help please???

Question

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, H, and O. Combustion of 19.81 mg terephthalic acid produces 41.98 mg CO2 and 6.45 mg H2O. If 0.242 mol of terephthalic acid has a mass of 40.2 g, determine the molecular formula for terphthalic acid.


SoI tried to figure out if 19.81mg = 41.98 mg CO2 and = 6.45 mg H2O then it's 2.119131752 times the acid for CO2 and 0.3255931348 times for H2O then 1 mol = 166.1157025g
then CO2 = 30% C and 70% O
and H2O = 11% H and 88% O
Then it's C9H6O18
But that's not correct can you help me?
What is the answer? and can you explain how you got it please.

Answer 1

You started with 19.81/40.2 * .242 = 0.11925 mm of T. acid (mm = millimole).

That produced 41.98 / 44 = 0.9541mm of CO2 and 6.45 / 18 = 0.3583 mm H2O. If you had started with 1 mm of T. acid, that would produce 0.9541/0.11925 = 8.00 mm CO2, which contains 8.00 mm of carbon. Therefore T. acid has 8 carbon atoms. Similarly, it would produce 0.3583/0.11925 = 3.00 mm of H20, which contains 6.00 mm of hydrogen, so T. acid has 6 hydrogen atoms, giving a partial formula

C8H6

The molecular mass of that portion is 8*12 + 6 = 102. The mol mass of T. is 40.2 g / 0.242 mole = 166. The remaining mass must be oxygen, or a total mol. mass of 64 for the oxygen, which has an atomic mass of 16, so this is 4 oxygen atoms, giving the formula

C8H6O4

Answer 2

it's too complicated..............