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Q.
The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A. What will be the ratio of the pressures acting on B and A?
$\frac{d}{p}=\frac{M}{RT}$
Let density of gas B be d.
$\therefore \quad$ density of gas A = 3d
and let molecular weight of A be M.
$\therefore \quad$ molecular weight of B = 2M
Since, R is gas constant and T is same for both gases, so
$p_{A}=\frac{d_{A}RT}{M_{A}}$ and $p_{B}=\frac{d_{B}RT}{M_{B}}$
$\frac{p_{B}}{p_{A}}=\frac{d_{B}}{d_{A}}\times\frac{M_{A}}{M_{B}}=\frac{d}{3d}\times\frac{M}{2M}=\frac{1}{6}$