Question

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m³ at a temperature of 27°C and 1 atm pressure.

Answer 1

Here, p = 1 atm = 1 x 1.01 x 10⁵ Pa

V = 25 m³

T = 27°C = 27 + 273 = 300 K

and R = 8.31 J mol^-1 K^-1

Now pV = uRT

⇒ u = pV/RT = {1.01 x 10⁵ x 25}/{831 x 300} = 1.013 x 10³ moles

Now, one mole of a gas contains = 6.023 x 10²³ molecules

∴ 1.013 x 10³ moles would contain

= 6.023 x 10²³ 1.013 x 10³ = 6.10 x 10²⁶ molecules