Question

The density of a gas $A$ is twice that of gas $B$ at the same temperature. The molecular weight of gas $B$ is twice that of gas $A$. The ratio of pressures of gases $A$ and $B$ will be:

• A. $1:6$
• B. $1:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is C $4:1$

Given, $\frac{\text{density of gas A}}{\text{density of gas B}}=\frac{\left(d_A\right)}{\left(d_B\right)}$ = $\frac{2}{1}$;
$\frac{\text{molecular mass of gas A}}{\text{molecular mass of gas B}}=\frac{\left(M_A\right)}{\left(M_B\right)}$ = $\frac{1}{2}$
$PM=nRT$
where $P$ = pressure of the gas A and B
dividing,
$=\frac{P_A}{P_B}\times \frac{M_A}{M_B}=\frac{d_A}{d_B}\times \frac{RT}{RT}$
$=\frac{P_A}{P_B}\times \frac{1}{2}=2$
$\frac{P_A}{P_B}=\frac{4}{1}$