SSACgnp.TD883.LV1.9
Core Quantitative Literacy Topics
Ratio and proportion
Supporting Quantitative Literacy Topics
Scientific notation
Unit conversions
Graph reading
Orders of magnitude
Core Geo-Enrivonmental Issue
Air Pollution
Len Vacher, Department of Geology, University of South Florida-Tampa
Susan Sachs, Appalachian Highlands Science Learning Center, Great Smoky Mountains National Park
© 2011 University of South Florida Libraries. All rights reserved.
This material is based upon work supported by the National Science Foundation under Grant Number NSF DUE-0836566.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

And you should also know where Great Smoky Mountains
National Park is and where the
Appalachian Trail goes.
Appalachian Trail
After completing this module you should be able to:
• Know the difference between “good ozone” and “bad ozone,” why “bad ozone” is bad, and where bad ozone comes from.
• Know what proportions are and be able to use them to solve problems.
• Be able to write numbers like 24 hundred million billion in scientific and Excel notation.
• Know these basic concepts of general science: what a mole is; how the volume of a gas varies with temperature and pressure; how atmospheric pressure varies with elevation.
Tennessee North
Carolina

Great Smoky Mountains National Park protects 524,000 acres of temperate mountains ranging in elevation from 875 to 6,640 feet in the Southern Appalachians. This range in altitude mimics the latitudinal changes you would experience driving north or south across the eastern United
States, say from Georgia to Maine. Plants and animals common in the southern United States thrive in the lowlands of the Smoky Mountains while species common in the northern states find suitable habitat at the higher elevations. This makes GRSM one of the most biologically diverse areas in the nation. In recognition of the park's unique natural resources, the United Nations has designated GRSSM as an International Biosphere Reserve. GRSM is also the most visited
National Park in the entire country, with over 9 million visitors each year.
A huge inventory of all species has added almost
900 new species to science and over 6,300 new park records. Pictured is a
Tardigrade, with 18 new species discovered.
Elk were reintroduced in the Smokies in 2001
The Smokies has over 2,000 miles of streams and 900 miles of trails.
The endemic Red-cheeked salamander (above). The park is referred to as the
Salamander Capital.

From the cover page of
Appalachian National Scenic
Trail: Resource Management
Plan
The Appalachian National Scenic Trail is a marked footpath that extends from Mt. Katahdin in Maine to Springer Mountain in Georgia, a distance of more than 2,100 miles. It is a hiking trail, within a day’s drive of two-thirds of the country’s population. NPS estimates that the AT has about 4 million hikers annually.
The AT passes through parts of
14 states. Can you identify them from this map?
State by state information
Detailed map
From The
Appalachian
Trail Home Page
Other national scenic trails include the Pacific
Crest NST , the Continental Divide NST , the Ice
Age NST , and the Florida NST .
4

The AT follows the ridgeline that defines the boundary between TN and NC in GRSM.
• Length: 71.4 miles.
• Elevation: 34 miles continuously above 5000 ft – the longest such stretch on the AT.
Clingmans Dome, elev. 6,643 ft
• Highest point in GRSM.
• Third highest mountain east of the Mississippi.
• Highest point on AT is where it crosses the dome .
5

The rocks of the Appalachian Mountains tell the geologic story of the opening and closing of an ocean basin (Iapetus Ocean) that preceded the Atlantic Ocean (
Endnote 1
). The main bedrock of GRSM is the Ocoee Supergroup, a thick sequence of terrigenous metasedimentary rocks deposited in continental basins in the supercontinent (Rodinia) as it was being rifted apart.
These rocks are classified stratigraphically (in ascending order) into the Snowbird, Great Smoky, and Walden Creek Groups. The 25,000 ft-thick Great Smoky Group in turn contains the Elkmont
Sandstone, Thunderhead Formation and Anakeesta Formation. The Thunderhead and
Anakeesta are ridge formers in the park. The Thunderhead is a massive metasandstone, presenting more-rounded ridgelines than the rugged outcrops of the Anakeesta, which consists of metasandstone interlayered with metasiltstones and phyllites. Clingmans Dome is held up by the erosionally resistant Thunderhead Formation. The Anakeesta Formation lines the slopes.
Left: Jagged Anakeesta ridgeline
Above: The .5 mile trail to Clingmans Dome
Right: Lookout tower at Clingmans Dome
6

Air pollution does not respect boundaries. NPS cannot fence off its park to pollutants, such as ozone, that are contained in the air.
Ground level ozone is a colorless gas. It forms in the atmosphere in the presence of sunlight by complex chemical reactions involving the ozone precursors nitrogen oxides (NOx) and VOCs (volatile organic compounds). Power plants, automobiles, and factories are the main producers of nitrogen oxides.
Automobile emissions, gasoline vapors, chemical solvents, and consumer products such as paints all contribute to VOCs.
Ozone is a powerful oxidant and a respiratory irritant for humans. It is a known trigger for asthma. It can cause coughing, sinus inflammation, chest pains, scratchy throat, even permanent damage to lung tissue and reduced immune system functions.
Children, the elderly, people with existing health problems, and active adults are most vulnerable.
Caution. See
Endnote 2 .
Source: EPA website

The Clean Air Act requires the Environmental Protection Agency to establish standards (the
National Ambient Air Quality Standards, NAAQS) for ground-level ozone, particulate matter, carbon monoxide, nitrogen oxides, sulfur dioxide, and lead. The new (2008) standard for ground-level ozone is 0.075 ppm for an 8hour average, implemented as follows: “to attain the standard, the 3-year average of the fourth-highest daily maximum 8-hour average ozone concentrations measured at each monitor within an area over each year must not exceed
0.075 ppm (effective May 27 2008).” (
EPA Web site )
Categories
Good
Moderate
AQI Value and
Color
0 – 50
Green
51 – 100
Yellow
O3 (ppm)
0.000 - 0.059
0.060 – 0.075
Unhealthy for
Sensitive
Groups
101 – 150
Orange
0.076 – 0.095
Unhealthy
Very Unhealthy
151 – 200
Red
201 – 300
Purple
0.096
0.116
– 0.115
– 0.374
The EPA also breaks the range for 8-hour average concentrations into five categories.
Anything coded orange or higher (red or purple) exceeds health standards.
The AQI value is the Air Quality Index , a summary index for reporting daily air quality. The scale runs from 0 to 500, with 100 generally corresponding to the national standard for the pollutant.

Current ozone concentrations are posted online at two air quality stations in GRSM.
The Purchase Knob station , on the eastern side of the park, posts ozone, weather and a photo that updates every 15 minutes. Look
Rock station , on the western side, posts those plus visibility and particulate information.
Ozone report.
It’s a green day (46 ppb)
Look Rock Air
Quality Station
Ground-level ozone exposures in
GRSM are among the highest in the
East and in recent years have exceeded levels that threaten human health. earlier standard
9

On average, ozone levels over the ridgetops of the park are up to two times higher than in nearby cities, including
Knoxville and Atlanta.
There is a road to Clingmans Dome and an observation tower affording 360
º views from the summit. The trail from the parking lot to the tower is paved and only ½ mile long. But it is steep, especially at the beginning.
You typically take in about a half liter during shallow breathing. When you exert yourself, as you do when you are hiking in the Smoky Mountains, you may inhale about nine times as much, around 4.5 L in a deep breath. Some times and especially in the higher elevations, the ozone level in the Park is “code red” exceeding 95 ppb.
How many molecules of ozone would you breathe in if you inhaled 4.5 L of air containing
95 ppb ozone after hiking to the summit of Clingmans Dome?
Return to Slide 12

Before getting to the problem, we should clear up something. The table on Slide 8 says that code red begins when ozone exceeds 0.095 ppm. On Slide 10, we stated the value as 95 ppb.
That’s the same concentration of ozone.
0.095 parts
One million parts
=
95 parts
One billion parts
Concentrations are expressed as ratios . Ppm and ppb are abbreviations for parts per million and parts per billion, respectively, in the same way that % (percent) is an abbreviation for per hundred. (Technically, it is ppmv and ppbv, where the “v” means “by volume.”)
What is 0.095 ppmv written as a percent by volume?
0.095 parts
One million parts
0.0000095 parts
=
One hundred parts
Answer: 0.0000095%
You can see why it’s preferable to write concentrations in ppm or ppb, if the concentration is very small.
The two equations are proportions : an equality of ratios. For example, the first one says
0.095 parts:1,000,000 parts::05 parts:1,000,000,000 parts
.
To convert the left side of the equation (ppm) to the right side (ppb), multiply by 1 in the form of
1,000/1,000. It’s just one more unit conversion.

The key to the problem stated on Slide 10 is the
concept of mole . A mole refers to a specific number of molecules. Think of a mole of molecules as something like a dozen eggs, only it’s a different number (not 12) and it refers to molecules (not eggs).
For now, suppose we told you that a dozen molecules of air at standard temperature and pressure occupied 0.25 L (liters), and that the concentration of ozone in the air is 15%. How many molecules of ozone would there be in 5 L of air?
You don’t need a calculator to do this one. If each dozen occupies 0.25 L, then there would have to be 20 (=5/0.25) dozen to make 5 L. That means there would be 240 (=20*12) molecules of air. If 15% of them were ozone, there would be 24 ozone molecules in the 5 L of air. The following spreadsheet works through the problem.
How would you change the spreadsheet to answer the problem
stated on Slide 10 ?
Click on the Excel worksheet above (left) and save immediately to your computer. Complete the spreadsheets at each of the tabs starting with “Slide 12.” Yellow cells contain given values, and orange cells contain formulas. The spreadsheet at the “EOM Answers” tab is for your answers to the end-of-module questions.

We just solved this problem: A dozen molecules of air at standard temperature and pressure occupies 0.25 L . The concentration of ozone in the air is 10% . How many molecules of ozone are there in 5 L of that air (at standard temperature and pressure)?
Now we want to solve this problem: A mole of air at standard temperature and pressure occupies 22.4 L . The concentration of ozone in the air is 95 ppb . How many molecules of ozone are there in 4.5 L of that air (at standard temperature and pressure)? Change your spreadsheet for the old problem to solve this new problem. (
Endnote 3 )
There is one more piece of information you need to know: the number of molecules in a mole.
(You already knew the number of molecules in a dozen molecules.)
The number is:
6.022
×10 23 , a really big number.
It is known as
Avogadro’s number
(
Endnote 4
).
Here’s the new spreadsheet
(“Slide 13” Tab.)
13

We answered the question for standard temperature and pressure . Standard temperature and pressure are 0

C (32

F) and 1 atmosphere (atm), respectively. On the day of your visit to
Clingmans Dome, it may not be 32
 F, and for sure the pressure will be less than 1 atm. Let’s examine temperature first; then we will think about pressure.
The volume of a quantity of gas expands when it is heated (at constant pressure). Imagine a vessel with a lid that is free to rise and fall. Imagine that it is weighted with a brick (which maintains the pressure). Heat the vessel from
T
1 to T
2
, and the lid rises; V
1 increases to V
2
.
V
1
V
2
Heat
Charles Law: If temperature is expressed as absolute temperature (degrees Kelvin), V is directly proportional to T.
Recreate this spreadsheet to find the volume of a mole at T = 70

F and standard pressure. Use Charles Law.
Directly proportional means that the ratio V
2
:V
1 equals the ratio T
2
:T
1
. For example, if you double the T, then the V will double also.
To obtain T in

K, add 273 to the T in

C.
You need to remember how to convert

F to

C.
14

Pressure works just the opposite as temperature. The volume of a quantity of gas is diminished if the pressure is increased. Imagine the same vessel with a lid that can rise and fall. Put another brick on the lid. P is forced down, and the gas is compressed. V
1
1 increases to P
2
. The lid decreases to V
2
.
Boyles Law: V is inversely proportional to P.
V
1
V
2
Use the given spreadsheet from Slide 12 to find the volume of a mole at T = 70

F and P = 1.25 atm. Use
Boyles Law for the formula in Cell C11.
Inversely proportional means that the ratio V
2
:V
1 equals the ratio P
1
:P
2
. For example, if you double the P (i.e. P
2
/P
1
= 2), then the V will be half its original value (V
2
/V
1
= ½).
Charles Law and Boyles Law are special cases of the Ideal Gas Law, which is well known to students who have had chemistry.
What can we say about the pressure at the summit of Clingmans Dome? It would not be 1.25 atm. Why not?
15

The standard pressure of 1 atm is appropriate for localities at sea level.
Atmospheric pressure should be considerably smaller along the
Appalachian Trail because the elevation is so much higher there. Atmospheric pressure is due to the weight of the overlying atmosphere. There is substantially less atmosphere above
5,000 ft elevation, say, than there is above 0 ft elevation (sea level).
Use the graph of elevation vs. pressure to estimate the pressure at the summit of
Clingmans Dome.
Modify your spreadsheet from
Slide 15 to determine the volume of a mole of air at the summit of
Clingmans Dome when the temperature is 70

F.
Return to End-of-module questions
16

Use the spreadsheet from “Slide 17” Tab to calculate the number of ozone molecules in 4.5 L volume at the summit of Clingmans Dome when the temperature is 70

F.
We get an answer of 8.3
×10 15 .
That’s 8.3 million billion. Right?
8.3 million billion is 8.3 × 10 6 × 10 9 .
It’s also 8.3 thousand trillion.
Not to mention 8.3 quadrillion.
Return to End-of-module questions
These are huge numbers of molecules in small volumes, of course, and that’s the take-home science concept from this module: Molecules are as incomprehensibly small as they are incomprehensibly many in a familiar quantity of material. Mathematically, the take-home concept is the usefulness of ratios and proportions. How many ways did we use them in this one simple problem?
17

Many national parks experience more air pollution than major cities. Ozone kills cells in leaves that we can see and cells in our lungs that we can’t see. Several national parks monitor damage to plants from ozone . In the
Smokies, this work is done by local students .
The reddish brown discoloration on this leaf is caused by exposure to ground-level ozone.
The pollution in the parks is not being generated within the parks. The NPS urges us all to help protect our national parks and our own health by reducing our contribution to air pollutants.
The EPA works with many partners to monitor ground-level ozone. Check out the AIRNow Web site to see current conditions in your area.

1.
The concentrations of oxygen (O
2
) and carbon dioxide (CO
2
) in air are 20.95% and 0.038%, respectively.
Use your spreadsheet from Slide 17
to calculate the number of oxygen and carbon dioxide molecules in a 2 L breath of air at sea level and 50 ºF. Use your spreadsheet again to calculate the number of oxygen and carbon dioxide molecules in a 2 L breath of air at the summit of Clingmans Dome and 50 ºF. Hand in both spreadsheets. Write a couple of sentences about what you find out, comparing the results using appropriate ratios. Include a comment on altitude sickness (Google ams oxygen).
2. What percentage of the AT is in GRSM? Which of the 14 states that the AT passes through have a smaller fraction of the trail?
3. How large is 4.5L? One L is 1000 cm 3 , which is the volume a cube 10 cm on an edge. How long does the edge length have to be for the cube to contain 4500 cm 3 ?
4. Use the graph of
Slide 16
to determine the atmospheric pressure at the following elevations 0 ft, 5,000 ft, and 10,000 ft. What is the ratio of the 5,000-ft result to the 0-ft result? What is the ratio of the 10,000-ft result to the 5,000 ft value. What would you estimate the pressure to be at 15,000 ft elevation?
5. Advanced students : the preceding question should be a clue. Determine the equation for pressure vs.
altitude. Create a graph like the graph found on Slide 16 by creating a table with x- and y-values. Then
plot the x- and y-values on a scatter plot. Use the trendline to determine the equation. (Hint: The R 2 value should be 1 and the equation to solve for pressure is an exponential function.) If you do not remember how to determine equations from a trendline please refer to Spreadsheet Warm-up for SSAC
Geology of National Parks, 2 .
6. Advanced students : Develop a spreadsheet that uses the ideal gas law (PV = nRT) to establish that a mole of gas occupies 22.4 L at standard temperature and pressure.
19

1. For the tectonic story of the Southern Appalachians, see the US
Geological Survey online booklet, Birth of the Mountains , by Sandra H. B.
Clark. Return to Slide 6
2. Do not confuse ground-level ozone with “good ozone.” Ozone occurs in two layers of the atmosphere. The layer closest to the Earth's surface is the troposphere. Here, ground-level or "bad" ozone is an air pollutant that is harmful to breathe and it damages crops, trees and other vegetation. It is a main ingredient of urban smog.
The stratosphere or "good" ozone layer extends upward from about 6 to
30 miles and protects life on Earth from the sun's harmful ultraviolet
(UV) rays.
Return to Slide 7
Source: EPA brochure “Good Up High, Bad Nearby”

3. Our strategy illustrates a useful technique in mathematical problem solving.
In How to Solve It , which has sold more than a million copies and has been translated into 17 languages, George Polya (1887-1995) breaks successful mathematical problem solving into four steps: understanding the problem, devising a plan, carrying out the plan, and looking back. Devising the plan is the difficult step. One of the techniques under that heading is to think
through the following question: What is a similar, easier problem? Return to
Slide 13
4. You might wonder where such a strange number comes from. The idea is that the mass of a mole of molecules is equal to the molecular mass in grams, and Avogadro’s number of the molecules is the number of molecules that aggregates to that number of grams. For example, the atomic mass of oxygen is 15.9994 (very nearly the number of neutrons and protons, 16, in an oxygen atom). So the molecular mass of the O
(=2*15.994), and Avogadro’s number of O
2
2 molecule is 31.988 molecules has a mass of 31.988 g, no matter what the pressure and temperature are. Similarly, the mass of 6.022
×10 23 molecules of O
3
(ozone) is 47.982 g (=3*15.994 g). All this works because a mole is defined as the amount of Carbon-12 that has a mass of exactly 12 g. The non-integer values for the other elements
result largely from the fact that many elements including carbon have isotopes. Return to
Slide 13