Two vessels A and B are of the same size and are at same temperat… - Vidyadip

MCQ

Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains $1 \mathrm{~g}$ of hydrogen and $B$ contains $1 \mathrm{~g}$ of oxygen. $\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are the pressures of the gases in $A$ and $\mathrm{B}$ respectively, then $\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}$ is:

✓
$16$
B
$8$
C
$4$
D
$32$

✓

Answer

Correct option: A.

$16$

a
$\frac{\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}} R \mathrm{RT}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}} \mathrm{RT}_{\mathrm{B}}}$

Given $V_A=V_B$

And $T_{\mathrm{A}}=T_{\mathrm{B}}$

$\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}}}$

$\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{1 / 2}{1 / 32}=16$

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