Final answer:
The mass of potassium nitrate needed can be calculated using the stoichiometry of the reaction and the ideal gas law equation. First, balance the equation and determine the moles of gas produced using the ideal gas law equation. Then, use the moles of the product and the molar mass of potassium nitrate to calculate the mass.
Step-by-step explanation:
To determine the mass of potassium nitrate needed to generate the given volume of gas, we can use the stoichiometry of the reaction and the ideal gas law equation.
First, let's balance the equation:
2N₂(g) + O₂(g) → 2NO(g)
Based on the balanced equation, we can see that 2 moles of N₂ produce 2 moles of NO, and 1 mole of O₂ is required.
Now, we can use the ideal gas law equation, PV = nRT, to calculate the moles of gas produced:
n = (PV) / (RT)
Substituting the given values (V = 209.0 L, P = 0.720 atm, T = 291 K, and R = 0.0821 L·atm/(mol·K)) into the equation, we can solve for n.
Once we have the moles of NO, we can use the molar mass of NO (46.0 g/mol) to calculate the mass of potassium nitrate needed using the stoichiometry of the reaction.
Let's calculate:
n(N₂) = (P(N₂) * V) / (R * T)
n(NO) = 2 * n(N₂)
Mass of KNO₃ = n(NO) * molar mass of KNO₃