A physics lecture room has a volume of 225 m3 . For a pressure of 1.00 atm and a

Question

A physics lecture room has a volume of 225 m3 .

For a pressure of 1.00 atm and a temperature of 27.0 C, use the ideal-gas law to estimate the number of air molecules in the room. Assume all the air is N2.

Express your answer to three significant figures and include the appropriate units.

Calculate the particle density-that is, the number of N2 molecules per cubic centimeter.

Express your answer to three significant figures and include the appropriate units.

Calculate the mass of the air in the room.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

V = 225 m^3, P = 1 atm ,

T = 27 oC = 27+273 = 300 K

gas constant R = 8.314 J/mol.K

from ideal gas equation

PV = nRT

n = N/NA

avagadro number NA = 6.023*10^23

1*1.01325*10^5*225 = N*8.314*300/(6.023*10^23)

Number of air molecules N = 5.51*10^27

N/V = 5.51*10^27/(225*10^6)

N/V = 2.45*10^19 molecules/cm^3

N/NA = m/M

molar mass of N2 = 28 g/mol

5.51*10^27/(6.023*10^23) = m/0.028

m = 256 kg

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