Q.15.C.27 - An Introduction to General, Organic, and Biological Chemistry

Question

The plastic known as PETE (Polytethylenetetraphathalate) is used to make plastic bottles and containers for shampoo and dishwashing agents. PETE is made of terephthalic acid and ethylene glycol liquids. Today PETE is the most widely recycled plastic. In one year 1.5*10⁹ lb of PETE is recycled. After it is separated from other plastics, PETE can be used in polyester fabrics, door mats, and tennis ball containers. The density of PETE is 1.38 g/mL.

a. Draw the line angle formula for the center 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 enter you draw in part a.

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

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

e. Suppose a landfill holds 2.7*10⁷ L of recycled PETE. If all the PETE that is recycled in one year were placed instead in landfills, how many would fir?

Step-by-Step Solution

Answer

a.

b. 

c. The mass of PETE is $6.8\times {10}^3 \mathrm{kg}$.

d. The volume of PETE is $4.9\times {10}^8 \mathrm{L}$.

e. It will fit into 22 landfills.

Step 1: Part (a) Given information

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

Step 2: Part (a) Explanation

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

Step 1: Part (b) 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. 

Step 2: Part (b) Explanation

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

Step 1: Part (c) Given information

Calculating the kilograms of PETE is recycled in one year. 

Step 2: Part (c) explanation

 In one year 1.5*10⁹ lb of PETE is recycled. 

Thus, the conversion of lb into kg can be shown as follows:

$1 \mathrm{lb}=0.453 \mathrm{kg}$

Therefore, for 1.5*10⁹ lb, the conversion will take place like this:

$$\begin{gathered} 1.5\times {10}^9 \mathrm{lb}=0.453 \times 1.5\times {10}^9 \mathrm{kg} \\ =0.675\times {10}^9 \mathrm{kg} \\ \approx 6.8\times {10}^8 \mathrm{kg} \end{gathered}$$

Hence, the kilograms of PETE recycled in one year is 6.8*10⁸ kg .

Step 1: Part (d) Given information

The density of PETE is 1.38 g/ml.

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

Step 2: Part (d) Explanation

Density is defined as the ratio of mass over volume.

The density is given that is 1.38 g/ml. 

The mass of PETE is calculated in the above part i.e., 6.8*10⁸ kg 

Therefore, the volume can be calculated as:

$$\begin{gathered} \mathrm{Density}=\frac{\mathrm{mass}}{\mathrm{volume}} \\ \mathrm{volume}=\frac{\mathrm{mass}}{\mathrm{density}} \\ =\frac{6.8\times {10}^8 \cancel{\mathrm{kg}}}{1.38 \cancel{\mathrm{g}} {\mathrm{mL}}^{-1}}\times \frac{1 \cancel{\mathrm{g}}}{1000 \cancel{\mathrm{kg}}} \\ =0.00492\times {10}^8 \mathrm{mL} \\ =4.9\times {10}^5 \mathrm{mL}\approx 4.9\times {10}^8 \mathrm{L} \end{gathered}$$

Thus, the volume is 4.9*10⁸ L.

Step 1: Part (e) Given information

A landfill holds  2.7*10⁷ L of recycled PETE.

Calculating the volume in landfills.

Step 2: Part (e) Explanation

A landfill holds  2.7*10⁷ L of recycled PETE.

The volume is 4.9*10⁸ L that is recycled in one year.

Thus, the number of landfills can be given as:

$$\begin{gathered} \mathrm{Number} \mathrm{of} \mathrm{landfills}= 4.9\times {10}^8-2.7\times {10}^7 \\ =2.2\times 10=22 \mathrm{landfills} \end{gathered}$$