What is the empirical formula of the polyethylene? Polyethylene is a polymer of only carbon and hydrogen.  If 2.300 g of the polymer is burned in the oxygen it produces 2.955 g H2O and 7.217 g CO2.  What is the empirical formula of the polyethylene?

So my method for this problem is 
1) find the mass of carbon from CO2
2) find mass of H from H20
3) Find mass of O by subtracting 
4) cont. answer with formula from % composition  

Therefore:  

(7.217 g x 1mole x 1 mole Carbon x 12 grams) /  44g CO2 = 1.96 g
(2.955 g x 1mole x 2 mole Hydrogen x 1g)     /  18g H2O = .328 g

1.96g / 12g = 0.163
.328  / 16g = .0205 (smallest #)

.163 / .0205 = 8 Carbon
.0205 / .0205 = 1 Hydrogen

The answer is CH2 :/, but I am having a hard time finding out where I slipped :(
$1 \dfrac{\rm{mole(C)}}{\rm{mole(\ce{CO2})}}*\dfrac{7.217 ~\rm{g(CO2)}}{44.01 ~\rm g(\ce{CO2})/\rm{mole(\ce{CO2})}} = 0.1640 ~\rm{mole(C)}$

$2 \dfrac{\rm{mole(H)}}{\rm{mole(H2O)}}*\dfrac{2.955 ~\rm{g(H2O)}}{18.015 ~\rm g(\ce{H2O})/\rm{mole(\ce{H2O})}} = 0.3281~\rm{mole(H)}$

Since fewer moles of C, normalize on C

$\rm C = 1$

$\rm H = \dfrac{0.3281}{0.1640} = 2.000 $

So the empirical formula is $\ce{CH2}$