Final answer:
The number of moles of KNO₃ that reacted to produce 409.87 grams of K₂O cannot be accurately determined without the stoichiometric reaction equation. Once the equation is known, the mole ratio would be used to calculate the number of moles of KNO₃.
Step-by-step explanation:
The question relates to a stoichiometry calculation in chemistry to determine the amount of moles of KNO₃ that have reacted to produce a certain mass of K₂O. To solve it, we need to use the molar mass of K₂O and convert the given 409.87 grams of K₂O to moles. K₂O has a molar mass of 94.2 g/mol (39.10 g/mol for each K, and 16.00 g/mol for O). Dividing 409.87 g of K₂O by the molar mass of K₂O (94.2 g/mol) gives us the number of moles.
Thus, the calculation will be:
Number of moles = 409.87 g / 94.2 g/mol = 4.35 moles.
However, this is not the final answer since we need to consider the stoichiometry of the reaction that creates K₂O from KNO₃. Unfortunately, the reaction equation is missing in the question. If we had the equation, we would use it to find the mole ratio between K₂O and KNO₃, and use that ratio to find the number of moles of KNO₃ reacted. Without the reaction equation, we cannot provide an accurate answer.