Need help with a Fermi problem of "Caeser's Last Breath"?

A famous example of a Fermi problem is "Caeser's last breath" which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. Assumptions: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The... show more A famous example of a Fermi problem is "Caeser's last breath" which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died.

Assumptions: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The atmosphere is 50 km thick, has an average temperature of 15 °C, and an average pressure of 0.20 atm. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500 mL.

Perform the following calculations, reporting all answers to two significant figures.
1. Calculate the total volume of the atmosphere in cubed meters.
2. Calculate the total number of gas molecules in the atmosphere.
3. Calculate the number of gas molecules in Caesar\'s last breath (37 °C and 1.0 atm).
4. What fraction of all air molecules came from Caesar\'s last breath?
5. About how many molecules from Caesar's last breath do you inhale each time you breathe?

Please help, I've gotten this question wrong fire times already!!!!
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