[Habib21]

I'm sorry for posting this as it may be an easy question for most, but it has been years since I took Chemistry and my background is in Microbiology.

I'll pose my question for anyone who has time to help:

I'm trying to use the data from research paper at the link here:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5549281/#eq3

I'm trying to make a model wherein one could predict the time necessary to decarboxylate an extract of THCa to THC at 110 degrees celsius.  My understanding is that this is a 1st order reaction, and the paper states that the rate constant k= 1.83x10^3 @110C.  They also state the Ea value as well. 

So how would I use this information to predict the rate and time it would take for another extract to reach completion?  I have a feeling this is really basic but I'm struggling.

Ex.

I have 150g of extract with a potency of 500mg/g Δ9THCA. (If I need to convert this to moles Δ9THCA Molar mass = 357.47 g/mol)

How would I calculated how long it needs at 110°C to fully decarboxylate.  And how could I set up an excel grid to show the theoretical amounts of THCA remaining at different points in time?

Any insight is GREATLY appreciated!

[Corribus]

On the one hand, it is a simple matter to look up the 1st order rate law expression and calculate a conversion time. In practice it is not so easy to do, particularly in scale up, because you have to worry about heat transfer rates, competitive side reactions, and so forth. In addition, you have to decide what "to completion" means. Even in the limit that equilibrium lies far to the right, the conversion probability slows as the reaction proceeds just as a matter of probability, so in reality no reaction ever truly reaches "completion".  Do you want 90%? 95%? 99%? The threshold you set for "completion" will significantly impact the theoretical reaction time.

[Habib21]

Corribus-

Thanks for the response.  Completion in this case would be around 97% THCA decarboxylation @110°C... as it is possible to go to 100% completion, but it doesn't correspond to an increase in Δ9THC much further according to the data.  Under the assumption that this is just the theoretical calculations and not taking into account all of the heat transfer rates, and competitive side reactions you mentioned .

So you are suggesting using ln([A]t/[A]0)=−kt

Where in my example:

[A]t= The 97% Conversion of 150g of 500mg/g THCa  (I assume I convert this to moles, Yes?) (.00629mol)

[A]0= Initial amount of THCa @ time 0
(.20981mol)

-k = -1.83x10^3 sec-1 (Listed in paper for 110°C)
t= is what I'm solving for (time to reach 97% of decarboxylated THCa)

If that is all accurate.... I'm not sure what I'm doing wrong.....as I did all the calculations and it came to .00192

That doesn't make sense at all? 

[Corribus]

First, my apologies for not reading your post carefully. I was thinking bimolecular reaction but I see this is basically a unimolecular reaction. You still need to define what completion means, but I see you did it, 97%, so good.

You can express the concentration as a function of time, based on initial concentration (A₀), using the equation

[tex]A_t = A_0*e^{-kt}[/tex]

The nice thing here is that the units of your concentrations don't really matter if you are expressing this as a function of % consumption. If you want 97% completion, then A/A₀ = 0.03), because at 97% completion there is only 3% left. The units on k for a first order reaction are inverse seconds.

So, plug and chug, I got 1916 s, or about 30 minutes. Looks like this is more or less what you got, but you are many orders of magnitude off. So, it's got to just be a calculation error somewhere. Check your math.

Note that if you put a 100% conversion in, A/A₀ = 0. The expression becomes undefined as it is impossible to solve for ln(0). Which basically means the reaction theoretically never reaches 100% conversion, even for a unimolecular reaction (assuming the number of reacting molecules approaches infinity). There's a physical, statistical reason for this that relates to the continuous distribution of decay times. Anyway. Don't be surprised if your real reaction time doesn't match the theoretical time, but maybe it provides a rough guide.

EDIT. I think I see what the problem is. Sorry for briefly deleting my post, butI read yours again and saw you had the rate constant listed as 1.83 x 10³ s^-1.When I solved this, I used 1.83 x 10^-3 s^-1, getting a calculated reaction time that makes more sense. If I use your value, I also got what you got, and that answer I agree doesn't make sense. I looked at the link you provided to the paper, and saw that the tabulated value lists the k value as 1.83, but it calls it "k x 10³ (sec^-1)". This is a thing you see a lot that I really hate, because it causes a lot of confusion.  If k x 10³ = 1.83 sec^-1, then k = 1.83 x 10^-3 sec^-1. It's easy to mistakenly interpret it as the unit being x10³ sec^-1. Does that make sense?

[Habib21]

THANK YOU SO MUCH!!!

Yes that is all extremely helpful, and I agree that the k x 103 (sec-1) is a confusing way of listing the value!  I really appreciate the time you took to help explain where I was going awry and how to move forward with this.