Answer to Question #277225 in Molecular Physics | Thermodynamics for Reign

Question

What is the mass of the air contained in a room 6m X 5m x 4m if the pressure is 100 kPa and the temperature is 25oC

Answer 1

$V = 6 \times 5 \times 4 = 120 \; m^3 = 120 \times 10^3 \;L \\ p= 100 \; kPa = 0.986923 \; atm \\ T = 25 + 273.15 = 298.15 \;K$

Ideal gas law

pV = nRT

R=0.082058 L×atm/(K×mol)

$n = \frac{pV}{RT} \\ n = \frac{0.986923 \times 120 \times 10^3 }{0.082058 \times 298.15} = 4840.70 \; mol M(air) = 28.97 \; g/mol \\ m = 4840.70 \times 28.97 = 140235.2 \; g = 140.23 \; kg$