Question

Two separate bulbs contain ideal gases $A$ and $B$. The density of $A$ is twice as that of gas $B$. The molecular mass of gas $A$ is half as that of $B$. If two gases are at same temperature, the ratio of the pressure of $A$ to that of $B$ is:

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

Answer 1

The correct option is C $4$

To find density :-

$PM=DRT$

$\therefore D=\frac{PM}{RT}$

Given :-

$D_1=2D_2$ $|$ $M_1=\frac{1}{2}{M}_2$ $|$ $T_1=T_2$

$\frac{D_1}{D_2}=2$ $|$ $\frac{M_1}{M_2}=\frac{1}{2}$

Now $D=PM$ $(\because R\&T$ are constant)

$\frac{D_1}{D_2}=\frac{P_1{M}_1}{P_2{M}_2}$

$2=\frac{P_1}{P_2}\times \frac{1}{2}$

$2\times 2=\frac{P_1}{P_2}$

$\therefore \frac{P_1}{P_2}=4$

Ans is C) 4