Question

Densities of two gases are in the ratio $1:2$ and their temperature are in the ratio $2:1$, then the ratio of their respective pressure is :

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

Answer 1

The correct option is A $1:1$

Densities of two gases are in the ratio 1:2 and their temperature are in the ratio 2:1

Then the ratio of their respective pressure is 1:1.
$PV=nRT=\frac{W}{M}RT$

$PM=\frac{W}{V}RT=dRT$

$\frac{P}{dT}=\frac{R}{M}=$ constant
$\frac{P}{dT}=\frac{P^{\prime }}{d^{\prime }{T}^{\prime }}$

$\frac{P}{P^{\prime }}=\frac{dT}{d^{\prime }{T}^{\prime }}$

$\frac{P}{P^{\prime }}=\frac{d}{d^{\prime }}\times \frac{T}{T^{\prime }}$
Densities of two gases are in the ratio 1:2
$\frac{d}{d^{\prime }}=\frac{1}{2}$

Their temperature is in the ratio 2:1

$\frac{T}{T^{\prime }}=\frac{2}{1}$
$\frac{P}{P^{\prime }}=\frac{d}{d^{\prime }}\times \frac{T}{T^{\prime }}$

$\frac{P}{P^{\prime }}=\frac{1}{2}\times \frac{2}{1}$

$\frac{P}{P^{\prime }}=\frac{1}{1}$

Therefore, the option is A.