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
Solution 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 = kBNT
Where,
KB is Boltzmann constant = 1.38 × 10–23 m2 kg s–2 K–1
N is the number of air molecules in the room
`:. N = (PV)/(k_BT)`
`= (1.013xx10^5xx25)/(1.38xx10^(-23)xx300) = 6.11 xx 10^(26)` molecules
Therefore, the total number of air molecules in the given room is 6.11 × 1026.
Solution 2
Here, Volume of room, `V= 25.0 m^3`, temperature, `T = 27 ^@C = 300 K` and
Pressure, `P = 1 "atm" = 1.01 xx 10^5 Pa`
According to gas equation, `PV = muRT = muN_A.k_BT`
Hence, total number of air molecules in the volume of given gas
`N = mu.N_A = PV/K_BT`
`:. N = (1.01 xx 10^5 xx25.0)/((1.38 xx 10^(-23))xx300) = 6.1 xx 10^(26)`
