Answers

Method of Initial Rates

How can you use rate data to determine the order of a reaction?

Why?
In most cases, the rate law for a chemical reaction cannot be derived theoretically. If the reaction is a
multi-step reaction, the rate law does not correspond to the balanced chemical equation. Finding the rate
law would be simple if we could observe the reactions at the molecular level, but that is not possible. We
must use indirect evidence. There are many experimental techniques that can be used to determine the
rate law for a reaction. Determining the initial rate of a reaction and seeing how that initial rate changes
when the concentrations of reactants are changed is one way of using experimental data to determine the
rate law.

Model 1 – The Effect of Exponents

y = kx n
where k = 5
x If n = 0, then y = ? If n = 1, then y = ? If n = 2, then y = ?

1
5 5 5
2
5 10 20
3
5 15 45
4
5 20 80
1. Consider the mathematical equation in Model 1.
a. What letter represents a constant in the equation?

K
b. What is the value of the constant?

k 5
c. What letter represents the exponent in the equation?

n
d. Does x in the equation represent the independent variable, dependent variable or a constant?

independent this is y
2. Fill in the table in Model 1 using the mathematical equation provided. Divide the work among
group members.

Method of Initial Rates 1

 3. Refer to Model 1. Use complete sentences to describe the change in y as x increases when n = 0.
Justify the pattern you see using your knowledge of mathematics.

does not change when n o as n o makes

y the value of X I
4. Refer to the column in the Model 1 table where n =regardless
1. of x's value
a. When x doubles, what happens to y?

doubles
b. When x triples, what happens to y?

triples
5. Use a complete sentence to describe the change in y as x increases when n = 1. Justify the pat-
tern you see using your knowledge of mathematics.

it is a direct 9
relationship
6. Refer to the column in the Model 1 table where n = 2.
a. When x triples, what happens to y?

multiplies by 9
b. When x quadruples, what happens to y?

multiplies by 16
7. Use a complete sentence to describe the change in y as x increases when n = 2. Justify the pat-
tern you see using your knowledge of mathematics.

it is an exponential 9
relationship
8. Consider the data below and determine the value of the exponent q. Justify your answer with an
explanation or a mathematical equation.
r = st q
t r
5 15

3x
2 1 10 30 742 3
15 45

is 1 direct
q relationship
9. Solve for the constant s in Question 8 above.

r st9 the constant

is 3
15 s 5
2 POGIL™ Activities for AP* Chemistry
3 5
 10. Consider the data below and determine the value of the exponent q. Justify your answer with an
explanation or a mathematical equation.
r = st q
t r
10 3
2 1 1 Nochange
20
30 1 3 3
3

5 5
q this will be
regardless
11. Consider the data below and determine the value of the exponent of the value of t
q. Justify your answer with an
explanation or a mathematical equation.
exp
r = st q rate
8
t
2
r
12
9 3
2 1 4 ax
4
6 1 3 48
108

2
q
12. Solve for the constant s in Question 11 above.

r st the constant is 3
12 5 2
3 S

Method of Initial Rates 3

Model 2 – Decolorization of a Dye
rate = k[dye]n Ratan
where k = 3.40 × 103

[dye] If n = 0, then rate = ? If n = 1, then rate = ? If n = 2, then rate = ?

m
0.10 M
3 40 103 1 3.40 102 1 34
0.20 M
3 40 103 It 6.80 102 ME 136 m
0.30 M
3 40 103 mots 1.02 103 1 306 met
13. Identify the reactant in the process being studied in Model 2.

the dye is the reactant

14. Refer to Model 2.
a. Circle the rate law for the decolorization of a dye in Model 2.

b. What variable represents the constant in the rate law?

k
c. What variable represents the order of the reaction?

h
15. Fill in the table in Model 2. Divide the work among group members. Note: The unit for rate
should be “molarity per second” in all cases.

16. How does the initial rate of reaction change as the concentration of the reactant increases when
the order of the reaction is zero?

the rate is unaffected

17. How does the initial rate of reaction change as the concentration of the reactant increases when
the order of the reaction is one?

when 2 rate x2 direct

relationship
18. How does the initial rate of the reaction change as the concentration of the reactant increases
when the order of the reaction is two?

when 7 2 rate 4 exponential

relationship

4 POGIL™ Activities for AP* Chemistry

 19. Consider the data below.
rate = k[O3]n
[O3] Initial Rate
0.44 atm 0.01848 atm/min
2 0.88 atm 0.03696 atm/min X2
a. Determine the order of the reaction with respect to ozone. Justify your answer with an expla-
nation or a mathematical equation.

whenT x 2 rate X2
direct relationship
r α 03
b. Use one set of data from the table to calculate the value and unit of k. Hint: What unit must
k have in order for the rate to have the unit atm/min?
rate K 03
K 0 t
20. Consider the data below. ftp fit 0421min or min
rate = k[KI]n
[KI] Initial Rate
0.10 M 8.4 × 10 −6 M/s
3 0.30 M 8
7.6 × 10 −5 M/s 7 9 why 786 9
a. Determine the order of the reaction with respect to potassium iodide. Justify your answer
with an explanation or a mathematical equation.

when KI 3 rate x 9 exponential

relationship
9 3 2
r α KI
b. Use one set of data from the table to calculate the value and unit of the rate constant k.
Hint: The units of k in this question will not be the same units as the k in Question 19.
2
rate K KI

8 4 10 k 0.10m
67

Method of Initial Rates 5

4
K 8.4 10 s
 21. Consider the data below.
rate = k[H2O2]n
[H2O2] Initial Rate
0.20 M 382 M/s
Cintreased 0.56 M 382 M/s Inchange
a. Determine the order of the reaction with respect to hydrogen peroxide. Justify your answer
with an explanation or a mathematical equation.

concentration increases ratedenotchange

2.8 increase
rα 420270
b. Use one set of data from the table to calculate the value and unit of the rate constant k.

rate K 4202 K
382m k 10.20 3827
me
Read This!
The rate of a reaction is obtained by determining the concentration of a reactant or product in the reac-
tion over time. This could occur through spectrophotometry for colored solutions, pressure changes for
gaseous components, temperature changes for highly endothermic or exothermic reactions or pH for acids
or bases—just to name a few. When concentration data are graphed versus time the slope of the curve is
the rate of the reaction at that moment. Because the rate may change as the concentrations of reactants
change the initial rate is the most dependable data point to use when determining the order of a reaction.

Model 3 – Reaction with Two Reactants

[N2] [H2] Initial Rate
Trial 1 4.3 × 10 −3 M 2.2 × 10 −4 M 9.60 × 10 −6 M/s
Trial 2 4.3 × 10 −3 M 4.4 × 10 −4 M 9.60 × 10 −6 M/s
Trial 3 8.6 × 10 −3 M 4.4 × 10 −4 M 1.92 × 10 −5 M/s

22. What are the reactants of the process being studied in Model 3?

N2 H2
23. Consider the data in Model 3.
a. Compare the concentration of nitrogen in trials 1 and 2.

same
b. Compare the concentration of nitrogen in trials 1 and 3.

doubled
6 POGIL™ Activities for AP* Chemistry
Read This!
When there are multiple reactants in a process, each reactant must be studied independently while the
other reactant is held at constant concentration. This allows the experimenter to determine the effect of
changing the concentration of a specific reactant on the initial rate.

24. Consider the data in Model 3.

a. Which trials should be considered when determining the order of reaction with respect to
nitrogen gas?
the conc
trial 2 3 changes
but conc of H2 doeynotage
b. Which trials should be considered when determining the order of reaction with respect to
hydrogen gas?
the conc
trial 1 2 changes
but conc
of Nz doennotage
25. Explain why no useful conclusion about the exponents of the rate law could be drawn by com-
paring the data in trials 1 and 3 of Model 3.

the concentration both reactants are

of rate tells
changing the resulting change
nothing
usto nitrogen.
26. Determine the order of reaction with respect

Nz Rate

2x 3 Mm
T.is Y stlis x2
direct relationship
27. Determine the order of reaction with respect to hydrogen.
r α N2 filter
Rate
2x 444 Éi.mn 8Thischange
x

no
relationship α HIT 89dm
28. Write the full rate law for the process in Model 3.

r K N2 H2
o r k Na
Method of Initial Rates 7
 29. Use data from Model 3 to determine the value and unit of the rate constant, k, in the rate law.

rate K N2
9.6 10 6Mls K 4.3 10 3M
K 2.23 103 or s
t
30. Use the data below to determine the rate law for the process shown. Include the value and units
on the rate constant k in your answer.
2NO (g) + O2 (g) → NO2 (g)

Initial [NO] Initial [O2] Initial Rate of Formation

Experiment
(mole L−1) (mole L−1) of NO2 (mole L−1s−1)
1 0.10 0.10 2.5 × 10 –4
2 2 1 0.20 0.10
3
5.0 × 10 –4
3 0.20 0.40 1 4 8.0 × 10 –3 6

ra NO rx 02
rate K NO 02
2.5 10 meds k 0.10m 0.10m

k
1 1st

8 POGIL™ Activities for AP* Chemistry