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?

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.

Well, let's break it down, shall we? The decomposition of potassium chlorate produces one mole of oxygen gas for every mole of potassium chlorate. So, to produce 15 moles of oxygen gas, you would need 15 moles of potassium chlorate. It's like a perfect match, they go hand in hand, or in this case, atom in atom. The oxygen gas would thank the potassium chlorate with a big "O2Mg, you're the best!"

To determine the number of moles of potassium chlorate needed to produce 15 mol of oxygen gas, we need to use the balanced chemical equation for the decomposition of potassium chlorate:

2KClO3 -> 2KCl + 3O2

From the balanced equation, we can see that 2 moles of potassium chlorate produce 3 moles of oxygen gas.

Using a proportion, we can set up the following equation:

2 moles KClO3 / 3 moles O2 = X moles KClO3 / 15 moles O2

Cross-multiplying, we have:

2 * 15 = 3 * X

30 = 3X

Dividing both sides by 3, we get:

X = 10

Therefore, 10 moles of potassium chlorate are needed to produce 15 moles of oxygen gas.

To find out how many moles of potassium chlorate are needed to produce 15 mol of oxygen gas, we need to use the balanced chemical equation for the decomposition reaction.

The balanced chemical equation for the decomposition of potassium chlorate is:
2 KClO3 -> 2 KCl + 3 O2

From the balanced equation, we can see that for every 2 moles of KClO3, we produce 3 moles of O2.

So, to find out how many moles of KClO3 are needed, we can use the following equation:

moles of KClO3 = (moles of O2) x (moles of KClO3 / moles of O2)

Substituting the given values:

moles of KClO3 = 15 mol x (2 mol KClO3 / 3 mol O2)

Calculating this gives us:

moles of KClO3 = 10 mol

Therefore, to produce 15 mol of oxygen gas, we need 10 moles of potassium chlorate.