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Just keep on trying till you run out of cake

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The mass of a fart
peek-a-baa
rho
A few years ago, I was listening to the radio (in the car with my mum on the way to the hospital to have my wisdom teeth removed, as it happens) and they had one of those inane "Strange but true" features that could only exist on the radio or in email forwards.

One of their alleged facts was that on average a fart weighs 5 grams.

This sounded rather dubious to me, so I did a quick calculation. If we assume so and so as the constituent gases of a fart, then use this, this and this as the relative atomic weights, then take that approximation of the ideal gas equation... then we wind up calculating that a 5 gram fart would have a volume somewhere in the region of 4 litres.

Now, it has to be stressed that that was a fairly rough and ready calculation, and I wouldn't put much stock in its accuracy. But as an order of magnitude approximation, it isn't too bad.

I don't know about you, but I've farted in the bath, where the bubbles make it easy to see the volume, and I'm quite, quite sure that even the biggest farts are nowhere even close to 4 litres.

Something is clearly amiss. Either the statement given by the radio was false, or various bits of science that I have learned were false (or both could be wrong, of course). I have absolutely no empirical evidence either way. I have never measured the mass of a fart. Nor, however, have I ever done a chemical analysis of a fart, nor measured relative atomic masses of carbon, hydrogen, oxygen, nitrogen, etc. The closest I've come to empirical evidence is seeing someone else perform demonstrations of Boyle's Law and Charles' Law, both of which are specific cases of the ideal gas law. The only real empirical evidence I have is the volume of the fart, which doesn't tell me which of the two propositions is right, only that they can't both be.

So, given this situation which of the two opposing theories would you be more inclined to believe, and more to the point why?

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Chemical Analysis of a Fart.

The average person farts 14 times each day. The total volume of these farts is about half a liter. So an average fart has a volume of 35.7 cubic centimeters.

The chemical composition of fart gas varies with person and diet, but the following are typical volume percentages: nitrogen 59%, hydrogen 21%, carbon dioxide 9%, methane 7%, oxygen 3%. The remaining one percent is the stinky stuff, mostly hydrogen sulfide, methyl mercaptan, methyl indol, and skatol.

That means a fart contains 21.0 ml nitrogen, 7.5 ml hydrogen, 3.2 ml carbon dioxide, 2.5 ml methane, 1.1 ml oxygen, and .357 ml of the stinky stuff.

A perfect gas at STP has a molar volume of 22.4 liters, and there are 6.0221415E+23 particles in a mole. Nitrogen, hydrogen and oxygen are all diatomic, forming molecules of N2, H2, and O2 at standard temperature and pressure.

So, in a fart, there are 0.000938 moles of nitrogen, 0.000335 moles of hydrogen, 0.000143 moles of CO2, 0.000112 moles of methane, 0.000049 moles oxygen, and 0.000016 moles of stinky stuff.

The molecular weights are N2 (28), H2 (2), CO2 (44), CH4 (16), O2 (32). The molecular weight of methyl mercaptan (CH3SH) is 48.1. The molecular weight of hydrogen sulfide (H2S) is 34.8.

There are several forms of methyl indol, and all of them are large molecules (molecular weight ~600). Skatol is huge (molecular weight ~56000). The main stink comes from methyl mercaptan and hydrogen sulfide though. The more exotic gases only serve to give the vintage fart a distinctive body and character. I'll assume that the mean molecular weight of the stinky stuff is 50 amu.

That means the masses of the gasses in a fart are...
Nitrogen: 0.0263 grams
Hydrogen: 0.0003 grams
Carbon dioxide: 0.0063 grams
methane: 0.0018 grams
oxygen: 0.0016 grams
stink: 0.0008 grams

The total mass of a fart is 0.0371 grams.

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