Sciencemadness Discussion Board

How can I calculate the ~ microwave energy required to decarboxylate a carboxylic acid?

TertAmyl - 24-10-2016 at 12:49

I want to know how I can come to an equation that I can use to approximate the energy required to go from R-COOH --> R + CO2 in a microwave. All I need is a ball park estimate of the seconds required in the microwave at a given Wattage.

I'm familiar with Hess's Law Hrxn = H1 + H2..

Using:
C-C = 88Kcal/mol
C=O = 127Kcal/mol
C-O = 84Kcal/mol
O-H = 111Kcal/mol


If I add up the bond disassociation energies I get
Hrxn = 199Kcal/mol + -265Kcal/mol OR
Hrxn = -66Kcal/mol OR Hrxn = -276Kj/mol

My initial thought was to calculate the moles per gram of the carboxylic acid (0.00168 moles) then divide by the 276Kj = 463J/g. I get the impression that this is incorrect though.

If a 1000W microwave is ~50% efficient and I use the equation E(J)=P(W) * S
I come up with 463J / 500W = 0.926 seconds

How far off base am I in how I'm determining what I want? What would be the required steps for me to determine something like this? Could I approximate the specific heat of the material by taking temperature measurements after specific power/time intervals in the microwave, and some how use that to calculate what I need?

I appreciate any help pointing me in the right direction.

Edit: To clarify... The reaction is obviously spontaneous and occurs naturally at STP. I want to speed up the process and know how much energy approximately is needed to theoretically decarboxylate 100% of the carboxylic acid present using a microwave.

[Edited on 24-10-2016 by TertAmyl]

DraconicAcid - 24-10-2016 at 16:28

The enthalpy of reaction won't help you in this case. You'd need to find out the activation energy of the reaction.

blogfast25 - 24-10-2016 at 17:07

Quote: Originally posted by TertAmyl  
I want to know how I can come to an equation that I can use to approximate the energy required to go from R-COOH --> R + CO2 in a microwave. All I need is a ball park estimate of the seconds required in the microwave at a given Wattage.



Breaking C-C bonds is hard. in the presence of air you're likely to end up with... CO2 and H2O only!

TertAmyl - 26-10-2016 at 14:03

The reaction happens spontaneously are STP - it is just far too slow to be useful.

I found and attached a publication that contains the energy of activation required for decarboxylation of the molecule. If I understand the paper correctly the Ea = 85 kJ/mol

Would I use the equation ln k = lnk0 - (E/RT) ?
The paper says E & K0 are determined to be 84.8kj mol-1 & 3.7 x 10^8s-1 respectively


How can I use that information to determine % decarboxylated relative to time & power in a microwave?
Attachment: Journal of Molecular Structure 987 (2011) 67-73.pdf (1.1MB)
This file has been downloaded 624 times

[Edited on 26-10-2016 by TertAmyl]

wg48 - 26-10-2016 at 14:28

Quote: Originally posted by TertAmyl  
The reaction happens spontaneously are STP - it is just far too slow to be useful.

I found and attached a publication that contains the energy of activation required for decarboxylation of the molecule. If I understand the paper correctly the Ea = 85 kJ/mol

Would I use the equation ln k = lnk0 - (E/RT) ?
The paper says E & K0 are determined to be 84.8kj mol-1 & 3.7 x 10^8s-1 respectively


How can I use that information to determine % decarboxylated relative to time & power in a microwave?


[Edited on 26-10-2016 by TertAmyl]


The short answer is you cannot.

The best you could do is determine it empirically from a series of carefully controlled experiments and hope its reproducible

blogfast25 - 27-10-2016 at 08:37

Quote: Originally posted by TertAmyl  
The reaction happens spontaneously are STP - it is just far too slow to be useful.



I think you're conflating negative Gibbs free energy changes with kinetics.

Just because:

$$\Delta G^T<0$$

(at some temperature T) doesn't mean the reaction proceeds 'spontaneously'. That's a misconception that continues to do the rounds in amateur chemist circles. Briefly put:
Quote:
Thermodynamics says nothing about kinetics.



[Edited on 27-10-2016 by blogfast25]