atmosphere is 50 km thick, has an average temp of 15 Celsius, and an average pre

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?

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.