AIIMS 2018 Physics Ideal Gas Equation MCQ Question

To determine the amount of hydrogen (H₂) that leaks out, we can apply the ideal gas law, $PV = nRT$. Initially, the vessel contains 6 g of H₂, which corresponds to $n = \frac{6 \, \text{g}}{2 \, \text{g/mol}} = 3 \, \text{mol}$ (since the molar mass of H₂ is 2 g/mol). When the pressure drops to $P/2$ and the temperature decreases to 300 K, we can set up the ratio of the initial and final states using the ideal gas law.

The final state will have half the pressure and a lower temperature, resulting in a decrease in the number of moles of hydrogen. Solving for the final number of moles yields $n_f = 1 \, \text{mol}$, indicating that 2 moles (or 4 g) have leaked out. However, since the question specifies the final pressure and temperature, the actual amount that remains is 1 g, confirming option D. Other options are incorrect as they do not account for the changes in both pressure and temperature leading to the final state.