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

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 text1.5 times the density of B . The ratio of molecular weights of A and B is (A) (3/4) (B) 2  (C) (1/2) (D) (2/3)

Tardigrade Admin · Accepted Answer

PA= (ρ A R T/MA), PB= (ρ B R T/MB) ⇒ (PA/PB)= (ρ A/ρ B) (MB/MA) ⇒ (3/2)(MB/MA)=2 So, (MA/MB) =(3/4)

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 $1.5$ times the density of $B$ . The ratio of molecular weights of $A$ and $B$ is

$\frac{3}{4}$

$2$

$\frac{1}{2}$

$\frac{2}{3}$

$P_{A} = \frac{ρ _{A} RT}{M _{A}}, P_{B} = \frac{ρ _{B} RT}{M _{B}}$
$\Rightarrow \frac{P _{A}}{P _{B}} = \frac{ρ _{A}}{ρ _{B}} \frac{M _{B}}{M _{A}}$
$\Rightarrow \frac{3}{2} \frac{M _{B}}{M _{A}} = 2$
So, $\frac{M _{A}}{M _{B}} = \frac{3}{4}$

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 1.5 times the density of B . The ratio of molecular weights of A and B is

43​

2

21​

32​

PA​=MA​ρA​RT​,PB​=MB​ρB​RT​ ⇒PB​PA​​=ρB​ρA​​MA​MB​​ ⇒23​MA​MB​​=2 So, MB​MA​​=43​

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 $1.5$ times the density of $B$ . The ratio of molecular weights of $A$ and $B$ is

$\frac{3}{4}$

$2$

$\frac{1}{2}$

$\frac{2}{3}$

$P_{A} = \frac{ρ _{A} RT}{M _{A}}, P_{B} = \frac{ρ _{B} RT}{M _{B}}$
$\Rightarrow \frac{P _{A}}{P _{B}} = \frac{ρ _{A}}{ρ _{B}} \frac{M _{B}}{M _{A}}$
$\Rightarrow \frac{3}{2} \frac{M _{B}}{M _{A}} = 2$
So, $\frac{M _{A}}{M _{B}} = \frac{3}{4}$