Q.27 - An Introduction to General, Organic, and Biological Chemistry

Question

The plastic known as PETE (polyethyleneterephthalate) is used to make plastic soft drink bottles and containers for salad dressing, shampoos, and dishwashing liquids. PETE is made from terephthalic acid and ethylene glycol. Today, PETE is the most widely recycled of all plastics. In one year, $1.5\times {10}^9\mathrm{lb}$ of PETE is recycled. After it is separated from other plastics, PETE can be used in polyester fabric, doormats, and tennis ball containers. The density of PETE is 1.38g/ml.

a. Draw the line-angle formula for the ester formed from one molecule of terephthalic acid and one molecule of ethylene glycol.

b. Draw the line-angle formula for the product formed when a second molecule of ethylene glycol reacts with the ester you drew in part a.

c. How many kilograms of PETE is recycled in one year?

d. What volume, in litres, of PETE is recycled in one year?

e. Suppose a landfill holds $2.7\times {10}^7$L of recycled PETE. If all the PETE that is recycled in a year were placed instead in landfills, how many would it fill?

Step-by-Step Solution

Answer

a. 

   

b. 

 

c. $6.8\times {10}^8\mathrm{kg}$

d. $4.9\times {10}^8\mathrm{L}$

e. $4.63\times {10}^8\mathrm{L}$

Part (a) Step 1: Given Information

The density of PETE is $1.38$g/ml.

Drawing the line-angle formula for the ester formed from one molecule of terephthalic acid and one molecule of ethylene glycol.

Part (a) Step 2: Explanation

The line-angle formula for the ester is formed from one molecule of terephthalic acid and one molecule of ethylene glycol. 

Part (b) Step 1: Given Information

Drawing the line-angle formula for the product formed when a second molecule of ethylene glycol reacts with the ester in part a. 

Part (b) Step 2: Explanation

The line-angle formula for the product is formed when a second molecule of ethylene glycol reacts with the ester in part a. 

Part (c) Step 1: Given Information

Calculating the kilograms of PETE is recycled in one year.

Part (c) Step 2: Explanation

Given,

Amount of PETE is recycled in one year = $1.5\times {10}^9\mathrm{lb}$

we know,

$1\mathrm{lb}=0.4535\mathrm{kg}$

$$\begin{gathered} =1.5\times {10}^9\times 0.4535\mathrm{kg} \\ =6.8\times {10}^8\text{kg} \end{gathered}$$

Hence $6.8\times {10}^8\text{kg}$of PETE is recycled in one year

Part (d) Step 1: Given Information

The density of PETE is $1.38$g/ml.

Calculating the volume, in litres, of PETE is recycled in one year.

Part (d) Step 2: Explanation

Given,

Density = $1.38$ g/ml

Volume = $\frac{\text{mass}}{\text{density}}$

$V=\frac{6.8\times {10}^8\mathrm{kg}}{1.38\mathrm{kg}/\mathrm{L}}=4.9\times {10}^{8}L$

Hence volume is $4.9\times {10}^{8}L$

Part (e) Step 1: Given Information

A landfill holds $2.7\times {10}^7$L of recycled PETE.

Calculating the volume in landfills.

Part (e) Step 2: Explanation

We know,

A landfill holds $2.7\times {10}^7$L of recycled PETE. 

The volume of PETE recycled in one year is $4.9\times {10}^8\mathrm{L}$

The volume in landfills is,

$$\begin{gathered} =4.9\times {10}^8\mathrm{L}-2.7\times {10}^7\mathrm{L} \\ =4.63\times {10}^8\mathrm{L} \end{gathered}$$

Hence the volume in landfills is $4.63\times {10}^{8}L$