Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. it contains only c, h, and o. combustion of 15.85 mg terephthalic acid produces 33.58 mg co2 and 5.16 mg h2o. if 0.250 mol of terephthalic acid has a mass of 41.5 g, determine the molecular formula of terephthalic acid. (type your answer using the format co2 for co2.)

Let x, y, and z be the number of carbon (C), hydrogen (H) and oxygen (O) of terephthalic acid. The combustion reaction of the given compound can be expressed as,

            CxHyOz + O2 --> CO2 + H2O

We are given that 0.250 mol of the acid is equal to 41.5 g. We calculate for the molar mass by dividing the mass by the number of moles.
                   M = (41.5 g)/ (0.250 mol) = 166 g/mol

Then, we calculate the number of moles of the given,
                     15.85 mg T acid / (41.5 g/0.250 mol) = 317/3320 mmol

Solving for the number of mols of CO2 in order to determine the number of mols of carbon,
                   (33.58 mg CO2) / (44 mg/1 mmol) = 0.763 mmol of CO2 (0.763 mmol of C)
 
For the number of mols of hydrogen from the produced water,
            (5.16 mg H2O) / (18 mg H2O/1 mmol) = 0.287 mmol H2O (0.573 mmol of H)
 
Solving for the amount of oxygen from the terephthalic acid,
    15.85 mg - (0.763 mmol C)(12 mg/1 mmol C) - (0.573 mmol H)(1 mg H/1 mmol H) 
          = 6.121 mg O

   number of mols of O = (6.121 mg O)(1 mmol O/16 mg O)
                                     = 0.383 mmol O

Thus, the empirical formula is,
               C0.763H0.573O0.383

Dividing the numbers by 0.383
                 C2H(3/2)O
Eliminating the fraction,
                    C₈H₆O₄