Caesar - kg/m s 2 )(5.10 x 10 14 m 2 ) Force = 5.15 x 10 19...

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Caesar's Las Breath Of the molecules in Caesar's last gasp, how many of them are in the breath you just took? Given: One breath= 2 liters of air at a pressure of 730 mmHg and 37 degrees Celsius. Earth is a sphere with a radius of 6370 Km and an average barometric pressure of 760mm Hg. (D of Hg=13.6g/cm 3 ) The avg. molecular mass of air is 29 g/mol. 1. Number of moles in Caesar’s last breathe: n = PV/RT = (0.96 atm)(2L)/(0.0821 L atm/mol K)(310 K) n = 0.075 mol 2. Number of moles in the atmosphere: a. Surface area of earth: Area = (4)( π )(r 2 ) Area = 5.10 x 10 14 square meters b. Pressure of the atmosphere on the earth’s surface: Pressure = 760 mm Hg = 1.01 x 10 5 Pascals = 1.01 x 10 5 Newtons/square meter Pressure = 1.01 x 10 5 kg/m s 2 c. Force of the atmosphere on the earth Pressure = Force/Area Therefore Force = (Pressure)(Area) Force = (1.01 x 10 5
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Unformatted text preview: kg/m s 2 )(5.10 x 10 14 m 2 ) Force = 5.15 x 10 19 kg m /s 2 d. Mass of the atmosphere Force = (mass)(acceleration) therefore mass = Force/acceleration mass = (5.15 x 10 19 kg m/s 2 )/(9.8 m/s 2 ) note: this is the acceleration due to gravity mass = 5.26 x 10 18 kg or 5.26 x 10 21 g e. Moles in the atmosphere mol = (5.26 x 10 21 g)(1 mol/29 g) mol = 1.81 x 10 20 mol 3. Fraction of atmosphere which represents molecules from Caesars last breath: (0.075 mol)/(1.81 x 10 20 mol) = 4.14 x 10-22 4. Moles of Caesars last breath in your last breath: Assume your breath holds 0.075 mol: (0.075 mol)(4.14 x 10-22 ) = 3.11 x 10-23 mol 5. Number of molecules: (6.022 x 10 23 molecules/mol)(3.11 x 10-23 mol) = 18.7 molecules ( An even more disconcerting fact is that he probably had flatulence as well. )...
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Caesar - kg/m s 2 )(5.10 x 10 14 m 2 ) Force = 5.15 x 10 19...

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