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Probability that Your Next Breath Contains a Molecule from Caesar's Last Breath

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Take a deep breath of air and assume it is one liter of air. What is the probability that the liter of air contains a molecule from Julius Caesar's last breath (also assume a liter of air)? Assume that the nitrogen that existed in the atmosphere ~ 2000 years ago is that which is currently present and that the liter of air has had a chance to randomly distribute in the atmosphere in the last 2000 years. Show calculations.

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The solution goes into great detail to explain the many steps required to approximate the answer to this question, drawing on resources across the web as well as logic.

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To answer this question we will need a bit of info...

First, the volume of the entire earth's atmosphere. And also the average temperature of the earth's atmosphere. We need that to calculate the number of molecules in the entire earth's atmosphere.

Second, the number of molecules in 1 liter. (That one's pretty easy). Let's do that one first.

n=(PV)/(RT) ideal gas law let T=298 K, P=1.0 atm, V=1.0 L

So n = (1.0 L*atm) / [(298 K * 0.08206 (L*atm)/(Mol*K)]
= 0.041 mol
= 2.5x10^22 molecules.

Now for the earth... I will do a little surfing to find the volume and average temp of the earth's atmosphere....

On this website I found a graph of the earth's temperature as a function of ...

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