Name _______________________________________________________Date ________________________
NORTH ALLEGHENY SENIOR HIGH SCHOOL
AP Chemistry
KINETICS: RATE LAW DETERMINATION OF THE CRYSTAL VIOLET/SODIUM
HYDROXIDE REACTION
INTRODUCTION:
The field of chemistry that is concerned with studies of reaction rates is called chemical kinetics.
It can be qualitative (e.g. a reaction can be described as being either "slow" or "fast") or it can be quantitative
with such terms as obtaining a "specific reaction rate constant" for a reaction, or obtaining an "order" of a
reaction. Quantitative studies lead to very important predictions not only about how fast a reaction proceeds and
how much of a product will form after a certain time, but detailed studies can lead to understanding mechanisms
of reactions.
Consider the general reaction:
A+B→C
[1]
The rate of this reaction can be measured by experimentally determining the amount of reactants A or B that is
consumed as a function of time, or the amount of C that is formed as a function of time. Choosing which species
to observe is usually a matter of convenience. Mathematically, the rate of reaction monitoring the concentration
of A can be expressed as follows:
Rate of disappearance of A =
_ change in concentration of A =
time required for change
_ ∆[A]
∆t
In most cases, the overall rate of the reaction will depend on the concentrations of the reactants.
Rate = k[A]m[B]n
[2]
where [A] and [B] are the molar concentrations of species A and B, m and n are the powers to which the
respective concentrations must be raised to describe the experimental rate, and k is the specific rate constant. A
main goal in kinetic studies is to determine the numerical values of m and n from experimental data. Suppose
that we found m = 2 and n = 1 for the hypothetical reaction shown in [1]. Then, the rate law would be expressed
as:
Rate = k[A]2[B]
[3]
It should be apparent from equation [3] that if the concentration of B were doubled (keeping [A]
the same) the reaction rate would double. On the other hand, if the concentration of A were to be doubled
(keeping [B] the same) the rate would increase by a factor of four because the rate of the reaction is proportional
to the square of the concentration of A. The powers to which the concentrations in the rate law are raised are
called the order of the reaction. In this last example, the reaction is referred to being second order in A and
first order in B. The overall order of the reaction is the sum of all the exponents: in the present example the
overall reaction would be described as being third order.
It is possible to experimentally determine the order of a reaction by noting the effects of changing
reagent concentrations on the rate at which the reaction proceeds as explained above. It should be noted,
however, that the order of a reaction is not necessarily dependent on the stoichiometry of the reaction. Thus a
reaction of the general form:
2A + B
→
C
[4]
may have a rate law that is first order with respect to A and first order with respect to B.
The k in the rate law is called the specific rate constant. It has a definite value that is
independent of the concentration. It is characteristic for a given reaction and is temperature dependent. Once
the rate of a reaction is known as a function of concentrations, the value of k can be calculated.
Determining the rate law, rate constant and reaction order of a chemical reaction.
There are several ways to determine the rate law, rate constant and reaction order of a chemical reaction. In this
experiment, you will determine how the concentration of a reactant changes as function of time. By comparing
how the experimental data follow concentration-time behavior for reactions with different rate laws, you can
determine whether the reaction follows a zero, first, or second order kinetic law.
As described in your text:
if a reaction is zero order, a plot of concentration [C] vs time gives a straight line
if a reaction is first order, a plot of ln [C] vs time gives a straight line and
if the reaction is second order, a plot of 1/[C] vs time gives a straight line
By analyzing the resulting plot, you can obtain the order of the reaction and evaluate the specific reaction
rate constant.
In this experiment, you will observe the reaction between crystal violet and sodium hydroxide. The
relationship between concentration of crystal violet and the time elapsed during the reaction will be studied
spectroscopically with the use of Spectronic 20 spectrophotometer. Under the assumption that absorbance is
proportional to concentration of crystal violet (Beer's Law) the order of the reaction with respect to crystal violet
will be determined by graphical analysis. The order with respect to sodium hydroxide will be determined next
by keeping the concentration of crystal violet constant and changing the concentration of sodium hydroxide.
Once the order with respect to crystal violet has been determined, you will also be finding the rate constant, k,
and the half-life for this reaction.
The Experiment:
The equation for the reaction between crystal violet and sodium hydroxide is shown below:
N(CH 3) 2
N(CH 3) 2
OH
+
C
–
N(CH 3) 2 + OH
C
2
N(CH 3) 2
N(CH 3) 2
N(CH 3) 2
A simplified version of the equation is:

CV+
+ OH- 
(crystal violet) (hydroxide)
CVOH
The rate law for this reaction is in the form: rate = k[CV+]m[OH-]n, where k is the rate constant for the
reaction, m is the order with respect to crystal violet (CV+), and n is the order with respect to the hydroxide ion.
By keeping the concentration of [OH-] very large compared to the concentration of [CV+], for all practical
purposes the concentration of [OH-] remains constant and does not change (the system is swamped with [OH-].
In fact the technique is called “swamping”. The concentration of crystal violet will change dramatically though,
allowing the order and rate constant with respect to crystal violet to be determined with only one reaction. The
rate constant obtained in this manner is called the pseudo rate constant (k’), because it only applies to part of the
reaction. The reaction is said to follow pseudo mth order kinetics.
Under these conditions, the rate equation simplifies to:
Rate = k’[CV+]m, where the pseudo rate constant k’ = k[OH-]n.
Now, in order to evaluate n and k, two kinetic runs with different excess concentrations of [OH-], say [OH,1]and
[OH-,2] are required. Each kinetic run will give different pseudo rate constants k1’ and k2’, where
k1’ = k[OH-,1]n
k2’ = k[OH-,2]n
If the two [OH-] concentrations are known, a simultaneous solution of these two equations provides the values
of the value of n and k.
k1’/k2’ = (k[OH-,1]n/k[OH-,2]n)
The above will allow you to calculate n, with a final substitution of m and n values to calculate k.
As the reaction proceeds, a violet-colored reactant will be slowly changing to a colorless product. Using
a Spectronic 20 set at a wavelength at 565 nm, you will monitor the absorbance of the crystal violet solution
with time. We will assume that absorbance is proportional to the concentration of crystal violet (Beer’s law).
Absorbance will be used in place of concentration in plotting the following three graphs:
• Absorbance vs. time:
• ln Absorbance vs. time:
• 1/Absorbance vs. time:
A linear plot indicates a zero order reaction (k = –slope).
A linear plot indicates a first order reaction (k = –slope).
A linear plot indicates a second order reaction (k = slope).
Analysis of the above graphs will provide the data needed for the completion of the lab report.
MATERIALS
0.10 M NaOH
0.20 M NaOH
1.6 X 10-5 M crystal violet
distilled water
100-mL beaker
stirring rod
two 10-mL graduated cylinders
one sample test tube
PROCEDURE
1. Use a 10-mL graduated cylinder to obtain 10.0 mL of 0.10 M NaOH solution. Use another 10-mL
graduated cylinder to obtain 10.0 mL of 1.6 X 10-5 M crystal violet solution.
2. We are now ready to calibrate the spectronic 20
• The right top panel knob on the Spec 20 controls the wavelength adjustment. Turn the knob to 565 nm,
the desired setting for this kinetic experiment.
• The bottom left knob on the Spec 20 (same as the on /off knob above) should be turned until the meter
reads 0.0% transmission. There must be no test tube in the instrument and the sample holder
cover must be closed.
• Next, by following the procedure below, we will set the Spec 20 to 100% transmittance.
a. The sample tube should be clean and free of any scratches or cracks.
b. Fill the test tube 3/4 full with the distilled water.
c. Wipe the outside of the tube with a Kimwipe and place the tube in the sample holder. The tubes
must be inserted with the same alignment every time. If there are no appropriate markings on your
tube, draw a vertical line at the top of your tube with a grease pencil to allow you to do this.
d. Close the cover.
e. Using the bottom right knob adjust the meter until it reads 100% transmission.
3. We are now ready to collect data.
To initiate the reaction, simultaneously pour the 10-mL portions of crystal violet and sodium
hydroxide into a 100-mL beaker and stir the reaction mixture with a stirring rod. Empty the water from
the sample test tube. Rinse the test tube with ~1 mL of the reaction mixture and then fill it 3/4 full(dry
the tube after). Place the sample tube in the sample slot of the Spec 20 and close the lid. Monitor
the absorbance reading on the Spec 20 for about 5 seconds (the absorbance reading should be
gradually decreasing). Begin recording absorbance vs. time data in 10 second intervals. Continue
this for at least 3 minutes of the reaction.
4. Repeat the above steps 1-3, this time using the same concentration of crystal violet and 0.20 M NaOH.
CALCULATIONS/CONCLUSION:
1. Using your data from the 0.10 M NaOH, determine the order of the reaction with respect to crystal violet.
Do this graphically using a program such as excel. Three plots should be made (you must make all three
even if you find the linear one) with a data table included that shows the mathematical manipulations of
the data.
2. Taking your linear plot, determine the equation of the line and show this on the graph. Using the slope of
the line, determine the pseudo rate constant for the reaction (we call this a pseudo rate constant at this
point because it is only with respect to crystal violet, not crystal violet and sodium hydroxide).
3. Using the half-life equation that goes with your reaction order, determine the half-life of this reaction.
Explain exactly what this value you found tells you about the reaction.
4. At this point you should already know the order of the reaction with respect to crystal violet. Take the
data from the 0.20 M NaOH trial and analyze as above, this time only doing the linear plot. Find the
equation of the line and determine the rate constant.
5. Determine the order of the reaction with respect to NaOH. Use the theory discussed in the introduction.
6. Write the overall rate expression for the reaction studied in this lab, giving the value for k in your
response.