Question

The pressure P, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2P, volume V/4 and temperature 2T, then the ratio of the number of molecules in the jar A and B will be

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 4 : 1

Answer 1

Answer: (D)

4 : 1

Answer 2

Ideal gas equation $PV = \mu RT = \left( \frac{N}{N_{A}} \right)RT$

where N = Number of molecule, N_A = Avogadro number

∴ $\frac{N_{1}}{N_{2}} = \left( \frac{P_{1}}{P_{2}} \right)\left( \frac{V_{1}}{V_{2}} \right)\left( \frac{T_{2}}{T_{1}} \right) = \left( \frac{P}{2P} \right)\left( \frac{V}{V ⥂ / ⥂ 4} \right)\left( \frac{2T}{T} \right) = \frac{4}{1}$.