Question

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only , , and . Combustion of 50.20 mg terephthalic acid produces 106.4 mg and 16.34 mg . If 0.170 mole of terephthalic acid has a mass of 28.2 g, determine the molecular formula for terephthalic acid.

Answer 1

Answer:

The molecular formula of Terephthalic acid = $C_8H_{6}O_4$

Explanation:

Taking incomplete things from the original source and assuming,

Mass of water obtained = 16.34 mg

1 mg = 10⁻³ g

Mass of water obtained = 16.34 ×10⁻³ g

Molar mass of water = 18 g/mol

Moles of $H_2O$ = 16.34 ×10⁻³ g /18 g/mol = 0.000907778 moles

2 moles of hydrogen atoms are present in 1 mole of water. So,

Moles of H = 2 x 0.000907778 = 0.0018156 moles

Molar mass of H atom = 1.008 g/mol

Mass of H in molecule = 0.0018156 x 1.008 = 0.00183 g

Mass of carbon dioxide obtained = 106.4 mg

1 mg = 10⁻³ g

Mass of carbon dioxide obtained = 106.4 ×10⁻³ g

Molar mass of carbon dioxide = 44.01 g/mol

Moles of $CO_2$ = 106.4 ×10⁻³ g  /44.01 g/mol = 0.002418 moles

1 mole of carbon atoms are present in 1 mole of carbon dioxide. So,

Moles of C = 0.002418 moles

Molar mass of C atom = 12.0107 g/mol

Mass of C in molecule = 0.002418 x 12.0107 = 0.029037 g

Given that the Terephthalic acid only contains hydrogen, oxygen and carbon. So,

Mass of O in the sample = Total mass - Mass of C  - Mass of H

Mass of the sample = 50.20 mg

1 mg = 10⁻³ g

Mass of the sample = 50.20 ×10⁻³ g

Mass of O in sample = 50.20 ×10⁻³ g - 0.029037 g  - 0.00183 g  = 0.019333 g

Molar mass of O = 15.999 g/mol

Moles of O  = 0.019333 / 15.999  = 0.0012083 moles

Taking the simplest ratio for H, O and C as:

0.0018156 : 0.0012083 : 0.002418

= 3 : 2 : 4

The empirical formula is = $C_4H_3O_2$

Molecular formulas is the actual number of atoms of each element in the compound while empirical formulas is the simplest or reduced ratio of the elements in the compound.

Thus,  

Molecular mass = n × Empirical mass

Where, n is any positive number from 1, 2, 3...

Mass from the Empirical formula = 4×12 + 8×1 + 16×2= 88 g/mol

Given, Mass = 28.2 g

Moles = 0.170 moles

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

Thus,

$0.170\ mole= \frac{28.2\ g}{Molar\ mass}$

Molar mass = 165.8824 g/mol

So,  

Molecular mass = n × Empirical mass

165.8824 = n × 88

⇒ n = 2

The molecular formula of Terephthalic acid = $C_8H_{6}O_4$