Question

A physics lecture room has a volume of 278 m^3 .

Part A

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.

N = ?    molecules

Part B

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.

particle density = ? molecules/cm^3

Part C

Calculate the mass of the air in the room.

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

m =   

Answer 1

part )

volume , V = 278 m^3

Pressure, P = 1.01 *10^5 Pa

T = 27 C = 300 K

Using ideal gas equation

P*V = n*RT

1.01 *10^5 * 278 = n * 8.314 * 300

n = 11257.3 moles

Number of molecules = 11257.3 * 6.022 *10^23

Number of molecules = 6.779 *10^27

the Number of molecules in room is 6.779 *10^27

part B)

particle density = 6.779 *10^27/278

particle density = 2.44 *10^25 molecules/m^3

the particle density in room is 2.44 *10^25 molecules/m^3

the particle density in room is 2.44 *10^19 molecules/cm^3

part C)

mass of air = n * 28

mass of air = 11257.3 * 28

mass of air = 315204.4 gm

the mass of air in room is315204.4 gm