Two vessels A and B are of the same size and are at same temperature. A contains 1 ~g of hydrogen and B contains 1 ~g of oxygen. P_A and P_B are the pressures of the gases in A and B respectively, then \fracP_AP_B is:

Heat and Thermodynamics PYQ — JEE Main 2024 · 29 Jan · Shift 1 · Q75 with Solution

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Correct answer: D

For a gas in a vessel, $PV=nRT$

Since vessels $A$ and $B$ have:

we get $P \propto n$

So, $\frac{P_A}{P_B}=\frac{n_A}{n_B}$

Hydrogen gas is $\mathrm{H_2}$ , so its molar mass is $M_{H_2}=2\ \text{g/mol}$

Given mass = $1\,\text{g}$ , $n_A=\frac{1}{2}\,\text{mol}$

Oxygen gas is $\mathrm{O_2}$ , so its molar mass is $M_{O_2}=32\ \text{g/mol}$

Given mass = $1\,\text{g}$ , $n_B=\frac{1}{32}\,\text{mol}$

$\frac{P_A}{P_B}=\frac{n_A}{n_B}=\frac{\frac{1}{2}}{\frac{1}{32}}=\frac{1}{2}\times 32=16$

The correct option is: $\boxed{16}$

So, Option D is correct.