Kinetics of the Crystal Violet-Hydroxide Reaction1
Frederick Wight
Manatee Community College
Factors Influencing the Reaction Rate
Several factors can influence the rate at which a reaction occurs. Two of these are the
concentration of the reactants and the temperature at which the reaction is performed. Most
often an increase in the concentration of the reactants also increases the rate of reaction. Likewise
an increase in temperature will increase the rate of the reaction in accordance with the activation
energy (Arrhenius Equation). In this lab we will examine both factors to determine the order of a
reaction and the activation energy.
The Rate Law and Order of Reaction
Since the reaction rate is often dependent on the concentrations of the reactants the rate law is
generally written in terms of these quantities.
For the reaction:
A+B→C
the rate law is:
Rate = k [A]x[B]y
Where:
k is the rate constant,
[A] is the concentration of A x is the order with respect to A
[B] is the concentration of B y is the order with respect to B
Determining the order of a reaction requires measuring the concentration of one of the reactants or
products as a function of time. We will use 2 different methods to find the rate law: the method of
initial rates and the graphical method.
Determining the Order of the Reaction by the Method of Initial Rates
One method of determining the order of reaction is to perform two experiments in which the
initial reaction rate is measured at different concentrations of one reactant. If only the
concentration of A is changed between these two experiments the change in rate was caused only
by the change in A and the order of the reaction with respect to A can be determined.
experiment #1:
Rate1 = k1 [A]1x [B]1y
experiment #2:
Rate2 = k2 [A]2x [B]2y
Since only [A] is changed k1 = k2 and [B]1 = [B]2. Taking the ratio of the two equations we get:
Rate1 = [A]1x
Rate2 [A]2x
Comparing the two rates and two concentrations allows us to calculate x.
Determining the Order of the Reaction by the Graphical Method
A second method of determining the order is by measuring the concentration of one reactant during
the course of a single experiment in which all other factors are kept as constant as possible. This is
1
Adapted from procedure developed by David W. Clarke, Albany College of Pharmacy.
often accomplished by using a large excess of the other reactants. During the course of the reaction
only a very small portion of the excess reactant is consumed and its concentration remains relatively
constant.
The order of the reaction with respect to the other reactant can be determined by plotting one of the
following: [A] vs. time, ln [A] vs. time or [A]-1 vs. time. A reaction which is zero order with respect to A
will give a linear plot if [A] is plotted vs. time. A plot of the ln [A] vs. time yields a straight line if the
reaction is first order with respect to A. Second order with respect to A is indicated by a linear plot of
[A]-1 vs. time. See Table below.
Reaction
Order
0
1st
2nd
Linear plot
[Conc.] vs. time
ln([Conc.]) vs. time
1/[Conc.] vs. time
Description of Experiment
We will study the rate of the reaction between hydroxide ion and the dye crystal violet (CV). CV is
purple in color while the other reactants and products are colorless. Therefore, if we measure the
rate of disappearance of the purple color, we know the rate of disappearance of the CV.
H3C
+
N
CH3
H3C
CH3
N
NaOH
H3C
CH3
N
H3C
CH3
N
N
CH3
CH3
H3C
Crystal Violet, CV (purple)
N
OH
CH3
(Colorless)
You will determine the rate law for this reaction:
Rate = k[CV]x[OH]y
You will measure the absorbance of the reaction mixture as a function of time using a
spectrophotometer which measures the intensity of the purple color. A spectrophotometer measures
the amount of light absorbed by a solution as a function of wavelength (See graph below for CV).
Absorbance is defined as:
A = log I0 =[c]l
It
Where I0 is the intensity of the incident light and It is the intensity of the light transmitted through the
sample. Absorbance is proportional to the concentration [c] where  is the proportionality constant
knows as the extinction coefficient and l is the path length (usually1 cm).
Crystal Violet Absorption Spectrum
Absorbance
1
0.8
0.6
0.4
0.2
0
400
450
500
550
600
650
700
Wavelength (nm)
We will assume that the concentration of CV is linearly proportional to the absorbance over the
entire range of concentrations. (This is known as Beer’s Law). As the reaction proceeds, the CV will
be consumed and the purple color will disappear and absorbance will drop in linear proportion to the
CV concentration. Using the graphical method (plotting the absorbance in place of [A]) you can
determine the order of the reaction with respect to CV.
The graphical method will give us the order of the reaction with respect to CV. By starting with the
hydroxide ion concentration ~500-1000 times that of CV, its concentration will not change
appreciably during the course of the reaction. The reaction rate will therefore depend primarily on
the concentration of CV present. The order of the reaction with respect to CV will be determined by
which plot is linear.
These are known as pseudo order conditions and the slope of the linear plot k' for this experiment is
actually:
Slope = k’1 = k[OH-]1y
The second trial will be performed in exactly the same way except that the hydroxide concentration
will be doubled.. The same plot that resulted in a straight line in the first trial should result in a
straight line in trial 2 as well. The slope of this line can be used to determine k' for this experiment:
k’2 = k[OH-]2y
The order with respect to the hydroxide ion can be found using a modified initial rate method. Under
pseudo order conditions the following rate laws can be written for the two experiments.
k’1 = k[OH-]1y
k’2 = k[OH-]2y
Since k1’ and k2’ are the slopes of the two plots and the two hydroxide concentrations are known, y,
the order with respect to [OH-] can be determined.
Determining the Activation Energy of a Reaction
Once the rate equation is known we can calculate the rate constant k at several temperatures and
determine the activation energy Ea, by the Arrhenius Equation:
ln(k) = -Ea + ln(A)
RT
Plotting ln(k) vs. 1/Temperature will yield a straight line with a slope of –Ea/R.
Experimental
Part I Calibration
To calibrate the spectrometer, choose CalibrateSpectrometer from the experiment menu. The
calibration dialog box will display the message:”waiting …seconds for lamp to warm up.” Wait for
3 minutes to warm up. Then follow the instructions in the dialog box. (Place a blank cuvette in
the device: click finish calibration. Then click OK.
Part II Measure the absorbance spectrum of Crystal violet solution. (Absorbance vs
Wavelength)
Obtain a 50-75mL sample of 2.0 x10-5 M CV solution in a 100 mL beaker. Obtain a 50-75 mL
solution of 0.10 M sodium hydroxide solution in another 100 mL beaker.
Fill a cuvette about ¾ full of 2.0x10-5 M crystal violet solution. Place the sample in the cuvette
holder of the spectrometer. Click on the Configure Spectrometer Data Collection Icon (rainbow
icon) and select Abs vs wavelength (under set collection mode) click OK. Then click Collect.
Examine the graph and record the wavelength region of maximum absorbance on your data
table.
Part III Determination of Reaction Order
Run 1
1. Click on the Configure Spectrometer Data Collection Icon. Then click Abs vs Time (under the
set collection Mode). Choose the wavelength that you get from part II. Click OK then NO.
2. Select data collection from the experiment menu. Click DONE.
2. Measure out 10.0 mL of CV in a graduated cylinder and pour it into a 50 mL beaker.
3. Measure out 10.0 mL of 0.10 M sodium hydroxide solution in a 2nd graduated cylinder.
4. Pour the sodium hydroxide into the 50 mL beaker of CV, swirl gently then immediately fill a
cuvette about 2ml (¾ full) of CV-NaOH solution. Place the cuvette in the cuvette holder of the
spectrometer. Click collect.
5. Record the Abs vs time data to your data table 1.
Run 2
1. Rinse and dry your 50mL reaction beaker and your cuvette into a waste beaker. (Do not use
a brush on the cuvette.)
2. Add 5.0 mL of CV stock solution to the reaction beaker.
3. Add 2.5 ml DI water to a clean graduated cylinder. Then add 2.5 mL of the 0.10 M sodium
hydroxide stock solution to the graduated cylinder.
4. Pour the sodium hydroxide into the 50 mL beaker of CV, swirl gently then immediately fill a
cuvette about 2ml (¾ full) of CV-NaOH solution. Place the cuvette in the cuvette holder of the
spectrometer. Click collect.
5. Record the Abs vs time data to your data table 2.
Part II Determination of Activation energy
To determine the activation energy run 2 will be performed at a different temperature.
1. Add 25.0 mL of stock CV solution to a 125 ml Erlenmeyer flask.
2. Add 12.5 mL DI water and 12.5 mL of 0.01M sodium hydroxide solution to a 2nd 125 mL
Erlenmeyer flask.
3. Place both flasks in a hot water bath and wait 10-15 minutes for the temperature to
equilibrate.
4. Pour the hydroxide solution into the CV Erlenmeyer, swirl gently and start the timer.
5. Using a disposable plastic pipet fill a cuvette with the reaction solution as soon as they are
mixed and measure the absorbance. Dispose of the solution in the cuvette as soon as you
take a reading (Only need to record the first reading) then click STOP to end the data
collection.
6. Repeat step 5 every 1-2 minutes. Record your Time and absorbance on your data table.
7. You should be able to obtain 6-7 readings.
Data Workup
Plot your data for each room temperature run in Microsoft Excel. Determine which plot produces a
linear fit and the order with respect to CV. Use the trend line option in Excel to get the slope of both
plots. From both slopes and the two hydroxide concentrations determine the order of reaction with
respect to hydroxide.
You can use Excel to obtain the activation energy. Convert your temperatures to 1/T (°K) and your
slopes into rates by dividing by the OH concentration.
Postlab Question
The data below has been taken for the reaction of an unknown dye with the hydroxide ion. The
reaction was performed at two different high (constant) hydroxide ion concentrations while the dye
concentration was kept constant. Find k, x and y in the rate law below.
Rate = k[Dye]x[OH]y
t (min)
0
1
2
3
4
abs
1.00
0.910
0.820
0.740
0.670
Run 1: [OH-] = 0.05 M
ln(abs)
1/abs
0.00
1.00
-0.0943
1.10
-0.198
1.22
-0.301
1.35
-0.400
1.49
abs
1.00
0.670
0.450
0.300
0.200
Run 2: [OH-] = 0.10 M
ln(abs)
1/abs
0.00
1.00
-0.400
1.49
-0.799
2.22
-1.204
3.33
-1.609
5.00
Data Table
Part II:
Wavelength of maximum absorbance=_________________ nm
Run 1
Calculate the [CV] and [OH ] in Run 1. (Note the concentration has been changed once you mix two
solutions together)
-
[CV] = ____________
Time (second)
1
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
[OH-] = ___________
Absorbance
(A)
Data Table Run 2
Calculate the [CV] and [OH-] in Run 1. (Note the concentration has been changed once you mix two
solutions together)
[CV] = ____________
Time (second)
1
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
[OH-] = ___________
Absorbance
(A)
Calculation Table
Find the rate order with respect to CV by graphing [abs] vs time; ln[abs] vs time and 1/[abs]
vs time. Print out your excel graphs and attach them to your lab report.
Run 1
CV Concentration in reaction mixture:__________________
NaOH Concentration in reaction mixture:________________
Best Fit Curve (circle 1): Absorbance
Slope of Plot:___________
ln(Absorbance)
1/(Absorbance)
Order of reaction with respect to CV:____
Run 2
CV Concentration in reaction mixture:__________________
NaOH Concentration in reaction mixture:________________
Slope of Plot:___________
Order of reaction with respect to Hydroxide:______
Actual Rate Constant k (Show calculations below):
Run1:___________
Run 2:______________
Room Temperature:____________
Rate Law (Include rate constant at room temperature and order for each reactant):
Rate = _________________________
Activation Energy Data Table
[OH-] = ___________
[CV] = _______________
Temperature of water bath=________
Time
Absorbance
(A)
Activation Energy Data
Temperature
1/Temp (°K)
Slope
Activation energy:_____________________
Rate Constant
Ln(k)