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  4. Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B . Under such conditions, the density of A is found to be text1.5 times the density of B . The ratio of molecular weights of A and B is

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Q. Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature, the pressure of $A$ being twice that of $B$ . Under such conditions, the density of $A$ is found to be $\text{1.5}$ times the density of $B$ . The ratio of molecular weights of $A$ and $B$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$P_{A}= \, \frac{\rho _{A} R T}{M_{A}}, \, P_{B}= \, \frac{\rho _{B} R T}{M_{B}}$
$\Rightarrow \, \frac{P_{A}}{P_{B}}= \, \frac{\rho _{A}}{\rho _{B}} \, \frac{M_{B}}{M_{A}}$
$\Rightarrow \frac{3}{2}\frac{M_{B}}{M_{A}}=2\,$
So, $\frac{M_{A}}{M_{B}} \, =\frac{3}{4}$