Quantification of Environmental Problems
Using SI units
I. Density = Mass / Volume
1. A student measures the mass of an 8 cm3 block of brown sugar to be 12.9 g. What is the density of the brown sugar?
2. A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density of the oil?
3. A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density of the aluminum?
4. Based on the density values list how the following liquids would layer in a beaker from top to bottom: glycerol (1.26 g / cm3), ethyl alcohol (.789 g / cm3), mercury (5.43 g / cm3), seawater (1.02 g / cm3), machine oil (.9 g / cm3) , water 1.0 g / cm3).
5. A teacher performing a demonstration finds that a piece of cork displaces 23.5 mL of water. The piece of cork has a mass of 5.7 g. What is the density of the cork?
6. A carver begins work on a block of granite that measures 20 cm by 10 cm by 5 cm. If the block of granite has a mass of 2700 g, what is the density of the granite?
7. A piece of PVC plumbing pipe displaces 60 mL when placed into a container of water. If the pipe has a mass of 78 g, what is the density of PVC?
8. An ice cube has a volume of 12 cm3, and a mass of 11 g. What is the density of the ice?
9. Gold is one of the densest substances on Earth. A gold bar 20 cm by 5 cm by 5 cm has a mass of 9.7 kg. What is the density of gold? Express your answer in g/cm3.
II. Using Time Conversions
PROBLEMS
Determine the number of people living in your community. Assume the average household size is four people and there arc approximately five water sources (faucets and toilets) in each household. Assume that two of the faucets leak at the rate of 1 drop/sec.
Always show your set-up and work. Use proper labels.
1. Calculate the volume of water lost by each household annually. Here are some useful
equivalences. Explain any other assumptions you make.
20 drops = 1 milliliter
3.78 liters = 1 gal
1 gal = 0.133ft3
2 What is the total water loss in your community (population 40,000)?
3.. What percent of the total water consumption does that community loss represent? Assume a typical person uses 95 gal of water per day, on average.
III. Temperature
C= 5/9(F-32)
F= 9/5 C+32
1. 75 °F = __________ °C
2. 0 °F = __________ °C
3. 98.6 °F = __________ °C
4. 160 °F = __________ °C
5. -10 °F = __________ °C
6. 45 °C = __________ °F
7. 30 °C = __________ °F
8. -10 °C = __________ °F
9. 200 °C = __________ °F
10. -40 °C = __________ °F
IV. Scientific Notation
In this problem set, we will explore two fundamental components of expressing and quantifying environmental problems: scientific notation and calculating percentage changes overtimes.
Exercise: Scientific Notation
Convert the following numbers into or; from scientific notation:
1. 678,950,000,000 =_________________
2. 1,000,000,000,000 =_________________
3. .00000004567 =_________________
4. 5,689,000,000 =_________________
5. 8923 =_________________
6. .000000045678963 = _______________
7. 2.223 X 10-9=-_________________
8. 7.47 X 1013 =________________
V. CALCULATING PERCENT CHANGE
Environmental scientists often analyze trends. A popular approach to communicating these trends is percentage increase/decrease over time. In calculating percentage of change (whether an increase or a decrease), you are concerned with the difference between two numbers and how much of the first number added to or subtracted from the first number will produce the second number.
The three steps to calculate a percentage are:
1. Subtract
2. Divide
3. Multiply
Subtract: New number - original number = change
Divide: by original number
Multiply: by 100
Thus, the basic formula is simple:
[pic]
Percent increases and decreases are calculated with respect to the value before the change took place— the original number.
A. In 2004, the level of acetone in the river was 100 parts per million (ppm). In 2004, the level increased by 12 ppm. What is the percentage increase in acetone?
12/100 = .12 X 100 = 12%
B. In 2000, the level of ammonia was 63 ppm. In 2004, the level is 112 ppm. What is the percentage of increase since 2000?
Step 1: Determine the amount of change.
112 -63 = 49
Step 2: Divide the change by the original number, then multiply by 100.
49/63 = .777 X 100 = 77.7%
Exercise: Calculating Percentage Changes
Solve the following.
1. 234.98 to 324.77 =____________% change
2. 324.77 to 234.98 =____________% change
3. 7.14 X 107 to 8.47 X 108 =____________% change
4. 100 increases by 300% =____________
5. 756 declines by 100% =____________
6. 756 increases by 100% =____________
7. A utility's total pollution control costs are broken down as follows:
Air pollution control = $234,000
Wastewater treatment = $167,000
Solid waste = $45,000
Hazardous waste = $12,000
What percentage does the company spend for each?
Air pollution control =_________%
Wastewater treatment =________%
Solid waste =_________%
Hazardous waste =__________%
8. The company's managers want to budget sufficient money for next year. Assuming that costs will increase by 2.4%, what will the costs be for next year for each category?
Air pollution control = $_________
Wastewater treatment = $__________
Solid waste = $_________
Hazardous waste = $_________
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