Question

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.

Answer 1

4.13×10²⁷ molecules of N₂ are in the room

Step-by-step 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