Kinetics Experiments
Determining the Rate Law for a Chemical Reaction and
Examining the Effect of Temperature on Reaction Rate
Purpose: 1. To determine the reaction orders,
rate law, and rate constant for the reaction
between persulfate ions, S2O8-2, and iodide ions,
I-.
2.: To measure reaction rate at different
temperatures for the reaction between persulfate
ions, S2O8-2, and iodide ions, I-, and thereby
determine the activation energy and frequency
factor for the reaction
Introduction
Chemical kinetics is the study of rates and mechanisms of chemical reactions.
Reaction rate refers to the change in concentration of a chemical species with time.
Reaction rate can often be determined by monitoring the disappearance of a reactant
with time, or the appearance of a product with time. The rate of a reaction depends on the
concentrations of the reactants in the reaction. In general, the lower the reactant
concentrations are, the slower will be the rate, and the higher the concentrations, the faster the
rate. The exact way in which the reaction rate varies with reactant concentrations is described
fully by the rate law, which expresses mathematically the rate of reaction in terms of reactant
concentrations raised to certain powers, called reaction orders. For the hypothetical equation
aA + bB  cC + dD
(eq. 1)
in which a, b, c, and d are the stoichiometric coefficients, we can state that
Rate ∝ [A]m[B]n
(eq. 2)
where m and n are the order of reaction with respect to a given reactant. In order to eliminate
the proportionality sign and replace it with an equality, we simply add a proportionality
constant k, called the rate constant.
Rate = k[A]m[B]n
(eq. 3)
This is the rate law for the reaction given in equation 1. We say that m is the order of reaction
with respect to A, and n is the reaction order with respect to B. It is important to recognize that
the reaction orders are not necessarily equal to the coefficients a and b. The reaction orders
must be determined experimentally, they can NOT be determined any other way. In the rate
law, the rate constant k is constant for a given reaction at a given temperature, but does change
when the temperature changes.
The purpose of this experiment, then, is to determine reaction rates with various starting
concentrations of reactants, and from that determine the orders of reaction with respect to all
reactants and then calculate the rate constant for the reaction. This information will then
provide the complete rate law for the reaction studied.
The Arrhenius equation is
k=Ae
-E a
RT
(eq. 4)
where k is the rate constant, A is called the frequency factor, Ea is the activation energy (in
J/mole), R is the gas constant 8.314 J/K-mole, and T is the Kelvin temperature. Taking the
natural logarithm of both sides of eq. 4 yields
E
(eq. 5)
ln k = ln A - a
RT
Rearranging slightly on the right side of the equation gives;
ln k = -
Ea
+ ln A
RT
(eq. 6)
Then factoring the constants out of the first term on the right;
 E 1
ln k =  - a  + ln A
 R T
which is of the form
y
=
(eq. 7)
m x + b
which, of course, you recognize as the equation for a straight line. So, if rate constants, k, are
determined at various temperatures, T, the data can be plotted as 1/T on the x axis, and ln k on
the y axis, with the resulting graph being a straight line whose slope is equal to –Ea/R and
whose y-intercept is equal to the natural logarithm of the frequency factor, ln A. Values of Ea
and A can thus be easily determined from the graph.
In this experiment, you will determine rate constants for the reaction at temperatures
about 10o above room temperature (i.e. about 35oC) and 20o above room temperature (i.e.
about 45oC). These rate constants, along with the room temperature rate constant will be
plotted as described above in order to determine values for the activation energy, Ea, and
frequency factor, A, for the reaction.
The Reaction
The reaction you will examine in this experiment is that between persulfate ions, S2O8-2,
and iodide ions, I-, in aqueous solution. The net ionic equation for the primary reaction is
S2O8-2(aq) + 3 I-(aq)  2SO4-2(aq) + I3-(aq)
(eq. 8)
The source of reactant ions in this case will be ammonium persulfate, (NH4)2S2O8, and
potassium iodide, KI. Both are soluble salts, so the ammonium ions (NH4+) and potassium ions
(K+) are spectator ions and do not participate in the reaction.
The difficulty with determining the rate of this reaction is that all species are colorless in
solution, so it would normally be impossible to monitor concentration changes effectively and
thus determine when the reactants were completely consumed. To eliminate this problem, you
will add starch solutions to each of the reaction mixtures. As soon as the triiodide ion, I3(produced in equation 8), reaches an appreciable concentration, it will react with any starch
present to form a deep blue colored complex. To prevent the solutions from immediately turning
blue, thiosulfate ions, S2O3-2, will be added to react with the triiodide ions, I3- produced in
equation 8 and thus prevent the triiodide from reacting with the starch to form the blue colored
complex until all the thiosulfate ions are consumed.
2S2O3-2(aq) + I3-(aq)  S4O6-2(aq) + 3 I-(aq)
(eq. 9)
In this way, the thiosulfate ion, S2O3-2, acts as a sort of “chemical stopwatch” since the blue
color cannot form until all the thiosulfate is consumed and the triiodide ion concentration can
then build up very quickly, reacting with starch to form a dark blue color. As long as
thiosulfate is present the blue color cannot form, but as soon as the thiosulfate is consumed
completely the blue color forms immediately. In this experiment, the amount of thiosulfate ion,
S2O3-2, will be constant for each determination that is performed, so the faster the reaction rate
the more quickly the thiosulfate will be consumed and the sooner the blue color forms.
You will thus monitor the reaction time as the time required for the appearance of the
blue complex signaling the disappearance of thiosulfate ion.
Reaction Rate Determination
The rate of reaction can be expressed as the change in concentration of a reactant in the
principal reaction (eq. 8) such as persulfate, S2O8-2, divided by the change in time in which that
concentration change occurred;
change in S2 O8-2 concentration
Rate = elapsed time
Rate = -
Δ[S2 O8-2 ]
Δt
(eq. 10)
(eq. 11)
Notice the negative sign in the rate expression in equations 10 and 11, indicating the
disappearance of a reactant and thus a decrease in concentration.
In order to get the change in persulfate ion concentration ∆[S2O8-2] in eq. 11 we will
need to start with the knowledge of the amount of thiosulfate ion, S2O3-2 , consumed, and use
stoichiometry to convert that to the amount of persulfate consumed. Since the volume and
concentration of thiosulfate added will be constant for all determinations (2.00 mL of 1.2 x 10-2
M Na2S2O3), so will the number of moles of thiosulfate be constant for ALL trials;
moles S2O3-2 = (2.0 x 10-3 L)(1.2 x 10-2 M) = 2.4 x 10-5 moles S2O3-2
for ALL trials. Thus the number of moles of persulfate consumed is constant for all trials also;
moles S2O8-2 = 2.4 x 10-5 moles S2O3-2 x
1 mole I3-
1 mole S2O8-2
= 1.2 x 10-5 moles S2O8-2
x
1 mole I3
2 moles S2O3-2
conversion factor
from eq. 9
conversion factor
from eq. 8
Since the total volume of the reaction mixture will be 19.0 mL for all determinations, the
change in the persulfate concentration for all determinations is;
∆[S2O8-2] = -1.2 x 10-5 moles = -6.3 x 10-4 M S2O8-2
0.0190 L
(eq. 12)
Note that the change in concentration is negative since persulfate is a reactant whose
concentration diminishes with time. Therefore the rate may be calculated as;
Δ[S2 O8-2 ] - (-6.3 x 10-4 M S2 O8-2 )
Rate = =
Δt
Δt
for ALL trials
Rate =
6.3 x 10-4 M
t
(eq. 13)
where t = elapsed time from mixing of reactants to appearance of blue color. Equation 13 is
thus used to calculate the reaction rate for all determinations performed in this experiment.
Determining Reaction Orders
You will use the method of initial rates to determine reaction orders for the reactants
in this experiment. The assumption is that the amounts of reactants consumed in the timed
interval are small compared to the total concentration of those reactants present in the reaction
mixture, and therefore the reaction rate is constant during that time. So it is the initial rate of
reaction that is being measured. The rate law for this reaction is of the form
Rate = -
Δ[S2 O8-2 ]
= k[S2O8-2]x[I-]y
Δt
(eq. 14)
Using subscripts to denote determination number yields
Rate1 = k1[S2O8-2]x1[I-]y1 for determination 1, and
Rate2 = k2[S2O8-2]x2[I-]y2 for determination 2
Dividing the first equation by the second gives
Rate1 = k1[S2 O8-2 ]x1[I- ]y1
Rate 2 = k 2 [S2 O8-2 ]x 2 [I- ]y 2
(eq. 15)
If the experiment is designed such that the concentration of iodide ion is the same for
determinations 1 and 2 (as they are in this experiment), these concentration terms will cancel,
as will the rate constants, since rate constant is constant for a given reaction at a given
temperature;
Rate1 = k1 [S2 O8-2 ]x1 [I- ]y1
(eq. 16)
Rate 2 = k 2 [S2 O8-2 ]x 2 [I- ]y 2
which reduces to
Rate1 = [S2 O8-2 ]x1
Rate 2 = [S2 O8-2 ]x 2
(eq. 17)
 [S O -2 ] 
[S O -2 ]x
Rate1
= 2 8-2 x 1 =  2 8-2 1 
Rate 2
[S2 O8 ] 2
 [S2 O8 ]2 
Or more simply,
 [S O -2 ] 
Rate1
=  2 8-2 1 
Rate 2
 [S2 O8 ]2 
x
(eq. 18)
x
(eq. 19)
Since both concentrations can be calculated from molarity and volume used, and both rates will
be calculated using equation 13, the only unknown in equation 19 is x, the order of reaction
with respect to persulfate ion.
A similar calculation using determinations in which the persulfate concentration
remains constant as the iodide ion concentration is varied (e.g. determinations 3 and 4) will
allow derivation of the analogous equation for calculating y, the order of reaction with respect
to iodide;
 [I- ] 
Rate 3
=  - 3
Rate 4
 [I ]4 
y
(eq. 20)
Mathematical note: In order to solve an equation like eq. 19 or eq. 20, you must use
logarithms to solve for x. Remember that log am = m log a. This identity allows isolation of the
unknown m (or x in eq. 19, or y in eq. 20), which is the exponent that corresponds to the
reaction order. You will need to use this relationship in calculating reaction orders in this
experiment, as well as in the post-lab questions.
Determining the Rate Constant
If the reaction rates, reactant concentrations, and reaction orders are all known, then it
is a simple matter of solving equation 21 for the rate constant, k, using data from any of the
determinations that you have done.
Rate = k[S2O8-2]x[I-]y
(eq. 21)
Theoretically, all determinations should give the same value for k, but experimental
variations will produce some slight differences. However, all determinations should have rate
constants that are fairly close to one another.
Procedure
SAFETY NOTE!!
The reagents used in this experiment are irritants. Avoid contact with your skin,
eyes, and clothing. If you do spill some on yourself, wash immediately with cold
water. Notify your instructor.
1.
You will need six burets to measure the solutions to be used in this experiment. See
Tables 1, 2, and 3 for the solutions and amounts to be used. It is imperative that you
clearly label each of the burets with the contents so as not to combine the solutions
incorrectly. After labeling each buret, rinse the buret several times with small (~2-3
mL) portions of the solution with which you will fill the buret. Be sure you rinse
through the buret tip, too. Then add enough solution to the buret to carry out all
determinations. That will vary depending on the solution; for example, only 1.00 mL of
the starch solution is needed for each of the determinations, so you would need, at
most, about 15 mL taking into account rinsing of the buret and any repeat
determinations. Make sure there are no air bubbles in the buret tip before starting the
titration. Make sure all your buret readings are read to the nearest 0.01 mL; that is, to
two digits to the right of the decimal point.
2.
Prepare two 50 mL Erlenmeyer flasks, labeled Flask A and Flask B, with the solutions
indicated in Table 1 for determination 1. Once both flasks are prepared, record in Data
Table 4 the room temperature and you are ready to perform determination 1. Be sure to
use precisely the volumes specified in Tables 1 and 2.
3.
This step requires teamwork. One of you will operate a stopwatch while the other mixes
the contents of Flasks A and B. As the person mixing begins to pour the contents of one
flask into the other, the person doing the timing watches carefully, and starts the
stopwatch when about half the liquid in the first flask has been transferred to the second
flask. Once all the liquid from both flasks has been combined into one flask, the person
mixing pours all the liquid back into the first flask, then pours it all back into the
second flask in order to completely mix the solutions. After three such pourings, the
reaction flask can be set down and watched carefully. The person timing should stop
the stopwatch as soon as the color of the reaction mixture changes from colorless to
deep blue. Record the reaction time on Data Table 1.
NOTE: Be very careful in reading the stopwatch. The stopwatch gives you a time in
minutes and seconds; thus a time of 1:27 is NOT 1.27 minutes, but rather it is 1 minute
and 27 seconds, or 87 seconds.
4.
Repeat determination 1 until two successive trials give reaction times within 10% of
each other. For example, if the reaction time was 80 seconds, 10% of 80 is 8 seconds,
so the times should be 80 ± 8 seconds. So in that example, the range of allowed times
for the second trial would be from 72 to 88 seconds. Record all times on Data Table 1.
5.
Repeat steps 3 and 4 for determinations 2 and 3. Do at least two trials of each
determination such that the times are within 10% of each other. Record all data on Data
Table 1.
6.
Thermostatically controlled constant temperature baths will be set up for use in
obtaining the temperatures about 10oC and 20oC above room temperature
(determinations 5 and 6, respectively). These two baths will automatically maintain a
constant temperature. For both baths, the temperature does not have to be exactly 35o
or 45o, but you will need to record in Data Table 3 exactly what the temperature is as
measured by the thermometer immersed in the bath. The only difference in these
determinations is that you must put flasks A and B separately into the constant
temperature bath, and allow both flasks and their contents to thermally equilibrate, that
is, come to the same temperature as the bath, before mixing the contents of the flasks.
There should be small (100 mL) beakers about half full of water, sitting on the bottom
of the constant temperature baths. The purpose of these beakers is to allow you to set
your 50 mL flasks A and B in the beakers in the bath without the flasks tipping over
and spilling their contents in the bath water. Label your flasks with your initials, and
allow the flasks to sit in the bath for at least 5-7 minutes to equilibrate before mixing.
Do not walk away from the water bath while the equilibration occurs. Either you or
your lab partner should remain there the entire time the equilibration is taking place.
7.
Once the flasks have equilibrated, follow the same procedure as in steps 3 and 4 to mix
the contents back and forth three times, as one person begins the timer. As soon as the
contents have been poured back and forth several times, the flask containing the
mixture must be returned to the constant temperature bath to remain at that
temperature while the reaction proceeds. Stop the timer when the reaction mixture
turns deep blue. Record your reaction times in Data Table 3. Also record the bath
temperature, in oC, in Data Table 7.
8.
Before cleaning your burets, show your data to your instructor to confirm that the
results are satisfactory. Rinse your burets thoroughly (including the tip) with lots of
water and store them in the buret stands upside down with the stopcocks open. All
waste from this experiment can be poured down the drain along with lots of water.
9.
Repeat each determination at least one more time until you have reaction times for each
determination that agree to within 10% of each other. Make sure you have recorded all
reaction times in Data Table 7.
Table 1 - Determining the Effect of S2O8-2 Concentration on Reaction Rate
FLASK A
FLASK B
-2
1.2x10 M
0.20 M
0.20 M
determination starch,
0.20 M
0.20 M
Na2S2O3,
(NH4)2S2O8,
(NH4)2SO4,
number
mL
KI, mL
KNO3, mL
mL
mL
mL
1
1.00
2.00
4.00
4.00
4.00
4.00
2
1.00
2.00
4.00
4.00
2.00
6.00
Table 2 - Determining the Effect of I- Concentration on Reaction Rate
FLASK A
FLASK B
1.2x10-2 M
0.20 M
0.20 M
determination starch,
0.20 M
0.20 M
Na2S2O3,
(NH4)2S2O8,
(NH4)2SO4,
number
mL
KI, mL
KNO3, mL
mL
mL
mL
3
1.00
2.00
8.00
0.00
4.00
4.00
4
1.00
2.00
4.00
4.00
4.00
4.00
Table 3 - Determining the Effect of Temperature on Reaction Rate
FLASK A
FLASK B
-2
determination starch, 1.2x10 M
0.20 M
0.20 M
0.20 M
0.20 M
number
mL
Na2S2O3,
KI, mL
KNO3, mL
(NH4)2S2O8,
(NH4)2SO4,
(temperature)
mL
mL
mL
2 (room T)
1.00
2.00
4.00
4.00
2.00
6.00
5 (35oC)
6 (45oC)
1.00
1.00
2.00
2.00
4.00
4.00
4.00
4.00
2.00
2.00
6.00
6.00
Calculations
1.
Calculate the initial concentration of iodide ions for each determination, and record
them on Data Table 2. “Initial” here means at the moment the solutions are mixed but
before any reaction has taken place. So this is, in effect, a dilution calculation. For
example, in determination 1, you have taken 4.00 mL of 0.20 M KI and diluted it to a
total volume of 19.00 mL. (Note that the total volume for all determinations is 19.00
mL.) You can use the dilution formula
M1V1 = M2V2
(eq. 22)
to calculate the initial concentration M2 at the moment of mixing, where M1 and M2 are
the undiluted and diluted molarities, and V1 and V2 are the undiluted and diluted
volumes, respectively.
2.
Calculate the initial concentration of persulfate ions for each determination using
volumes and concentrations of (NH4)2S2O8 along with equation 22. Record these initial
concentrations on Data Table 2.
3.
Calculate the average reaction time for each of the four determinations, and record on
both Data Table 1 and Data Table 2.
4.
Calculate the reaction rate for each determination using equation 11. Use your average
reaction times for t in equation 13. Record the rates on Data Table 2, including correct
units with your rates.
Using your data for determinations 1 and 2, calculate the reaction order with respect
to persulfate ion by solving for x in equation 19. Calculate x to two digits to the right
of the decimal point by taking the logarithm of both sides (see mathematical note.
Record the results on Data Table 3.
5.
6.
Using your data for determinations 3 and 4, calculate the reaction order with respect
to iodide ion by solving for y in equation 20. Calculate y to two digits to the right of
the decimal point. Record the results on Data Table 3.
7.
Using equation 21, calculate the rate constant, k, for each of the determinations. Record
your results on Data Table 4. Be sure to include correct units with your rate constants.
8.
On the bottom line of Data Table 4, write the complete rate law for the reaction you
studied in this experiment. Include the average of your calculated values for the rate
constant, k, and your reaction orders rounded off to an integer.
9.
For determinations 5 and 6, calculate the initial concentrations of iodide ion, persulfate
ion, the average reaction time, and reaction rates. Record your results in Data Table 6.
10.
Using eq. 21 calculate values of the rate constant k for each of the three determinations.
Use the reaction orders you determined in Data Table 4. Record your results in Data
Table 7.
11.
Convert the Celsius temperatures at which you carried out the reaction into Kelvin, and
record the results in Data Table 7.
12.
Using the Microsoft Excel spreadsheet in the Science Learning Center, make a plot of
ln k on the y-axis versus 1/T on the x-axis. Go to the Science Learning Center website
at http://www.montgomerycollege.edu/Departments/scilcgt/, click on Online Study
Material, then choose CH102, and then click on Excel Graphs for Lab. Make sure the
Excel window is maximized, and choose the appropriate tab at the bottom of the
window.
13.
Use the linear regression analysis on the graph to obtain the slope (m) and the yintercept (b) of your plot. Use those values to calculate Ea and A. Remember,
the slope = -Ea/R, and the y-intercept = ln A. Record the results on Data Table 8.
14.
Include a copy of the printout of your graph with your lab report.
Determining the Rate Law for a Chemical Reaction
Data Table 1
Reaction Times (s)
determination
trial 1
trial 2
trial 3
average time (s)
1
2
3
4
Data Table 2
determination
initial [S2O8-2]
initial [I-]
average time
(s)
rate
(include correct units)
1
2
3
4
Data Table 3
Reaction Orders
(x is order for S2O8-2, y is order for I-)
determinations used
x
determinations used
1 and 2
3 and 4
Data Table 4
determination
rate constant, k
(include correct units)
1
2
3
4
Rate Law:
at ______oC
y
Examining the Effect of Temperature on Reaction Rate
Data Table 5
Reaction Times (s)
determination
trial 1
trial 2
trial 3
5
6
Data Table 6
determination
initial [S2O8-2]
initial [I-]
average time
(s)
rate
(include correct units)
5
6
Data Table 7
determination
temperature, oC
temperature, K
k
(include correct units)
2
5
6
Data Table 8
Activation energy, Ea
Frequency Factor, A
Kinetics Experiments : Determining the Rate Law for a Chemical Reaction
and Examining the Effect of Temperature on Reaction Rate
Pre-laboratory Assignment
1.
Write the general form for a rate law and explain what each part means.
2.
Explain the purpose of performing the reaction shown as equation 9.
3.
Do Calculations 1, 2, and 9 under the calculations section and record the results of your
calculations in the appropriate spaces in Data Table 2and 6. Write them also below and
show how you did each calculation.