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

Volume of the room, V = 25.0 m3

Temperature of the room, T = 27°C = 300 K

Pressure in the room, P = 1 atm = 1 × 1.013 × 105 pa

The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T) can be written as:

PV = kB NT

Where,

KB is Boltzmann constant = 1.38 × 10-23 m-23 m2 lg s-2 K-1

N is the number of air molecules in the room

∴ $N=\frac{PV}{K_BT}$

$=\frac{1.013×10^5×25}{1.38×10^{-23}×300}$ = 6.11 × 1026 molecules

= 6.11 × 10

Therefore, the total number of air molecules in the given room is 6.11 × 1026