This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
To solve this problem, we need to use stoichiometry based on the given balanced chemical equation: 4KNO_3(s) → 2K_2O(s) + 2N_2(g) + 5O_2(g) We are given that 56.6 kg of oxygen (O_2) is produced. First, we need the molar masses: Molar mass of O_2 = 2 × 16.00 g/mol = 32.00 g/mol Molar mass of KNO_3 = 39.10 g/mol (K) + 14.01 g/mol (N) + (3 × 16.00 g/mol (O)) = 101.11 g/mol a) Moles of KNO_3 must be heated: Step 1: Convert the mass of oxygen from kilograms to grams. Mass of O_2 = 56.6 kg × 1000 g1 kg = 56600 g Step 2: Calculate the moles of oxygen produced. Moles of O_2 = Mass of O_2Molar mass of O_2 = 56600 g32.00 g/mol = 1768.75 mol Step 3: Use the mole ratio from the balanced equation to find the moles of KNO_3. From the equation, 4 moles of KNO_3 produce 5 moles of O_2. Moles of KNO_3 = 1768.75 mol O_2 × 4 mol KNO_35 mol O_2 = 1415 mol KNO_3 Rounding to three significant figures: 1.42 × 10^3 mol KNO_3 b) Grams of KNO_3 must be heated: Step 1: Use the moles of KNO_3 calculated in part (a) and its molar mass to find the mass in grams. Mass of KNO_3 = Moles of KNO_3 × Molar mass of KNO_3 Mass of KNO_3 = 1415 mol × 101.11 g/mol = 143080.65 g Rounding to three significant figures: 1.43 × 10^5 g KNO_3 What's next?