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

The correct option is D $4:1$

We have ideal gas equation $pV=nRT=\left(\frac{N}{N_A}\right)RT$

where, $N=$ number of molecule, $N_A$$=$ Avogadro number

$\therefore \frac{N_1}{N_2}=\left(\frac{p_1}{p_2}\right)\left(\frac{V_1}{V_2}\right)\left(\frac{T_1}{T_2}\right)=\left(\frac{p}{2p}\right)\left(\frac{V}{V/4}\right)\left(\frac{2T}{T}\right)=\frac{4}{1}$