The closed containers of the same capacity and at the same temperature are filled with 44g of in one — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Solution **Step 1: Find the number of moles in each container** For $H_2$: $$n_{H_2} = \frac{44 \text{ g}}{2 \text{ g/mol}} = 22 \text{ mol}$$ For $CO_2$: $$n_{CO_2} = \frac{44 \text{ g}}{44 \text{ g/mol}} = 1 \text{ mol}$$ **Step 2: Apply ideal gas law** Since both containers have: - Same volume ($V$) - Same temperature ($T$) - Same capacity Using $PV = nRT$, we get: $$P = \frac{nRT}{V}$$ Therefore, pressure is directly proportional to the number of moles: $$\frac{P_{H_2}}{P_{CO_2}} = \frac{n_{H_2}}{n_{CO_2}}$$ **Step 3: Calculate pressure of hydrogen** $$\frac{P_{H_2}}{1 \text{ atm}} = \frac{22}{1}$$ $$P_{H_2} = 22 \text{ atm}$$ **Answer: The pressure of hydrogen in the first container is 22 atm** (Option C) The key insight is that at constant V and T, pressure depends only on the number of moles—even though $H_2$ and $CO_2$ have different molar masses, the 44g of $H_2$ contains 22 times more moles than 44g of $CO_2$, producing 22 times higher pressure.