Program Area

This activity provides practice in graphing, working with fractions and powers, and manipulative skills with numbers. It may be used in the Grade 9 Mathematics, Science and Technology Program, or in the advanced and general Grade 10 Mathematics courses as a supplement to any section on number manipulation skills, graphing, fractions, powers, or as enrichment material.

Learning Outcomes

Teaching, learning and evaluation will focus in the student's ability to:

• Practice number skills, operations with fractions, powers, and graphing;
• Learn about how exhaust gases are cleaned;
• Learn to do calculations which involve reducing exhaust gas emissions;
• Learn about the term "acid rain" and discuss some of the harmful effects.

Classroom Development

1. Use this activity as a supplement to sections on number skills, fractions, powers, or as enrichment.
2. A discussion of acid rain should precede work on this activity.
3. Point out to students that removal of contaminants from exhaust gas is an example of exponential decay. Students should also note that removal of all contaminants is not possible and that an acceptable level has to be determined. Discuss what is meant by "acceptable."
4. Students should do the questions on the attached pages. Working cooperatively in groups would be appropriate.
5. Have the solutions presented by groups of students and use these solutions to encourage discussion of acid rain and air pollution in general.

Timing

Allow 2 periods (70 min)

Resources

This activity was adapted from Frank Ebos, Paul Zolis. Math Matters, Book 4. Scarborough: Nelson, 1988. Page 83.

Cross-disciplinary Links

The introduction to acid rain should be an integral part of this lesson in the Grade 9 program. This introduction could be provided by the science teacher if this activity is done at the Grade 10 level. Communicative skills are an important part of this lesson.

Student Activities

Air Pollution

Emissions from vehicles and from industrial plants get mixed with the air that we breathe. Two of the more common pollutants in the air are nitrogen dioxide and sulphur dioxide. The rain dissolves these and other substances and they come back to the earth in the form of "acid rain." This rain falls everywhere and causes environmental damage.

To help prevent this, cars and factories have devices which "scrub" their exhaust. These scrubbers remove some of the pollutants from the exhaust before they can enter the atmosphere and produce acid rain.

The concentration of pollutants in exhaust is measured in parts per million (ppm).

Doing the questions that follow will help you to increase your understanding of the mathematics of cleaner air.

1. A scrubber unit installed in a factory removes half of the pollutants each time the exhaust gas passes through it. Untreated exhaust contains 2000 ppm of contaminants.

   (a) Complete the table of values below which show values of

   n - number of times the exhaust gas passes through the scrubber

   and

   c - the concentration in ppm of contaminants that remain in the exhaust gas.

   n	1	2	3	4	5	6
   c

   
   

    

    

   (b) Plot the ordered pairs from the table of values in part (a). Number of times breathed on the x axis and concentration in ppm on the y axis shown below, after you have looked back at the example on the previous page.

   (c) Could all of the contaminants in the exhaust gas be removed in this way? Explain.

    
   

2. A company installed a scrubber which removes one-third of the pollutants each time exhaust gas passes through it. Untreated exhaust contains 1500 ppm of sulphur dioxide. In its annual report the company states that by passing exhaust gas through the scrubber three times, all of the sulphur dioxide will be removed. You believe this statement to be false. Write a short letter to the company which explains and corrects its error.

    

3. A scrubber removes two-thirds of the pollutants each time exhaust gas passes through it. Before treatment, the gas contains 1200 ppm of contaminants.
   (a) What is the concentration of contaminants in the gas after it has passed through the scrubber 2 times?

   (b) After the gas has passed through the scrubber 2 times, what fraction of the contaminants has been removed and what fraction remains?
   
   

    

4. Before exhaust gas can be released into the air, it must contain less than 200 ppm of sulphur dioxide. If untreated exhaust contains 3600 ppm of sulphur dioxide and if a scrubber can remove half of the pollutants each time the gas passes through it, how many times should the gas be treated before it is released?  

    

5. A manufacturing plant passes its exhaust gas through three cleaning stations before it is released into the atmosphere. Station A removes three-quarters of the pollutants, station B removes one-third of the pollutants, and station C removes half of the pollutants.

    

   (a) What fraction of the pollutants will be removed after the gas passes through all three stations?

   (b) Does it matter in which order the gas passes through the three stations? Explain.

   (c) If untreated exhaust contains 4500 ppm of pollutants, what will be the concentration of pollutants after the gas has been cleaned by all three stations?

   (d) A problem with station B is causing it to work at 50% efficiency. What percent of the pollutants will be emitted into the atmosphere after treatment by all three stations?