

27.[39.]

[40.] The following data were obtained from a study of the decomposition of a sample of HI on the surface of a gold wire. (a) Plot the data to find the order of the reaction, the rate constant, and the rate equation. (b) Calculate the HI concentration in mmol/L at 600 seconds.

t (seconds) [HI] (mmol/L)0 5.46250 4.10500 2.73750 1.37

[41.] 33The dimerization of butadiene 2C4H6(g) C8H12(g)

was studied at 500 K, and the following data were obtained.

Time (s) [C4H6] (mol/L)195 1.6 x 10-2

604 1.5 x 10-2

1246 1.3 x 10-2

2180 1.1 x 10-2

6210 0.68 x 10-2

Assuming: Rate= - -∆[C4H6]/ ∆t, determine the form of the rate law, the integrated rate law, and the rate constant for this reaction. (These are actual experiments so the line may not be perfectly straight.)28.

29. The rate of the reaction O(g)+NO2(g)NO(g)+O2(g)

was studied at a certain temperature. In the first set of experiments, NO2 was in large excess, at a concentration of 1.0x1013 molecules/cm3 with the following data collected:

Time(s) [O] (atoms/cm3 )0 5.0x109 1.0x10-2 1.9x109 2.0x10-2 6.8x108 3.0x10-2 2.5x108

a. 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.

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30. The following data were measured for the reaction BF3 (g) + NH3 (g) F3BNH3 (g)

Expt [BF3] (M) [NH3] (M) Initial Rate (M/s)

1 0.250 0.250 0.21302 0.250 0.125 0.10653 0.200 0.100 0.06824 0.350 0.100 0.11935 0.175 0.100 0.0596

a. What is the rate law for the reaction?b. What is the overall order of the reaction?c. What is the value of the rate constant for the

reaction?

[42.] The reaction A B + C is known to be zero order in A and to have a rate constant of 5.0x10-2 mol/L]

[43.] ◦s at 25°C where [A]0=1.0x10-3 M.a. Write the integrated rate law for this reaction.b.[a.] Calculate the half-life for the reaction

c.[b.] Calculate the concentration of B after 5.0x10- 3 s has elapsed.

31. The radioactive isotope 32 P 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 for 32 P to decay?

32. A first-order reaction is 38.5% complete in 480sa. Calculate the rate constant?b. What is the value of the half-life?c. How long will it take for the reaction to go to 25%, 75%, and 95% completion?

33. It took 143 s for 50.0% of a particular substance to decompose. If the initial concentration was 0.060 M and the decomposition reaction follows second-order kinetics, what is the value of the rate constant?

34.[44.] The decomposition of SO2Cl2 in the gas phase, SO2Cl2 SO2 + Cl2

can be studied by measuring the concentration of Cl2 as the reaction proceeds. We begin with [SO2Cl2]0 = 0.250 M.

Holding the temperature constant at 320o C, we monitor the Cl2 concentration, with the following results.

t(hours) [Cl2] (mol/L)0.00 0.0002.00 0.0374.00 0.0686.00 0.0958.00 0.11710.00 0.13712.00 0.15314.00 0.16816.00 0.18018.00 0.19020.00 0.199

Plot [Cl2] versus t. (b) Plot [SO2Cl2] versus t. (c) Determine the rate law for this reaction. (d) What is the value, with units, for the specific rate constant at 320°C? (e) How long would it take for 95% of the original SO2Cl2 to react?

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Arrhenius Equation

35.[45.] Temperature Dependence of Rate Constant for Iodide Plus Bromomethane Reaction

Calculate the frequency factor and the activation energy.

36.[46.] These data were obtained for the rate constant for reaction of an unknown compound with water:

[a.] Calculate the activation energy and frequency factor for this reaction.

a.[b.] Estimate the rate constant of the reaction at a temperature of 100.0°C

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T (K) k273 4.18E-05280 9.68E-05290 2.00E-04300 8.60E-04310 2.31E-03320 5.82E-03330 1.39E-02340 3.14E-02350 6.80E-02360 1.41E-01370 2.81E-01

T (°C) K (s1-) T (°C) k (s1-) 25.0 7.95x10-8 56.2 1.04x10-5

30.0 2.37 x10-7 78.2 1.45 x10-4