CHEM 1032
esolutions
in_this_experiment_q.pdf
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KINETICS I: DETERMINATION OF A RATE LAW
ADDITIONAL READING
The concepts in this experiment are also discussed in sections 13.2 and 13.3 of Principles of Chemistry – A
Molecular Approach, by Tro.
ABSTRACT
In this experiment you will qualitatively measure the rate of reaction using the initial rate method. This method
involves measuring the rate of reaction before any of the reactant concentrations have decreased significantly or,
in this case, measuring the amount of product formed before it increases significantly. Hydrogen peroxide is a
relatively unstable liquid and will decompose quickly in the presence of many different catalysts. In this
experiment we will use potassium iodide, KI, to catalyze the decomposition, where the iodide ion, I – (aq), acts as
the catalyst. Catalysts remain unchanged (or are regenerated) at the end of a reaction. We can write the
reaction as:
2 H2O2(aq) + I – (aq) 2 H2O() + O2(g) + I
– (aq) (1)
Note that the iodide ion is a reactant but it is also a product. The actual reaction is more complex than this and
involves more than one step. We will investigate the kinetics of the overall reaction by systematically varying the
concentration of the hydrogen peroxide while keeping concentration of the iodide fixed. The rate of reaction is to
be expressed in terms of the rate of formation of oxygen gas formed whose change in pressure will be measured
using a gas pressure sensor linked to a Vernier LabQuest computer interface. Also, we will vary the
concentration of the iodide while keeping concentration of the hydrogen peroxide fixed. The data will be analyzed
graphically to determine the order of the reaction for hydrogen peroxide and for iodide as well as the rate
constant.
BACKGROUND
Reactions do not occur instantaneously; they take time. In this experiment we shall examine one of the many
ways in which we can determine just which factors influence the speed (or rate) of a reaction.
The average rate of a chemical reaction is often expressed as the change in the concentration of one of the
reactants, or one of the products, divided by the time required for the change to take place. In this experiment the
average rate can be defined in terms of the decrease in the concentration of hydrogen peroxide, or the decrease
in concentration of iodide, or the increase in concentration of oxygen gas. Using the Greek letter delta, Δ, to
signify "the change in"; square brackets, [ ], to indicate "molar concentration of..."; and Δt to represent the time
needed for the given concentration change to take place (the change in time), expressions for the average
reaction rate can be written:
Δt
]Δ[O
1
1
Δt
]Δ[I
1
1
Δt
]OΔ[H
2
1 Rate 222
(2)
Note that the term "average" is commonly omitted, although all rates are "average" unless Δt is infinitely small.
Since [H2O2] and [I – ] decrease as the reaction proceeds, Δ[H2O2] and Δ[I
– ] are negative quantities (Δ[H2O2] =
[H2O2]final – [H2O2]initial); the rate of a reaction should be positive, so the terms containing Δ[H2O2] and Δ[I – ] are
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preceded by minus signs. Since from the balanced equation two moles of H2O2 disappear for every one mole of I –
that disappears, and since one mole of O2 is formed for every two moles of H2O2 that disappears, the term
containing Δ[H2O2] is multiplied by 1/2, and those for Δ[I – ] and Δ[O2] are multiplied by 1. (See Tro, page 478).
For the reaction of hydrogen peroxide with iodide, the term "Rate" in a rate law can signify any one of these
changes with time.
It should be remembered that the term "Rate" when used in a rate law refers not to the average rate, but to the
instantaneous rate. The instantaneous rate is analogous to the reading on a car's speedometer at any given
instant; the average rate would be analogous to the value obtained by dividing the total distance driven by the
total amount of time needed to make the trip.
As a reaction proceeds, and the reactants diminish in concentration, it is reasonable to expect that the rate of the
reaction will slow down. Fewer and fewer reactant molecules are available, making it less and less likely that
those remaining will react successfully. The rate of reaction, then, should depend upon the concentrations of the
reactants:
Rate = k[H2O2] p [I
– ] q (3)
The proportionality constant, k, in the equation above is called the rate constant. The value of k, as well as the
values of the exponents p and q, can only be obtained by experiment. Note that the order with respect to each
reactant is usually not the same as the stoichiometric coefficient from the balanced reaction, i.e., we cannot
assume that p = 2. There is no way to predict on the basis of the balanced chemical equation alone what the
values will be.
In this experiment we will use the initial rate method to determine values for the rate constant, k, and the two
exponent’s p and q. We will carry out two sets of experiments, one set varying [H2O2] while holding [I – ] constant,
and the other varying [I – ] while holding [H2O2] constant. The exponent p will be determined in the first set of runs,
since holding the I – (aq) concentration constant focuses attention on the effect of [H2O2]. The situation will be
reversed in the second set of experiments, leading to the determination of the exponent q.
The initial rate (which we shall now refer to as the rate) will be determined by measuring the change in pressure
of the oxygen gas that is formed over a five minute period. Using a gas pressure sensor and the Vernier system,
you will obtain data similar to the following:
Figure 1
Since the change in partial pressure of the oxygen, ∆PO2, is proportional to its change in concentration, ∆[O2],
then we can write the reaction rate can be expressed as:
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Rate = Δt
ΔP 2O (4)
The slope of the linear part of the curve between 50 and 100 seconds in Figure 1 is, to a good approximation, the
rate of the reaction. Combining equation 3 and 4, we can write the rate law as:
Rate = Δt
ΔP 2O = k[H2O2]
p [I
– ] q (5)
The effect of a reactant's concentration on the reaction rate can be found by varying its concentration in several
repetitions of the reaction. In the first set of experiments, we will use varying initial concentrations of H2O2, but the
use same amount of I – for each determination, thus keeping [I
– ] constant. Since the reaction order with respect to
iodide, q, is a constant, [I – ] q will be constant for this set of reactions. This allows us to simplify Equation 5 even
further:
Rate = k' [H2O2] p (where k' = k [I
– ] q ) (6)
It is useful to take the natural logarithm of both sides of Equation 6, to give:
ln(Rate) = p ln[H2O2] + lnk' (7)
Equation 7 has the form of the equation of a straight line, y = m x + b. A plot of ln(Rate) on the y-axis versus
ln[H2O2] on the x-axis will yield a straight line of slope p, which is the order of the reaction with respect to
hydrogen peroxide.
Using the same type of procedure with constant [H2O2], we can obtain the same type of information for [I – ] and q.
The equations that would apply are:
Rate = k" [I – ] q (where k" = k [H2O2]
p ) (8)
ln(Rate) = q ln[I – ] + lnk" (9)
For these experiments, a plot of ln(Rate) versus ln[I – ] should give a line having a slope equal to the order of the
reaction with respect to iodide, namely q.
SAFETY/HYGIENE/WASTE DISPOSAL
1. As always wear your goggles!
2. Caution: concentrated acids are corrosive. You should wear gloves and be sure your skin is not exposed.
Discard the gloves after use, and wash your hands. Acid exposure may result in an itchy sensation. If you
have any sensation of itching, burning, or tingling, thoroughly flush the area with water. Inform your lab
instructor while flushing the area should you experience any of the symptoms listed. Don’t wait until several
minutes have passed.
3. Never raise containers of solution, especially corrosive solutions, to eye level or above. In particular, avoid
this when filling a buret.
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4. Never weigh chemicals directly on a balance pan. Use weighing paper, glassware, or other secondary
container.
5. Waste solutions from this experiment should be disposed of in a designated container.
PROCEDURE
Your lab instructor will divide the class into pairs.
Equipment and Chemicals Provided in Lab:
Vernier Lab Quest computer interface
gas pressure sensor
black stopper assembly
plastic tubing with one connector
125-mL Erlenmeyer flask
small beakers
graduated cylinder
thermometer
ring stand and utility clamp
stirrer/hot plate
stir bar magnet
burets filled with 0.880 M H2O2(aq) (prepared by diluting 90.0 mL of 30% H2O2 to 1 L)
burets filled with 0.500 M KI(aq) (prepared by dissolving 83.00 g of KI in 1 L of DI water)
1. Connect the gas pressure sensor to Channel 1 of the Vernier LabQuest computer interface (which will now be
referred to as LabQuest). The pressure (kPa) should be displayed in a box on the LabQuest screen. The
value will fluctuate a little. If you do not see a pressure reading displayed, consult your lab instructor.
2. Check the following settings (in upper right of the screen):
Mode: Time Based Rate: 5.0 samples/s Length: 300.0 s
If you need to change the settings, follow the procedure that you used in previous experiments.
3. Assemble the apparatus as shown in Figure 2 below. Use the clear tubing to connect the black rubber
stopper to the gas pressure sensor; about one half turn of the fittings will secure the tubing tightly. Twist the
black stopper snugly into the neck of the Erlenmeyer flask (which should be clean) so as to avoid losing any
of the oxygen gas that will be produced. The flask should not contain any solutions at this stage, only the bar
magnet.
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4. Using the volumes shown in the table below for Run 1, dispense the required amount of H2O2 and KI
solutions from the burets into separate small, dry beakers. Measure the volume of DI water required using a
graduated cylinder. Let the solutions sit for a few minutes so that they will come to the same temperature.
Since the solution were prepared in advance there temperatures should had a chance to equilibrate, that is
the temperatures difference should be within 1 C of each other. It is advisable to construct a table in your lab notebook similar to that shown below and with an additional column for rate (see Data Sheet).
Run Volume H2O2(aq), (mL) Volume KI(aq), mL Volume water, mL
1 10.00 5.00 45.0
2 15.00 5.00 40.0
3 20.00 5.00 35.0
4 5.00 10.00 45.0
5 5.00 15.00 40.0
6 5.00 20.00 35.0
7* 10.00 5.00 45.0
*For Run 7, add a small amount (tip of the spatula) of iron(III) chloride hexahydrate (FeCl3•6H2O) to the water.
5. Remove the black stopper from the flask and add the water. Adjust the dial so that the bar magnet stirs at a
moderate speed.
6. Add the H2O2 solution followed by the KI solution and replace the stopper securely in the flask. Why do you
think the solution turns a yellow color? Start collecting pressure data by tapping the green arrow on the lower
left of the screen with the stylus. The pressure may fall slightly before it starts to increase. If the pressure
exceeds about 120 kPa the stopper may pop off (which can be prevented by holding down the stopper). This
is OK as long as the curve has a linear portion and data has been collected for at least 200 seconds.
7. After Run 1 has finished you have to determine the rate of the reaction. The screen may look something like
this. If your graph is not scaled like this, choose the Graph Option in the menu bar and tap on Autoscale
Once.
Note that in this case the pressure suddenly dropped because the pressure approached 120 kPa and the
stopper popped off! Place the stylus on the screen at the lower end of the linear portion and then drag to the
upper end, then release (this is similar to using a mouse to highlight text or a figure on a computer). Then tap
the Analyze menu and select Curve Fit and tap the box next to Pressure. From the Choose Fit Equation
menu, select Linear. The equation of the straight line, y = mx + b, should appear followed by the values of m
and b. Record the value of the slope (m) in your lab notebook. This value is equal to the rate of the reaction.
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8. Remove the black stopper from the flask and empty the solution into the appropriate waster container.
9. Repeat steps 4 – 8 for Runs 2 – 7. Before starting a new Run, you should tap the file cabinet icon (next to the
box that reads Run 1) with the stylus. This will create a new graph for the new Run. Note that Run 7 is the
same as Run 1 with a small amount (tip of the spatula) of iron(III) chloride hexahydrate, FeCl3•6H2O, added to
the water.
10. Rinse out all of the glassware and return it to the bench. Disconnect the tubing from the black stopper and
the gas pressure sensor.
11. Delete any stored data from the computer interface by tapping the “File” menu with the stylus and selecting
“New”. The LabQuest should be left turned on for the next lab section. If the lab is scheduled to end at 4:50
PM or 8:20 PM then the LabQuest should be turned off by pressing the silver button on the top left of the
device.
12. Hand in a copy of your data (recorded in your lab notebook) to your lab instructor.
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CALCULATIONS AND RESULTS
When working with reactions that occur in solution, the concentration of the stock solution is defined as the initial
concentration before mixing (BM), upon mixing the initial concentration will change because of dilutions. The
concentration after mixing depends on the volume of the reaction mixture.
In Run 1 the [H2O2]BM = 0.880 M, and the initial volume is 10.00 mL. When all the chemicals are mixed the final
volume of the reaction mixture will be 60.0 mL. What we need to determine in this experiment are the initial
concentrations of the reaction components after mixing, [H2O2]AM. To determine the concentration after mixing
we will use the dilution equation, M1V1 = M2V2, where 1 is the initial values before mixing and 2 are the initial
values after mixing. The concentration of hydrogen peroxide after mixing is calculated in the following way:
M1V1 = M2V2
[H2O2]BM V1 = [H2O2]AM V2
(0.880 M) x (10.00 mL) = [H2O2]AM x (60.0 mL)
[H2O2]AM = 0.147 M
For each run you will have to calculate the concentrations of H2O2(aq) and I (aq) after mixing using the method
described above.
You will estimate the values for p and q using the data in your rate table. At home you will use Excel to
plot your data and verify the values of p and q which were estimated in lab.
The orders of the reaction, p and q, are found by plotting graphs of ln(Rate) on the y-axis versus the natural log of
the concentration of one of the reactants (after mixing) on the x-axis. The slope of the straight line will be the
order of the reaction with respect to that reactant. Runs 1 – 3 will yield the value of the order in hydrogen
peroxide (p), since the concentration of the iodide was held constant. Runs 4 – 6 will yield the value of the order
in iodide (q), since the concentration of the hydrogen peroxide was held constant.
Calculating the rate constant, k, is straightforward. Once you have the values for p and q, and the concentrations
of both reactants after mixing for Runs 1 – 6, substitute them into Equation 5. The values of k should be about
the same for each run, and an average value should be calculated. You should think carefully about the units for
k.
In Run 7, a small amount of an additional catalyst, FeCl3•6H2O, was used. You should be able to calculate k for
Run 7 and compare it with the average value for Runs 1 – 6. You should be able to conclude something about
how this catalyst affects the rate of the reaction.
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DATA SHEET
Complete the following table:
Run [H2O2]AM, mol/L [I ]AM, mol/L ln[H2O2]AM ln[I
]AM Rate, kPa/s ln(Rate)
1
2
3
4
5
6
7
Show how you calculated [H2O2]AM and [I ]AM for Run 2:
Using your rate table you now will approximately determine the values for p and q. Each member within the
group will do one set of calculation shown in the table below. You will then compare your values for p and q to
determine if your runs are consistent. The table below indicates which pairs of run can be used to determine the
values of p and q.
Runs Runs Runs
p 1 & 2 1 & 3 2 & 3
q 4 & 5 4 & 6 5 & 6
To determine the order for H2O2, the value for p, using run 1 and 2
To determine the order for [I ], the value for q, using run 4 and 5
Order in hydrogen peroxide _____ Order in iodide _____
(value of p to nearest whole number) (value of q to nearest whole number)
To verify your values for p and q calculated above, you will plot two graph, using Excel. The first graph will be a
plot of ln(Rate) vs. ln[H2O2]AM using data from runs 1 through 3 in which the iodide concentration was held
constant. The second graph will be a plot of ln(Rate) vs. ln[I ]AM using data from runs 4 through 6 in which the
hydrogen peroxide concentration was held constant. Use the “Add Trendline” feature to draw the best straight
line through the data points for each graph. The equation of the line as well as the R 2 value should appear on
your graph. Based on the discussion on page 3 the slope of the best fit line represents the order of reaction for
each component
([H2O2]2/[H2O2]1) p = R2/R1
n p = m
p = ln(m)/ln(n)
([I ]5/[I
]4)
q = R5/R4
n q = m
q = ln(m)/ln(n)
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POST-LAB EXERCISES
1. Calculate the value of the rate constant, k for Runs 1 – 6. Show a sample calculation for Run 2.
Determine the average value of k. What are the units of k?
Run k
1
2
3
4
5
6
Ave.
2. Compare the rate of Run 1 with that of Run 7. How much faster does the reaction occur when a small
amount of iron(III) chloride hexahydrate is present compared to the reaction without this compound? What is
the role of the iron(III) chloride hexahydrate, i.e., why does it affect the rate of the reaction?
3. Suppose we were able to measure the amount of oxygen gas formed in units of moles/L, and the rate of
formation of oxygen was found to be 0.0125 M/s.
a. Using the rate law for this reaction and the units associated with each variable, show what the derived
units for the rate law constant would be.
(b) What would be the rate of decomposition of the hydrogen peroxide? Explain your answer.
Name: _________________________ Lab Day: M T W R F Instructor: __________________
Room: 103 109 117 125 Lab Time: __________________
