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Ideal Gas Equation from KTG

Estimate the ...

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.

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Solution

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

∴

= 6.11 × 10²⁶ molecules

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

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