Assumptions: 1. The gas molecules from Caesar\\\'s last breath are now evenly di

Question

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. Calculate the total volume of the atmosphere.

Calculate the total number of gas molecules in the atmosphere.
_____ m3

Calculate the number of gas molecules in Caesar's last breath (37 °C and 1.0 atm).
_____ molecules

What fraction of all air molecules came from Caesar's last breath?
_____ molecules

About how many molecules from Caesar's last breath do you inhale each time you breathe?
_____

Explanation / Answer

Volume of Sphere = 4/3*pi*r^3 (given 50 km thick layer)

Volume of atmosphere = [4/3*pi*(6450km)^3 - 4/3*pi*(6400km)^2] * (1000L/1Km)^3 = 2.6 * 10^*(19) m^3

Using ideal gas equation

PV = nRT

n = PV/RT = (0.20 * 2.6 * 10^(19) * 1000)/(0.0821*288)

=> 2.19 * 10^(20) moles

Number of molecules = number of moles * avogadro number

=> 2.19 * 10^(20) * (6.022x10^23 molecules / mol) = 1.3x10^44 molecules

2) n = PV/RT

=> 1 * 0.5/0.0821*310

=> 0.0196 moles

number of molecules = 0.0196 moles * (6.022x10^23 molecules / mol) = 1.23 * 10^(22) molecules

3) Fraction = Molecules in Caesar breath/ Total volume

=> 1.23 * 10^(22) molecules/1.3x10^44 molecules

=> 8.98 * 10^(-22)

4) (1.23x10^22 molecules air / breath) x (9.0x10^-23 molecules Caesar molecules / 1 molecule air) = 1.0 Caesar molecules per breath.

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