terephthalic acid used in the production of polyester fibers and films is composed of carbon, hydrogen, and oxygen. When 0.6943 h og acid is subjected to combustion analysis it produced 1.471 g CO2 and 0.391 g h20. What is its empirical and molecular formula if its molar mass is 172 g/mol

Empirical formula: C₂H₃O

Molecular formula: C₈H₁₂O₄

Explanation:

After the reaction, all the carbon will form CO₂ and all the hydrogen will form H₂O, so the number of moles of each element will be the same as in the terephthalic acid. Knowing the molar masses: C = 12 g/mol, H = 1 g/mol, and O = 16 g/mol. CO₂ = 12 + 2x16 = 44 g/mol, H₂O = 2x1 + 16 = 18 g/mol.

The number of the moles of the compounds are the mass divided by the molar mass so:

CO₂ = 1.471/44 = 0.0334 mol

H₂O = 0.391/18 = 0.0217 mol

There is 1 mol of C in each mol of CO₂, so there is 0.0334 mol of C.

There are 2 mol of H in each mol of H₂O, so there is 0.0434 mol of H.

Which are the same of in the acid. The masses of the compounds are:

mC = 0.0334x12 = 0.400 g

mH = 0.0434x1 = 0.0434 g

mO = 0.6943 - (0.4 + 0.0434) = 0.2509 g

The number of moles of O is: 0.2509/16 = 0.0157 mol

To know the empirical formula, let's divide the number of moles of the elements for the samllest: 0.0157 mol

C = 0.0334/0.0157 = 2

H = 0.0434/0.0157 = 3

O = 0.0157/0.0157 = 1

The empirical formula is C₂H₃O

The molecular formula will be the empirical multiplied by a factor (n):

n (C₂H₃O), so the molar mass will be: nx (2x12 + 3x1 + 16) = 172

43n = 172

n = 4

So the molecular formula is 4x (C₂H₃O) = C₈H₁₂O₄.