Question

atmosphere is 50 km thick, has an average temp of 15 Celsius, and an average pressure of .20atm. radius of the Earth is 6400km and the volume of a single breath is 500mL. calculate the total volume of the atmosphere then calculate the total # of gas molecules in the atmosphere then calculate the # of molecules in Caesar's last breath(37°C and 1.0 ATM). what fraction of all air molecules came from Caesar's last breath? about how many molecules from Caesar's last breath do you inhale each time you breathe?

Answer 1

a) Volume of the atmosphere

=> Volume of sphere with radius (6400+50)km - Volume of sphere with radius (6400)km

=> [4/3 * pi * (6450)^3] - [4/3 * pi * (6400)^3]

=> 2.593 * 10^(10) Km^3

Now 1Km^3 = (1000m)^3 = 10^9 m^3

Volume in m^3 = 2.593 * 10^(19) m^3

b)

Using the ideal gas equation

PV = nRT

1 m^3 = 1000L

(0.20)(2.593 * 10^(22)) = n * 0.0821 * (273+15)

n = 2.192 * 10^(20) moles

Total number of gas molecules = 2.192 * 10^(20) * 6.023 * 10^(23) = 1.3202 * 10^(44) molecules

c)

Using the ideal gas equation

PV = nRT

(1)(0.500) = n * 0.0821 * (273+37)

n = 0.01964 moles

Number of molecules in the breath = 0.01964 * 6.023 * 10^(23) = 1.183 * 10^(22) molecules

d)

Fraction of air coming from caesar breath = 1.183 * 10^(22)/1.3202 * 10^(44) = 8.960 * 10^(-23)

e)

Number of molecules of Caesar breath inhaled = 1.183 * 10^(22) * 8.960 * 10^(-23) = 1 molecule per breath