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

Question

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...

Answer 1

*** 1 ***
volume of a sphere = 4/3 x pi x r³

and we want volume of sphere with diameter 6450km - volume of sphere with diameter = 6400km. this gives volume of the atmosphere..

Vatm = [(4/3 x pi x (6450km)³) - (4/3 x pi x (6400km)³)] x (1000m / 1km)³ = 2.6x10^19 m³

*** 2 ***
PV = nRT
n = PV/(RT) = (0.20atm) x (2.59x10^19 m³ x 1000L/1m³) / ((0.08206 Latm/molK) x (288.15K))
n = 2.19x10^20 moles

and number of molecules...
2.19x10^20 mol x (6.022x10^23 molecules / mol) = 1.3x10^44

*** 3 ***
PV = nRT
n = PV/(RT) = (1.0atm) x (0.500L) / ((0.08206 Latm/moLK) x (310.15K)) = 0.0196 mol

number of molecules..
0.0196 mol x (6.022x10^23 molecules / mol) = 1.2x10^22 molecules

*** 4 ***
volume fraction = (1.2x10^22 molecules Caesar exhaust / 1.3x10^44 air) = 9.0x10^-23 molecules / molecule

*** 5 ***
assuming your lung capacity is also 500mL at 37°C and 1.0atm

you breathe in..
(1.2x10^22 molecules air / breath) x (9.0x10^-23 molecules Caesar molecules / 1 molecule air) = 1.0 Caesar molecules per breath.

Answer 2

Fermi Problem

Answer 3

God bless you