Calculating Activation Energy of Crystal Violet/NaOH Reaction

[kevinnn]

So we just completed an experiment and we are now expected to calculate the activation energy of the reaction we ran using our data. The reaction was between crystal violet and sodium hydroxide. The reaction was performed under pseudo order conditions (sodium hydroxide concentration did not noticeably change) and I was able to determine from those conditions that the reaction is first order for the hydroxide ion and second order for crystal violet. These were confirmed by my professor and I then went on to calculate little k.
I have the value of k for room temperature. We ran the reaction at two other temperatures and my goal now is to determine the k values for the reaction performed at the two other temperatures. I want to do this so I can get a line of best fit through my three data points where ln(k) is a function of the inverse of the temperature and the slope of the line is the activation energy divided by R. Like I said, I was able to determine k and the order of the reaction but now I'm stuck Some help on a proper way to determine the k's at the two other temperatures is much appreciated. Thanks!

 

[Borek]

Where did you got k for the room temperature from?

 

[kevinnn]

We calculated k for room temperature by running two experiments, each one with the same concentration of dye but a different concentration of sodium hydroxide. We then set up a ratio of the two experiments to calculate the order of the reaction for sodium hydroxide. From this we calculated k by plug and chug using one of our pseudo order condition equations.
For the reactions at different temperatures we only have one run each. We can't set up a ratio of the reaction at two temperatures because the value of k will be different for each. our professor said we didn't need to run the experiment twice for each temperature so i know there is an alternate way to calculate k at the two different temperatures. I just don't know how to do it yet.

 

[Chestermiller]

We calculated k for room temperature by running two experiments, each one with the same concentration of dye but a different concentration of sodium hydroxide. We then set up a ratio of the two experiments to calculate the order of the reaction for sodium hydroxide. From this we calculated k by plug and chug using one of our pseudo order condition equations.
For the reactions at different temperatures we only have one run each. We can't set up a ratio of the reaction at two temperatures because the value of k will be different for each. our professor said we didn't need to run the experiment twice for each temperature so i know there is an alternate way to calculate k at the two different temperatures. I just don't know how to do it yet.

At the other two temperatures, you have measured the reaction rate at some set of conditions, and you know the mathematical expression for the reaction rate as a function of the concentrations of the reactants. Use this relationship to back out what the value of k is at that temperature.

 

[DeeNos]

First of all, congratulations on completing your experiment and determining the order of the reaction. Calculating the activation energy of a reaction can be a challenging but important step in understanding the underlying mechanisms of a chemical reaction.

To determine the k values at the two other temperatures, you can use the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea), the gas constant (R), and the temperature (T):

k = A * e^(-Ea/RT)

Where A is the pre-exponential factor, which can be determined from your room temperature k value.

To solve for Ea, you will need to rearrange the equation to:

ln(k) = ln(A) – (Ea/R) * (1/T)

This equation is similar to the one you mentioned in your question, where ln(k) is a function of the inverse of the temperature. By plotting ln(k) against 1/T for the three different temperatures, you should be able to obtain a straight line with a slope equal to -Ea/R. From this, you can calculate the activation energy by multiplying the slope by R.

It's important to note that the Arrhenius equation assumes a constant value for the pre-exponential factor (A), which may not always be the case. If you notice significant variations in A between your three temperatures, you may need to use a more complex equation, such as the Eyring equation, to accurately determine the activation energy.

I hope this helps you in your calculations. If you have any further questions, don't hesitate to consult with your professor or reach out to other experts in the field. Good luck!