Use the ideal-gas law to estimate the number of air molecules in your physics lab room, assuming all the air is N2. Assume a room size of 18 ft * 18 ft * 18 ft. Assume a temperature of 20∘C.

4.13*10²⁷ molecules of N₂ are in the room

Explanation:

ideal gases Law → P. V = n. R. T

Pressure. volume = moles. Ideal Gases Constant. T° K

T°K = T°C + 273 → 20°C + 273 = 293K

Let's determine the volume of the room:

18 ft. 18 ft. 18ft = 5832 ft³

We convert the ft³ to L → 5832 ft³. 28.3L / 1 ft³ = 165045.6 L

1 atm. 165045.6 L = n. 0.082 L. atm/mol. K. 293K

(1 atm. 165045.6 L) / 0.082 L. atm/mol. K. 293K = n

6869.4 moles of N₂ are in the room

If we want to find out the number of molecules we multiply the moles by NA

6869.4 mol. 6.02*10²³ = 4.13*10²⁷ molecules