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CHEMISTRY HIGHER LEVEL INTERNAL ASSESSMENT
AN INVESTIGATION TO DETERMINE THE RATE LAW OF THE CHEMILUMINESCENT OXIDATION OF
LUMINOL BY SODIUM HYDROXIDE AND HYDROGEN PEROXIDE
RESEARCH QUESTION
What is the rate law of the chemiluminescent oxidation of luminol ( C 8 H 7 N 3 O 2 ) by sodium hydroxide ( NaOH ) and hydrogen peroxide ( H 2 O 2 )?
AIM OF THE INTERNAL ASSESSMENT The aim of this experiment is to experimentally derive the rate law for the chemiluminescent oxidation of luminol by determining the reaction orders with respect to each reactant. This will be done by varying the concentrations of each reactant and determining the effect this has on the rate of photon emission, as measured by the change in illuminance of the reaction mixture over time.
INTRODUCTION I found myself initially interested in exploring chemical kinetics after a conversation with a classmate about the real-life applications of the field. After some discussion, we came to appreciate the large scope of applications of chemical kinetics, particularly in phenomena which we would encounter on a day to day basis such as the corrosion of metal and the shelf life of food products. Following this conversation, I began further researching chemical kinetics when I encountered an application which particularly excited me; the chemiluminescence of luminol. As somewhat of a crime drama fanatic, I was very familiar with the spray used by forensic investigators to make blood almost magically glow in crime scenes, yet I never really understood the science behind this process. The chemiluminescence of luminol was exactly this; a reaction catalyzed by the heme iron in blood which would emit a distinct glow 1 and thus allow the blood tracings in crime scenes to be visualized. Ultimately, I chose to use this investigation to explore the kinetics behind this reaction, specifically scrutinizing the effect which the concentration of each reactant has on the reaction rate while the ultimate goal of determining the order of reaction with respect to each reactant and, subsequently, the rate law for the reaction.
BACKGROUND INFORMATION Within chemistry there exists the field of chemical kinetics which is concerned with “the effects of different factors on the rates of reaction, reaction mechanisms and forming models to predict reaction rates”. One of^2 the elementary concepts of chemical kinetics is the “rate” of a reaction, defined as the “change in the concentration of the reactants or products of a reaction per unit time”. To explain why different reactions occur at different^3 rates the collision theory is utilized, which is composed of three principles that must be true for a reaction to occur. The first principle of the collision^4 theory is that reactant particles must collide. The second principle of the collision theory is that reactant particles must collide with the correct orientation in order to “allow atoms that bond together to be in contact with one another”. The last principle of the collision theory is that particles must^5 collide with sufficient energy that is equal or greater than the activation energy - “the minimum energy which particles must possess in order to break pre-existing bonds in the reactants and form new bonds in the products”. Critically, any factor which influences the rate of a reaction must^6 influence one of these defining principles.^7
(^1) “NCATS Inxight: Drugs - LUMINOL.” Inxight Drugs. US Department of Health & Human Services. Accessed November 24, 2019. https://drugs.ncats.io/drug/5EXP385Q4F. (^2) Helmenstine, Anne Marie. “Understand Chemical Kinetics and Rate of Reaction.” ThoughtCo. ThoughtCo, March 2, 2019. https://www.thoughtco.com/definition-of-chemical-kinetics-604907. (^3) “Reaction Rate.” Chemistry LibreTexts. Libretexts, September 30, 2019. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretica l_Chemistry)/Kinetics/Reaction_Rates/Reaction_Rate. (^4) “The Collision Theory.” Chemistry LibreTexts. Libretexts, September 30, 2019. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretica l_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/The_Collision_Theory. (^5) “Collision Theory.” Chemistry. PressCorp. Accessed November 24, 2019. https://opentextbc.ca/chemistry/chapter/12-5-collision-theory/. (^6) “Activation Energy.” Definition of Activation Energy | Chegg.com. CheggStudy. Accessed November 24, 2019. https://www.chegg.com/homework-help/definitions/activation-energy-6. (^7) “The Collision Theory.” Chemistry LibreTexts. Libretexts, September 30, 2019. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretica l_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/The_Collision_Theory.
One example of a factor which influences the rate of a reaction is the concentration of the reactants. Increasing the concentration of the reactants increases the molar amount of reactant particles per unit volume, thus increasing the frequency of successful collisions between particles and hence the rate of the reaction. Moreover, an increased concentration will result in a greater number of reactant particles possessing energy greater or equal to the activation energy, further causing the frequency of successful collisions to increase and thus increasing the rate of the reaction. This phenomenon is illustrated in the Boltzmann distribution curve in Figure 1. As can be seen, while an increased concentration of the reactants ( c 1 ) doesn’t alter the shape of the Boltzmann curve, meaning that the mean kinetic energy of particles remains the same, the area under the c 1 curve is greater, resulting in a greater number of particles possessing energy that is larger or equal to the activation energy ( Ea ). The relationship between the rate of a reaction and the concentration of its reactants can be expressed in a rate law , for example:^8
For the hypothetical reaction aA + bB → cC , the rate law can be expressed as rate = k [ A ] [ x^ B ] y
In the above rate law, [A] and [B] represent the concentrations of the two reactions in mol dm-3. The constant k is known as the rate constant and is a coefficient of proportionality which represents the relationship between the rate of the reaction and the concentration of the reactants. The rate constant is specific for the reaction at a particular temperature^9 10 and its units depend on the number of reactants in the rate equation and the units expressing the rate of the reaction. The two coefficients, x and y , represent the order of the reaction with respect to each reactant. These coefficients don’t necessarily correspond to the stoichiometric coefficient in the reaction equation. The order of reaction with respect to a reactant is the “power dependency”^11 of the rate on the concentration of the reactant. Commonly, the order of reaction with respect to a reactant will be zero-order,^12 first-order or second-order. The zero-order reactant is raised to the zeroth power, meaning that the reaction rate is independent of that reactant’s concentration. A first-order reaction is raised to the first power, meaning that the reaction rate is directly proportional to its concentration. A second-order reactant is raised to the second power, meaning that the relationship between the reaction rate and the reactant’s concentration is exponential. If these different orders of reaction were to be illustrated on a concentration against rate graph, a zero-order reaction will be a horizontal line, a first-order reaction will be a linear graph starting at the origin and a second-order reaction will be an exponential graph starting at the origin.
The reaction explored in this investigation is the chemiluminescent oxidation of luminol. This reaction is exothermic, meaning that the energy of the reactants is greater than the energy of the products and there’s thus a net release of energy by the reaction. However, unlike most exothermic reactions that release energy in the form of heat, this reaction releases^13 energy in the form of photons, or light. This is what the term “chemiluminescence” refers to; the emission of cold light (light accompanied by little or no heat ) due to the relaxation of an excited state. The reactant which is primarily responsible for^14 the chemiluminescent characteristics of this reaction is luminol (formally known as 5-amino-2,3-dihydro-1,4-phthalazinedione ), an organic compound that exhibits chemiluminescence when activated by an^16 oxidizing agent in an alkaline solution in the presence of a catalyst. In this specific reaction, the oxidizing agent is hydrogen^17 peroxide (H 2 O 2 ), the base is sodium hydroxide (NaOH) and the catalyst is potassium ferricyanide (K 3 [Fe(CN) 6 ]). The full reaction is represented by the equation below.
C 8 H N O 7 3 (^) 2 ( s ) + 2 H 2 O (^) 2 ( aq ) + 2 N aOH (^) ( aq ) → C 8 H N O 5 (^) 4 2−( aq ) + N (^) 2 ( g ) + 4 H O 2 (^) ( l ) + 2 N a +( aq ) + hv
One of the products of this reaction, hv , represents the energy of the light emitted by the reaction. The particle-wave duality of light allows for the energy of a light ‘particle’ (a photon) to be expressed as a function of the light wave’s frequency. This relationship is expressed by Planck’s equation: " E = hv "^18 , which states that the energy of a photon is equal to the product of the frequency of the light wave ( v ) and Planck’s constant ( h ).
(^8) “The Rate Law.” Chemistry LibreTexts. Libretexts, June 5, 2019. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretica l_Chemistry)/Kinetics/Rate_Laws/The_Rate_Law. (^9) Ball, David W., and Jessie A. Key. “Rate Laws.” Introductory Chemistry 1st Canadian Edition. BCcampus, September 16, 2014. https://opentextbc.ca/introductorychemistry/chapter/rate-laws-2/. (^10) Ibid. (^11) Ibid. (^12) Bagshaw, Clive R. 2013. “Order of Reaction.” In Encyclopedia of Biophysics, edited by Gordon C. K. Roberts, 1807–8. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-16712-6_575. (^13) Firuz, Akmal. "Chemiluminescence." n.d. PPT. (^14) “Cold Light.” The Free Dictionary. Farlex. Accessed November 24, 2019. https://www.thefreedictionary.com/cold light. (^15) “Luminol.” Chemistry LibreTexts. Libretexts, June 5, 2019. https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Analytical_Chemiluminescence/2: _Chemiluminescence_Reagents/2.01:_Luminol. (^16) Clegg, Brian. “Luminol.” Chemistry World, April 16, 2014. https://www.chemistryworld.com/podcasts/luminol/7272.article. (^17) Lodovico, Ray. “Luminol and Chemiluminescence.” PhysicsOpenLab, February 6, 2019. http://physicsopenlab.org/2019/02/06/luminol-2/. (^18) “E=Hv.” PhysicsMatters.org: Quantum: E=hv. American Physical Society, 2012. http://www.physicsmatters.org/quantum/ehv.html.
HYPOTHESIS
From the reaction mechanism shown in Figure 2 it can be predicted that both luminol and NaOH are part of the rate law, given that they are both required to form dianion (A) which proceeds to react with O 2. However, if the reaction between dianion (A) and the O 2 molecule is the slow, rate-determining step then O 2 , and thus H 2 O 2 , may also be part of the rate law. Given this, it is necessary to use a method to predict the rate law. The steady-state approximation is used to estimate the rate laws of reactions by assuming that “the concentration of all reaction intermediates remains constant throughout the experiment”. Another assumption made as part of the steady-state approximation is that the “overall rate law will be the^28 final step in the reaction mechanism”. In order to better understand the reaction, it is easiest to deconstruct the reaction^29 mechanism presented in Figure 2 into elementary steps. For simplicity’s sake, I have drawn out some of the compounds which take part in the reaction, as indicated in the reaction mechanism, and have labelled them accordingly in Figures 3 to 6.
Figure 3: Luminol (I) Figure 4: Intermediate 1 (II) Figure 5: Intermediate 2 (III) Figure 6: Product (IV)
As such, the following reaction mechanism was constructed, following the findings of White et al.^30 :
Given the steady-state approximation, the concentration of intermediate 1 (II) and intermediate 2 (III) will remain constant throughout the reaction, meaning that they will be produced at the same rate that they are consumed by the reaction. Using the reaction mechanism outlined above, it is possible to express the rate of production and consumption of each intermediate in the form of a rate law. These rate laws will be equal to each other and, via some basic arithmetical operations, an expression can be deduced for the concentration of each intermediate in terms of the rate constants of other elementary steps and the concentration of the original reactants. For example, the expression for the concentration of intermediate 1 (II) is derived in the following way:
r ate of production of Ⅱ = rate of consumption of Ⅱ k 1 [Ⅰ][ OH −^ ] = k 2 [Ⅱ][ OH −] [ Ⅱ ]= (^) k [ OH ] 2 −
k (^) 1 [Ⅰ][ OH −] = k 2
k (^) 1 [Ⅰ]
Similarly, an expression for the concentration of intermediate 2 (III) can be derived. Given that III is involved in the equilibrium step 2, its rate of consumption will be equal to the sum of the rate of the backwards reaction in step 2 and the rate of step 3.
r ate of production of Ⅲ = rate of consumption of Ⅲ k 2 [Ⅱ][ OH −]^ = k −2[ Ⅲ][ H O 2 ] + k 3 [Ⅲ][ O (^) 2 ] k 2 [Ⅱ][ OH −]^ = [Ⅲ ]( k (^) −2[ H O 2 ] + k 3 [ O (^) 2 ])
(^28) Mott, Vallerie. “Steady-State Approximation.” Introduction to Chemistry. Lumen. Accessed November 24, 2019. https://courses.lumenlearning.com/introchem/chapter/steady-state-approximation/. (^29) Ibid. (^30) White, Emil H., Oliver. Zafiriou, Heinz H. Kagi, and John H. M. Hill. 1964. “Chemiluminescence of Luminol: The Chemical Reaction.” Journal of the American Chemical Society 86 (5): 940–41. https://doi.org/10.1021/ja01059a050.
[Ⅲ ]=
k (^) 2 [ Ⅱ][ OH −] ( k (^) −2[ H O 2 ]+ k (^) 3 [ O (^) 2 ])
Ultimately, the overall rate law can be generated by substituting the derived values for the concentrations of intermediate 1 (II) and intermediate 2 (III). The assumption that the overall rate law is equal to the rate law of the final step (step 3) is illustrated here.
When generating this overall rate law, two further assumptions were made. The first assumption is that the value for k-2 is much larger than the value of k 3 ( k −2 >> k 3 ), meaning that the value of k 3 [O 2 ] is negligible in comparison to the value of k-2[O 2 ]. This assumption based on the fact that “there is a lot more water in an aqueous solution than there is O 2 from the decomposition of H 2 O 2 ”. Ultimately, this assumption allows us to remove^31 k 3 [O 2 ] from the rate law. The second assumption is that water has “unit activity”, meaning that its concentration has no effect on the reaction rate. This is because water acts^32 as a solvent in this reaction and its concentration is therefore “extremely large and virtually constant”. This allows us to^33 remove the concentration of water from the rate law. Ultimately, a new rate constant ( k’ ), is formed from^ k kk^3 −2^1 , making the
overall rate law equal to rate = k’[I][OH-][O 2 ]. Critically, the steady-state approximation suggests that the chemiluminescent oxidation of luminol is first order with respect to luminol, OH-^ ions and O 2. This will act as my hypothesis for this investigation.
APPROACH TO THE RESEARCH QUESTION When considering the research question, it was clear to me that I needed to construct a method which would alter the concentrations of each reactant and measure the rate of the luminol reaction at different combinations of reactant concentrations. This would ultimately allow me to construct a graph of concentration against reaction rate for each reactant to determine its order of reaction. Initially, I needed to determine a suitable way to measure the rate of the reaction. Given the characteristic chemiluminescence of the reaction in question, it was evident to me that calculating the reaction rate as the change in illuminance of the reaction mixture over the change in time would be most suitable. Illuminance, measured in lux (lx), is a measure of total luminous flux per unit area and is proportional to light intensity (measured in candela).^34 In this reaction, concentration can be considered proportional to illuminance given that, as concentration increases, the rate of the reaction increases, leading to the formation of more unstable 3-aminophthalate* transition states per unit time. The greater the number of unstable transition states, the more will decay into a more stable state and emit light per unit time. This will translate into a greater intensity of light emitted by the reaction mixture and hence, given that illuminance is proportional to light intensity, a greater illuminance value. I wasn’t able to find any online methodology that determined the rate law for this specific reaction so I decided to adapt pre-existing methodologies that dealt with the oxidation of luminol such that I was able to alter the concentrations of the reactants and determine the rate law. I ultimately chose to alter the methodology proposed by the department of chemistry at the North Carolina State University (NCSU) , which instructed the use of two solutions^35 which would be mixed together to initiate the reaction. In preliminary testing, I adapted this methodology by conducting the experiment inside a box to block external light and by using a light meter to measure the change in illumination of the reaction mixture over time. By graphing these two variables against each other, I was able to identify the spike in illuminance caused by the emission of light once the reaction was initiated. By subtracting
(^31) Fleming, Declan. “Mechanism of the Reaction.” The Chemiluminescence of Luminol - Home. Accessed November 24, 2019. http://www.chm.bris.ac.uk/webprojects2002/fleming/mechanism.htm. (^32) “Rate Laws: An Introduction.” Chemistry LibreTexts. Libretexts, April 27, 2019. https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:Chemistry(Zumdahl_and_Decoste)/15:Chemical_Kinetics/15.2_Rate_Laws: An_Introduction. (^33) “Acid and Base Ionization Constants.” Chemistry for Non-Majors. Lumen. Accessed November 24, 2019. https://courses.lumenlearning.com/cheminter/chapter/acid-and-base-ionization-constants/. (^34) Keim, Robert. “Understanding Illuminance: What's in a Lux? - Technical Articles.” All About Circuits, January 11, 2016. https://www.allaboutcircuits.com/technical-articles/understanding-illuminance-whats-in-a-lux/. (^35) "Chemiluminescence with Luminol." North Carolina State University Department of Chemistry. n.d. Raleigh. PDF.
(black, opaque bin bag material) in order to prevent external light from passing into the box through any pre-existing holes or cavities.
3. Distance of the reaction vessel from the light sensor: The intensity of light at different distances from a light source is described by the inverse-square law. Critically, the intensity of light is inversely proportional to the square of the^38 distance, meaning that the light intensity decreases as the distance from the light source increases. Given that illuminance is proportional to light intensity, the distance of the reaction vessel (the “light source”) from the light sensor will affect the illuminance value recorded and must therefore be controlled. To ensure this variable remains constant, a circular marking will be made on the inside of the light-blocking box to indicate where the reaction vessel (a 50 cm^3 beaker) should be placed during each experimental trial. This circular marking will be made to ensure that the closest face of this beaker will be an insignificant 1 cm away from the light sensor. This was measured using a 30 cm ruler. 4. Mass of potassium ferricyanide catalyst used: In this reaction, potassium ferricyanide acts as a catalyst to speed up the rate of the reaction. In its processed form, potassium ferricyanide exists as small salt granules. Ultimately, a larger mass of potassium ferricyanide would increase the total surface area of the catalyst used, meaning that collisions between the catalyst and the reactant particles would be more frequent and hence the rate of reaction would increase. Critically, this illustrates why the mass of potassium ferricyanide used needs to be controlled. To ensure this variable remains constant, the same mass of potassium ferricyanide (3.00 grams) was measured using an electronic weighing scale and added to each oxidizing solution, as recommended by the NCSU’s methodology.^39 5. Volume of alkaline luminol solution and oxidizing solution mixed : Larger volumes of both the alkaline luminol and oxidizing solutions would contain a greater number of moles of the reactants used. Given this, larger volumes of, for example, the oxidizing solution would result in more light being produced by the reaction and hence a higher illuminance value being recorded. To ensure this variable remains constant, the volume of the alkaline luminol and oxidizing solutions was kept constant at 10 cm^3 (meaning that 10 cm^3 of each solution were mixed together to initiate the reaction). This was measured using a 10 cm^3 volumetric pipette (used for the alkaline luminol solution) and a 10 cm^3 syringe (used for the oxidizing solution).
APPARATUS WITH UNCERTAINTIES
(1) light sensor ± 0.0001 lx (1) 10 cm^3 syringe ± 0.5 cm^3
(6) 250 cm^3 volumetric flask ± 0.12 cm^3 (1) 10 cm^3 volumetric pipette ± 0.03 cm^3
(1) electronic weighing scale ± 0.005g (1) 10 cm^3 graduated pipette ± 0.05 cm^3
METHODOLOGY
The method for this experiment can be separated into five parts: A) PART 1: constructing the apparatus
- Take a cardboard box and cut two openings into it using a pair of scissors, as illustrated in Diagram 1. One of the openings, the beaker opening, should be a 6 x 6 cm square on the top of the box that is 12 cm from either edge of the box. The other opening, the light sensor opening, should be a circle that’s 2 cm in diameter whose centre is 1 cm from the bottom edge of the box and 15 cm from the side edges of the box.
- It is necessary to make a circular marking inside the box to act as an indication of where to place the 50 cm^3 beaker (with a diameter of 5 cm) during each experimental trial. Use a permanent marker and a 30 cm ruler to measure and mark a point on the bottom of the box from the inside which is 3.5 cm away from the light sensor opening. Subsequently, use a protractor to draw out a circle which has a radius of 2.5 cm, using the marked point as the centre of the circle.
- Using sellotape, cover all sides of the box with a black, opaque material, such as a bin bag. Make sure that the beaker opening and light sensor opening are not covered by the bin bag material.
- Using a pair of scissors, cut out a 7 x 7 cm square out of the bin bag material. Pierce a hole into the center of this square using scissors.
- Stick one side of this square to the top of the box in order to cover the beaker opening. It is essential that this square is only stuck on one side so that it acts as a flap which can be opened and closed to reveal and cover the beaker opening. B) PART 2: setting up the apparatus
- Connect the LabQuest data logger to the computer and, to it, connect the Vernier light sensor. Make sure that the light sensor is switched to collect data in the “0-600 lux” range, given that this is the most suitable range for this experimental procedure.
- Make sure that the Logger Pro data logging software is loaded and set the sampling duration to 60 seconds and the sampling rate to 2 samples per second.
(^38) “Inverse Square Law Formula.” SoftSchools.com. Soft Schools. Accessed November 24, 2019. http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/. (^39) "Chemiluminescence with Luminol." North Carolina State University Department of Chemistry. n.d. Raleigh. PDF.
- Stick the end of the light sensor into the light sensor opening in the box, ensuring that the end of the light sensor fits snugly in the opening but doesn’t protrude into the box itself. Critically, the end of the light sensor should be situated 1 cm from the face of the beaker inside the box. C) PART 3: preparing the solutions
- To prepare the different alkaline luminol solutions, place a 500 cm^3 beaker on the electronic weighing scale and tare the scale. Hereafter, weigh 100 grams of distilled water in the beaker.
- Transfer the distilled water in the beaker to a 250 cm^3 volumetric flask and place this flask on the magnetic stirrer. Set the magnetic stirrer to the maximum speed.
- Using a 10 cm^3 graduated pipette, measure out the 5 cm^3 of NaOH. Add this NaOH to the volumetric flask.
- Using the electronic weighing scale, weigh out the appropriate mass of luminol on a weigh boat as indicated in Table 1. Add this luminol to the volumetric flask as well and allow it to dissolve. Once all the luminol has dissolved, top up the volumetric flask with distilled water to the 250 cm^3 mark.
- Repeat steps 9 to 12 in order to prepare the 3 different alkaline luminol solutions, as indicated in Table 1.
- To prepare the 3 different oxidizing solutions, repeat steps 9 to 13. However, instead of adding NaOH and luminol, measure out the appropriate volumes of H 2 O 2 and mass of K 3 [Fe(CN) 6 ] respectively, as indicated by Table 2. D) PART 4: conducting the experiment
- Using a 10 cm^3 volumetric pipette, transfer 10 cm^3 of an appropriate alkaline luminol solution into a 50 cm^3 beaker. Transfer this beaker through the beaker opening into the box and place it on the indicated circular marking. Subsequently, close the beaker opening flap.
- Use a 10 cm^3 syringe to withdraw 10 cm^3 of an appropriate oxidizing solution. Start recording the illuminance and, after 5 seconds, inject the oxidizing solution through the hole in the beaker opening flap into the beaker containing the alkaline luminol solution.
- Allow the light sensor to record the illuminance for the remaining 55 seconds of the sampling duration. Once the sampling is complete, make sure to save the data file.
- Repeat steps 15 to 17 two more times to achieve three experimental trials for the run in question, making sure to create a new data file for each trial.
- Repeat steps 15 to 18 for the remaining runs of the experiment, ensuring that three experimental trials are conducted per run. Utilize Table 3 to determine the appropriate solutions to use for each run. E) PART 5: data processing
- Open up a chosen data file on the Logger Pro data logging software and, under the ‘Analyze’ tab, select ‘Examine’. This function will allow you to trace the graphed data points.
- Locate the spike in illuminance caused by the emission of light by the reaction. Using the examine function, identify the data point at the peak of the spike (the “final” illuminance) and the data point prior to the spike (the “initial” illuminance).
- Using these two points, calculate the change in illuminance and the change in time. The change in illuminance can be calculated by subtracting the “final” illuminance value from the “initial” illuminance value while the change in time can be calculated by subtracting the “final” time value from the “initial” time value (refer to Figure 7).
- Repeat steps 20 to 22 for all 3 trials of each run of the experiment in order to determine the change in illuminance and change in time for each experimental trial.
Table 1: the different alkaline luminol solutions and their contents Solution number Contents Concentration of luminol dianions Millimoles per unit volume / mmol dm- 1 0.20 g luminol in 5 cm^3 of 1 M NaOH and diluted to 250 cm^3 with distilled water 6. 2 0.10 g luminol in 5 cm^3 of 1 M NaOH and diluted to 250 cm^3 with distilled water 3. 3 0.05 g luminol in 5 cm^3 of 1 M NaOH and diluted to 250 cm^3 with distilled water 1.
A sample calculation for the concentration of luminol dianions is shown below. As established previously, the concentration of luminol dianions is equal to the concentration of luminol given that 1 luminol molecule reacts with two OH-^ ions to form 1 luminol dianion (as illustrated in Figure 2). Given this, the concentration of luminol dianions and the concentration of luminol will be made synonymous henceforth in this investigation.
Sample calculation for the concentration of luminol dianions in solution 1 M olar amount of luminol = (^) molarmass mass = (^) 117.160.200 = 0 .00170 moles M olar amount of luminol = molar amount of luminol dianions , ∴ molar amount of luminol dianions =0.00170 mol C oncentration of luminol dianions =^ molarvolume^ amount^ = 0.001700.250^ = 0 .00680 mol dm −3^ = 6 .80 mmol dm −
in the near vicinity, including the eye-wash station, shower and fire extinguisher, before conducting the experiment. In case of skin or eye contact with any of the chemicals, make sure to take off any contaminated clothing and rinse the skin/eyes with water. It is necessary to dispose of the reactant solutions in a suitable chemical disposal container given that some of the reactants, particularly potassium ferricyanide and sodium hydroxide, are toxic to marine life 44 45,^. A further environmental consideration to note is the need to make larger batches of the reactant solutions than necessary, meaning that a substantial volume of the solutions will be unused and disposed of. This is due to the fact that very small masses of the reactants are used to make these solutions, meaning that the smallest batch size that could be made for each solution using the available measuring apparatus is 250 cm^3. Given this, and the fact that only 10 cm^3 of each solution (alkaline luminol and oxidizing solution) is used per trial, a total of 1500 cm^3 of solution will be prepared while only 300 cm^3 of solution will be used in the experiment.
DATA COLLECTION AND PROCESSING After conducting all trials and runs of the experiment, the values for the initial illuminance and final illuminance were recorded in Table 4 below:
Table 4: raw data collection showing the initial and final illuminance and time for each trial of each run
Run
Concentration of luminol moles per unit volume / mol dm-
Concentration of O 2 moles per unit volume / mol dm-
Initial illuminance illuminance / lx ±0.0001 lx
Final illuminance illuminance / lx ±0.0001 lx
Initial time seconds / s ±0.0001 s
Final time seconds / s ±0.0001 s Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 A 0.0068^ 0.294 1.1036^ 2.3680^ 1.9269^ 9.8010^ 9.4908^ 8.7438^ 0.0750^ 0.0500^ 0.0875^ 0.1000^ 0.0750^ 0. B 0.0068 0.147 1.6919 1.7506 1.7271 7.2733 7.1887 6.9556 0.0875 0.0750 0.0250 0.1250 0.1125 0. C 0.0068^ 0.0735 3.1723^ 1.6684^ 1.6331^ 4.4735^ 3.0365^ 3.9375^ 0.0750^ 0.0875^ 0.1250^ 0.1000^ 0.1125^ 0. D 0.0034 0.294 1.7506^ 1.9504^ 1.5744^ 5.1757^ 5.5582^ 3.4279^ 0.0750^ 0.0625^ 0.0750^ 0.1000^ 0.0875^ 0. E 0.0017 0.294 1.9504^ 1.5509^ 2.3506^ 5.0945^ 4.6125^ 3.9984^ 0.0875^ 0.1625^ 0.0750^ 0.1325^ 0.2125^ 0.
Following this, it was necessary to calculate the changes in illuminance and time for each trial of each run. Sample calculations for the changes in illuminance and time and their respective absolute uncertainties are shown below. Given that the calculations for the change in illuminance and time only involved a subtraction, the absolute uncertainties of the initial and final illuminance and time were added in order to find the absolute uncertainty of the change in illuminance and time respectively. Critically, the absolute uncertainty for all of the change in illuminance and change in time values is ±0.0002 lx and ±0.0002 s respectively, given that all the illuminance and time values in Table 4 have an absolute uncertainty of ±0. lx / ±0.001 s.
Sample calculation for the change in illuminance for trial 1 of run A c hange in illuminance = f inal illuminance − initial illuminance = 9 .8018 − 1 .1036 = 8 .6974 lx ( correct to 4 decimal points )
Sample calculation for the change in time for trial 1 of run A c hange in time = f inal time − initial time = 0 .1000 − 0 .0750 = 0 .0250 s ( correct to 4 decimal points )
Sample calculation for the absolute uncertainty of the change in illuminance/time
Δ a = Δ b + Δ c = Δ a = 0 .0001 + 0. = Δ a = 0 .0002 lx / 0.0002 s
Δ a = absolute uncertainty of the change in illuminance / time Δ b = absolute uncertainty of the initial illuminance / time Δ c = absolute uncertainty of the f inal illuminance / time
The values for the change in illuminance and change in time for each trial of each run were recorded in Table 5 below. Using these values, the rate of reaction for each trial, the mean rate of reaction and the absolute uncertainty of the mean rate of reaction could be calculated.
(^41) "SAFETY DATA SHEET POTASSIUM FERRICYANIDE." Sigma Aldrich, January 6, 2019. PDF. (^42) "SAFETY DATA SHEET Hydrogen Peroxide 10%." PeroxyChem, April 8, 2015. PDF. (^43) "Sodium Hydroxide Safety Data Sheet." LabChem, March 26, 2012. PDF. (^44) Ibid. (^45) "SAFETY DATA SHEET POTASSIUM FERRICYANIDE." Sigma Aldrich, January 6, 2019. PDF.
Table 5: processed data showing the change in illuminance, change in time and the rate of reaction for each trial as well as the mean rate of reaction and its absolute uncertainty for each run
Run
Concentration of luminol moles per unit volume / mol dm-
Concentration of O 2 moles per unit volume / mol dm-
Change in illuminance illuminance / lx ±0.0002 lx
Change in time seconds / s ±0.0002 s
Rate of reaction illuminance over time / lx s-
Mean rate of reaction illuminance over time / lx s-
Absolute uncertainty of the mean rate of reaction illuminance over Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 time / lx s-
A 0.0068 0.294 8.6974 7.1228 6.8169 1.5000 1.5000 1.5000 5.7983 4.7485 4.5446 4.6466 0. B 0.0068^ 0.147 5.5814 5.4381 5.2284 2.2500 2.2500 3.2500 2.4806 2.4169 1.5844 2.4488 0. C 0.0068^ 0.0735 1.3012 1.3681 2.3044 1.5000 1.5000 3.0000 0.9375 0.9121 0.8881 0.9149 0. D 0.0034 0.294 3.4250 3.6078 1.8535 1.5000 1.5000 0.7500 2.2834 2.4052 2.4713 2.3866 0. E 0.0017 0.294 3.1441 3.0616 1.6478 2.7000 3.0000 1.5000 1.1645 1.0205 1.0985 1.0945 0.
Sample calculations for the rate of reaction in each trial, the mean rate of reaction and the absolute uncertainty of the mean rate of reaction are shown below.
Sample calculation for the rate of reaction for trial 1 of run B r ate =^ changechange^ in^ illuminance in time^ = (^) 2.2500^ 5.5814^ = 2 .4806 lx^ s^ −1( correct^ to^^5 signif icant^ f igures )
Sample calculation for the mean rate of reaction for run B (accounted for anomaly) M ean =^ sumnumber^ of^ individual of trials^ trials^ = 2.4806+2.4169 2 = 2 .4488 lx s −1( correct to 5 signif icant f igures )
Sample calculation for the absolute uncertainty of the mean rate of reaction for run B: a bsolute uncertainty =^ range 2^ =^ max.^ value^ 2 −^ min.^ value^ = 2.4806−2.4169 2 = ± 0.0319 lx s −1( correct to 4 decimal places )
In Table 5 it can be seen that two rate of reaction values in runs A and B are highlighted in orange - identifying them as anomalies. This is evidenced by the fact that the removal of these two values (5.7983 and 1.5844 lx s-1) substantially decreased the absolute uncertainty of the mean rate of reaction in their respective runs. For example, the removal of the 5.7983 lx s-1^ data point from run A reduced the absolute uncertainty of the mean rate of reaction from ± 0.6269 lx s-1^ to ± 0.1020 lx s-1. Ultimately, these anomalous results were ignored when calculating the mean rate of reaction in order to enhance the accuracy of this calculation. Additionally, qualitative observations were made throughout the experiment and recorded in Table 6. These observations may aid in the interpretation of the experiment's results.
Table 6: qualitative observations made throughout the experiment Run(s) Qualitative observations
A, D, E In runs A, D and E, which used solutions with the highest oxygen concentrations, light effervescence of oxygen bubbles was observed in the oxidizing solution prior to the reaction. This effervescence was most prominent when the oxidized solution was disturbed (e.g. when a syringe was used to withdraw the solution). While the oxygen effervescence was also observed in oxidizing solutions with lower concentrations of oxygen (e.g. runs B and C), this was much fainter than in runs A, D and E.
All runs Luminol was least soluble in the runs where it was used at the highest concentration (runs A, B and C), yet was also observed to be relatively insoluble in the other runs of the experiment. Due to this limited solubility, the alkaline luminol solutions needed to be stirred excessively (particularly in runs A, B and C) in order to dissolve as much luminol as possible. Despite these efforts, a precipitate of undissolved luminol remained at the bottom of the alkaline luminol solutions used (a larger amount of precipitate was observed in runs A, B and C), indicating that not all of it had dissolved.
All runs In all of the trials it was seen that the baseline illuminance reading fluctuated slightly above zero (usually at 0.7 lux).
Ultimately, the mean rate of reaction determined in Table 5 was graphed against the concentration of luminol and O 2 , as is shown in Graphs 1 and 2. In these graphs, the error bars represent the absolute uncertainty of the mean rate of reaction.
luminol molecule and two OH-^ ions, the reaction should be second order with respect to the OH-^ ions. Evidently, it is difficult to conclude which of these orders of reaction is experimentally observed. The high precision of the collected data is also apparent when considering the uncertainty of my results. This is demonstrated by, for example, the high coefficient of determination (R^2 ) values in Graphs 1 and 2 (R^2 = 0.9986 and 0. respectively), which indicate that there is very minimal variance of the data points from the linear trendline. However, it^46 can further be seen that the coefficient of determination value is lower for Graph 3 than for Graph 2 , suggesting that a random error affected the precision of the data collected for the varying concentrations of O 2. A possible source of this error was a random error commented upon in the qualitative observations in Table 6; the effervescence of the oxidizing solution. The fact that hydrogen peroxide decomposes into oxygen gas was overlooked in this investigation and resulted in the inevitable loss of oxygen from the oxidizing solution throughout the experiment. The effervescence of oxygen was evident in all solutions yet was most prevalent in the oxidizing solution used in trials A, D and E which contained the highest concentration of O 2. This observation, alongside the fact that the runs and trials in this investigation weren't conducted in chronological order, would’ve most likely resulted in greater variance in the collected data as the concentration of O 2 in the oxidizing solution would decrease over time as O 2 was lost as gas. This variance was also reflected in the small error margin of the data. The absolute uncertainty of the mean rate of reaction values was very small, ranging from ±0.0319 lx s-1^ to ±0.1020 lx s-1, and the error bars in Graph 1 and 2 are thus barely visible, supporting the high precision of the data. However, while the trendline in Graph 1 passes through all of these error bars, the trendline in Graph 2 does not, which demonstrates the relatively lower precision of the collected data in Graph 2 in comparison to the data in Graph 1. This observation could also be explained by the oxygen loss observed and may further suggest that the error margins for this investigation were too small (and hence underestimated). One way in which the accuracy of the collected data was ensured was through the identification and removal of anomalous data in Table 5, effectively reducing the likelihood of an erroneous correlation being identified. Despite this, both Graphs 1 and 2 demonstrated a systematic shift of the trendline, as is indicated by the extrapolated trendline which intersects the y-axis below the origin. The cause of this systematic shift may partly be due to a prominent systematic error which was commented upon in the qualitative observations in Table 6; the solubility of luminol in the alkaline luminol solution. This phenomenon was observed throughout the experiment, as the beakers with the alkaline luminol solutions had a layer of undissolved luminol precipitate despite intensive and sustained stirring. Due to this, the concentration of luminol was consistently underestimated, given that the actual concentration of luminol in the alkaline luminol solutions was consistently lower than was theoretically calculated, which explains the systematic (rightward) shift of the trendline. Prior to conducting the experiment, no consideration was given to the solubility of luminol in water; the primary solvent used. Unsurprisingly, subsequent research revealed that luminol is “comparatively insoluble in water, but quite soluble in base”, thus explaining the insolubility of luminol in water and further indicating that the pH of the alkaline luminol solution (despite the addition of the NaOH base) was too low. Another possible cause of this systematic shift would be due to the underestimation of the change in illuminance caused by the emission of photons. In the qualitative observations in Table 6, it was noted that the baseline illuminance value recorded in all trials of all runs fluctuated slightly above 0 lx. Due to this zero error, the change in illuminance would’ve been consistently underestimated throughout the experiment, meaning that the rates of reaction would be consistently underestimated (given that the rate of reaction was calculated as the change in illuminance over time). This, ultimately, provides an explanation for the systematic (downwards) shift of the trendline. Both of these systematic errors - the solubility of luminol and underestimation of the change in illuminance - are valid explanations for the systematic shift of the data, and aiming to overcome both of these errors would therefore improve the accuracy of the data collection.
ERRORS AND IMPROVEMENTS SYSTEMATIC ERRORS
1. Solubility of luminol: the solubility of luminol was a significant error in this investigation as it was thought to partly cause the systematic shift of the data, as explained previously. One way to increase the solubility of luminol, and thus overcome this error, would be to adjust the contents of the alkaline luminol solutions to initially contain less distilled water or more NaOH, both of which will increase the concentration of OH-^ ions in the solution and hence increase the solution’s pH. Alternatively, it would be possible to add other bases that wouldn’t react with either NaOH or luminol (e.g. sodium carbonate and ammonium carbonate) in order to raise the pH of the alkaline luminol solution and thus increase the solubility of luminol. 2. Zero error : the other potential cause of the systematic shift of the data was due to the underestimation of the change in illuminance, caused by the positive zero error in the light sensor. This zero error indicates that the inside of the light-blocking box wasn’t entirely dark and that there were therefore sources of external light whose illuminance was recorded from inside the box. This error is significant given that it may have caused the systematic shift of the data, but it doesn’t refute the trendline found given that the same apparatus (light-blocking box) was used throughout the experiment. To improve upon this error, one could construct a light-blocking box from a more suitable, light-blocking
(^46) Frost, Jim. 2018. How To Interpret R-squared in Regression Analysis. February 24. Accessed November 12, 2019. https://statisticsbyjim.com/regression/interpret-r-squared-regression/.
material (e.g. a large film canister) in order to better block out external light. Furthermore, the entire experiment could be conducted in a dark laboratory room in order to reduce the amount of external light which needs to be blocked by the light-blocking box.
3. Limited range and number of reactant concentrations: this experiment tested only 3 different concentrations of each reactant in order to determine their respective orders of reaction. While this resulted in an observable trend, the limited range and number of different concentrations meant that it was difficult to deduce if, for whatever reason, the mean rate of reaction in one (or more) runs was anomalous, given that a trendline needed to be fitted to only 3 different data points in each graph. Ultimately, this error can be overcome by using a greater number and range of different reactant concentrations, effectively increasing the reliability of the trends observed in Graphs 1 and 2. For example, a wider range of 5 different concentrations could be investigated.
RANDOM ERRORS
1. Loss of oxygen from the oxidizing solution: the loss of oxygen from the oxidizing solution is a significant error as it was thought to greatly increase the variance and thus reduce the precision of the collected data. Critically, this error was caused by the flawed assumption that the concentration of O 2 in the oxidizing solutions would be equal to the concentration of H 2 O 2 since the loss of oxygen gas from the oxidizing solution was overlooked. Ultimately, this error could be improved upon by creating the oxidizing solutions such that their O 2 concentration is lower, given the fact that the oxidizing solutions with a higher O 2 concentration were seen to produce the most effervescence. This lower concentration could be achieved by using a lower percentage concentration of H 2 O 2 or by adding lower volumes of H 2 O 2 to the oxidizing solutions. While this methodological improvement won’t eliminate the presence of effervescence it will greatly reduce it such that the assumption that the concentration of O 2 in the oxidizing solutions would be equal to the concentration of H 2 O 2 is more accurate. 2. Limited number of trials: in the experiment, only 3 trials for each run was conducted. While this allowed me to calculate the mean rate of reaction using three different data points in most runs, removing an anomalous data point (as was done in runs A and B) would mean that the mean of only two values was taken, which isn’t very reliable. Moreover, given that the absolute uncertainty of the mean was calculated as the range of data points divided by 2, removing anomalous data points would possibly result in the underestimation of the error margins in the experiment, as was outlined in Graph 2. Ultimately, in order to improve upon this error one would need to conduct a larger number of trials, say five, in the experiment.
EXTENSIONS An obvious extension to this investigation would be to determine the order of the reaction with respect to OH-^ ions, but the methodology required to do this is beyond my level of understanding and requires the use of more elegant equipment due to the presence of three different reactants. A more realistic extension to this investigation would be to consider the energy lost as heat in the reaction. One of the assumptions made in this experiment is that the energy released by the reaction is released as light, following the definition of “cold light”. However, this is a slight simplification given that there will always be a certain amount of energy which is released as thermal energy, although this amount of energy may not be so significant in this reaction. Nevertheless, by keeping track of the temperature change of the reaction mixture as the reaction progresses, one could take into account the energy lost as heat and integrate this with the energy lost in the form of light in order to get a more accurate estimation of the enthalpy change of the reaction. This could, ultimately, be used to derive a more accurate value for the change in energy emission over time.
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"Chemiluminescence with Luminol." North Carolina State University Department of Chemistry. n.d. Raleigh. PDF. Clegg, Brian. “Luminol.” Chemistry World, April 16, 2014. https://www.chemistryworld.com/podcasts/luminol/7272.article. “Cold Light.” The Free Dictionary. Farlex. Accessed November 24, 2019. https://www.thefreedictionary.com/cold light.
Images: Figure 1: Boltzmann Distribution Illustrating the Effect of Concentration on the Number of Particles with Energy Greater than the Activation Energy. Les Facteurs Qui Influencent La Vitesse De Réaction. Alloprof. Accessed November 24, 2019. http://www.alloprof.qc.ca/BV/pages/c1028.aspx. Figure 2: Fleming, Declan. Multi-Step Mechanism of Luminol Oxidation. Mechanism of the Reaction. Accessed November 24, 2019. http://www.chm.bris.ac.uk/webprojects2002/fleming/mechanism.htm.
