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Chemistry Internal Assessment: Activation Energy of Sodium hypochlorite

I Aim

To quantify the activation energy of the reaction between bleach and dye producing a colorless solution, by
assessing the time required to complete the reaction in temperature range of 25-75℃ in increments of 10℃.

II Research Question

What is the activation energy of the reaction between Sodium hypochlorite and Azorubine dye determined
by measuring rate of reaction via Spectrophotometry (Beer’s law), in various temperature, by the application
of Arrhenius Equation?

III Motivation for research

As a child, I had nasal allergy (Rhinitis) which caused frequent nosebleeds. I remember once staining my
brand-new white shirt with my nose blood, and I tried to remove the stain using bleach in room temperature
water. However, it was proven to be ineffective, as it was time consuming and resulted in a shirt with a slight
hint of red. This is when I went to my mother for assistance, and she suggested soaking my white shirt in hot
water with diluted bleach, as a result it removed the stain flawlessly and easily. Wanting to rebuke this absurd
idea, I resorted to the internet and soon found out that various industry involving oxidizing agent such as
bleach, tend perform the reaction in an environment greater than 60℃. Thus, it prompted me to investigate
the relationship between bleaching and temperature, by investigating the kinetics of dye bleaching.

To simulate nose blood, I decided to go with general food coloring for hygienic reasoning and to serve a
more “effective” learning experience regarding the mechanism between bleach and coloring. The
investigation will be predominantly based around the concept of kinetics, as by measuring the rate of reaction,
it will enable the calculation of activation energy using the Arrhenius equation.

In additional to satisfactory of answering the research question, by determining an ideal temperature for
which bleach should be used, it will allow us to conform to a greener world and save capital without
sacrificing the efficiency of the reaction.

IV Scientific Background Information

Azorubine Red Dye Molecular Formula: 𝐶20 𝐻12 𝑁2 𝑁𝑎2 𝑂7 𝑆2 (502.431 𝑔𝑚𝑜𝑙−1 ) (𝑃𝑢𝑏𝐶ℎ𝑒𝑚)

Dissociation of Sodium Hypochlorite in the presents of water: 𝑁𝑎𝐶𝑙𝑂(𝑎𝑞) → 𝑁𝑎(𝑎𝑞)

+
+ 𝐶𝑙𝑂(𝑎𝑞)
−

Reaction Studied: 𝐶20 𝐻12 𝑁2 𝑁𝑎2 𝑂7 𝑆+2 (𝑎𝑞) + 𝑁𝑎𝑂𝐶𝑙(𝑎𝑞) → 𝐶20 𝐻12 𝑁2 𝑁𝑎2 𝑂8 𝑆+2
2(𝑎𝑞) + 𝑁𝑎(𝑎𝑞) + 𝐶𝑙(𝑎𝑞) (𝑇ℎ𝑜𝑚𝑝𝑠𝑜𝑛)
+ −

The reaction will undergo an exothermic redox reaction. Through the

addition of Sodium hydrochloride, the nitrogen double (𝜋) bond in
Azorubine will be broken via the addition of Oxygen, where two new
𝛿 bonds are created in place of the original bond, resulting in a
colorless product, this process is known as Electrophilic addition.

The following mechanism will be explained in detailed under the Figure 1 Wiki, Skeletal Formula of
Chromophore selection. Azorubine
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IV.I Chromophore (Color Science)
The observation of color is a result of absorption and reflections of specific wavelength. When light is
incident on a molecule, the molecule will absorb a specific range of the electromagnetic spectrum, while the
remaining segments will be reflected in all orientations. If the wavelength of the reflected light falls within
the visible spectrum (~400 nm to 700 nm), our macula in our eye
will translate the wavelength into its respective color (Britannica).
Thus, the color observed is the complementary color to the light
(wavelength) that is absorbed on the color wheel.

There are two general molecule responsible for the creation of color
in chemistry; fluorophores and chromophores. The molecules that Figure 2 Richard-59, The mechanism
are responsible the coloring in red dye are chromophores. of chromophore
Chromophores is a region in a molecule where the energy gap between an occupied orbital and an empty
orbital is within the visible spectrum (Britannica).

The mechanism of chromophores goes as follow, when an incident light (photon) hits the molecule with a
corresponding energy, the photon will be absorbed, and an electron will be excited to be promoted from a
lower to a higher-level empty orbital. Where the complementary color will be observed (Britannica).

IV.II Bleaching (Redox)

Household bleaches consist of a mixture of chemicals, but it’s mainly consisted of Sodium hypochlorite
(𝑁𝑎𝐶𝑙𝑂), Calcium hypochlorite (𝐶𝑎𝐶𝑙𝑂) , or Hydrogen Peroxide (𝐻2 𝑂2 ) . Whom of each are strong
oxidizing agents. For this experiment the bleach is used is composed of 8.25% diluted 𝑁𝑎𝐶𝑙𝑂 (NTUC).

Firstly, the bleach as the oxidizing agent reduces by  2[LGL]HVLQFUHDVHVLQR[LGDWLRQVWDWH 

gaining the electrons from the oxidation of the dye as
'\HDT&O2DTĺFRORUOHVVSURGXFWDT&ODT
the reducing agent, altering the physical structure of the
molecule. In turn this, removes the ability of electrons  5HGXFHVGHFUHDVHLQR[LGDWLRQVWDWH 
to become excited, thus photons are not released Figure 3 Created by author, Redox reaction between
(ThoguhtCo). Dye and Hypochlorite ions

Secondly, Sodium Hypochlorite bleach work by breaking the double bonds of a chromophore into a single
via the addition of Sodium ions, which alters the electron configuration of the molecule, therefore the energy
difference between the filled and empty orbitals would also differ. With smaller changes the color might
appear to be different, for example high energy photons in such can disrupt bonds to decolorize molecule,
but with larger changes it can inactivate the chromophore and result in a colorless product (Britannica).

IV.III Rate Equation

The rate law expresses the relationship between the rate of reaction and the concentration of the reactant:

𝑟𝑎𝑡𝑒 = 𝑘[𝑑𝑦𝑒]1 [𝑁𝑎𝐶𝑙𝑂]1 (𝐴𝑟𝑐𝑒)

𝑥[𝑑𝑦𝑒] + 𝑦[𝑏𝑙𝑒𝑎𝑐ℎ] → 𝑧[𝑝𝑟𝑜𝑑𝑢𝑐𝑡], 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑜𝑟𝑑𝑒𝑟 = 𝑥 + 𝑦 = 2

Within the rate law, [𝑑𝑦𝑒] and [𝑏𝑙𝑒𝑎𝑐ℎ] represent the concentration of the reactants with units of 𝑚𝑜𝑙𝑑𝑚−3 .
The variable k denotes the rate constant of the reaction, the rate constant is specific to a reaction at a specific
temperature and its unit depends on the order of reaction The two coefficients 𝑥 and 𝑦 correspond to the
reaction’s order and the sum of 𝑥 and 𝑦, will give you the overall order. A zero-order states that the rate is
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unaffected by the concentration of its reactant. While a first-order rate states that it is proportional to the
concentration of its reactant. Where a second order states that the rate is proportional to the square of the
concentration of one reactant (Libretexts). By using a greater concentration and volume of bleach compared
to the amount of dye, the reaction will be forced into pseudo-first order (“fake” first order). Thus, [𝑏𝑙𝑒𝑎𝑐ℎ]
will remain essentially unchanged over the course of the reaction and the experimentally determined rate
constant, k’ known as apparent rate constant can be expressed as in terms of the actual rate constant k
(LibreTexts). Therefore, the rate law of the reaction studies can be assumed as:
𝑟𝑎𝑡𝑒 = 𝑘[𝑑𝑦𝑒]1 , 𝑤ℎ𝑒𝑟𝑒 𝑘 = 𝑘′ [𝑏𝑙𝑒𝑎𝑐ℎ] (1)
IV.IV Activation Energy
Activation energy refers to the least amount of energy needed for a
chemical reaction to occur. And according to the collision model as
the temperature increase, the rate of reaction and rate constant also
increases. This is a result of increase in kinetic energy.

An increase in temperature will increase the velocity of the particles,

which results in a higher frequency of collision, thus an increase in
successful collision. And in-turn it will increase the rate of reaction.
Figure 4 Drvanderveen, Maxwell-
Additionally, an increase in kinetic energy will in-turn increase the Boltzmann graph
total energy of the system. This increase in energy will result in a greater proportion of molecules will be
greater or sufficient energy to overcome the activation energy, thus the frequency of successful collision
between reactant increase, therefore rate of reaction increase. As shown by the Maxwell-Boltzmann curve.

The relationship between temperature and rate law can be defined by the Arrhenius equation.
𝐸𝑎
𝑘 = 𝐴 × 𝑒−𝑅𝑇
1
By rearranging and linearizing the Arrhenius equation, ln 𝑘 can be expressed in terms of 𝑇
where the
activation energy can be determined graphically by calculating the gradient (𝑚) as shown below (Puffelen).
𝐸𝑎 𝑘 = 𝑟𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝑚𝑜𝑙−1 𝑑𝑚3 𝑠−1 )
ln 𝑘 = ln 𝐴 + (− )
𝑅×𝑇 𝐸𝑎 = 𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑔𝑟𝑦 (𝐽 )
𝐸𝑎 1
(2): ln 𝑘 = − × + ln 𝐴
𝑇 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 (𝐾)
𝑅 𝑇 𝑅 = 𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (8.31 𝐽 𝐾 −1 𝑚𝑜𝑙−1 )
(3): 𝐸𝑎 = 𝑚 × −𝑅 𝐴 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
IV.V Colorimetry
The concentration of the reactant is proportional to absorbance, according to Beer-Lambert's law. Which is
expressed by the following expression; 𝐴 = 𝜀 × 𝑐 × 𝜆, where 𝐴 denotes absorbance, 𝜀 denotes absorption
coefficient and 𝑐 denotes concentration. Dye consists of molecules with strong absorbance against a specific
wavelength, resulting in a maximum absorbance reading. Therefore, by monitoring the absorbance at the
maximum wavelength the concentration is computable (Gilchrist).

V Hypothesis

According to the collision model, as temperature increases the reactant would have greater thermal energy,
hence more energetic and resulting in higher frequency of collusion. Furthermore, the peak of the curve shifts
toward the right, therefore a greater proportion of particles will have sufficient energy to surpass the 𝐸𝑎, as
illustrated in Figure 4. This would decrease the time required for the redox reaction to completed. Therefore,
it is hypothesized as temperature increase will follow exponential, as suggested by (2).
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VI Independent, Dependent and Controlled Variables

Independent Variable How does it change

This range of temperature is selected for the simplicity to conduct in the lab, using
a standard water bath. Furthermore, by using increments of 10℃, the uncertainty in
water bath temperature (±0.2℃) is reduced to a negligible level. Considering most
household’s tap deliver water up to 65℃ a range of 25 − 65℃ is used, with 25 being
Temperature room temperature (Sea Temperatures). Following the industrial recommended
(25,35,45,55,65,75℃) temperature of 70 − 80℃, a temperature range of 25 − 75℃ was chosen (Wang).
In order to compute the activation energy, Equation 3 is used, where the slope of the
Arrhenius graph equate to − 𝐸𝑎
𝑅
× 𝑇1 , while ln 𝐴 is the y-intercept. By changing
temperature then plotting (ln 𝑘) against (𝑇1 ), we will be able to multiple the slope by
the Ideal Gas constant to compute for the activation energy of the reaction.

Dependent Variable How does it change

Using the full-wavelength spectrum on Vernier’s Colorimeter, a maximized
wavelength 𝜆𝑚𝑎𝑥 will be determined. Using 𝜆𝑚𝑎𝑥 , a cuvette containing the required
Initial Rate of concertation of dye and bleach, will be put through the colorimeter. Where the initial
reaction: Change
rate of reaction can be found by measuring the gradient of the tangent of the graph
in absorbance over
time of absorbance vs time. By applying Beer’s Law, a calibration-graph will be
established. Allowing change in absorbance to be translated into concentration, and
the rate constant can be measured at each trial temperature using (1).

Controlled Variables Explanation

To avoid unwanted deviation, 1.5 ml of dye and 0.75ml of bleach at 1 uM and 1M
Volume & will be used respectively throughout the experiment. Where the reactants will be
Concentration of measured using a 1000µl [±2.5 µl] Micropipette, limiting random errors. The studied
Reactants reaction is a second order reaction, therefore any changes in concentration will affect
the rate of reaction to the power of two, thus affecting the calculated rate constant.

At different wavelengths the dye will display different levels of absorbance,

resulting in discrepancy between measurements. Therefore, all experiments will be
Spectroscopic performed using Vernier’s Spectro-Vis Plus set at 515 nm, smooth pathlength of 1
measurements cm and distilled water used for the 100%T reference and calibration of the
colorimeter. Furthermore, calibration will be conducted at the beginning of each
trial, to reduce systematic error.

Before the experiment is underway, a thermometer will be used to measure the room
temperature, ensuring throughout the duration of the experiment room temperature
is 22.3℃. Similarly, the atmospheric pressure will be measured at 101 𝑘𝑃𝑎 using
Experimental the Barometer. And since the atmospheric pressure in Singapore does not fluctuate
condition much, it can be considered a control variable. According to the collision model,
external heat energy from the surrounding would influence the kinetic energy of
particles, hence it has the potential of influencing the rate of reaction, therefore
impacting the rate of reaction. Due to the stability of pressure, there will not be a
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large impact on the volume of dye or bleach, this variable will be further monitored
to ensure the accuracy of the experimental data.

No catalyst will be introduced in this experiment. As catalyst provide the reaction

Introduction of with an alternative pathway with lower Activation energy. The introduction of a
Catalyst catalyst would increase the rate of reaction recorded, therefore lowering the
activation energy computed, thus making the data not reliable.

Given the spontaneity of oxidizing agent and the sensitively of the colorimeter, there
is a time delay between data logging, cuvette insertion, and reaction, thus resulting
Time-delay between
in a reduction in the reading of the initial rate of reaction. As a controlled variable,
measurements
the process of mixing and insertions will be performed within 9 seconds, while data
logging will begin 20 seconds following the initiation.

VII Chemical and Apparatus List

Chemicals:
o Distilled Water × 500𝑚𝑙
o Azorubine Solution - Bake King’s Red Color [~10−3 𝑀] × 75𝑚𝑙
o Sodium Hypochlorite (Solid) × 7.44g (disposal at hazardous waste dump)
Apparatus:
o Vernier’s Spectro-Vis Plus [±1 𝐴𝑈] o 3𝑚𝑙 [±0.05] Luerslip syringe× 3
o 100𝑚𝑙 [±0.1] Volumetric-Flask× 1 o Water Bath [±0.2℃] × 1
o 50𝑚𝑙 Beaker × 2 o Electronic [±0.01 g] scale
o 1000𝜇𝑙 [±2.5] Micropipette× 1 o Lab spoon × 1
o Cuvette × 5 o Stopwatch [±0.01𝑠𝑒𝑐] × 1
VIII Risk Assessment & Ethical Consideration
Table 1 Safety precautions regarding the chemicals involved in this experiment (PubChem)
Chemicals Hazard Card Risks and Method to prevent risk
Sodium Hypochlorite is an oxidizing agent, which could result in
server burns to skin, and inhaling it could cause damage to your
Sodium lungs. To maximize safety, lab coats, glasses, and enclosed
Hypochlorite footwear should be worn at all times within the laboratory.
Sodium Hypochlorite is also a hazard to the environment;
therefore, it should dispose in a waste bucket.

Azorubine The chemical has been verified to be of low concern.

Table 2 Safety precautions regarding the apparatus involved in this experiment

Apparatus Hazard Card Risks and Method to prevent risk

The water-bath will reach temperature that could result in severe
Water Bath burn to skin, to prevent unnecessary injuries, always use heat
insulted gloves to extract the solution.

Waste Management: Considering the ethical and environmental implications of using the above-mentioned
chemical, which can cause corrosion and pose a risk to the environment. The amount of Sodium Hypochlorite
used in excess during this experiment will be limited to 10%. While excess chemical will be disposed of
according to the lab technician's instructions.
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IX Methodology

IX.I Data Collection (adapted from thermoscientific “How does bleach keep our whites, white?”)
Standard Solution Preparation 8. Set the display to every 1 second for 60 second
1uM Azorubine Dye solution and record the maximum absorbance
9. Conduct 3 trials for each concentration listed
1. Measure 10 ml of red dye into a 50 mL beaker
in step 1.
2. Transfer 0.1ml of dye into a 100 ml volumetric
flask using a 1000 microliter micropipette Determine the effect of temperature and activation
3. Fill the flask up to the 100 ml mark with energy

distilled water 1. Set the water bath to the desired temperature

4. Cap the flask and invert the solution several 2. Fill 3 test tube with 1.50 ml of 1M bleach
times to mix well. Label the solution as 1uM solution
Azorubine solution using masking tape. 3. Cap the test tube and immerse it into the hot
1M Sodium Hypochlorite Solution water bath for 25 min
4. Using a 1000 microliter micropipette transfer
1. Weight 7.444 g of Sodium Hypochlorite
0.75 ml of 1uM Azorubine solution into 3
transfer it into a 100ml volumetric flask using
cuvettes
a lab spoon
5. Insert the cuvette with red dye into the
2. Fill the flask until the 100ml mark with
calorimeter, select “start” on vernier spectral
distilled water. Label the solution as 1M
analysis at 515 nm (as determined during
Sodium Hypochlorite solution using making
preliminary investigation and compared
tape.
against data collected by EU Food
Absorbance measurements [Beer’s Law]
improvement Agents, 516nm)
1. Prepare four solutions of Azorubine with 6. Swiftly Add the bleach when the timer reaches
respective concentration of 1,0.8,0.6 and 0.2 20 seconds, and only record the data when
uM. *Use glove to prevent staining absorbance reading at ~0 AU.
2. Obtain 5 well-matched cuvettes 7. Repeat step 1-6 with 3 trials each at 5 different
3. Fill the first cuvettes with distilled water to temperatures in total (25, 35, 45, 55, 65, 75).
serve as blank and for calibration for 100%T
Clean up
4. Place the cuvette with 1 uM Azorubine
1. Remove all sample from the
solution into the spectrophotometer and select
spectrophotometer
“Full Wavelength” option.
2. Discard all solution into “the chemical
5. Record the maximum wavelength using the
dustbin”
spreadsheet feature
3. Wash and rinse glassware and apparatus
6. Set the spectrophotometer to the maximum
thoroughly to remove bleach and red dye
wavelength and place the cuvette with
residue
distilled water and select “Calibration”
4. Shutdown the spectrophotometer as instructed
7. Place the remaining 4 cuvettes into
spectrophotometer and,
IX.II Data Processing
1. The rate constant will be calculated using the rate of reaction and concentration of bleaching, and in order
to produce the Arrhenius plot the reaction will be conducted under various temp
2. The Arrhenius plot will be produced by plotting 𝑇1 values as the x-axis against the y-axis ln 𝑘
3. Where the activation energy will be determined by measuring the gradient of the graph
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X Data Analysis

X.I Qualitative Data

Table 3 Qualitative Observation
Before During After
Bleach: The Sodium hypochlorite Color: Upon adding the bleach Color: The final solutions are
is a colorless and transparent there’s an instant change in color tinted in orange, and after leaving
solution. And exhibits a strong from red to dark orange. the solution in room temperature
chlorine-like odor. for around 3 min the solution
Changes: And as temperature
Red Dye: The Azorubine solution become colorless to the naked eye.
increases this change becomes
is a red solution, that closely
resembles the color of nose blood. more spontaneous. This is the Odor: A strong odor of bleach still
And it exhibits no smell nor odor. most noticeable at 75℃. remains in the final solution.

X.II Quantitative Data

Table 4 Calibration data between Figure 5 Beer's law: Relation between 𝑎𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 and [𝑑𝑦𝑒](𝑢𝑀 )
[𝑑𝑦𝑒] and average absorbance *y-intercept is set at (0,0)
Avg Absorbance 1.2
Concentration
(@515 𝑛𝑚)
±0.01 𝜇𝑀
Absorbance [515nm] (A.U.)

1
±0.001 AU
0.8
0.20 0.401
0.6
0.40 0.602
0.4
0.60 0.814 Absorbance Line of Best Line y = 1.3085x
± 0.001 Au R² = 0.9918
0.2
0.80 1.034
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.00 1.242 [dye] (uM)

Table 5 Sample data of absorbance reading of the acted solution at 75.0℃ for 29 seconds
Absorbance ±0.001 A. U.
Time ±0.01𝑠𝑒𝑐
Trial 1 Trial 2 Trial 3
0.00 1.241 1.240 1.240

3.00 1.104 1.094 1.001

6.00 0.708 0.801 0.981

9.00 0.699 0.754 0.839

12.00 0.695 0.732 0.801

15.00 0.685 0.701 0.785

18.00 0.677 0.682 0.771

22.00 0.663 0.612 0.758

23.00 0.659 0.598 0.741

26.00 0.651 0.579 0.739

29.00 0.641 0.568 0.736

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Table 6 Data for change in absorbance within the first 24 seconds at different trial temperature
Change in Absorbance ±0.001 A. U.
Temperature ±0.2℃
Trial 1 Trial 2 Trial 3 Average
25.0 0.018 0.016 0.017 0.017
35.0 0.015 0.020 0.019 0.018
45.0 0.022 0.020 0.019 0.020
55.0 0.021 0.022 0.024 0.022
65.0 0.027 0.026 0.025 0.026
75.0 0.031 0.034 0.028 0.031

Line of best fit obtained from Figure 5:

𝑦 = 1.3085 × 𝑥 (4)
Where 𝑦 equals to absorbance reading at 𝜆𝑛𝑚 = 515 𝑛𝑚 and 𝑥 equals to [𝑑𝑦𝑒] measured in uM

Table 7 Table of uncertainty in the apparatus and equipment used in this experiment

Measurement Apparatus Used Uncertainty

Volume (𝑚𝑙) Analog Micropipette Δ𝑃𝑖𝑝𝑒𝑡𝑡𝑒 = 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡

2 = ±0.0025 𝑚𝑙
Mass (g) Digital Scale Δ𝑆𝑐𝑎𝑙𝑒 = ±𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 = ±0.01 g
Absorbance (𝐴. 𝑈) Digital Colorimeter Δ𝐶𝑜𝑙𝑜𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = ±0.001 𝐴. 𝑈
Temperature (℃) Digital Water bath Δ𝑊𝑎𝑡𝑒𝑟 𝑏𝑎𝑡ℎ = 0.2℃
Time (s) Digital Timer Δ𝑡𝑖𝑚𝑒𝑟 = ±0.01𝑠

XI Processed Data

Table 8 Calculated Averaged rate and rate constant for bleaching at each respective trial temperature
Temperature 𝚫Conc Rate of bleaching Rate Constant
± 0.2℃ 10−8
𝑀 (𝑚𝑜𝑙 𝑑𝑚−3 ) × 10−10 𝑚𝑜𝑙 𝑑𝑚−3 𝑠−1 × 10−4 𝑚𝑜𝑙−1 𝑑𝑚3 𝑠−1
25.0 1.30 ± 0.09 5.41 ± 0.36 5.41 ± 0.36
35.0 1.37 ± 0.09 5.73 ± 0.36 5.73 ± 0.36
45.0 1.55 ± 0.09 6.47 ± 0.37 6.47 ± 0.37
55.0 1.70 ± 0.09 7.10 ± 0.38 7.10 ± 0.38
65.0 1.98 ± 0.09 8.27 ± 0.39 8.27 ± 0.39
75.0 2.37 ± 0.09 8.60 ± 0.40 8.60 ± 0.39
Through the application of equilibrium concept, Sodium hypochlorite is a weak base with an accepted pH of 13 in
most household’s bleach, while Azorubine is coined as a weak acid a pH of 6 for the concentration used In this
experiment. And since [𝑏𝑙𝑒𝑎𝑐ℎ] ≫ [𝑑𝑦𝑒] by a magnitude of 106 , it is safe to assume that the 𝐾𝑏 ≫ 103 , therefore
as the experiment progresses, the decrease in [𝑏𝑙𝑒𝑎𝑐ℎ] have negligible effect on the experiment. Hence, the average
slope obtained in table 8 are equals to k in (1) the rate expression.

Table 9 Sample Calculation for Rate Constant of Bleaching Red Dye for 75℃ trial

Data Processing: Uncertainties Propagation:

Instantaneous rate @75℃ Uncertainty in instantaneous rate @75℃

The instantaneous rate of change was found by computing 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟: 0.001 + 0.001 = ±0.002
the difference in absorbance during the first 24 seconds of 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟: ± 0.1
the reaction.
∆𝑅𝑎𝑡𝑒
= ∆𝐴𝑏 ∆𝑇𝑖𝑚𝑒
𝐴𝑏 + 𝑇𝑖𝑚𝑒
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − @24𝑠𝑒𝑐 1.241 − 0.641 𝑅𝑎𝑡𝑒
= = 0.0250
𝑡𝑖𝑚𝑒 24.00 Δ𝑅𝑎𝑡𝑒𝑖 = 0.025(0.002
0.600 + 24.00) = ±0.0001
00.01
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Average Instantaneous Rate of Change @75℃ Uncertainty in Averaged Instantaneous rate @75℃

𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡𝑟𝑖𝑎𝑙𝑠 0.0250 + 0.0281 + 0.0212 0.000093 + 0.000095 + 0.000092

= = 0.0271 = = ±0.0001
𝑁𝑢𝑚𝑏𝑒𝑟𝑠 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠 3 3
Change in Concentration of Azorubine / Δ[𝑑𝑦𝑒] Uncertainty in Concentration of Azorubine / Δ[𝑑𝑦𝑒]

The uncertainty in the linear equation’s coefficients and

𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒@ = 1.31 × [𝑑𝑦𝑒] (4) constants are ± the smallest Sig.Fig.
𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 Δ𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 Δ𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
[𝑑𝑦𝑒] = Δ[𝑑𝑦𝑒] = [𝑑𝑦𝑒] ( + )
1.31 𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
𝛥𝐴𝑏 0.0271 0.001 0.01
= 2.37 × 10−8 ( )
𝛥[𝑑𝑦𝑒] = = × 10−6 = 2.37 × 10−8 +
0.027 1.31
1.31 1.31
= ±9.215 × 10−10 = 0.09 × 10−8
Rate of Bleaching @75.0℃ Uncertainty in Rate of bleaching @75.0℃
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝛥𝑅𝑎𝑡𝑒 𝛥𝐶𝑜𝑛𝑐 𝛥𝑇𝑖𝑚𝑒
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
= +
𝑅𝑎𝑡𝑒 𝐶𝑜𝑛𝑐 𝑇𝑖𝑚𝑒
= 8.60 × 10−10 𝑚𝑜𝑙𝑑𝑚−3 𝑠−1 Δ𝑅𝑎𝑡𝑒 = 8.60 × 10−10 (2.37×10 −8 + 24.00) = 0.38 × 10
−8 0.09×10 −8 0.01
= 2.37×10
24.00
−10

Rate Constant @75.0℃ / 𝑘 Uncertainty in Rate constant @75.0℃ / 𝑘

𝑟𝑎𝑡𝑒 = 𝑘[𝑑𝑦𝑒] (1) UC in [𝑑𝑦𝑒] = 10−6 (2.5×10 )

−3
0.1
10 + 100
8.60 × 10−10 0.38 × 10−10 1.2 × 10−9
𝑘= 𝛥𝑘 = 8.60 × 10−4 × ( + )
10−6 8.60 × 10−10 10−6
= 8.60 × 10−4 𝑚𝑜𝑙−1 𝑑𝑚3 𝑠−1 Δ𝑘 = 0.39 × 10−4

Percentage of Uncertainty in Rate Constant @75℃

𝑈𝐶 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑒 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 0.39

× 100 = × 100
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑒 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 8.60
Percentage of Uncertainty in Average Rate of reaction = 4. 53%

Figure 6 Arrhenius plot: Relationship between ln 𝑘 and 𝑇1 which is used to compute activation energy
lnk Min Max Line of Best-fit Min Max
-6.80

-6.90

-7.00

y = -1.0078x - 4.07
-7.10
ln(k)

y = -1.2201x - 3.4787
R² = 0.9589
-7.20

y = -1.4453x - 2.7337
-7.30

-7.40

-7.50

-7.60
2.85 2.95 3.05 3.15 3.25 3.35
1/T (K⁻¹) [×10⁻³]
Graphical Analysis: The slope of the Arrhenius plot shown a slope that equals to − 𝐸𝑎
𝑅
, where𝑅 is the ideal gas
constant, 8.31 𝐽𝑚𝑜𝑙−1 𝐾 −1 , thus 𝐸𝑎 is computed as 10.1 𝑘𝐽𝑚𝑜𝑙−1 . The coefficient of determination, 𝑅2 was found
to be 0.958 for the line of best fit, which suggest a strong negative correlation, which also comments on the high
precision of the data.
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Table 10 Processed data displaying ln 𝑘 at different temperature against reciprocal value of temperature

𝐥𝐧 𝒌 Temperature ± 0.2𝐾
𝟏
𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞
× 10−3 𝐾 −1

−7.52 ± 0.07 298.0 3.355 ± 0.032

−7.47 ± 0.06 308.0 3.246 ± 0.030
−7.34 ± 0.06 318.0 3.144 ± 0.027
−7.25 ± 0.05 328.0 3.049 ± 0.023
−7.10 ± 0.05 338.0 2.958 ± 0.021
−7.06 ± 0.05 348.0 2.873 ± 0.017

Table 11 Sample Calculation for Activation Energy of Bleaching Azorubine Solution

Data Processing Uncertainties Propagation

Convert temperatures from degrees Celsius to Kelvin Uncertainty in reciprocal value of temperature
𝑋℃ + 273 = 75 + 273 = 348𝐾 ±℃ = ±𝐾 = ±0.2𝐾
0.2
Compute reciprocal value of temperature 𝑃𝑟𝑒𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑈𝐶 𝐾 −1 = × 100 = 0.0574%
348.0
Δ𝐾 −1 = 0.58 × 2.87 × 10−3 = ± 0.017 × 10−3
1 1
= = 2.873 × 10−3 𝐾 −1
𝑇 348.0
Compute natural log of the rate constant Uncertainty in 𝑙𝑛 𝑘
𝛥𝑘
Δ ln(𝑘 ± Δ𝑘) = ln 𝑘 ±
ln 𝑘 = ln(8.60 × 10 ) = −7.06
−4 𝑘
0.39 × 10−4
Δ ln 𝑘 = = ±0.05
8.60 × 10−4
Activation energy from the slope of the Arrhenius plot Uncertainty in Activation energy
𝑚𝑎𝑥𝑠𝑙𝑜𝑝𝑒 − 𝑚𝑖𝑛𝑠𝑙𝑜𝑝𝑒
Δ𝑚 =
According to (2); 𝑙𝑛𝑘 = − 𝐸𝑎 × 𝑇1 + ln 𝐴 2
−1445 − (−1007.8)
𝑅

The gradient of the Arrhenius Plot, 𝑚 = − 𝐸𝑎

𝑅
= −1220 Δ𝑚 = = ±220
2
(3): 𝐸𝑎 = 𝑚 × −𝑅 = −1220 × −8.31 = 10138𝐽 −220
Δ𝐸𝑎 = 10138 ( ) = ±1828
−1220
Activation Energy of bleaching of Azorubine Solution = 10.1 ± 1.8 𝑘𝐽𝑚𝑜𝑙−1 (3 𝑆. 𝑓)
*In order to fully factor the degree of uncertainty, the method which propagates the greatest uncertainty is used.
Percentage Error in Activation Energy Percentage of Uncertainty in Activation Energy
|𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 − 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑|
𝑈𝐶 𝐴𝑐𝑡𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑒𝑟𝑔𝑦 1.8
× 100 = × 100 = 18%
%𝑒𝑟𝑟𝑜𝑟 =
𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑
𝐴𝑐𝑡𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑒𝑟𝑔𝑦 10.1
%𝑒𝑟𝑟𝑜𝑟 = 42.6−10.1
42.6
× 100 = 76% (Steinfeld)

XII Conclusion

The raw data, documented the change in absorbance at varying temperature from 25 − 75℃ by increments of 10℃
for 29 seconds between 1uM of Azorubine solution in the presence of 1ml of 1M Sodium Hypochlorite, where a
colourless solution is produced. In turn, the change in absorbance over time, allowed the measuring average rate
of reaction, which is then processed into rate constant using (1) and (4). By plotting natural log of rate constant
against reciprocal of the trial temperature as expressed by equation (2), a Arrhenius plot is plotted. To calculate
the activation energy the slope of the graph is multiplied by −𝑅, −8.31𝐽𝑚𝑜𝑙−1 𝐾 −1 . This was computed to be 10.1 ±
1.8 𝑘𝐽𝑚𝑜𝑙−1 , thus the aim of the investigation – determine the Activation Energy of the reaction, are met.

Going back to my motivation that started this investigation, for a surface area of 50𝑐𝑚2 such a piece of cloth with
a pigment concertation of 0.001𝑀 , it is calculated that a total of 5.3𝑘𝐽 of energy is required to achieve the reaction.
Through the application of (4) and data collected, stains can be effectively removed using the optimal temperature,
thus conforming to green chemistry and showcases how kinetics could reduce our carbon footprint.
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Despite the fact that the scientific procedure and experiment were scrutinized for accuracy, there were some
uncertainty in both the rate constant and activation energy - the uncertainty is processed to be ±5%and ±18%
respectively. Though uncertainty exist in both, the propagated Activation energy is considerably higher. This is
likely attributed to minuscule used on the y-axis, which resulted in the vast difference between max and min
coordinates.
The data was sufficient to achieve the objective of the experiment, as the averaged values reflected the rate of
reaction between Azorubine and Sodium Hypochlorite across three trials. The data, however, cannot be considered
reliable due to its low accuracy, as the percentage error is significantly above the generally recognized 5 − 10%
error range, according to LibreTexts. The use of three experimental trials, on the other hand, considerably
decreases one-time errors or inconsistencies, limiting the influence of random error and suggestive of the existence
of predominant systematic errors. This is further confirmed by the fact that the percentage error is nearly fourfold
the percentage uncertainty; 76% 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟 ≫ 18% 𝑜𝑓 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦, suggestive that the experiment is more precise
than accurate (Thoughtco). Therefore, it can be said that the experiment was only somewhat successful.

XIII Evaluation

XIII.I Strengths
Multiple trials per temperature: Due to the conduction of three trials per trial temperature, this investigation is
considered to be more precise and reliable, as the value used to compute the activation energy between the reaction
of Sodium hypochlorite and Azorubine are averaged values acquired from three independent trials. This reduces
any random errors and eliminates outliers from having a significant impact on the calculation, allowing the derived
conclusion to be more statistically significant by minimizing the investigation's overall random error.
Random Error: Another area of success in this experiment is the relatively low uncertainty in the rate constant.
This is the result of using highly precise instruments when recording the concentration of Azorubine, Sodium
Hypochlorite, and absorbance. For example, the uncertainty in absorbance is ±0.001 AU, which is converted into
concentration of dye using (4), and because of their relatively low uncertainty the computed rate constant has an
averaged percentage of uncertainty of 0.006%. This reflects the low random error in the experiment regarding rate
constant. Furthermore, the accuracy of the experiment is reflected by the 𝑅2 value of 0.958, which suggests a
strong and positive correlation between the data and the trend line.
Methodology : To determine the effect of temperature on Sodium Hypochlorite’s oxidizing ability, the kinetics of
the reaction is investigated rather than a comparative study between the rate of reaction at various temperature.
This allows the experimental activation energy value to be evaluated against literature values, gauging the accuracy
of the investigation, adding creditability to the investigation.

XIII.II Weaknesses
Average rate instead of initial rate: During the preliminary trial it was noted that seconds after the addition of the
bleach there was a considerable decrease in absorbance reading, and because the drop was so significant the initial
rate is not computable. As a solution the average rate is used to compute the rate constant, which would have
contributed to the systematic error of the investigation. As a solution to this limitation, a colorimeter with a smaller
time increment could have been used instead to produce a smoother curve, where the initial rate can be measured.
Temperature loss: It is inaccurate to assume that the temperature of the reactant and the environment where the
reaction occurs are in equilibrium with the water-bath, because there will be constant heat radiating into the
surrounding environment during mixing and data logging, resulting in systematic error. The use of a cover can
only aid in maintaining a consistent insulated environment during data logging in order to reduce external cooling.
Additionally, as the Azorubine solution is not heated during the experiment, after the addition of the dye, the acted
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solution would decrease in temperature. In an ideal situation, both the Azorubine and the Sodium Hypochlorite
solution will be heated, while data logging will occur in an environmental where the temperature is controllable,
such as colorimeter used for Water Analysis “CHROMA Model 260”.
Reactant Evaporation: The Sodium Hypochlorite solutions were kept at a high temperature for hours during the
temperature trials. For highly volatile and reactive substances such as Sodium hypochlorite, evaporation occur at
20℃. Which means at room temperature it is sufficient to cause evaporation, thus resulting in systematic error in
that period (PubChem). This evaporation-related limitation could have been mitigated by lowering the temperature
range to, say, 0 − 20℃, as well as using a stopper on top of the test tube to prevent exposure to the environment.
Reduced exposure to toxic fumes and spillage would be an added benefit of this improvement.
Impure Food Dye: The food dye used is produced by Bakeking and as stated on their website the dye used in this
experiment consist of Glycerin (E422), Propylene Glycol (E1520) and Permitted Food Color Carnosine. These
chemicals are unaccounted for when processing the rate law and rate constant. A possible solution would be the
use of pure Lyophilized Azorubine to produce standardized Azorubine solutions, this will allow the mechanism of
the reaction to be studied in detail and reducing the systematic error of the experiment.
Impure Bleach: The experiment is conducted over a period of two days, where the bleach solutions are left in the
air with a varying degree of exposure to 𝑂2 . Considering the solutions are stored in air sealed containers it may
not exert a big difference, nonetheless it will have a certain influence over the concentration of the bleach solution,
hence the rate constant computed may not be an accurate representation. A possible solution would be filling the
containers with less-reactive gas such as 𝐶𝑂2 and 𝑁2 limiting the impact of 𝑂2 oxidation, reducing systematic
error.
Decomposition of Sodium hypochlorite: Under ultra-violent and high temperature (> 40℃) conditions, Sodium
hypochlorite is subjected to two known degradation pathway, as shown below (Wiley):
−
3𝐶𝑙𝑂(𝑎𝑞) → 2𝐶𝑙−
(𝑎𝑞) + 𝐶𝑙𝑂3 (𝑎𝑞) (5) & 2𝑂𝐶𝑙(𝑎𝑞) → 2𝐶𝑙(𝑎𝑞) + 𝑂2 (𝑔) (6)
− − −

The reaction shown in (6) occurs to a negligible extent, without the catalyzation of transitional metals. On the
other hand, the reaction shown in (5) is applicable in this investigation, due to the high temperature used. According
to Tyagi’s research in 2009, when comparing the electrode potential between hypochlorite and chlorate, Chlorate
(𝐶𝑙𝑂3− ) is proven to be ineffectiveness as an oxidizer compared to Hypochlorite. This is a result of increased
number of 𝜋 bonds involved in 𝐶𝑙𝑂3− , which increases the stability of the ion, making it unreactive (Tyagi).
Furthermore, according to Lister’s research at 60℃, with NaOCl and NaCl concentration of 0.862M and 2.23M
respectively, Chlorate is produced with ~30% efficiency (Lister). As observed by Lister’s research the Chlorate
producing reaction predominates at 𝑝𝐻 > 6 , therefore, to prevent the decomposition of Hypochlorite into the
weaker oxidizer Chlorate, the experiment should be performed in acidic condition (𝐻𝐶𝑙 𝑎𝑛𝑑 𝐻2 𝑆𝑂4 ), 𝑝𝐻 < 6.

XIV Extension
This investigation merely explored the relationship between temperature and the oxidizing power of Sodium
hypochlorite, introducing other factors such as catalysis via the addition of transitional metal and alteration
in pH level, would allow a better insight into Sodium hypochlorite’s alterative degradation pathways. All
these factors would broaden our conceptual knowledge in the kinetics of bleaching and in-turn allow
industries to develop a better understanding the control of the oxidizing power of Sodium hypochlorite,
further pursuing green chemistry and chemistry amniotomy. To further lend creditably to this research, the rate
law could be investigated by the application of the integrated rate law, by linearizing the concentration vs time
plot using the relevant order's integrated rate law (zero, first, or second order), rather than basing it off of Arce’s
research.
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