SSACgnp.TD883.LV1.9
Take a Deep Breath on the Appalachian Trail
in Great Smoky National Park
How Many Molecules of Ozone Do You Inhale?
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
© 2010 University of South Florida Libraries. All rights reserved.
1
Getting started
After completing this module you
should be able to:
Appalachian Trail
And you should also know
where Great Smoky Mountains
National Park is and where the
Appalachian Trail goes.
• 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
2
The setting – Great Smoky Mountains National Park (GRSM)
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.
3
The setting – the Appalachian Trail (AT)
From the cover page of
Appalachian National Scenic
Trail: Resource Management
Plan
The AT passes
through parts of
14 states. Can
you identify them
from this map?
State by state information
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.
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.
Detailed map
4
The setting – the AT in GRSM
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 setting – Clingmans Dome
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
Environmental issue: ozone
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
7
Air quality standards
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 8-hour 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
AQI Value and
Color
O3 (ppm)
Good
0 – 50
Green
0.000 - 0.059
Moderate
51 – 100
Yellow
0.060 – 0.075
Unhealthy for
Sensitive
Groups
101 – 150
Orange
0.076 – 0.095
Unhealthy
151 – 200
Red
0.096 – 0.115
Very Unhealthy
201 – 300
Purple
0.116 – 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.
8
Ozone monitoring at Great Smoky Mountains National Park
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
The problem
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 360º 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
10
Concentration: ppm and ppb
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.
11
Returning to the problem. The concept of mole
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.
12
The concept of mole (2)
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:
6.022×1023, a really
big number.
It is known as
Avogadro’s number
(Endnote 4).
Here’s the new spreadsheet
(“Slide 13” Tab.)
13
Adjusting for a different temperature
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
T1 to T2, and the lid rises; V1 increases to V2.
Charles Law: If temperature is
expressed as absolute
temperature (degrees Kelvin), V
is directly proportional to T.
V1
Recreate this spreadsheet to find the
volume of a mole at T = 70F and
standard pressure. Use Charles Law.
V2
Heat
Directly proportional means that the
ratio V2:V1 equals the ratio T2:T1. 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
Adjusting for a different pressure
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. P1 increases to P2. The lid
is forced down, and the gas is compressed. V1 decreases to V2.
Boyles Law: V is inversely
proportional to P.
V1
V2
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 V2:V1 equals the ratio P1:P2. For
example, if you double the P (i.e. P2/P1
= 2), then the V will be half its original
value (V2/V1 = 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
Finding the volume of a mole of air at the elevation of Clingmans Dome
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
Answering the question
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 8.3×1015.
That’s 8.3 million billion. Right?
8.3 million billion is 8.3 × 106 × 109.
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
Concluding thought: ozone in the parks
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 EPA works with many partners to
monitor ground-level ozone. Check out
the AIRNow Web site to see current
conditions in your area.
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.
18
End-of-module assignment
1.
The concentrations of oxygen (O2) and carbon dioxide (CO2) 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 50ºF. 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 50ºF. 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 cm3, 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 cm3?
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 R2
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
Endnotes
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”
20
Endnotes (2)
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 O2 molecule is 31.988
(=2*15.994), and Avogadro’s number of O2 molecules has a mass of 31.988 g, no matter
what the pressure and temperature are. Similarly, the mass of 6.022×1023 molecules of O3
(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
21