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Air
Pollution
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
- Use this
activity as a supplement to sections on number skills, fractions,
powers, or as enrichment.
- A discussion
of acid rain should precede work on this activity.
- 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."
- Students
should do the questions on the attached pages. Working cooperatively
in groups would be appropriate.
- 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.
- 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.
-
-
- (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.
-
- 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.
- 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?
-
- 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?
- 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?
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