Question

Soft drink bottles are made of polyethylene terephthalate (PET), a polymer composed of carbon, hydrogen, and oxygen. If 1.9022 g PET is burned in oxygen it produces 0.6585 g H₂O and 4.0216 g CO₂. What is the empirical formula of PET?

Answer 1

Let us find the mass of H from the given mass of H2O

The combustion reaction produces 0.6585 g H2O. From this, let's find mass of H

0.6585 g H2O * ( 1 mol H2O / 18.01 g H2O) * ( 2 mol H / 1 mol H2O) * ( 1.008 g H / 1 mol H ) = 0.0737 g H

The combustion reaction produces 4.0216 g CO2. From this, let's find mass of C

4.0216 g CO2 * ( 1 mol CO2/ 44.01 g CO2) * ( 1 mol C / 1 mol CO2) * ( 12.01 g C / 1 mol C) = 1.0975 g C

Mass of the compound = 1.9022 g

Mass of C & H = 1.0975 + 0.0737 = 1.1712 g

Mass of O = Mass of compound - Total mass of C & H

Mass of O = 1.9022 - 1.1712 = 0.731 g

Therefore we have

Mass of C = 1.0975 g

Mass of H = 0.0737 g

Mass of O = 0.731 g

Let's convert above values to moles

1.0975 g C * 1 mol C/ 12.01 g C = 0.09138 mol C

0.0737 g H * 1 mol H / 1.008 g H = 0.07312 mol H

0.731 g O * 1 mol O / 15.9998 g O = 0.04569 mol O

Now we divide each of the above mol by smallest mol value

0.09138 mol C/ 0.04569 mol : 0.07312 mol H / 0.04569 mol : 0.04569 mol O / 0.04569 mol

2.0 C : 1.6 H : 1 O

We have decimal value for H , we need to convert it to a whole number.

For this, we multiply the whole equation by such an integer, which would convert 1.6 to a whole number.

Given below are some possibilities

2 * [2 C : 1.6 H : 1 O ] = 4 C : 3.2 H : 2 O

3* [2.0 C : 1.6 H : 1 O ] = 6 C : 4.8 H : 3 O

4* [2.0 C : 1.6 H : 1 O ] = 8 C : 6.4 H : 4 O

5* [2.0 C : 1.6 H : 1 O ] = 10 C: 8 H : 5 O

From the above possibilities, we can say that integer 5 convert H to a whole number.

Therefore the correct ratio is

10 C : 8 H : 5 O

We write the coefficients in this ratio as subscripts to get the empirical formula

C₁₀H₈O₅

The empirical formula of PET is C₁₀H₈O₅