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
Question
The closed containers of the same capacity and at the same temperature are filled with 44g of $H_2$ in one and 44g of $CO_2$ in the other. If the pressure of carbon dioxide in the second container is 1 atm. That of hydrogen in the first container would be :
💡 Solution & Explanation
# Solution **Step 1: Calculate moles of each gas** For $H_2$: Molar mass = 2 g/mol $$n_{H_2} = \frac{44}{2} = 22 \text{ mol}$$ For $CO_2$: Molar mass = 44 g/mol $$n_{CO_2} = \frac{44}{44} = 1 \text{ mol}$$ **Step 2: Apply ideal gas law** Since both containers have: - Same volume ($V$) - Same temperature ($T$) Using $PV = nRT$, at constant $V$ and $T$: $$P \propto n$$ **Step 3: Find pressure ratio** $$\frac{P_{H_2}}{P_{CO_2}} = \frac{n_{H_2}}{n_{CO_2}} = \frac{22}{1} = 22$$ **Step 4: Calculate $P_{H_2}$** Given $P_{CO_2} = 1$ atm: $$P_{H_2} = 22 \times 1 = \boxed{22 \text{ atm}}$$ **Why this is correct:** The number of moles of gas determines pressure in a fixed volume at constant temperature. With 22 times more moles of $H_2$, its pressure must be 22 times higher than $CO_2$.