Find Moles of O2 produced:
48g of O2 * 1mol/32grams O2 = 1.5 moles of 02
Mole Ratio to get moles of KClO3 needed to produce 1.5 moles of O2
1.5 moles of 02 * 2 mol KCLO3/3 mol O2 = 1 mol of KClO3 produced from 48 grams of O2
Convert Moles to grams:
1 mol of KClO3 = 122.5 grams KClO3
I think the key is to realize its a decomposition reaction, and getting the correct balanced equation. The rest is just stoichiometry, except normally you're finding the grams of products produced rather than the grams of reactants needed to produce the products.
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