Complete and Incomplete Combustion of Isooctane?

Question

I have this chemistry problem that I have been trying to answer since last week, but still I can't figure it out. Please help!

Petroleum based fuels like gasoline consist mainly of hydrocarbons, compounds containing only hydrogen and carbon. One of the compounds in gasoline is isooctane, C8H18. When burned in a car's engine, some isooctane conbusts completely to form carbon dioxide and water, as shown in equation (1), and some combusts incompletely to form carbon monoxide and water, as shown in equation (2).

(1) 2 C8H18 + 25 O2 --> 16 CO2 + 18 H2O

(2) 2 C8H18 + 17 O2 --> 16 CO + 18 H2O

If 50.0 g of isooctane burns to produce 221.2 g of total gaseous products ( a mixture of CO2, CO, and H2O), determine the percent by mass of isooctane that reacts by complete combustion.

Answer 1

Step 1.) Find out how many moles of isooctane you have.
1 mole of C8H18 =
C * 8 + H * 18
12 * 8 + 18 = 96 + 18 = 114 g.
50 / 114 = 0.43859649 moles.

Step 2.) Define the difference between complete and incomplete combustion. In this case, complete combustion of 2 moles of C8H18 incorporates 16 more moles of Oxygen than incomplete combustion does.

Step 4.) Find out the weight of the byproducts if you have 0% complete combustion.
0% - 2 moles of C8H18 produce:
16 (12+16) + 18 (2 + 16) = 16 (28) + 18 (18) = 448 + 324 = 772

thus 1 mole produces 386 g total products.
and 0.43859649 moles of C8H18 produces 169.29824514g total products.

Step 4: Take the difference in weight between 0% complete combustion, and your actual weight of products, then convert that to moles of Oxygen.
221.2g - 169.3g = 51.9g in extra oxygen

51.9g = 3.24375 moles of Oxygen.

Step 5: Divide the difference of your answer in step 4 with the moles of oxygen from 100% complete combustion:

2 moles of C8H18 produces 16 extra moles of Oxygen when completely burned, thus 0.43859649 moles of C8H18 produces 3.50877192 moles of Oxygen.

3.24375 / 3.50877192 moles = 92.446875% complete burn.

Check:
0.43859649 * .92446875 =
.4054687 moles of complete burn + .03312779 moles of incomplete burn.

Incomplete burn: 1 mole produces 386 g total products.
.03312779 moles produces 12.78732694 g total products

Complete burn: using the equation for incomplete burn: 2 mole produces 772g total products (from incomplete) + 16 moles of oxygen (difference between complete and incomplete) (16 * 16 = 256) = 1028g.
thus 1 mole produces 514g.
.4054687 moles produces 208.7g total products

208.4109118 + 12.78732694 = 221.19823874g = 221.2g.