Final answer:
The question requires using stoichiometry and the ideal gas law to determine the mass of potassium nitrate needed to produce a given volume of nitrogen and oxygen gases at specific conditions.
Step-by-step explanation:
The question involves finding the mass of potassium nitrate that is needed to generate a specific volume of gas, composed of nitrogen and oxygen, under given conditions using chemical reactions. To solve this problem, you will need to use the stoichiometry of gaseous substances and apply the ideal gas law (PV=nRT) to determine the number of moles of gas produced. The stoichiometric coefficients from the balanced chemical reaction indicate the molar ratios of the reactants and products. By applying the gas law, you can find the moles of N₂ and O₂ gas, then backtrack using stoichiometry to determine the mass of potassium nitrate (KNO₃) needed for the reaction. This process requires a solid understanding of chemical reactions, stoichiometry, and the behavior of gases.