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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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Well, the 4 litres sounds more like the daily volume of farts that people produce.

How, you might well as, do I know this?

Other than the fact that I'm, well, me, there is a book at Empire that my friends and I read, called - I forget what it's called, but it's all about farting. I forget just what it said was the size/volume of an average fart, but I can read the book again. :)

I wonder if it's on WikiPedia.

*ask

Seems to me I gave us a bit more credit (?) - Here's the Wiki article.

Isn't a fart in water going to occupy less volume than a fart in air? And isn't it likely that some of the gases will dissolve in the bathwater?

Yes in both cases, but not enoughto make a significant difference. The volume would decrease slightly due to the increased pressure, and some small amount of gas would probably disolve, but neither effect would be nearly large enough to make up for the several orders of magnitude difference. (Unless, of course, you want to postulate that both the radio show and the science I used to estimate the required volume were right, but that the science that says those two things would only make a negligible difference was wrong.)

I'm inclined to believe you, because you at least suggested some working :).

I'm with you. It's the bath bubbles that wins me over, because a litre would take long enough to expel (assuming you set it up so that it had the same release rate as the anus), and produce a hell of a lot more bubbles. Multiply that by four, and you'd probably find yourself being able to take off by fart power.

Plus, I know gases are funny things, but 4 litres at one time? Wouldn't you, like, explode before it got to that volume? 'cos where would it be stored? Little and often sounds saner to me.

I'd be inclined to believe you, because you showed your work, and because I know that those sorts of "strange but true" things are passed along from one person/place to another, often carelessly and with no fact-checking. It's entirely possible that someone dropped a decimal point in transcribing, or that the original was "a cow fart" and someone assumed that the number applied to humans as well.

I was inclined to believe you when I first read this this morning. Your numbers sound much more reasonable. However I can't resist a chance to do an experiment (you can see where this is going can't you?).

Aim: To measure the volume and hence the mass of a fart.

Method: One bath with a disposable plastic cup and waterproof pen. Fart and catch bubbles in the inverted water filled cup. Mark gas level on cup with pen. Determine volume of gas by weighing water in same cup filled to gas line.

Results: 115 cm^3 of gas (+- 5) was released. Bath temp was about 29 degrees. At STP this gives 0.0046 mols of gas. Assuming the gas is 100% methane, it isn't, but for this example I'll claim it is, I get a total of 0.074g of methane.

Comment on your results: There isn't a lot to say about this, I have no way of knowing if this was an average fart. The weight determined from this experiment is much less than that given in the radio show. In fact even if I'd been farting pure Radon, the recorded volume of gas would still only weigh just over 1g.



I belive NASA did fairly extensive research into this sort of thing as part of the Skylab programme, maybe you can find some of their papers?

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.

Another opinion on the mass of a fart.

Over at http://www.bikeforums.net/archive/index.php/t-194893.html
a poster named "cmcenroe" estimated that farts weigh 1.3 grams per liter. Our average fart contained 1/28th of a liter of gas, and that would work out to 0.0464 grams. Same ballpark as my estimate just above.

(Deleted comment)
Let's assume that a person farts 5g per day on average. I have no clue how accurate that is but it seems reasonable for an order of magnitude calculation.

5g is 1/200 of a kg, so it would take (1.31 * 10^22) * 200 = 2.62 * 10^24 days to fart it all out. Converting that to years give (2.62 * 10^24) / 365 = 7.18 * 10^21 years. Or seven thousand billion billion years.

For comparison, the universe is about 13 billion years old, so to fart out the whole of Pluto would take five hundred billion times as long as the universe has existed. Hopefully that will dissuade your daughter from trying to head out to the Kuiper Belt for a snack.

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