Final answer:
To find the mass of potassium nitrate needed, calculate the moles of N₂ and O₂ using the ideal gas law, then apply stoichiometry based on the chemical equation(s) involving KNO₃ to produce N₂ and O₂.
Step-by-step explanation:
To calculate the mass of potassium nitrate (KNO₃) needed to generate 155.0 L of gas composed of 107.0 L of N₂ and 48.0 L of O₂ at 0.720 atm and 289 K, we need to first use the ideal gas law to determine the number of moles of N₂ and O₂ produced. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in kelvins.
For N₂:
n = (P * V) / (R * T) = (0.720 atm * 107.0 L) / (0.0821 L·atm/mol·K * 289 K)
For O₂:
n = (P * V) / (R * T) = (0.720 atm * 48.0 L) / (0.0821 L·atm/mol·K * 289 K)
Once the moles of each gas are calculated, you would then use stoichiometry to find the amount of KNO₃ needed to react to produce these quantities of N₂ and O₂ based on the balanced chemical equation(s) given.