Chemiluminescence Questions

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For my IA, I'm trying to find the activation energy of a glowstick reaction (phenyl oxalate ester + hydrogen peroxide). Using the Arrhenius equation and the integrated rate laws, and using this link as a guide (https://www.westminster.edu/about/community/sim/pdf/SLIGHTSTICKKINETICS_001.pdf), I was able to come up to a certain point. I have two questions.

In the link, I see that it used first-order kinetics in order to create an equation that relates rate of reaction to temperature (with activation energy/R being the slope). However, as far as I know, first-order kinetics only applies to chemical reactions with one reactant. I then looked at another source, which breaks up the chemiluminescence process into several steps, as shown by this source (http://cartwright.chem.ox.ac.uk/tlab/experiments/X3_kinetics.pdf). Was the formula in the first link regarding the decomposition of the peroxyacid ester?

My second question is that in the first document, it creates an equation that shows a linear relationship between rate of reaction and illumination. Would illumination be illuminance which could be measured in lux?

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The rate law is always empirically derived, and is independent of the number of reactants present. You can have only one reactant in a higher ordered reaction, or multiple reactants but zeroth or first ordered. In particular, Arrhenius equation only describes how temperature changes the rate constant, and it does not care about the order of reaction the rate constant is for. You should read more about how to derive rate laws for reactions of multiple steps, specifically regarding the equilibrium assumption and the pseudo steady state assumption. Maybe also review limiting reagents.

Answer to Q1. The formula is for the reaction Fluorophore* -------> Fluorophore + Light. But you can assume that that rate is reflective of the original phenyl oxalate ester / H2O2 reaction. You should clearly justify this assumption.

Answer to Q2. The short answer is yes. The long answer is that it doesn't matter. Digital probes rarely directly measures the quantity it outputs. Usually some conversion/calculation is done by the probe from an original measurement in resistance or pressure change to the desired quantity, such as illumination. It does not matter whether illumination is the same as illuminance; it's important that illumination (or whatever the output reading is) is proportional to the concentration of the fluorophore, or another chemical species of interest.

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Thanks! So I did some digging up regarding deriving rate laws for reactions of multiple steps.

Regarding the chemiluminescence reaction, would the reason we can assume that the rate is reflective of the phenyl oxalate ester/H2O2 reaction is because it is the rate determining reaction (slowest reaction)?

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I think so. You should justify it in your IA.

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