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How can you calculate the total bond energy of $\ce{CO2}$? I've searched for the bond energy of C=O and found it was 745 kJ/mol, but sometimes 799 kJ/mol. Which one is the right one to use? And do those numbers mean the bond energy of $\ce{CO2}$?

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    $\begingroup$ there are many C=O bonds with different chemical environments, bearing slightly different energies. Usually the reported value is an average of many instances of that bond. $\endgroup$
    – khaverim
    Feb 7, 2016 at 21:47

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I wouldn't worry too much about the slight differences in the bond enthalpy for the C$=$O. I will discuss why after the next paragraph.

The bond enthalpy is the amount of energy (in kJ) that is required to break 1 mol of that bond. Therefore, it is also a measurement of how much energy is released as 1 mol of that same bond is formed. The bond enthalpy is dependent upon the strength of the bond. The higher the strength, the larger the bond enthalpy.

The bond enthalpy is more of an average value than an accurate figure. For example, the energy required to break the first double bond between the central carbon atom and the oxygen is different from the energy required to break the second double bond. This is because the strength of the bond is dependent upon its environment. When you break off that first oxygen atom, it changes the environment.

So you can use any one of those bond enthalpy values.

Source(s): Any good textbook in General Chemistry should discuss how enthalpy bonds are calculated. Personally, I used the Pearson Baccalaureate Textbook for IB Chemistry HL.

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    $\begingroup$ Thanks! This helped. But what is the total bond energy of CO2? $\endgroup$ Feb 7, 2016 at 21:52
  • $\begingroup$ In $\ce{CO2}$, the potential energy in the carbon-oxygen double bonds is equal to the number of such bonds in the molecule multiplied with the average bond enthalpy. If you are in doubt, it is always useful to draw the Lewis Structure of the molecule to help define the bonds. $\endgroup$
    – Mattias
    Feb 7, 2016 at 22:02
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You're asking a pretty complex question. The short answer is that to calculate such an energy you have to utilize quantum mechanical calculations, or otherwise perform macroscopic experiments on bulk $\ce{CO2}$.

A quick ab initio calculation of a O=C=O molecule with a bond length of 1.164 Angstroms (quite close to experimental and theoretically deduced length) yields the following Hartree-Fock SCF energy (using the 6-31G* basis set):

-187.634176090515 Hartrees, which is -492633.5668524824 kJ/mol

This is a huge negative energy, and rightly so -- it is how much energy is theoretically required to break the $\ce{CO2}$ molecule entirely into subatomic particles. In other words, it is the energy holding $\ce{CO2}$ together -- the energy that defines the molecule.

Better approximations can be made with higher levels of theory but don't deviate from these values by much.

The simplistic route is to add up collective bonds from a data table provided in your textbook, e.g. $2 \times$ C=O = total molecular bond energy. This is not the same thing as the total molecular energy though: the latter includes the energetic contribution of the nuclear-electron interactions, not just atomic bonds.

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I know that at this point I'm basically necroposting, but none of these answers actually directly answered the question you were (mostly probably) trying to ask, which was somewhat disappointing to me since I came here looking for the answer to this same question, and yet after 7 years, nobody actually answered it, at least not that I could determine. So now I think I will take a crack at answering it.

First lets address the question actually being asked: "What is the total bond energy of CO2" and I notice that you're referring to chemical bonds because you also said: " I've searched for the bond energy of C=O and found it was 745, but sometimes 799. Which one is the right one to use?" based off your question, it sounds like you're looking for a more simple high-school-level answer, not a full breakdown with perfect technical accuracy, so I will try to answer it as such.

Well, now we have a question that we can actually answer.

To start off, it would be good to know how to navigate the online data accurately. So, a few pointers:

#1 when a molecule that has 2 bonds (CO2 for instance) loses one of the bonds, the strength of the other is affected, so there isn't a single value to accurately describe the energy of any one C=O bond in CO2. Thankfully most websites will just take the average of the values, so it really shouldn't matter, but that's only as long as you're either just looking for the average energy of a C=O bond in CO2, or if you want the total bond energy of CO2. Fortunately you were just wanting the total, so this should be as simple as multiplying the energy of a C=O bond (from CO2) by 2, and I guess that also answers your "how to calculate" question.

#2 C=O bonds in CO2 will have a different strength than C=O bonds in other molecules, and that's simply because the configuration of the molecules themselves (bond angle and distance etc.) are significantly different between molecules.

#3 As (I think) you mentioned, the value that is provided online can either be for the molecule as a whole, or just for one of the double bonds. What's nice is that no matter which of these values it ends up being, we can derive you're answer from it. Now, usually its pretty easy to tell (upon reading the value that they provide) whether its referring to just one of the double bonds or the whole molecule, because it will either say "per mol of CO2" which is both bonds, or "per mol of C=O bonds" which would only be one. Generally just checking the phrasing will get you the answer, additionally its good to check for notes at the bottom of the paragraph or at the bottom of the page to see if they specify which it is (and they really should for scientific information like this).

Now to tackle the online data: When I search for the value online, I get a lot of the same 2 values you got, one around ~750 and another around ~800. Obviously this difference is large enough to cause errors if we were to use the wrong one, and so its necessary to pinpoint which one is the correct one to use. Additionally, we need to know if the values refer to a single double bond or the molecule as a whole (both double bonds). When I looked around online, almost all the sites suggesting the ~750 value were primarily discussing carbonyl groups. such as: The Carbonyl Group - Chemistry Libre Texts which is strictly referring to carbonyl groups, and doesn't even mention CO2 a single time. And if we take a look at that site, we find the following statement:

"The double bond lengths of a carbonyl group is about 1.2 angstroms and the strength is about 176-179 kcal/mol."

Converting kcal/mol to kJ/mol we get ~748kJ/mol for carbonyl double bonds, and converting angstroms to picometers we get 120 pm for bond length which we'll reference again in a moment. Just based off the phrasing its pretty obvious that they are referring to the individual C=O double bonds of carbonyls. These are C=O groups within other molecules that are not CO2. And if you remember from earlier, the strength of the C=O bond can vary significantly depending on what molecule its in. And since we just found out that the ~750 value belongs to the carbonyls, we know that its very likely that the ~800 value belongs to CO2. When I looked on Wikipedia: Carbon-oxygen bond - Wikipedia I found the following paragraph:

"Bond lengths of C=O bonds are around 123 pm in carbonyl compounds. The C=O bond length in carbon dioxide is 116 pm. The C=O bonds in acyl halides have partial triple bond character and are consequently very short: 117 pm."

Notice the bond lengths, they are 123pm for carbonyls (which agrees decently with the value we got from the previous website), 116pm for carbon dioxide, and 117pm for acyl halides. Now remember that the shorter the bond length, usually the significantly stronger the bond, and the ones in CO2 actually have the shortest bond length of all the ones listed here, even surpassing the acyl halides with their sort-of triple bond character. So, this means that of all the energy values for C=O bonds in various molecules, the ones for CO2 should have the highest bond strength of basically all of them.

So, we now have 3 pieces of evidence that the value for individual C=O bonds in CO2 is the ~800 value, and that its not the ~750 value. Firstly that the websites suggesting the ~750 value are primarily referring to carbonyls and not CO2, and secondly that CO2 has some very strong bonds even when compared to the acyl halides which have "triple bond character" (triple bonds are very strong) meaning that CO2 should be the stronger of the two. And finally we know that they have to be referring to the individual C=O bonds not only for carbonyls, but also for CO2 because the bond strength of C=O bonds in CO2 has to be stronger than the carbonyls, and if ~800 were for the whole CO2 molecule then 800/2 (just one double bond) would only be 400 which is less than the carbonyls ~750 which has to be wrong, and so we know that both values refer to individual bonds.

And to really drive it all home, Bond Energies - Chemistry Libre Texts says the following:

"Table 1: Average Bond Energies (kJ/mol) ... O=O 495, C=O* 745, C≡O 1072, ..."

And at the bottom of the table it follows up the asterisk with:

"*C == O(CO2) = 799"

And that, along with everything else, makes it pretty clear, the ~750 value belongs to C=O groups from random compounds and carbonyls, and the ~800 value belongs to CO2 specifically, meaning that everything checks out, nothing contradicts, and we have come to an answer.

Fully written out it would be: The average bond strength in kJ/mol of individual C=O bonds for CO2 is ~800 kJ/mol, that's 1,600kJ/mol of CO2 molecules formed, that's 1.6MJ/mol of carbon dioxide, and that's a lot of energy!

-Metal Master

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  • $\begingroup$ CO2 is a too complex molecule to perform such a back of the envelope calculation. Unfortunately this post is very long, without saying much. I don't actually think it's answering the question. But then again the question is really hard to answer. $\endgroup$ Feb 2 at 1:07
  • $\begingroup$ @Martin-マーチン thanks for the feedback, as I'm quite new here and would like to refine my ability to answer questions effectively. however I should point out that my post did not claim to definitively answer the question, it was only meant to point people in the right direction. I was also later able to find more definitive references which aligned very closely with my answer. $\endgroup$ Feb 2 at 16:05

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