Final answer:
To produce 15 moles of oxygen gas from the decomposition of potassium chlorate, 10 moles of potassium chlorate are required according to the molar stoichiometry of the balanced chemical reaction.
Step-by-step explanation:
The decomposition of potassium chlorate (KClO3) produces potassium chloride (KCl) and oxygen gas (O2) based on the balanced chemical equation:
2 KClO3 (s) → 2 KCl (s) + 3 O2 (g)
From the equation, 2 moles of KClO3 produce 3 moles of O2. To find out how many moles of KClO3 are needed to produce 15 moles of O2, we set up a proportion:
(2 moles KClO3 / 3 moles O2) = (x moles KClO3 / 15 moles O2)
Solving this for x gives us:
x = (2 moles KClO3 / 3 moles O2) * 15 moles O2
x = 10 moles KClO3
Therefore, 10 moles of potassium chlorate are needed to produce 15 moles of oxygen gas. This calculation is based on molar stoichiometry and the balanced chemical equation provided.