Question

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 $1.5\, times$ the density of $B$. The ratio of molecular weight of $A$ and $B$ is :

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. 2

Answer 1

The Correct Option is C

${{\rho }_{A}}=1.5{{\rho }_{B}}$
${{\rho }_{A}}=2{{\rho }_{B}}$

According to ideal gas equation, we have Pressure,$p=\frac{\rho RT}{M}$
, where M is molecular weight of ideal gas.
Such that, $\frac{p}{\rho }=\frac{RT}{M}\Rightarrow M=\frac{\rho RT}{p}$
where, R and T are constant.
So, $M\propto \frac{\rho }{p}$
$\Rightarrow \,\,\frac{{{M}_{A}}}{{{M}_{B}}}=\frac{{{\rho }_{A}}}{{{\rho }_{B}}}\times \frac{{{p}_{B}}}{{{p}_{A}}}=1.5\times \frac{1}{2}=0.75=\frac{3}{4}$