I recently heard that due to the amount of air that is in the atmosphere and the amount of air molecules that is in every breath of air that during every breath there is a 1 in 3 chance that I will be breathing in one of the molecules of air that Van Gogh breathed in during his last moments of life. My question is if my motorcycle has a 4 gallon tank and I have filled it 100 times and that I only fill it when it has reached 1/10 th of a tank. How many gasoline molecules are in my tank that were in the tank when I originally bought it.
I would say, disregarding the number of molecules that have returned in later fillings (because that would be really small) your answer is (1/10)^100 or the 1x10^-100th part of your original tank.
A gallon of gas weighs about 6.15 pounds, so (converting to SI) 4 gallons weighs 11,168 grams.
a mole of gasoline molecules (that’s 6.02x10[sup]23[/sup] of them) weighs 114 grams.
So 4 gallons of gasoline contains 5.9x10[sup]25[/sup] molecules of gasoline.
Pitchmeister’s nailed the dilution: each refill cuts the concentration of original molecules by a factor of ten, and you did it 100 times, so your tank contains 1/10[sup]100[/sup] of the original showroom gasoline.
1/10[sup]100[/sup] of 5.9x10[sup]25[/sup] molecules is far, far less than one.
Bottom line, it’s very likely that your tank does not contain any of the original gasoline molecules.
[sub]Someone check my math?[/sub]
So you get left with homeopathic gasoline and you should never run out again. 
Is the OP’s premise about molecule’s of VanGogh’s last breath(s) accurate? Without really knowing what I’m talking about, 1 in 3 seems to be considerably off for chances of encountering a molecule from VanGogh’s last breath or handful of breaths.
Seems more along the lines of a molecule he breathed at some point, but I could be way off there too.
lung tidal volume = 500 mL. For ideal gas, there are 6.02x10[sup]23[/sup] molecules per 22.4 liters, so Van Gogh’s final breath had 1.34x10[sup]22[/sup] molecules in it.
The atmosphere has a total mass of 5x10[sup]18[/sup] kg. At standard temperature and pressure, that’s a volume of 4.17x10[sup]21[/sup] liters. When Van Gogh breathed his last, that lungful of air got diluted in the atmosphere by a factor of 0.5/(4.17x10[sup]21[/sup]), or 1.2x10[sup]-22[/sup].
So the next breath of air you inhale will have 1.34x10[sup]22[/sup] molecules in it, and you would expect it to have 1.34x10[sup]22[/sup] * 1.2x10[sup]-22[/sup] molecules from Van Gogh’s last breath, or 1.1 molecules.
If the number of molecules in a breath of air were far lower (think single digits), then the distribution of them could be very uneven, and any given breath may or may not have some of Van Gogh’s air in it. But since each lungful of air has a very large number of molecules in it, it’s statistically very likely that each breath you take has one (or occasionally two) molecules in it from Vincent Van Gogh’s last breath.
That is so cool. Thanks Machine Elf.
Don’t these calculations assume that the molecules from Van Gogh’s last breathe after being expelled from his lungs were evenly distributed around the world? That’s quite an assumption. I could just as easily assume that they are circulating in the air above Europe and so there is little chance that I in America am breathing any of them.
Van Gogh died in 1890, allowing 110 years for atmospheric mixing to take place. Volcanic eruptions and various other episodes of atmospheric pollution (e.g. Chernobyl) have demonstrated how bulk air masses can move thousands of miles in just a few days. The nature of nature - atmospheric transport/fluid mechanics, diffusion, and entropy - is such that in 110 years’ time, it is extremely unlikely for Van Gogh’s last breath to be distributed in anything other than a very even fashion. In the same way that your awful beer fart permeates the entire living room in a matter of seconds, Van Gogh’s last breath has, no doubt, spread round the entire globe over the past century.
The atmospheric mixing time is on the order of 1-10 years. There is some amount of partitioning between the northern and southern hemispheres, but the atmosphere as a whole is very well-mixed on decadal timescales.
edit: Cite
This doesn’t take into account the amount of oxygen being used to form sugar molecules in a photosynthesis reaction, or nitrogen being fixed into biologically accessible forms. Your next steak likely has some of Van Gogh’s last breath in it.
If your next steak smells like Van Gogh’s last breath, no need to call the waiter. It is perfectly natural.
Great, so not only am I breathing in molecules from Van Gogh’s last breath, there is probably a molecule from Hitler’s beer farts during the Putsch up in the mix.
'scuse me, I gotta go gargle with Listerine.
/I’m not sure if this is a hijack, but:/
Our skin cells are dying off and being replaced at x times a day. (I could not find a cite for this). Now, that means at some time our entire integument (nice word I think) is entirely changed. We are no longer ourselves to the face of the world. (Stephen Daedalus in Ulysess uses this argument to get out of a debt.)
So, I am Leo Bloom.
When will I be Leo Bloom the II, etc.?
ISTR reading somewhere relatively authoritative that every cell of your body has died and been replaced every seven years. So you’re a whole new you every seven years. Dunno if that’s true.