Kinetics

(Revised 4 March 2026)

Introduction

Chemical kinetics¹

Studying the kinetics of a reaction means an investigation of the rate of a reaction. Several factors can influence the rate of a chemical reaction: temperature, nature and concentration of reactants, surface area and the presence of a catalyst. By studying the variation in the concentration of reactants over the course of a reaction, it is possible to determine its rate law. This experiment will focus on the decomposition of a Brilliant Blue food colorant (Brilliant Blue FCF, shown below) in the presence of bleach, whose active ingredient is sodium hypochlorite.

Since several products are obtained in this reaction, the general reaction will be written in the following way:

Blue (aq) + NaOCl (aq) equilarrow

products (aq) (equation 1)

Thus, the rate law of this reaction is given by the following expression:

rate = k [Blue]^m [NaOCl]ⁿ (equation 2)

in which k is the rate constant, while m and n represent the order of the reaction according to each reactant. The overall objective of this experiment is then to determine the rate law for the bleaching of Brilliant Blue food colorant by sodium hypochlorite (bleach), and, thus, to find the values of k, m and n.

In this experiment, the concentration of bleach is much larger than the concentration of the blue food colorant. Thus, since hypochlorite ions are present in great excess in the solution, the change in their concentration during the reaction will be very small, and, thus, their concentration is assumed to be constant throughout the reaction. This kind of approach is called swamping. Under these conditions, we can use a new rate constant, k_obs:

k_obs= k [NaOCl]ⁿ(equation 3)

Substituting equation 3 into equation 2, the rate law for the bleaching reaction under swamping conditions can be simplified to:

rate = k_obs [Blue]^m(equation 4)

The concentration of hypochlorite ions in bleach is known from the results of a previous experiment or it will be given to you by the professor.

The concentration of the blue food colorant in solution will monitored by using spectrophotometry, also known as ultraviolet-visible spectroscopy, or UV-Vis spectroscopy (see the section Introduction to Ultraviolet-Visible (UV-Vis) Spectrophotometry and Beer's Law below). In fact, the change in coloration during the reaction is also clearly visible to the eye.

In Part 1, the wavelength of maximum absorbance ( Lambda

max) of the colorant will be determined.

In Part 2, the concentration of blue colorant will be measured as a function of time by measuring the absorbance of the solution at 10-second intervals. Remember that a colored substance absorbs a fraction of the visible light that goes through it and transmits the rest.

If a solution is dilute enough, the amount of light absorbed is proportional to the concentration of the substance (colorant) absorbing the light, as illustrated by the Beer-Lambert Law:

A = abc (equation 5)

in which:

A is the absorbance. For best results, measurements of absorbance should be measured at the max. It would be of little use to try to measure the concentration of a colored substance at a wavelength of light that it does not absorb;
a is the molar absorptivity coefficient or the extinction coefficient (units M^-1cm^-1). The extinction coefficient is constant for a species at a given wavelength and represents how much light is absorbed at a particular wavelength. The extinction coefficient varires with wavelength so it must be reported with reference to a wavelength of light;
b is the path length in cm (1.00 cm in the instrument used in this experiment);
c is the concentration in M.

Thus, in Part 3, a calibration curve will be constructed using aqueous solutions of the blue food colorant of known concentration to verify that the Beer-Lambert law applies. It is important to make sure that the absorbance of the solution remains proportional to the concentration over the full range of concentrations observed during the reaction.

Introduction to Ultraviolet-Visible (UV-Vis) Spectrophotometry and Beer's Law²

Every chemical substance possesses its own unique set of electronic, vibrational and rotational energy levels. When electromagnetic radiation falls upon an atom or molecule, only the energy that corresponds exactly to the difference between two energy levels in the atom or molecule is absorbed. The remainder of the electromagnetic radiation passes on through the sample. This decrease in the amount of radiation is exactly what a spectrophotometer measures. In the visible region of the electromagnetic spectrum, most absorptions result in the transition of an electron from a lower to a higher electronic state in the sample. These transitions are responsible for the colors we ascribe to samples, for example, if red is absorbed the sample will appear green (the complementary color of red). Several factors control the amount of light absorbed by a sample:

The concentration of the absorbing species
The sample length
The probability of light absorption by the absorbing species (called the molar absorptivity coefficient or extinction coefficient)

The equation below relates these quantities:

(equation 6)

Where:

I_o is the intensity of incident light;
I_t is the intensity of transmitted light;
a is the molar absorptivity coefficient (constant for a species at a given wavelength);
b is the path length in cm;
c is the concentration in moles/liter (M).

Furthermore, log(Io/It)

is also called the absorbance (A), and the equation A = a b c is called Beer's Law. From this equation, A versus c should be a straight line.

You may find the video below about UV-Visible spectroscopy helpful.³

Data Analysis

In Part 1, determine the wavelength of maximum absorption ( Lambda

max) and compare to the theoretical value. Calculate the molar absorptivity (provide the correct units) and compare to the theoretical value.

As for the analysis of the data, several graphs will be prepared from the results obtained in Part 2 with the goal of determining the complete rate law:

Graph 1 - the absorbance as a function ot time. Place all trials on the same set of axes.
Graph 2 - the natural logarithm of the absorbance vs. time, placing all trials on the same set of axes.
Graph 3 - the reciprocal of the absorbance vs. time, combining all trials on the same set of axes.

For graphs 2 and 3, it is assumed that the concentration and the absorbance are proportional. This is what we verify in Part 3 by graphing absorbance versus concentration and ensuring that it is, in fact, linear.

Among the graphs 2 and 3, the one that shows a straight line determines the order (m) of the reaction according to the blue food colorant. Therefore, identify the graph that shows a straight line and gives the equation of the line and the regression coefficient. The slope of the line is equal to the magnitude of the constant k_obs. Obtain the k_obs constant for trials 1 and 2. The k_obs constant will also be obtained for trial 3 with a diluted solution of bleach (see procedure below: Part 2 Kinetic Study, step 7).

The order (n) of the reaction according to NaOCl will be obtained by comparing k_obs value of trial 3 with trial 1 using the following equation: k_obs _{trial 3}/ k_obs _{trial 1} = k [NaOCl]ⁿ _{trial 3} / k [NaOCl]ⁿ _{trial 1} (this method is called the initial rates method). Inthis equation, you want to know the value of n. What is the value of n if approximtely equal values are obtained on the left and right side of the equal sign in?

Calculate the actual rate constant, k, by substituting k_obsand [NaOCl]ⁿin the k_obs= k [NaOCl]ⁿequation. Write the complete rate law, including the value for k (with the correct units) and the values of m and n. Compare the rate law and the value of the rate constant with the literature.

For Part 3, a calibration curve is obtained along with, thhe equation of the line and the regression coefficient. Calculate the extinction coefficient of the blue food colorant. Provide the correct units. Compare to the literature value and to the value you determined in Part 1.

Safety

Where a lab coat and gloves. The blue food colorant my stain your hands.

Prelab

Search the Journal of Chemical Education (JCE) to find an article containing the:

Theoretical values for the maximum wavelength of absorption (max) in water (solvent) and the molar absorptivity in water (solvent) of the blue food colorant, Brilliant Blue;
Rate constant, k, for the bleaching of Brilliant Blue by sodium hypochlorite.
Provide your reference.

For Part 1:

Calculate the concentration of the diluted blue dye solution (blue reaction solution).

For Part 3:

Calculate the concentration of calibration solutions 2 to 5.
Create a table containing the solution number, and, for solutions 2 to 5 include the number of mL pipetted of the previous solution and the total volume. Also include in the table, the final concentration of each of the 5 calibration solutions, the absorbance at the max. Complete the table with all the values exept the absorbance at the max.
Prepare a table of observations.

Procedure

Part 1 - Determine Lambda

max of Brilliant Blue

Pipette 10 mL of 0.100 mM stock blue food colorant solution into a 100-mL volumetric flask. The concentration of blue food colorant is an approximate concentration. The actual concentration of the stock solution will be given to you on the day of the experiment.
Fill the flask to the mark with distilled water and mix thoroughly. This blue reaction solution will be used for Part 2.
Using a plastic pipette, fill a cuvette with the solution you just prepared.
Place the cuvette into the sample holder of the spectrophotometer.
Determine the wavelength of maximum absorbance by obtaining the visible spectrum of the blue dye between 450 and 750 nm. Use distilled water as the blank. To use the spectrophotometer, follow the instructions of the professor.

Part 2- Kinetic study of the bleaching of Brilliant blue by sodium hypochlorite

The professor will guide you when using the spectrophotometer. Choose the kinetics mode of the instrument. Set the instrument to measure the absorbance of the kinetic solutions at the max, every 5 seconds for 60 seconds, every 10 seconds for 60 seconds and finally every 20 seconds for 120 seconds (total time period = 240 seconds or 4 minutes).

Trial 1 - using the concentrated bleach solution

In a small beaker, pipette 20 mL of the blue reaction solution prepared in Part 1.
When the instrument is ready, use an Eppendorf pipette and quickly add 800 µL of bleach to the beaker containing blue reaction solution. It is important to add the bleach only when the instrument is ready, not before and not after, as the blue color of the dye solution will begin to fade immediately upon the addition of the bleach.
Mix thoroughly and transfer part of the mixture into a cuvette as quickly as possible. Without delay, place the cuvette into the sample holder of the spectrophotometer.
Immediately begin measuring the concentration of the blue colorant solution as a function of time.
Since it is not possible to observe what is happening in the cuvette inside the spectrophotometer, observe the contents of the beaker to see what happens over the 4-minute time interval.

Trial 2 - using the concentrated bleach solution

Perform a second trial by adding to a clean beaker, in the following order: 20 mL of blue reaction solution, then 800 µL of bleach. Remember that the bleach should only be added to the beaker when the instrument is ready!! The professor will be there to help you.

Trial 3 - using the diluted bleach solution

Next perform one last trial by adding 20 mL of blue reaction solution, then 800 µL of diluted bleach solution (that is half the concentration of the one used in trials 1 and 2) to a clean beaker.
During the waiting times, you may begin to prepare the solutions for the calibration curve in Part 3.

Part 3 - Verify the Beer-Lambert law with the construction of a calibration curve

In order to prepare the calibration curve, a serial dilution of the blue reaction solution will be performed. Prepare these solutions during the waiting times of the kinetics experiment performed in Part 2.
A serial dilution is the stepwise dilution of a substance in solution. Usually, the dilution factor is constant at each step, resulting in the progressive lowering of the concentration in logarithmic fashion. In this experiment, a two-fold serial dilution will be made because each solution is half the concentration of the next most concentrated solution.
Using a graduated pipette, add 25 mL of the blue reaction solution (solution 1) to a 50-mL volumetric flask. Fill the flask to the mark with distilled water and mix thoroughly. This represents solution 2.
Next, pipette 25 mL of solution 2 and place it into another 50-mL volumetric flask. Add distilled water to the mark and thoroughly mix. This represents solution 3.
Then, pipette 25 mL of solution 3 and place it into another 50-mL volumetric flask. Add distilled water to the mark and thoroughly mix. This represents solution 4.
Finally, pipette 25 mL of solution 4 and place it into another 50-mL volumetric flask. Add distilled water to the mark and thoroughly mix. This represents solution 5.
Using the max, measure the absorbance of each solution. The professor will guide you when using the spectrophotometer.
Create a calibration curve (absorbance vs. concentration).

References

Arce J, Betancourt R, Rivera Y, Pijem J. The reaction of a food colorant with sodium hypochlorite: a student-designed kinetics experiment. J Chem Educ [Internet]. 1998 Sep [cited 2024 Feb 19];75(9):1142. Available from: https://pubs.acs.org/doi/abs/10.1021/ed075p1142
Brown TL, LeMay HE Jr., Bursten BE, Murphy CJ, Woodward PM, Stoltzfus MW, Lufaso MW. Chemistry: The Central Science, 14th edition. USA: Pearson Education, Inc.; c2018. Chapter 14, Chemical Kinetics, p576
Professor Davis, ChemSurvival. How a simple UV-Visible spectrophotometer works [Internet]. YouTube; 2014 [cited 16 Feb 2023]. Available from: https://www.youtube.com/watch?v=oysDkHz1pgA