Chemistry 212 Lab
Spring 2012
Chemical Kinetics I, A Survey:
I.
II.
III.
Graphical Determination of Reaction Order for Crystal Violet Dye
Determination of the Complete Rate Law
Estimation of Activation Energy
Purpose
For a simple reaction system consisting of an organic dye and aqueous base, determine
the order of the reaction with respect to the organic dye. This general method involves
monitoring a reaction by visible spectroscopy, and obtaining data sets of percent transmittance
versus time. Later processing of these data sets will lead to the unambiguous assignment of
reactant order by a graphical method.
Introduction
Kinetics is a large and diverse field of study within chemistry. It is primarily concerned
with discovering, and if possible controlling, those factors that govern the rates of reaction.
Starting with the relatively simple reaction system A → B, immediately two ways to determine
rate become apparent:
• Determine the rate at which the reactant, A, is consumed, or
• Determine the rate at which the product, B, is formed
Such a simple analysis leads to the construction of a general rate expression for this system,
mathematically expressing the two general methods outlined above:
𝑅𝑎𝑡𝑒 = −
𝑑[𝐴]
𝑑[𝐵]
=
𝑑𝑡
𝑑𝑡
This general rate expression can be read in terms of either A or B. For the reactant A: "Rate is
equal to minus the change in the concentration of A over the change in time." For the product B:
"Rate is equal to the change in the concentration of B over the change in time." This treatment
allows the reaction rates to have positive values for [A] and [B], and for the two rates to be
expressed in terms of one another.
What this general expression really says mathematically, is something that is intuitively
obvious physically: that the rate at which product B forms cannot be any faster than the rate at
which reactant A is being consumed to produce it. General rate expressions become more
complicated, but keep these same features, when a reaction system under study becomes more
complex.
Below is a more complicated general reaction equation, and a corresponding general rate
expression for that reaction:
𝑎𝐴 + 𝑏𝐵 → 𝑐𝐶 + 𝑑𝐷
𝑅𝑎𝑡𝑒 = −
1 𝑑[𝐴]
1 𝑑[𝐵]
1 𝑑[𝐶]
1 𝑑[𝐷]
∙
= − ∙
= + ∙
= + ∙
𝑎 𝑑𝑡
𝑏 𝑑𝑡
𝑐 𝑑𝑡
𝑑 𝑑𝑡
The introduction of reaction coefficients brings one additional term to each reactant and product
in the general rate expression.
Relevant Background Information:
The more complicated general rate expression above can still be read the same way as the
simple one, and has the same utility. Being able to measure the change in concentration as a
function of time for any single reactant or product allows the measurement of the rate of change
over time for any of the other reactants or products. In this experiment, the disappearance of the
color of one of the reactants can be used, if one so desires, to characterize the rates for all
chemical species in the reaction system.
Thus the design of this experiment is to monitor, by visible spectroscopy, this
disappearance of color, and convert that information into a general expression for how a
particular reactant behaves. One can assume the disappearance of color to be related directly to
the consumption of the reactant and an appearance of product. You will also determine the
order of reaction with respect to this consumed reactant, which becomes part of what is called
the rate law for the reaction.
You will be concerned with how the change in concentration versus time can be turned
into a reactant order for a given reactant. Usually reaction orders have integer values, or zero.
They can also be fractional, and can even be negative. The reaction under study is one of the
type A(color) → B(colorless), and the rate can be conveniently expressed in terms of
disappearance of color:
𝑅𝑎𝑡𝑒 = −
Δ[𝐴]
= 𝑘[𝐴]𝑥
Δ𝑡
The reaction order, x, can be found in one of two ways. In the first general method, the
rate can be found by varying the concentration of A. For example, a 'baseline' concentration of 1
for A, yields a corresponding 'baseline' rate, also of 1. If you were to then double the
concentration of A to 2, assuming all other factors remain the same, the rate of reaction could
again be measured. The dependence of changing the concentration of A on rate could be
measured directly, and the order solved mathematically by:
𝑅𝑎𝑡𝑒 = [2]𝑥
If the rate were observed to increase by a factor of two, this expression simplifies to:
2 = [2]𝑥
The reaction order, x, is therefore equal to 1. The reaction can then be said to be, "first-order
with respect to A." Convince yourself that if doubling the concentration of A led to no change in
the observed rate, that the reaction order x would be 0. Also, if doubling the concentration of A
led to a factor of 4 increase in rate, that the reaction order x would be 2.
In the second general method, the use of integrated rate law expressions is used to
determine reaction order. The results for zero-, first-, and second-order reactions are presented
in the following table.
Zero-Order
First-Order
k[A]0
Rate Law
Second-Order
k[A]1
k[A]2
Integrated Rate Expression
[A]t = kt + [A]0
ln[A]t = kt + ln[A]0
1/[A]t = kt + 1/[A]0
Linear graph
[A] versus time
ln[A] versus time
1/[A] versus time
Slope
k
k
k
Relevant Chemistry and Experimental Details
I. Determination of Reaction Order with respect to Crystal Violet Dye
The reaction of the organic dye crystal violet with aqueous base is a relatively simple
one, whose progress can be tracked over time by the disappearance of a purple color:
crystV(aq) + OH(aq) --------> crystVOH(aq)
(purple)
(colorless)
A general rate expression for this reaction can be written:
Δ[𝑐𝑟𝑦𝑠𝑡𝑉 + ]
𝑅𝑎𝑡𝑒 = −
= 𝑘[𝑐𝑟𝑦𝑠𝑡𝑉 + ]𝑥
Δ𝑡
The complete rate law for this system is:
𝑅𝑎𝑡𝑒 = 𝑘[𝑐𝑟𝑦𝑠𝑡𝑉 + ]𝑥 [𝑂𝐻 − ]𝑦
The disappearance of the purple color, indicating the consumption of the crystal violet dye, can
be monitored over time with a Spectronic 20 visible spectrometer. This instrument is able to
determine how much of a given incident beam of light is being allowed through a sample at a
given wavelength. The more color, the less light passing through. As the reaction proceeds, and
the color fades, more of the incident light is allowed through. The experimental procedure asks
that readings from the spectrometer be taken in percent transmittance, which should be seen to
increase as a function of time. This would be indicative of an initially "rich" color fading over
time, thus allowing more of the incident light to be 'transmitted' through it. Percent transmittance
readings should be converted to absorbance with this equation:
Absorbance = log(%T/100)
Absorbance can be related to concentration (although the exact concentration of the crystal violet
dye is neither found nor needed, as is shown shortly) using the Beer-Lambert Law.
Use of the Beer-Lambert Law -- Exploiting the Absorbance/Concentration Relationship
The Beer-Lambert Law is a simple relationship between the amount of incident light a given
analyte absorbs as a function of the concentration of that analyte:
A = 0 b c
The terms 0 (extinction coefficient) and b (path length) are constant under the conditions of this
experiment, allowing the further simplification
absorbance (is directly proportional to) concentration
Without this simplification, it would be necessary to determine the actual concentrations of
crystal violet dye at every time measurement. Since the absorbance is directly proportional to
the concentration of crystal violet dye, the data sets collected will actually be of absorbance
versus time information. You will assume this proportionality is true, and that your measured
absorbances will be treated as if they were actually concentrations of crystal violet dye. It does
not change any of the attributes of the integrated rate laws to use absorbances in place of
concentrations under the conditions of this experiment.
Additional Treatments of Experimental Data: Complete Rate Law and Activation Energy
II.
Determination of the Complete Rate Law
Once the order of reaction with respect to crystal violet dye has been determined, it is possible to
find the complete rate law by also determining the order of reaction with respect to aqueous
hydroxide, OH. The method used takes advantage of two facts:
• the rate constant, k, is unchanged if the temperature is unchanged
• the concentration of crystal violet dye is constant under the experimental conditions
The rate law can accordingly be simplified to a form such as this:
original rate law:
modified rate law:
Rate = k [crystV]x [OH]y
Rate = k' [crystV]x
where k' = k [OH]y
The new symbol k' assumes the crystal violet dye concentration, and the rate constant, are in fact
constant. It should now be possible, by varying the hydroxide ion concentration, to determine
the exponent y, the order of reaction with respect to hydroxide. It is a consequence of using the
modified rate law that now, the actual rate constant, k, is dependent on hydroxide ion
concentration. The slope of the graph prepared that reveals the reaction order with respect to
crystal violet dye is in fact this term k', and not the actual rate constant, k. Therefore it is
necessary to determine the reaction order with respect to crystal violet dye before attempting to
determine the order with respect to hydroxide ion concentration. This simplification cannot be
made and used without knowing the exponent x.
If, therefore, a series of experiments were run in which the hydroxide concentrations
were varied, a dependence of this variance on the rate would be obtained directly, and would
reveal itself as hydroxide ion-dependent values for k'. If two such experiments with varying
hydroxide ion concentrations were run (denoted by "[OH]1y" and "[OH]2y") the order with
respect to hydroxide ion could be found with the following relationships.
k1'
k [OH]1y
---= --------------k2'
k [OH]2y
which can be simplified to (k1' / k2' ) = ([OH]1 / [OH]2)y. This method has the additional
benefit if being able to provide a value for the actual rate constant, k, with just a little extra math.
It is not necessary to know the rate constant to construct the complete rate law, only the
exponents.
Since this method uses actual experimental numbers, and does not rely on a fitted straight
line, it is important to point out that while most reaction orders are whole numbers, it is unlikely
actual data will lead directly to a whole number result. When considering which order to assign
a given reactant by this method, select the nearest whole number for the reaction order. An
answer of 1.124, for example, is best rounded back to 1, and so on.
Estimation of Activation Energy
The rate law expression for the crystal violet dye/hydroxide ion is shown below:
Rate = k [crystV]x [OH]y
The rate constant, k, has a dependence with temperature. Generally it is true that a given
reaction's rate increases as a function of increasing temperature. It can therefore be assumed that
this increase in rate is due to an increase in the value of the rate constant. So it is possible, by
carrying out the reaction of crystal violet dye with hydroxide at various temperatures, to obtain a
variety of values for temperature-dependent rate constants (k1 at T1, k2 at T2, etc).
With such data points, it is possible to estimate the activation energy. The Arrhenius
Equation has a relatively simple form, and relates temperature, rate constant, and activation
energy for a given reaction:
k = A ea/RT
"A" is a term called the "frequency factor", which accounts for the number and orientation of
molecular collisions. For our purposes, this frequency factor term is essentially a constant.
k is the rate constant at the absolute (K) temperature T.
R is the thermodynamic gas constant, 8.314 J/mol K.
Ea is the activation energy in J/mol.
To get rid of the exponential function, take the natural log of each side and re-arrange:
ln k = Ea/RT + ln A
Notice the similarity of this to
y = m
x +
b
Here is the key to estimating activation energy, Ea, for this system. This natural log rearrangement of the Arrhenius Equation has, as its slope, the quantity Ea/R. The 'y' values are
the rate constants at various temperatures (Kelvin), and the 'x' values are equal to 1 divided by
those absolute temperatures.
Thus, collecting %T versus time data at various temperatures, T, and finding the rate constants at
those temperatures, allows you to construct a plot of ln k versus 1/T. The slope of a line fitted to
this plot is equal to Ea/R. Or to make things as convenient as possible:
slope x R = Ea, in J/mol
A second experimental procedure guides you through a process for obtaining %T versus time
data at several temperatures. At your Instructor's option, you may be asked to perform this
procedure, as well as the collection of %T versus concentration data at a constant temperature,
differing the hydroxide ion concentration. Make sure you are familiar with both procedures.
Experimental Procedure
Collection of %T versus Time Data, Constant Temperature
Data sets are to be collected individually, and for two different concentrations, of aqueous
sodium hydroxide solution with crystal violet dye. Standard concentrations might include 0.025
M NaOH, and 0.0125 M NaOH. Be sure to check the reagent bottles in your laboratory section
for the exact concentrations available.
Begin by turning on a Spectronic 20 and letting it warm up for at least 15 minutes. Be sure the
wavelength indicator is set to 540 nm, and do not adjust it again for the remainder of the
experiment. When the instrument has warmed up, use a clean small test tube from your drawer,
filled 2/3 with the first NaOH solution you plan to use, as a blank to set 0% and 100%
transmittance.
You will be taking a %T reading every minute for at least 15 minutes, so it may be convenient to
wait until the room clock's second hand approaches 12 before beginning the following
procedure. Add one single drop of the crystal violet dye solution, invert to mix the contents of
the test tube, and carefully place the tube into the instrument. When the drop hits the surface is
your "time zero", and one minute later you will begin taking readings of %T. Leave the sample
tube in the instrument throughout the data collection process. Obtain readings of %T every
minute for at least 15 minutes. Record %T values to one decimal place, as this allows you to
convert to absorbance and retain three significant figures.
When you have taken your 15th and final reading, remove the sample tube from the instrument
and prepare to re-zero the instrument with a new NaOH blank in another test tube. Then repeat
the entire 15-minute data collection a second time.
Remember, everyone will be required to measure a full 15-minute data set on two different
NaOH samples of differing concentration. The real work of this experiment comes in the data
analysis, only some of which you will be required to do in the laboratory.
When you and your partner have finished collecting data, turn off the instrument, discard your
samples down the drain, and carefully clean the test tubes you used. Enter whatever data is
required into the 212 database before you leave for the day.
Ater consulting the table of reaction orders and their attributes, the order of the crystal violet dye
should make itself apparent if, after collecting the absorbance and time data, three graphical plots
are prepared:
• One graph of absorbance vs. time
• One graph of ln(absorbance) vs. time
• One graph of 1/absorbance vs. time
Only one of these should be a straight line. This is therefore a direct, graphical determination of
the order of reaction with respect to crystal violet dye.
Experimental Procedure
Collection of %T versus Time Data, Variable Temperatures
Data sets are to be collected in groups of no more than 2. Only one concentration of NaOH
solution will be available for this portion of the experiment. Be sure to check the reagent bottles
in your laboratory section for the exact concentration used.
Begin by turning on a Spectronic 20 and letting it warm up for at least 15 minutes. Be sure the
wavelength indicator is set to 540 nm, and do not adjust it again for the remainder of the
experiment. When the instrument has warmed up, use a clean small test tube from your drawer,
filled 2/3 with the NaOH solution you plan to use, as a blank to set 0% and 100% transmittance.
Set up a water bath with a 250 mL beaker on a hot plate. Place at least 4 clean small test tubes
filled 2/3 with the aqueous NaOH solution into the water bath and heat to NO HIGHER THAN
50°C. When the bath has reached 50°C, remove it from the hot plate, shut off the hot plate, and
allow the bath to begin cooling on the bench top. As soon as the bath reaches 40°C, and for
samples every 5°C after that, measure absorbance and time data according to the following
procedure.
You will be taking a %T reading every minute for at least 10 minutes, so it may be convenient to
wait until the room clock's second hand approaches 12 before beginning the following
procedure. Add one single drop of the crystal violet dye solution, invert to mix the contents of
the test tube, and carefully place the tube into the instrument. When the drop hits the surface is
your "time zero", and one minute later you will begin taking readings of %T. Leave the sample
tube in the instrument throughout the data collection process. Obtain readings of %T every
minute for at least 10 minutes. Record %T values to one decimal place, as this allows you to
convert to absorbance and retain three significant figures.
When you have taken your 10th and final reading, remove the sample tube from the instrument
and prepare to re-zero the instrument with the NaOH blank. Then repeat the entire 10-minute
data collection when the bath temperature has reached 35°C. By the time a given temperature's
data is collected (say the set from 40°C), it should nearly be time for the 35°C set to be taken,
and so on for 30°C and 25°C. This should afford you 4 data sets at temperatures above room
temperature, and to complete the Arrhenius plot, you are to use the data from the same NaOH
concentration as you used this week, room temperature.
Remember, every group will be required to measure full 10-minute data sets on at least three
samples at differing temperatures. Do not be too concerned about the temperature not staying
exactly constant during the data collection process—this is designed to be a rough approximation
method for determining the activation energy. An exercise, if you will, in handling the data
necessary to obtain such a value.
Data Tables -- Percent Transmittance versus Time, Constant Temperature
Concentration of NaOH Solution
__________
Concentration of Crystal Violet Dye Solution
__________
Room Temperature
(assumed to be reaction temperature)
__________
Trial #1
Time(min)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Trial #2
%T
__________
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Time(min)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
%T
__________
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Data Tables -- Percent Transmittance versus Time, Constant Temperature
Concentration of NaOH Solution
__________
Concentration of Crystal Violet Dye Solution
__________
Room Temperature
(assumed to be reaction temperature)
__________
Trial #1
Time(min)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Trial #2
%T
__________
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__________
Time(min)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
%T
__________
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__________
__________
__________
__________
__________
__________
Data Tables -- Percent Transmittance versus Time, Variable Temperature
Concentration of NaOH Solution
__________
Concentration of Crystal Violet Dye Solution
__________
Trial #1
Trial # 2
Trial #3
Temp. (°C)
________
________
________
Temp. (K)
________
________
________
Time(min)
%T
Time(min)
%T
Time(min)
%T
1
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