The Decomposition of potassium chlorate, KClO3, into KCl and O2 is used as a source of oxygen in the laboratory. How many moles of potassium chlorate are needed to produce 15 mol of oxygen gas?

Answer 1

2KClO3 ==> 2KCl + 3O2
First you balance the equation as I've done above. Then you let the coefficients convert mols of any one material into any other material. You know you have 15 mols O2. Convert that to mols KClO3 using the coefficients as follows:
15 mols O2 x (2 mols KClO3/3 mols O2) = 15 x 2/3 = ?
Notice that mols O2 in the numerator cancel with mols O2 in the denominator which leaves mols KClO3 remaining and that's what you are looking for. Canceling of units and leaving units you want are how you know that the fraction KClO3/O2 is set up that way and NOT O2/KClO3.