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

Concept :- use, PV = n.Kb.T
When , n = number of molecules or atoms
Kb = Boltzman's constant = 1.38 × 10^-23 m²/s².K

Volume of the room ( V) = 250 m³
Temperature ( T) = 27°C
= 273 + 27 = 300 K
Pressure ( P) = 1 atm
= 1.013 × 10^5 N/m²

Use formula,
PV = n.Kb.T
n = PV/Kb.T
= 1.013 × 10^5 × 25/1.38 × 10^-23 × 300
= 6.11 × 10^26 molecules .

Answer 2

Answer:

6.11 × 10²⁶ molecules

Explanation:

Here we shall use the concept PV = Kь×N×T

Now...

• P = 1 atm = 1.103 × 10⁵ Pascals
• V = 25m³
• Kb = Boltzmann constant ( 1.38 × 10 ⁻²³ J/K)
• T = 27°C = 300 K

SO ..

PV = Kb*N*T

∴N = P*V/Kb*T

∴N = 1.103 * 10⁵ * 25/ 1.38 * 10⁻²³ *300

∴N = 0.0611 * 10²⁸

∴N ≈ 6.11 * 10²⁶ molecules

Here is your answer...HOPE it helps