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 = k_BNT

Where,

K_B 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.

Answer 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)`