[stanmancan]

I have no clue what I'm talking about but this piqued my interest. If I ask WolframAlpha:

   Q:how many carbon molecules in 2.4 tons
   A: 1.092×10^29 molecules

X molecules of pure carbon carbon would theoretically require 2X molecules of oxygen to turn into CO2

   Q: how much does (10^29)*2 molecules of oxygen weight in us tons
   A: 5.827 tons

So 2.4 tons of Carbon + 5.827 tons of Oxygen = 8.227 tons of CO2? Maybe? What am I missing to have 2.4 tons of fuel turn into 16.8 tons of CO2 emissions? I'm not doubting it, and I'm sure it's WAY more complicated than above, but just genuinely curious!*

[undersuit]

Kerosene(jet fuel) has between 6 and 20 carbon atoms per molecule. https://en.wikipedia.org/wiki/Kerosene#Properties_and_grades

Have fun with the math!

[stanmancan]

Hm, does that change anything? Atoms per molecule doesn’t seem important when we’re talking about the total weight. If anything jet fuel isn’t pure carbon so the math works out to create less CO2 than I calculated?

[thayne]

I don't think the number of atoms directly matters. However, the amount of energy that is released when kerosene burns has a _small_ impact. Because that energy was contributing to the mass of the kerosene (E=mc^2). But, that difference in mass will be tiny. Far surpassed by the mass of the non-carbon atoms in kerosene.

[tonymillion]

You also missed the carbon monoxide and water vapor that would be produced. Along with nitric and sulfur oxides. So it’s probably not as bad.

[thaumasiotes]

No need to ask WolframAlpha; you can do those computations yourself very easily.

Avogadro's number is the conversion factor between grams and "atomic mass units", 6.023e+23†.

1.102e-6 is the conversion factor between grams and tons.

The atomic weight of carbon is 12.01 amu.

So 2.4 tons of pure carbon should contain 1.312e+30 atoms of carbon. The concept of a "carbon molecule" is not well defined; theoretically you could arrange all of these into one big diamond, or a bunch of graphite, or whatever.

The atomic weight of oxygen is 16.00 amu. If you're making carbon dioxide, every 12.01 units of carbon mass will correspond to 32.00 units of oxygen mass, so 2.4 tons of carbon would require 2.4 * (32.00/12.01) = 6.4 tons of oxygen.

There are a few comments we can make:

- "What you're missing" appears to be that the emissions are described as "equivalent to" a certain amount of carbon dioxide by some metric, not as actually containing that much carbon dioxide.

- Wolfram Alpha, at first glance, does not appear to be capable of answering your question correctly, but it's also in the right ballpark. Something is up.

- Could be that your question is posed too poorly to get a good response.

- Could be that the mass of a carbon dioxide molecule is greater than the sum of the masses of the one carbon and two oxygen atoms that it contains. I am told that in fact these two quantities are not equal - there is energy in the molecular bonds which ultimately equates to mass - but I don't know whether the molecule or the independent atoms should be heavier, and I feel sure that, if it's the molecule that's heavier, it is not heavier by a factor of 12, which is what the WolframAlpha answer requires.

- Your second question, "how much does 2e+29 molecules of oxygen weigh in US tons", is perfectly well defined, although it is incorrect given your goals. One molecule of oxygen contains two oxygen atoms, so you only need one molecule of oxygen per carbon atom to make carbon dioxide.

But WolframAlpha should have been able to answer this one unambiguously, and it couldn't. The correct result:

2e+29 molecule_O × 2 atom_O/molecule_O × 16.00 amu/atom_O ÷ 6.022e+23 amu/g × 1.102e-6 g/ton_US = 11.71 US tons

Something went very wrong in the WolframAlpha answer. Mostly it seems to have mistaken molecules for atoms, but I can't explain the difference between 5.855 and 5.827. On the other hand, that difference is small enough that if you said it was the effect of the "mass" of the molecular bonds, I wouldn't just dismiss the idea out of hand.

A larger lesson here might be that just because an automated system (or a human!) claims that it understands you, that doesn't mean it actually does.

† I just checked wikipedia and they have 6.022e+23. This doesn't make a significant difference to this calculation, so I'll ignore it.

[stanmancan]

This was a fantastic answer, thank you!