AIIMS 2018 Physics Ideal Gas Equation MCQ Question

To determine how much hydrogen (H₂) leaks out, we can use the ideal gas law $PV = nRT$. Initially, the number of moles of hydrogen is calculated as $n = \frac{m}{M} = \frac{6 \, \text{g}}{2 \, \text{g/mol}} = 3 \, \text{mol}$. When the pressure drops to $P/2$ and the temperature decreases to 300 K, we can find the final number of moles using the ideal gas law, which results in $n' = \frac{(P/2)V}{R \cdot 300}$. This gives $n' = 1.5 \, \text{mol}$, indicating that 1.5 moles (or 3 g) of hydrogen have leaked out, leaving 3 g remaining, thus confirming that 3 g of hydrogen has escaped.

Options A (2 g), B (3 g), and D (1 g) are incorrect because they do not account for the correct final number of moles based on the changes in pressure and temperature, leading to an inaccurate calculation of the mass of hydrogen that has leaked.