SPECTROPHOTOMETRIC STUDY OF DYE KINETICS
Theory
Crystal Violet (CV) is a highly colored compound whose formula may be represented below by
one of its many resonance structures.
(CH3)2 N
(CH3)2 N
OH
+
N (CH3)2
C
Cl
OH
–
C
N(CH3)2
–
(CH3)2 N
(CH3)2 N
violet
colorless
In the presence of hydroxide ion, CV undergoes a change to a colorless carbinol as shown above.
Therefore the reaction can be studied by monitoring the color change at a selected wavelength.
The absorption spectrum and molar absorptivity of CV have been determined and the absorption
maximum occurs at 590 nm.
In this experiment, the kinetics of hydrolysis of crystal violet in basic solution are studied at
298K. The order of reaction, specific rate constant, and dependence of the rate on ionic strength
are determined. Since the dye is colored, a convenient way to determine the reaction rate is to
monitor the absorbance of the dye as a function of time. Carrying out the reaction in large excess
[OH-], a technique called isolation (or flooding) assures that the concentration of the OHremains constant throughout each kinetics experiment (run). Under these circumstances the
changes in absorbance at the wavelength maximum in the dye absorbance spectrum give the time
dependence of the dye concentration. From these data the order of reaction with respect to the
[CV] can be deduced.
The rate law has the general form
d [CV ]
= − k[CV ] x [OH − ] y
dt
(1)
where:
k is the specific rate constant
x is the order of the reaction with respect to CV
y is the order of the reaction with respect to OH-
Gentry, 2013
If the [OH-] is present in high enough excess concentration, then it can be assumed that [OH-] is
approximately constant during the course of the experiment. This allows the rate law to be rewritten as:
(2)
d [CV ]
= − k eff [CV ] x where keff = k [OH ]
dt
y
This still leaves the question unanswered as to whether the [CV] has an exponent of x = 1 (first
order in CV) or x = 2+ (higher order in CV)
One way to determine if the reaction is 1st order in CV is to plot the natural logarithm of [CV] vs.
time. First order kinetics should give a ln[CV] vs. time plot that is linear.
(3)
d [CV ]
= − k eff [CV ]
dt
for x = 1
The first order differential equation integrates to
(4)
ln[CV] = ln[CV] o – keff ·t
Thus, the logarithm of the concentration versus time is a linear function of the time with [CV] o
equal to the initial concentration at time zero (as the OH- is being added to the reaction vessel)
and slope equal to keff.
If the graph of ln A vs. t is not linear then we can conclude the reaction is not first order in [CV].
In this case, use the data to plot ( l/[CV ]) vs. time. The linearity of such a plot would indicate a
second order dependence on [CV]. If this plot were nonlinear, we would try a third order
dependence.
When a pseudo-first-order reaction is carried out at a number of different excess initial
concentrations of hydroxide [OH-] o, the order of the reaction in hydroxide (y) can be determined
from a graph, and the specific rate constant for the reaction can also be calculated.
(5)
keff = k[OH-] o y
(6)
ln(keff) = ln(k) + y·ln[OH-] o
A plot of ln keff vs. ln[OH-] o (y axis vs. x axis) should be linear with slope y.
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B) Rate Constant as Function of Ionic Strength
In certain chemical reactions, the rate changes when the ionic strength of the medium is altered.
This is often the case when the reactants are ionic species.
(7)
AZa + BZb → products
where Zi is the ionic charge on each of the respective chemical species.
Because of the ionic charges on the reactants, the reaction rate can be influenced by electrostatic
attraction (or repulsion) between the ions. These electrostatic forces, in turn, are influenced by
the ionic strength of the surrounding solution. This influence is often called the "salt effect", and
is reflected in changes of the activity coefficients of the ions.
For real solutions,
(8)
ai = xi · γi,
where ai = activity, xi = true mole ratio, γi = activity coefficients.
These activity coefficents can be used to correct the concentrations in the rate law. Renaming the
rate constants gives:
(9)
k = ko ( γ A ⋅ γ B )
where k = observed rate constant, and ko is the “specific rate constant” which describes the
kinetic behavior if the chemical species were in an ideal solution with no ions present.
The ionic activity coefficients for each charged species can be estimated from the Debye-Huckel
theory, using base-10 logs:
log γi = – A · Zi2 · I
with Zi = the ionic charge on each ion,
A is a constant that depends on the solvent. For water at 298K, A = 0.509
1
I =−
2
∑
m j z 2j
= the ionic strength,
mj = molality of ion j
j = all ions
It can be shown that:
(10)
log k = log ko + 2A ZA ZB I 1/2
This indicates that a plot of log k vs. I 1/2 (y vs. x axis) would have an intercept of log ko and a
slope of 2(0.509) Za Zb. To determine the salt effect, the reaction is run several times with the
same initial concentrations of CV and OH- while varying the ionic strength of the solutions by
addition of an inert electrolyte, such as KNO3, which regulates the ionic strength but does not
take part in the bleaching of the CV.
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EXPERIMENTAL DETAILS
Solutions:
0.15 M
NaOH
2 * 10-5 M Crystal Violet
1.00 M
KNO3
For best results, mix the amounts of standard NaOH and water in a vial, and place the CV in a
separate vial. Thermostat the vials in the temperature bath for about five minutes. For the salt
effect, the portions of 1.00 M KNO3, water, and NaOH can be mixed in one vial and
thermostated.
During each run the computer will display the absorbance and time. Each run should be allowed
to go at least two half lives of the reaction so that enough points are obtained to assure correct
graphical interpretation.
The reaction starts as soon as the standard sodium hydroxide solution is added. After mixing the
components as outlined in the table. A different concentration of sodium hydroxide is used in
each of the four runs.
The table below summarizes the volumes required for the first four runs. The first four runs are
used to establish the rate law with respect to dye and hydroxide.
Run#
1
2
3
4
dye
(mL)
10
10
10
10
water
(mL)
8
6
4
0
NaOH
(mL)
2
4
6
10
The salt effect is determined by the following five runs in which the concentration of KNO3 is
varied. Each solution is prepared by starting with a dry vial, adding the complementary volume
of water, the needed volume of KNO3, and finally the required NaOH. The vial containing this
mixture and the vial with 10mL of dye is thermostated.
Run#
5
6
7
8
9
Dye
(mL)
10
10
10
10
10
H2 O
(mL)
5
4
3
2
1
- 4 -
1M KNO3
(mL)
1
2
3
4
5
NaOH
(mL)
4
4
4
4
4
VERNIER LOGGER-PRO PROCEDURE USING SPECTRAVIS SPECTROMETER
1) Set-up instrument
a) Plug in SpectraVis to computer with USB cable – do not need LoggerPro controller.
b) After Spetravue is connected, run LoggerPro software
c) Wait for LoggerPro to recognize SpectraVis – will give readings for absorbance
2) Calibrate device using cuvette + water
a) Select absorbance as y-axis output
Experiment / Change Units / Spectrometer 1 / Absorbance
b) Start calibration and follow instructions
Experiment / Calibrate / Spectrometer 1
This process calibrates 100% transmission through the cuvette. You must then use the
same cuvette for the rest of experiment. Make sure that the clear faces of cuvette are
aligned with direction of light beam.
3) Prepare a sample of 10mL water + 10mL dye.
Collect an Absorbance vs. Wavelength scan a sample of the dye.
Store the spectrum using File / Export as… / .txt or .csv format
This spectrum should be included in lab report
Note the wavelength corresponding to peak absorbance as well as the absorbance level.
4) Switch to Absorbance vs. Time mode
a) Click on the Configure Spectrometer Data Collection icon,
, on the top toolbar.
c) Under “Configure Collection…”
- select Absorbance vs. Time
- select wavelength you wish to monitor as function of time (i.e. peak wavelength)
d) Go to Experiment / Data Collection and click on box for Continuous Scan.
5) When ready to collect data for kinetic scan
a) Pour the NaOH and crystal violet solutions into a single beaker. Immediately start the
computer collection by clicking on
. This should be done even though the
sample is not yet in the spectrometer. This will insure that your times are accurate
for when the reaction first began.
b) After gentle mixing, transfer material to a cuvette and insert into the spectrometer.
c) Record the starting temperature by measuring the temp. in the left-over sample.
d) If software stops collecting prematurely – then re-hit “Collect” and select “Append”
Alternatively can re-specify sample rate and length by going to:
Experiment / Data Collection
e) Continue running for at least 2 half-lives
6) To prepare to collect data for another trial, choose Store Latest Run from the Experiment
menu. To save data to disk for use with Excel, use File / Export As… / .txt or .csv
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CALCULATIONS
For Part A – Determining Kinetic Exponents
For each run you must first convert your absorbances into concentrations of CV. [You will need
to use Beer’s law to find the molar absorptivity (ε) from your initial wavelength scan and then
convert the rest of the absorbance data to concentrations.] You can then determine if the reaction
follows first-order kinetics by plotting ln[CV] vs. t (y axis vs. x axis). If your plot is linear, then
use Eqn. 4 to find keff. If it is not linear then test for a 2nd order reaction by plotting 1/[CV] vs.
time. Repeat the analysis for each of the first four runs, creating a table that compares keff to
[OH-].
The results from each run can then be combined into a single plot of ln keff versus ln [OH-].
This can be used to graphically determine the order of the reaction in hydroxide as wells as the
value for the rate constant k. [Eq. 6]
What is the value of k, the observed rate constant, that is obtained from your graph?
For Part B – Determining the Specific Rate Constant (ideal dilute solution limit)
Using the data for the samples containing various levels of KNO3 as well as using your
knowledge of the rate law exponents, find the observed rate constant, k, for each run.
Combine the results from each run in a graph of log10 k versus (ionic strength)1/2. Remember to
include ALL of the ions that are present including the KNO3 as well as the reactants and their
counter ions. Use the graph to determine ko. (Eq. 10)
QUESTIONS
What is the order of the reaction in crystal violet dye? What is the evidence for this in the results
you obtained (Read the Theory section again)?
How is the specific rate constant, ko, obtained in this experiment?
We may assume that the rate determining step in the reaction is the bimolecular reaction of a dye
molecule and the hydroxide ion. From your experimental data, what is the charge on the
dye molecule?
Is the reaction faster at high ionic strength or low ionic strength? Explain. What is the
significance of ko relative to this discussionon ionic strength?
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