Question

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, H, and O. Combustion of 20.30 mg terephthalic acid produces 43.02 mg CO2 and 6.60 mg H2O. If 0.258 moles of terephthalic acid has a mass of 42.9 g, determine the molecular formula for terephthalic acid.

Answer 1

Step 1:

let in compound number of moles of C, H and O be x, y and z respectively

Number of moles of CO2 = mass of CO2 / molar mass CO2

= 0.04302/44

= 9.777*10^-4

Number of moles of H2O = mass of H2O / molar mass H2O

= 0.0066/18

= 3.667*10^-4

Since 1 mol of CO2 has 1 mol of C

Number of moles of C in CO2= 9.777*10^-4

so, x = 9.777*10^-4

Since 1 mol of H2O has 2 mol of H

Number of moles of H = 2*3.667*10^-4 = 7.333*10^-4

Molar mass of O = 16 g/mol

mass O = total mass - mass of C and H

= 0.0203 - 9.777*10^-4*12 - 7.333*10^-4*1

= 7.834*10^-3

number of mol of O = mass of O / molar mass of O

= 7.834*10^-3/16.0

= 4.896*10^-4

so, z = 4.896*10^-4

Divide by smallest:

C: 9.777*10^-4/4.896*10^-4 = 2

H: 7.333*10^-4/4.896*10^-4 = 1.5

O: 4.896*10^-4/4.896*10^-4 = 1

Multiply by 2 to get simplest whole number ratio:

C: 2*2 = 4

H: 1.5*2 = 3

O: 1*2 = 2

So empirical formula is:C4H3O2

Step 2:

number of mol = mass / molar mass

0.258 = 42.9 / molar mass

molar mass = 166.3 g/mol

Step 3:

Molar mass of C4H3O2,

MM = 4*MM(C) + 3*MM(H) + 2*MM(O)

= 4*12.01 + 3*1.008 + 2*16.0

= 83.064 g/mol

Now we have:

Molar mass = 166.3 g/mol

Empirical formula mass = 83.064 g/mol

Multiplying factor = molar mass / empirical formula mass

= 166.3/83.064

= 2

So molecular formula is:C8H6O4

Answer: C8H6O4