How Do I Calculate the Correct Percent Composition of Oxygen in a Compound?

[limofunder]

Homework Statement

I am running an experiment in which I have a compound of SiO₂ Na₂ K₂O PbO I am trying to figure out the percent composition of oxygen given that the percent composition of the compound is:
46% SiO₂
5% Na₂
4% K₂O
and 45% PbO

Homework Equations

46% SiO₂
5% Na₂
4% K₂O
and 45% PbO

The Attempt at a Solution

So I figured given the previous percentages, the compound is made of
$$.46 SiO_2 * \frac{2 mol O }{1 mol SiO_2} + .04 K_2O * \frac{1 mol O}{1 mol K_2O} + .45 PbO * \frac{1 mol O}{1 mol PbO} = .46*2+.04+.45 = 1.41$$

but this gives me 141% oxygen composition, what am I doing wrong here? Its been a while since I took general chem (about 3 years ago) and my stoichiometry is not at its best right now.
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[limofunder]

would it be more correct to say that the percent composition of oxygen is:

$$0.46* \frac{2}{3}O + .04* \frac{1}{2}O+ 0.45* \frac{1}{2}O$$
= .5516 = 55.2%?

 

[limofunder]

or would it be easier if I do the calculation by breaking it down into atomic masses, add the total of oxygen mass divided by the total mass of the compound?

 

[limofunder]

thanks fellas, once again, couldn't have done it without yall.

 

[Borek]

$$.46 SiO_2 * \frac{2 mol O }{1 mol SiO_2} + .04 K_2O * \frac{1 mol O}{1 mol K_2O} + .45 PbO * \frac{1 mol O}{1 mol PbO} = .46*2+.04+.45 = 1.41$$

but this gives me 141% oxygen composition, what am I doing wrong here?

You are adding apples and oranges. Each of these oxides contains different amount of oxygen (mass of oxygen per mass of the oxide), you can't add them this way. As you have already (and correctly) noticed, that gives idiotic results (percentage above 100%).

Your last approach is correct. Think this way: SiO₂ is 46% of the substance. Assume you start with 100 g of the substance. How many grams of SiO₂? How many grams of O in these grams of SiO₂? (That's where the molar masses come into play).