Final answer:
To find the mass of potassium nitrate needed to generate the given volume of gas, calculate the moles of nitrogen and oxygen in the gas mixture using the ideal gas law. Use the stoichiometry of the reaction to determine the moles of potassium nitrate needed. Convert the moles of potassium nitrate to grams using its molar mass.
Step-by-step explanation:
In order to find the mass of potassium nitrate needed to generate the given volume of gas, we need to first determine the moles of nitrogen and oxygen in the gas mixture. From the given volumes, we can calculate the moles of each gas using the ideal gas law. Then, using the stoichiometry of the reaction N₂(g) + O₂(g) → 2NO(g), we can find the moles of potassium nitrate required. Finally, we can convert the moles of potassium nitrate to grams using its molar mass.
Step 1: Calculate the moles of nitrogen (N₂) and oxygen (O₂) using the ideal gas law,
n = PV/RT
Step 2: Use the stoichiometry of the reaction to determine the moles of potassium nitrate (KNO₃) needed.
Step 3: Convert the moles of KNO₃ to grams using its molar mass (74.5 g/mol for KNO₃). The mass of potassium nitrate needed is:
mass = moles × molar mass = ___ g