Phys. Chem. Lab., 2010, Fall, Expt.3
Iodate Reduction: Using the Iodine Clock Reaction to
Determine the Rate Law and Activation Energy
Trinda Wheeler,* Jason Smarkera
Physical Chemistry Laboratory, 4014 Malott Hall, Department of Chemistry, University of Kansas
*
Corresponding author: [email protected], aLab Partner, CHEM 649
Received: November 1, 2010
Initial rates of reaction for the reduction of iodate were measured for a variety of reactant concentrations. Comparing the initial rates of reaction with the known concentrations of reactants allowed us
to determine the rate law to be: r kT [ IO3 ][ I ]2 [ H ]2 . This rate law allowed us to evaluate the plausibility of several proposed reaction mechanisms. Further tests were run, keeping all reactant concentrations equivalent but varying the ambient temperature of the reaction in order to generate an Arrhenius plot of ln(kT) vs. 1/T. The linear relationship then allowed us to calculate an activation energy (Ea)
for the reaction of 16.86 0.07kJ/mol, and a frequency factor (A) of 3.56x1012 4x1010s-1.
I. Introduction
Chemical kinetics is the study of reaction rates and
reaction mechanisms. A reaction rate is the rate at
which a chemical reaction takes place, and is measured
by the rate of formation of the product(s), or the rate of
disappearance of the reactants3. This can also be stated
as the change in concentration of reactants or products
over time. A reaction mechanism is the way in which a
chemical reaction takes place, which is expressed in a
series of chemical equations, or reaction steps3. Kinetics helps us understand the molecular changes that take
place during the reaction from reactants to products.
There are different ways in which molecules can
react. A unimolecular reaction involves the break-up of
a molecule into constituent parts; a bimolecular reaction
involves two atoms or molecules combining to form a
new molecule; and a termolecular reaction involves
three atoms or molecules combining to form a new molecule. Because these different types of reactions exist,
multiple reaction mechanisms can be proposed to explain the kinetics of a particular reaction. Proposed
reaction mechanisms can be evaluated by determining
the rate law that corresponds to a reaction mechanism
and comparing it with an experimentally determined
rate law for the reaction1.
The rate law for a reaction can be expressed as:
r
kT [ A]m [ B]n [C ] p ...
(1)
where r is the rate of the reaction, kT is the temperaturedependent rate constant, [A] etc. is the concentration of
a reactant and m etc. are the orders of reaction with
respect to their corresponding reactants. These orders
can be determined from the stoichiometry of the ratedetermining (slow) step of the reaction mechanism, or
experimentally by systematically varying the concentration of one or more reactants in the method of initial
rates1.
In this experiment, we examined the initial reaction
rate, or the rate before any significant changes in concentration occur3, of the reduction of iodate:
IO3
8I
6H
3I 3
3H 2O
(2)
whose rate law can be written generically as:
r
kT [ IO3 ]m [ I ]n [ H ] p
(3)
The iodine clock reaction allows us to quantify the
amount of I 3 (triiodide) produced over a measured period of time by including a starch solution and a small,
calculated amount of arsenious acid, H 3 AsO3 . Triiodide reacts with starch to produce a dark blue solution;
however arsenious acid reacts quickly and completely
with triiodide in the reaction2:
(4)
H 3 AsO3 I 3 H 2O HAsO42 3I 4H
which quenches the triiodide until all the arsenious acid
has reacted. At that point, the triiodide reacts with the
starch and the solution turns blue2. Since the stoichiometric ratio of triiodide to arsenious acid in equation 4
is 1:1, we know that once the solution turns blue, an
equivalent number of moles of triiodide has been
formed as the number of moles of arsenious acid that
were added to the solution.
The initial rate of reaction is then calculated as the
change in concentration of triiodide over time:
Lab Report, Page 1
r
1 d[I3 ]
3 dt
(5)
Phys. Chem. Lab. I, 2010, Fall, Expt. 3
Note that the reaction rate is the rate of formation of
triiodide divided by 3 to account for the stoichiometry
in equation 2. Multiple test runs were conducted, systematically changing the concentration of one reactant
at a time which affected the rate of reaction according
to the order of reaction with respect to that reactant.
Once two test runs have been completed where only the
concentration of one reactant was changed, that order of
reaction can be calculated using the equation:
r1 k[ IO3 ]1a [ I ]1b [ H ]1c
(6)
r2 k[ IO3 ]a2 [ I ]b2 [ H ]c2
since r1 and r2 are calculated values (equation 5), and
all values except the concentration of the reactant in
question will cancel out. The process is repeated until
all three orders are determined. Orders are generally
integers, unless the stoichiometry of the reaction mechanism dictates a fraction, so experimental values are
rounded to the nearest integer1. Once the rate law is
determined, it can be compared with the rate laws of
proposed reaction mechanisms to determine which, if
any, are plausible.
NaAc●3H2O and 1.25mL HAc from the laboratory
chemical storage shelf, and 20mL of a starch solution
which was prepared and provided by the TA with distilled water in a 500mL volumetric flask. The experimental method1 called for anhydrous sodium acetate,
and it was not until after Buffer A was prepared that the
TA pointed out to us that we had used NaAc●3H2O.
The final pH of Buffer A was 4.75, as measured with a
pH meter. An additional 10mL of starch solution was
added to Buffer A on the second lab day, which slightly
altered the pH to 4.76. Buffer B was prepared using
3.07g anhydrous NaAc and 0.63mL HAc from the laboratory chemical storage shelf and 10mL of starch
solution provided by the TA with distilled water in a
250mL volumetric flask. Our preparation calculations
for Buffer B had to be altered in lab to prepare the appropriate volume of Buffer B, and we miscalculated the
required volume of HAc, which should have been approximately double what we used. The final pH of
Buffer B was 4.64 as measured with a pH meter. See
Appendix A for calculations of stock solution concentrations and propagation of error.
Knowing the rate law not only allows us to evaluate reaction mechanisms, but also to determine the
activation energy (Ea) and frequency factor (A) of the
reaction using the Arrhenius equation2:
(7)
kT Ae Ea / RT
which becomes a linear equation by taking the log of
both sides,
Ea 1
ln( kT )
ln A
(8)
R T
therefore, Ea (slope x -R) and A (y-intercept) can be
determined by plotting ln(kT) vs. 1/T, where kT is calculated from the completed equation 3, in which r is calculated using equation 5, at temperature T. The activation energy is the change in potential energy of the
reactants required in order to begin the reaction 3, and
the frequency factor is related to the collision frequency
of molecules in the solution.
A. Concentration dependent test runs Each test
run was completed in triplicate in 25mL Erlenmeyer
flasks. Three flasks were loaded with 5mL I - solution.
Three additional flasks were loaded with H3AsO3 solution, IO3- solution, and a buffer as listed in Table 1 with
mechanical pipettes. All test runs were completed at
room temperature on the lab bench. A digital Fisher
Scientific timer was started concurrently with the initial
mixing of the flasks and the reaction time was recorded
to the second by watching for the first moment of color
change.
Test
Run
1
2
3
4
5
H3AsO3
(mL)
1
1
1
1
1
IO3(mL)
1
2
1
1
2
Buffer A
(mL)
13
12
8
7
Buffer B
(mL)
13
-
Table 1. Stock Solution Volumes
II. Experimental Approach
In the first lab period, stock solutions of 0.03M
H3AsO3, 0.1M IO3-, 0.2M I-, and “Buffer A” were prepared. The final stock solution, “Buffer B,” was prepared in the second lab period. The H3AsO3 solution
was prepared using 0.1933g NaAsO2 and 86 L glacial
acetic acid (HAc) from the laboratory chemical storage
shelf with distilled water in a 50mL volumetric flask.
The IO3- solution was prepared with 1.0708g KIO3
from the laboratory chemical storage shelf and distilled
water in a 50mL volumetric flask. The I - solution was
prepared with 8.3056g KI from the laboratory chemical
storage shelf and distilled water in a 250mL volumetric
flask.
“Buffer A” was prepared using 6.1602g
Once the stock solution concentrations were calculated, and taking the above volumes into account, the
concentrations of the reactants in the test solutions can
be determined. These values are shown in Table 2.
Test
Run
1
2
3
4
5
[IO3-]
mol/L
5.00x10-4
1.00x10-3
5.00x10-4
5.00x10-4
1.00x10-3
[I-]
mol/L
5.00x10-2
5.00x10-2
1.00x10-1
5.00x10-2
1.00x10-1
[H+]
mol/L
1.74x10-5
1.74x10-5
1.74x10-5
2.29x10-5
1.74x10-5
[H3AsO3]
mol/L
1.49x10-3
1.49x10-3
1.49x10-3
1.49x10-3
1.49x10-3
Table 2. Reactant Concentrations in Test Solutions
Lab Report, Page 2
Phys. Chem. Lab. I, 2010, Fall, Expt. 3
B. Temperature dependent test runs Each test
run was completed in triplicate in 25mL Erlenmeyer
flasks. Three flasks were loaded with 1mL H3AsO3
solution, 1mL IO3- solution, and 13mL Buffer A using
mechanical pipettes. Three additional flasks were
loaded with 5mL I- solution. Prior to mixing the contents from the first flasks with the second flasks, all
flasks were allowed to equilibrate to the test temperature. Table 4 includes the temperatures at which the
test runs were completed. With the exception of run 1,
which was completed at room temperature on the lab
bench, the flasks were heated in a water bath with a
digital temperature control and display. The actual
temperature of the water bath was recorded using a
standard thermometer. A digital Fisher Scientific timer
was started concurrently with the initial mixing of the
flasks and the reaction time was recorded to the second
by watching for the first moment of color change.
Test
Temperature
21.9 C
Rate Constant (95% confidence)
3.85x109 5x107
33.8 C
4.69x109
6 x107
45.1 C
5.88x109 8x107
55.1 C
7.39 x109 1x108
64.9 C
8.81x109 1x108
73.8 C
1.06 x1010 1x108
Table 4. Temperature-Dependent Rate Constants
Once kT was calculated, ln kT was then plotted vs.
1/T to generate the Arrhenius plot shown as Figure 1.
III. Results and Analysis
A. Determining the rate law The initial rate for
the reaction in each flask in each run was calculated
using equation 5. Recall that from equation 4, [I3-] =
[H3AsO3], which is listed in Table 2. An average rate was
then calculated for each test run. These rates are presented
in Table 3. See Appendix A for these calculations and
propagation of error.
Test Run
1
Figure 1. Arrhenius Plot of Temperature Dependent
Rate Tests
Reaction Rate (95% confidence)
1.52 x10
6
8
2
3.55x10
6
6.2 x10 8 mol / L s
3
7.40x10
6
1.4 x10 7 mol / L s
4
2.33x10
6
4.0 x10 8 mol / L s
5
6.50 x10
5
5.1x10 6 mol / L s
2.6 x10 mol / L s
The activation energy and frequency factor were
then calculated as described in the introduction section.
The calculated activation energy (Ea) for the reaction
was 16.86 0.07kJ/mol (95% confidence), and the calculated frequency factor (A) was 3.56x1012 4x1010s-1
(95% confidence). See Appendix A for these calculations.
Table 3. Calculated Reaction Rates
Equation 6 was then employed to solve for the orders in equation 3, leading to the rate law:
r
kT [ IO3 ][ I ]2 [ H ]2
(9)
See Appendix A for these calculations.
B. Determining the activation energy and frequency factor Solving for kT in equation 9 allows the
temperature-dependent rate constant to be calculated for
each flask in each temperature run. An average kT was
then calculated for each temperature. Note that the rate
constant at room temperature (21.9 C) corresponds to
the rate constant for the rate-law determining test runs.
These rate constants are presented in Table 4. See Appendix A for these calculations and propagation of error.
IV. Discussion
Experimental determination of the rate law for the
reduction of iodate allows us to evaluate the plausibility
of proposed reaction mechanisms. A partial list of proposed mechanisms is provided in the textbook1, and
those are discussed below. Each mechanism is preceded by the name(s) of its proposer and is succeeded
by the derivation of its corresponding rate law. Recall
that the rate law is based on the stoichiometry of the
rate-determining (slow) step. However, when any of
the reactants of the rate-determining step are not reactants in the overall reaction, i.e. it is an intermediate
species, the reactant in the rate-determining step must
be replaced by the reactant(s) from its generation. Depending on the complexity of the reaction mechanism,
this process may need to be reiterated until only reac-
Lab Report, Page 3
Phys. Chem. Lab. I, 2010, Fall, Expt. 3
tants from the overall reaction are represented in the
rate law.
A. Abel and Hilferding
IO3
I
K
H
HIO3
kT [ IOIO ]
[ IOIO ] K eq '[ IO2 ][ I ]
[ IO2 ] K eq [ IO3 ][ H ]
HIO3 ( fast )
K'
H
r
r
HI ( fast )
k
HI
HIO
kT '[ IO3 ][ I ][ H ]
E. Dushman
HIO2 ( slow)
IO3
r
Followed by fast reactions
kT [ HIO3 ][ HI ]
2I
k
Followed by fast reactions
[ HIO3 ] K eq [ IO3 ][ H ]
[ HI ] K eq '[ I ][ H ]
(10)
I
K
2H
k
H 2 I 2O3
IO3
I 2O2
H 2 I 2O3 ( fast )
HIO
2HIO IO ( slow)
r
kT '[ IO3 ][ I ]2 [ H ]2
I
2H
H 2 I 2O3
B. Bray
IO3
2H
I
K'
K
I 2O2
k
H 2 I 2O3 ( fast )
H 2O( fast )
I 3O2 ( slow )
Followed by fast reactions
HIO2 ( slow )
Followed by fast reactions
r
r
[ I 2O2 ] K eq '[ H 2 I 2O3 ]
kT [ H 2 I 2O3 ]
kT '[ IO3 ][ I ][ H ]2
K
H
H
OH
IO2
K'
I
IOIO
IO2
1/ K w
I
OH ( fast )
H 2O( fast )
IOIO ( fast )
k
I
2 IO ( slow )
Followed by fast reactions
r
kT [ IOIO ][ I ]
[ IOIO ] K eq '[ IO2 ][ I ]
[ IO2 ] K eq [ IO3 ][ H ]
kT '[ IO3 ][ I ]2 [ H ]
r
D. Morgon, Peard, and Cullis
IO3
H
IO2
IOIO
K
H
OH
K'
I
k
IO2
1/ K w
I
OH ( fast )
H 2O( fast )
IOIO ( fast )
IO
IO ( slow)
Followed by fast reactions
r
(11)
C. Morgon, Peard, and Cullis
IO3
kT [ I 2O2 ][ I ]
[ H 2 I 2O3 ] K eq [ IO3 ][ I ][ H ]2
[ H 2 I 2O3 ] K eq [ IO3 ][ I ][ H ]2
r
(14)
F. Bray
kT '[ IO3 ][ I ][ H ]2
r
(13)
(12)
kT '[ IO3 ][ I ]2 [ H ]2
(15)
Our experimental results led us to equation 9,
which corresponds to both equations 14 and 15, indicating that both these proposed mechanisms, E and F, are
plausible. Mechanism E includes a termolecular reaction as its slow step, which is feasible, as termolecular
reactions are generally slow. Mechanism F, on the other hand includes a termolecular reaction as a fast step,
which is less likely. This leads us to the opinion that
mechanism E is the most promising of the presented
mechanisms given our experimental results. It should
be noted, however, that the calculations to determine
the orders of the reaction were less conclusive for H+
than for the other reactants, possibly due to the error in
the preparation of the buffer solutions, however equation 6 should account for less-than-ideal difference in
pH between the solutions. The calculated value was
1.56, which was rounded to 2 (see Appendix A). It is
possible then, that reaction mechanism C, which differs
only by the order of H+, is contributing to the reaction,
along with mechanism E, and perhaps even mechanism
F1.
While determining the rate law allows us to evaluate reaction mechanisms, which helps us improve our
understanding of the reaction, the calculated activation
energy also gives us information about the reaction.
The reaction we are studying, along with all other
Lab Report, Page 4
Phys. Chem. Lab. I, 2010, Fall, Expt. 3
chemical reactions, results from collisions between the
reactant molecules. Not every collision, however, results in reaction, which is why some reactions take
longer4. For a collision to result in reaction, the molecules must come together with specific orientation to
each other, and with enough kinetic energy to overcome
the energy barrier that is represented by the activation
energy5. See Figure 2 for a graphic representation of
activation energy.
VI. References
1.
Garland, C. W. (2009). Experiments in Physical
Chemistry (Eighth Edition ed.). New York, NY:
McGraw-Hill.
2.
Kinetics of the Iodine Clock Reaction. (2010, Fall).
3.
Myers, R. T., Oldham, K. B., & Tocci, S. (2006).
Chemistry. Holt, Rinehart and Winston.
4.
Sibert, G. (n.d.). Notes on Kinetics: Activation
Energy. Retrieved October 2010, from Virginia
Tech Department of Chemistry:
http://www.files.chem.vt.edu/RVGS/ACT/notes/ac
t_energy.html
Activation Energy. (n.d.). Retrieved October 2010,
from Purdue Department of Chemistry:
http://chemed.chem.purdue.edu/genchem/topicrevi
ew/bp/ch22/activate.html
5.
6.
Figure 2. Activation Energy is the energy barrier between the potential energy of the reactants and the
potential energy of the products.
Collision Frequency. (2008, September). Retrieved
October 2010, from Wikipedia:
http://en.wikipedia.org/wiki/Collision_frequency
Reaction rates increase with increased concentration of reactants and with increased temperature, as we
saw in this experiment. Increased concentration leads
to an increased number of collisions, increasing the
likelihood of reaction-resulting (successful) collisions4,
and increased temperature leads to increased energy in
each molecule, also increasing the likelihood of successful collisions5. It follows then, that activation energy is also related to reaction rate. Reactions with higher activation energies, and therefore requiring more
frequent and higher energy collisions, generally proceed more slowly than reactions with lower activation
energies4.
The frequency factor also tells us about the reaction in that it relates directly to the number of collisions
that occur per unit of time, which is known as collision
frequency. Collision frequency is a theoretical value,
while frequency factor is an empirical value. They are
related by the steric factor, which varies with the reaction in question. The closer the two values are to each
other for a reaction, the better the chemical kinetic
theory used to determine the collision frequency applies
to the reaction6.
V. Conclusions
The experimentally determined rate law points to
Dushman’s1 proposed mechanism as the most promising of the available reaction mechanisms. Varying the
concentrations and temperatures (internal energy) clearly showed the relationship between increased frequency
and energy of molecular collisions and rate of reaction.
Lab Report, Page 5