EXPERIMENTAL DETERMINATION OF THE

ACTIVATION ENERGY OF A LIGHT STICK

Purpose:

To determine, experimentally, the activation energy (Ea) and

frequency factor (A) of a light stick using graphical analysis

Background Information:

Rate constants, as you already know, can be experimentally determined from a graph obtained by conducting various reactions. Rate constants for most chemical reactions closely follow an equation of the form:

k = Ae-Ea/RT

which demonstrates how the rate constant depends on temperature. This equation is commonly known as the Arrhenius equation, and it allows us to determine the activation energy required to initiate a reaction given its temperature. The symbol A, which is assumed to be a constant for each substance, is known as the frequency factor. The frequency factor is related to the frequency of molecular or atomic collisions with proper orientation (pZ) necessary to initiate a chemical reaction. R, the gas constant, is 8.314 J/(K· mol). Logically, it makes sense that a reaction’s rate constant would depend on temperature, because temperature will affect the ability of molecules to collide, interact, and react with predictable frequency. Notice that as the activation energy increases for a reaction, the exponent becomes more negative, the fraction of the reacting molecules with an energy greater than that of Ea decreases, the rate constant becomes smaller, and the rate of the reaction decreases. As temperature increases, the exponent becomes less negative, the fraction of the reacting molecules with an energy greater than that of Ea increases, the rate constant becomes larger, and the rate of the reaction increases.

Exponentially, the initial form of the Arrhenius equation is not very useful. By taking the natural logarithm of both sides, we can arrive at the following:

ln k = ln A e-Ea/RT

This can be rearranged to the following:

ln k = ln A + ln e-Ea/RT

Which, reduced, becomes:

ln k = ln A + -Ea

RT

Or,

ln k = -Ea + ln A

RT

Which, practically, takes the linear form y = mx + b. From this, both the activation energy, and the frequency factor, of any naturally occurring or synthesized reaction, may be obtained.

The light stick has two separate chambers, one that houses hydrogen peroxide, and one that houses a phenyl oxalate ester. When broken, the hydrogen peroxide oxidizes a phenyl oxalate ester, to form phenol and an unstable peroxyacid ester. The unstable peroxyacid ester decomposes, resulting in another phenol and a cyclic peroxy compound. The cyclic peroxy compound decomposes to carbon dioxide. This decomposition reaction releases the energy that excites the dye. The electrons in the dye atoms jump to a higher level, then fall back down, releasing energy in the form of light:

In this particular experiment, the light producing reaction above follows first order kinetics, where [X] is the reaction concentration of the phenyl oxalate ester:

Rate = k[X]1

Substitution using the Arrhenius equation gives us the following:

Rate = [X]1 · Ae-Ea/RT

The light intensity, I, at a fixed point in the light stick should be proportional to the rate of the chemiluminescence reaction, by a factor of some proportionality constant, C:

Rate = C[I]

Substitution once again gives us the following:

[I] = [X]1 · Ae-Ea/RT

C

Taking the natural logarithm of both sides, and rearrangement, gives us the following:

ln[I] = ln [X]1 · A - Ea or

C RT

ln[I] = - Ea + ln (A ·[X]1 )

RT C

Materials:

ComputerLabproLight sensor

Temperature probeWooden blockWater bath

Test tubeFilm canisterTape

Procedure:

  1. Your task is to observe the chemical reaction in a light stick through measurement of its illumination, which will change according to a predictable pattern as the reaction progresses. Open the logger pro experiment entitled “Activation Energy” on the desktop. Make sure that the experiment is set to run for 10 minutes, collecting 4 samples a minute.
  2. Make sure that the light sensor is plugged into channel one and the temperature probe is plugged into channel two. In addition, make sure that “Illumination” in lux is being graphed on the y-axis, and “Time” in minutes is being graphed on the x-axis. We will also be monitoring temperature, as illumination changes as a function of temperature. Make sure appropriate units are being used for all measurements. Make sure the temperature probe is calibrated, and the light sensor is calibrated to its most sensitive setting (0-600 lux). Make sure you have a live readout for temperature and lux!
  3. Mount the light sensor into the side of the wooden block.
  4. Prepare a 500C water bath to heat the contents of the reaction. Snap the glow stick, and shake the contents. Allow the glow stick reaction to proceed for five minutes, to allow the first part of the mechanism to take place. Then, cut the top off the glow stick, and pour the contents into a test tube. Place the glow stick into the water bath and allow it to come to 500C.
  5. Remove the test tube from the water bath, dry it, and place the temperature probe into the test tube. Place the test tube into the wooden block and cover it with a film canister. You might need to place electrical tape around the opening to ensure darkness. You should have an initial lux readout of around 400-500 lux!
  6. Hit the “collect” button and let the experiment run for the duration.

Graphs and Data:

Notice that the relationship between illumination and time is not linear. Create a graph that allows you to determine both the activation energy and the frequency factor of the light stick reaction graphically.

Calculations and Conclusions:

  1. Using your initial graph for analysis, what happened to the illumination of the light stick as the reaction progressed? How can this be related to chemical concentration?
  2. Write an experimental equation for the light stick, using the Arrhenius equation as a model. Use appropriate units!
  3. What is the activation energy of the light stick? Perform this calculation, and use appropriate units when reporting this!
  4. Is this a “true” value of activation energy, in an SI definition of the term? Explain your answer.
  5. What is the frequency factor of the light stick? Calculate this as a function of the proportionality constant and concentration – meaning, you will only be able to solve for the expression A · [X]1 .

C

  1. Is this a “true” value of frequency factor, in an SI definition of the term? Explain your answer.
  2. How could the frequency factor of this particular light stick be useful, if comparing it to other frequency factors of other light sticks? Explain your answer!
  3. Examine the “pseudo” frequency factor of other light sticks from other groups. Which light stick has the highest “pseudo” frequency factor? What does this tell you regarding that particular light stick?