
Purpose
Students gain an
appreciation for the partpermillion and partperbillion
units used to measure contaminant concentrations in the environment.
Students learn to calculate these ratios and analyze a sample
chemical spill to determine if cleanup action is necessary.


Background
Some toxic substances are
dangerous even in very small amounts. "Partpermillion" (ppm) and "partperbillion"
(ppb) are the units of measure scientists use to describe the concentration
of a hazardous substance or contaminant found within a large volume
of another substance. For instance, you could find 500 ppm of a pesticide
in a lake.
Expressing the amount of
contamination in ppm or ppb is measuring the concentration of the substance.
This way, a scientist can take a relatively small sample of water, from
the lake in our example, and measure the concentration of one or more
contaminants in that sample, then assume that the concentration is the
same in the whole lake without testing the entire lake.
For more information on
the science of detecting and measuring contamination, see the Suggested
Reading list found at the end of the HazEd materials. Other HazEd
materials that are related to this topic include Activity
7: Identifying Risks at a Superfund Site and Activity
9: Making Decisions About Hazardous Waste Cleanup.
Preparation

Gather the following
materials:
Procedure

Hand out the Student
Worksheet, The Numbers Game, and
have the students take the quiz in Part A. Part
A is intended to gauge the students' intuitive grasp of how small
a "partpermillion" and a "partperbillion"" are. Instruct the students
to guess if necessary to answer these three questions. They will actually
calculate the correct answers in Part B.

After they have completed
the quiz, go on to Part B. Work with them to
calculate each answer choice and, from that information, determine
the correct answers to the quiz in Part A.
 Finally, work through
the Lake Jasmine spill scenario in Part C with
the students.
WarmUp 3: The Numbers
Game
Correct answers are boxed.
Part A
Just how small is a part per
million? A part per billion? Answer the following three questions based
on your "gut reaction." Guess if you need to.
 One part per million
is equivalent to 1 minute in
a. 1 day 



c. 6 weeks 
 One part per billion
is equivalent to 1 second in
a. 3 weeks 

b. 17 months 


Part B
Now go back and calculate
each of the answers you chose in Part A. Use the
procedure below for each calculation.
To calculate the relationship
between 2 quantities, first convert both quantities to the same unit
of measure. For example, to compare years to seconds, convert the
years to seconds. To do this, convert the years to days, then the days
to hours, the hours to minutes and the minutes to seconds:
365
days

x 
24
hours

= 
8,760
hours




1
year

1
day

1
year

8,760
hours

x 
60
minutes

= 
525,600
minutes




1
year

1
hour

1
year

525,600
minutes

x 
60
seconds

= 
31,536,000
seconds




1
year

1
minute

1
year

1. 
Use the space below to calculate
(a) 1 minute per day, (b) 1 minute per 2 years, and (c) 1 minute per
6 weeks to find the answer to question 1 of part A. After you have
completed the conversion to the same units (e.g., expressing hours,
days, or weeks in minutes or seconds), you may have to round your
answers to the nearest thousand, million or billion.

a) 
1
minute

x 
1
day

x 
1
hour

= 
1
minute


1 
=> 
1
part per 1,500






1
day

24
hours

60
minutes

1,440
minutes

1,500 

b) 
1
minute

x 
1
year

x 
1
day

x 
1
hour

= 
1
minute


1 
=> 
1 part per
million







2
years

365
days

24
hours

60
minutes

1,051,200 
1,000,000 


c) 
1
minute

x 
1
week

x 
1
day

x 
1
hour

= 
1
minute


1 
=> 
1 part per 60,000 






6
weeks

7
days

24
hours

60
minutes

60,480
min.

60,000 

2. 
Use the space below to calculate
(a) 1 second per 3 weeks, (b) 1 second per 17 years, and (c) 1 second
per 32 years to find the answer to question 2 of Part A.

1) 
1
second

x 
1
week

x 
1
day

= 
1
hour

x 
1
minute

= 
1
second







3
weeks

7
days

24
hours

60
minutes

60
seconds

18,144,400
seconds



1 
=> 
1
part per 18 million


18,000,000 


2) 
1
second

x 
1
year

x 
1
day

x 
1
hour

= 
1
second






17
years

365
days

24
hours

3,600
seconds

536,112,000
seconds



1 
=> 
1
part per 500,000,000


500,000,000 


3) 
1
second

x 
1
year

x 
1
day

x 
1
hour

= 
1
second






32
years

365
days

24
hours

3,600
seconds

1,009,152,000
seconds



1 
=> 
1
part per billion


1,000,000,000 



Part
C
If the conversion of units leads to a fraction with a numerator other
than 1, a different method can be used to determine parts per million
or parts per billion. Be sure your fraction has a smaller number on
top and larger number on the bottom and divide.
To express the decimal answer
in parts per million, move the decimal point 6 places
to the right. To express the answer in parts per billion, move
the decimal point 9 places to the right.
Moving the decimal place
6 places to the right gives 1,250 parts per million.
Moving the decimal place 9 places to the right gives 1,250,000 parts
per billion. (You would probably not see a number this large expressed
in parts per billion. It is better expressed as a smaller number
of parts per million.)
Moving the decimal place
6 places to the right gives 34.37, or about 34.4 parts per million.
Moving the decimal place 9 places to the right gives 34,370, or about
34,000 parts per billion.
(NOTE: Depending on the
skill level of your class, you may need to let students practice calculating
and converting measures of volume. Since students may associate volume
with rectangular objects, you may want to use a swimming pool for this
same problem. Assume that a 50gallon container of chlorine is spilled
into a swimming pool, which is 100 feet long by 50 feet wide by 10 feet
deep.)
Based on the scenario described
below and the table of legally allowable concentrations of contaminants
in surface water, decide whether local public health officials should
take measures to keep vacationers near Lake Jasmine out of the water.
Allowable Quantities: 
Fuel Oil A 
2.2 ppm in recreational waters 
(concentrations of contaminants 
Pesticide B 
4.7 ppm in recreational waters 
above these levels require action) 
Solvent C 
1.3 ppm in recreational waters 
Conversion
Table:

1 acre = 43,560 square feet 
1 gallon = 0.1337 cubic feet 
1 cubic foot = 7.48 gallons 
SCENARIO
Lake Jasmine is a 20acre lake with an average depth of 30 feet. Yesterday
afternoon, four 55gallon drums of Fuel Oil A and six 55gallon drums
of Solvent C fell off a truck during an accident, rolled into lake Jasmine
and burst open on the rocky shore. The entire contents of all the drums
spilled into the lake.
STEP 1
Calculate the concentration of each contaminant (in ppm) in Lake Jasmine.
To do this you must compare the volume of the contaminants (gallons)
to the volume of the lake (cubic feet).
Start by converting both
to cubic feet. To calculate the volume of the lake, multiply the area
(in square feet) by the depth (in feet) to get cubic feet.
Calculate volume of
contaminants:
4 x 55 gallons of Fuel Oil
A x 1 cubic foot/7.48 gallons = 29.42 cubic feet Fuel Oil A
and
6 x 55 gallons Solvent C x 1 cubic foot/7.48 gallons = 44.12 cubic feet
of solvent C
Calculate volume of
Lake Jasmine:
20 acres x 30 feet x 43,560
square feet/acre = 26,136,000 cubic feet of water in Lake Jasmine
Comparison:
29.42 cubic feet Fuel Oil
A/26,136,000 cubic feet Lake Jasmine
= 29.42/26,136,000
= 0.0000011
Moving the decimal point 6 places to the right gives 1.1 ppm Fuel
Oil A
44.12 cubic feet Solvent
C/26,136,000 cubic feet Lake Jasmine
= 44.12/26,136,000
= 0.0000016
Moving the decimal point 6 places to the right gives 1.6 ppm Solvent
C
STEP 2
Compare these levels to the values in the chart of allowable quantities
to see if they exceed the legally allowable levels.
Allowable Quantities:
(concentrations of contaminants above these levels require action)
Fuel Oil A 
2.2 ppm in recreational waters 
Pesticide B 
4.7 ppm in recreational waters 
Solvent C 
1.3 ppm in recreational waters 
1.1 ppm Fuel Oil A does not
exceed allowable concentration of 2.2 ppm. If that were the only chemical
spilled, no action would be necessary.
However, since 1.6 ppm Solvent
C does exceed the limit, local health officials will have to keep Lake
Jasmine residents out of the water until the levels of contaminants
are lowered.
