Final answer:
To calculate the theoretical yield of O₂, we need to determine the molar ratio between KClO₃ and O₂, convert the mass of KClO₃ to moles, use the mole ratio to find the moles of O₂, and convert the moles of O₂ to grams using its molar mass.
Step-by-step explanation:
To calculate the theoretical yield of O₂, we first need to determine the molar ratio between KClO₃ and O₂. From the balanced equation, we can see that 2 moles of KClO₃ produce 3 moles of O₂. Now we can convert the mass of KClO₃ to moles using its molar mass (122.55 g/mol).
Given that we have 47.5 g of KClO₃, we can calculate the moles of KClO₃:
Moles of KClO₃ = 47.5 g / 122.55 g/mol = 0.387 mol KClO₃
Next, we use the mole ratio to find the moles of O₂:
Moles of O₂ = 0.387 mol KClO₃ x (3 mol O₂ / 2 mol KClO₃) = 0.5815 mol O₂
Finally, we convert the moles of O₂ to grams using its molar mass (32.00 g/mol):
Mass of O₂ = 0.5815 mol O₂ x 32.00 g/mol = 18.57 g
Therefore, the theoretical yield of O₂ when 47.5 g of KClO₃ is completely decomposed is 18.57 g.