0 Unit 1 Teacher Notes

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Unit 1 - Physical Properties of Matter
Instructional goals
1. Define mass as the measure of atomic “stuff”; contrast with volume - the amount of space an
object occupies.
2. Use a multiple beam or double-pan balance to determine the mass of various objects.
3. Record the value of an object’s mass in a manner consistent with the limit of precision of the
balance.
4. Represent class data using a histogram; use the histogram to interpret trends in the data.
5. Develop, from experimental evidence, the law of conservation of system mass.
6. Relate the volume of a container (in cm3) to the volume of liquid it contains (in mL).
7. Recognize that instruments have a limit to their precision; relate the data recorded to the quality
of the measurement.
8. Given a graph of mass vs. volume of a various substances, relate the slope to the density of the
substances.
9. Recognize that density is a characteristic property of matter (i.e., it can be used to help identify an
unknown substance).
10. Use density as a conversion factor between mass and volume; apply this to quantitative
problems.
11. Use differences in density of solids, liquids and gases as evidence for differences in the structure
of matter in these phases.
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Sequence
1. Demonstration: Using particles to describe chemical change
2. Lab: Mass and change
3. Worksheet 1
4. Activity: Comparing units of volume
5. Notes on measurement, precision and accuracy
6. Worksheet 2 – reading scales
7. Lab: Mass and volume
8. Worksheet 3
9. Worksheet 4 – applications
10. Quiz 1
11. Lab: Density of a gas
12. Activity: Thickness of a sheet of aluminum foil
13. Worksheet 5 – Size of Things
14. Review—The Model so Far . . .
15. Test
Overview
We start the course with a demonstration of a phenomenon that surprises most students – the
exploding can demo. Students are asked to try to describe what is taking place at various stages of
the reaction using particle models. The difficulty they encounter doing so helps them realize that
they need find better ways to describe change.
Next, we develop the concept that mass is a property of an object that tells how much matter is
present, and that the balance (not scale – the difference is important!) is the instrument used to
measure mass. The episode - Mass - from the video series Eureka1 - Force and Motion, part 1,
reinforces the idea that mass is a measure of the amount of stuff present in a sample of material. In
the lab: Mass and Change2, students develop skill in the use of the balance and go on to learn that in
a variety of situations in which the physical appearance of a sample changes, the mass remains
1
2
Eureka, Films for the Humanities and Sciences,
This suite of labs is adapted from the Introductory Physical Science curriculum.
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constant (conservation of mass). The video resources described in the Instructional Notes (Eureka
and The Ring of Truth) do an excellent job of reinforcing these key concepts; they should not be
considered as merely entertainment. Worksheet 1 reinforces what students have learned in the
series of experiments.
Next the discussion shifts to volume as another measure of how much stuff is present in a sample.
Students review calculation of the volume of a regular solid V  A h and are introduced to the
program Graphical Analysis™ or Logger Pro™ from Vernier Software to prepare graphs from data
collected in the lab. In the next activity: Comparing Units of Volume, they plot volume (in mL) vs.
volume in cm3 and find that the slope of the graph is very nearly one. This is clear evidence that
these are equivalent units of volume. Since the slope of the line is not exactly one, this is the ideal
time for a discussion of limitations of measurement and how best to report data. Links to a website, a
reading and Worksheet 2 give students the opportunity to read and report values from scales.
After a brief discussion of how one can find the volume of an object by water displacement, students
perform the lab: Mass and Volume, in which they attempt to find a relationship between the mass
and volume of sets of samples of iron and aluminum. For students who have yet to take physics, this
may be their first exposure to the notion that the slope of a graph has physical meaning. Students
should find two distinct lines of best fit, corresponding to the densities of the two materials. For
students to really grasp the concept of density they have to be able to make the distinction between
what it represents (the mass of a unit volume) and how one goes about calculating it. Arnold Arons
writes3:
“Even if students correctly say ‘mass per unit volume’ rather than ‘mass per volume’ in
interpreting M/V, there is no conclusive assurance that they really understand the meaning.
Some do, but others have merely memorized the locution. It is important to lead all students
into giving simple interpretation in everyday language before accepting a regular use of ‘per.’
Many students do not know what the word ‘ratio’ means. Those having difficulty with
reasoning and interpretation should always be asked, at an early stage, for the meaning of the
word if they, the text, or the teacher invoke it.”
In Worksheet 3 students make comparisons of the mass, volume and density of pairs of objects
based on particle representations. Worksheet 4 further reinforces the notion that the slope of a
graph has physical meaning. The first quiz requires students to determine the slope and perform
standard calculations involving density. In the next activity: Density of a gas, students determine
the density of carbon dioxide. The fact that the value is 3 orders of magnitude smaller than that of
liquids and solids sets the stage for the discussion of an atomic model of matter that accounts for this
difference.
In the activity: Thickness of a thin layer, students apply the tools they have learned thus far
(V=M/D, h = V/A) to calculate the thickness of sheet of Al foil –this gives an upper limit for the size
of atoms. Students are asked to estimate, and then calculate the number of layers of atoms in a sheet
of Al. A better approximation is made when they see the experiment in which the thickness of a
layer of oil is calculated. Students then visit the Size of Things website4 to relate the prefixes milli,
micro, nano, and kilo to objects in the physical world.
3
4
A Arons, Teaching Introductory Physics, John Wiley & Sons, 1997.
http://www.vendian.org/howbig/
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Instructional Notes
1. Demo/discussion: Exploding coffee can
Apparatus
2 lb coffee can with lid. A small hole is drilled in the bottom of the can and another, larger hole is
drilled in the side, near the top.
Demo performance notes
Start the demonstration by filling the can with natural gas. Caution: propane will not work with this
demonstration since its density is greater than that of air. [An alternative approach can be found in
the document hydrogen.doc.] Explain to students that the can is filled with methane, a gas that is
lighter than air. Dim the room lights, then ignite the gas escaping through the hole in the top.
At first, the flame is large (7-10 cm) tall and very luminous. As the methane is
consumed, the flame gradually becomes bluer and smaller. Ask the students to
try to visualize what is going on inside the can and in the flame at the particle
level.
After 2-4 minutes, the flame appears to disappear. Students expect that as the
methane is exhausted the flame will go out quietly. They are usually quite surprised when the flame
enters the can and ignites the methane-air mixture explosively.
Post-lab discussion
Ask the students to divide their whiteboards into three panes. In the first pane they should represent
the contents of the can at the particle level when the flame is burning brightly. In the 2nd, they
represent the contents when the flame is about to go out. In the final pane they should represent what
they think is happening inside the can when the explosion occurs. Have the lab groups present their
ideas to their fellow students. Don’t be surprised if their descriptions miss the mark. Students have
all sorts of ideas about the contents of the can and how the explosion occurs. Try to get the students
to be as clear as they can about what they think is taking place, yet resist telling them the answer.
Explain that later they will be studying combustion in considerable detail and will eventually be able
to answer the question for themselves. Watch Alan Alda's Flame Test Challenge, described in a
video clip found at PBS (http://video.pbs.org/video/2252507384/) to remind us that we need to
remember that "naming" is not the same as "explaining." A link to the winning video is provided in
the StResources page.
2. Lab: Mass and Change
Pre-lab discussion
Due to the considerable variation in the way students represented the changes that occurred during the
combustion of the methane in the coffee can leading to the eventual explosion, we need some tools to
describe matter in a quantitative way. One useful property of matter that we can measure to
determine how much “stuff” we have is mass. The balance is the tool to measure the mass of an
object.
If available, the Eureka video on mass (5 min) is a great resource here to give a historical perspective
on our concept of mass. Demonstrate an equal arm or double-pan balance; then show a multiplebeam balance. Explain how it differs from the others – how it differs from an equal arm-balance.
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Introduce the 6-part lab: Mass and Change as an opportunity to examine a number of instances in
which the appearance of the system changes to see if the mass also changes. Help them set up a
general table for data and calculations.
Part 1 – Mass of steel wool
Apparatus
Balance
Small wad of steel wool (~ 1/4 of a pad of #1 steel wool)
Pre-lab discussion
It is likely that students may confuse volume and mass as measures of the “amount of stuff” in a
sample. Display a small tightly wadded ball of steel wool. Ask students to predict whether the mass
will change if the wad of steel wool is pulled apart.
Lab performance notes
•
•
•
Students should determine the mass of the wad of steel wool.
Students should carefully pull the wad apart so that it occupies a volume roughly twice as great
as before.
Students then determine the mass of the expanded wad of steel wool.
Post-lab discussion
•
Have the students report any change in mass by doing the following calculation:
Mass steel wool-after- Mass steel wool-before
Change in mass
The lab groups should report their results on the board so that the entire class data can be recorded.
Change should be recorded as + (for a gain) or – (for a loss).
Group
Change in mass (g)
This is the ideal time to introduce the use of a histogram as a way to represent the class results. The
only real difficulty with the use of this tool is in introducing the idea of “bins” to store the results.
But before you treat experimental data, use a more familiar example: the range of test scores for the
class. Math teachers typically label their bins with ranges of values. Place a set of trays on the desk
and label them as shown below.
60-69
70-79
80-89
90-99
Using “scores” written on index cards, have a
student “sort” the scores by placing them in the
trays. Once that task is completed, count the cards
in each bin and sketch a histogram, labeling the
bins with ranges of values – the height of each bar
corresponds to the number of scores in a given bin.
See figure at right.
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Another way to specify bins is to label the
endpoints. A question that arises is where to place a
score that falls on the junction of two bins; e.g., a
70. If you adopt the rule that this score fall into the
bin right of the junction, you obtain a histogram
very much like the one shown at right.
This method of labeling bins is more convenient when the bin size is small or if each bin represents a
range of decimal fractions. Suppose that you determined that the limit of precision of the balance
was ± 0.01 g. Then a histogram centered around 0 = no change in mass would have bins like the
ones below.
–0.05
–0.03
–0.01
+0.01
+0.03
+0.05
0
Change in mass (g)
Students could write tally marks in each of the bins, or make a bar chart in which the height of each
column would be the number of time a value fell into a particular bin. When students make a
histogram of their class data they should find that some of the values fall in the “zero” bin, with most
groups getting a decrease in mass ranging from 0.03 – 0.07 g.
Post-lab discussion
Ask the students if these results were what they expected. Some students may express surprise,
arguing that the mass should have remained the same, since simply pulling the steel wool apart did
not remove any material. Elicit a possible explanation for their results. A student most certainly will
volunteer that he/she noted that when they pulled the steel wool apart, small pieces broke off and fell
onto the table. At this point, you should ask, “But you swept those pieces up as best you could and
added them to the balance pan, right? Most will sheepishly admit that they did not, and immediately
realize that the real reason the mass appeared to decrease is because they allowed some matter to
escape; had they kept track of all the material, the mass would have remained the same. Draw a box
with a number of small circles or dots to represent the particles of the steel wool when it is
compressed. Then ask the students how they would represent the steel wool in its expanded state.
Most should be able to say that there are the same number of particles and the particles remain the
same size; the increase in size of the steel wool is accounted for by the fact that the particles are
farther apart.
For homework, students should visit the website http://quarknet.fnal.gov/toolkits/ati/histograms.html
to get more information about histograms and to follow links to an interactive website.
Part 2 – Mass of ice and water
Apparatus
Balance
Small vial and chip of ice
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Pre-lab discussion
Remind students what happens when they leave a soft drink in the freezer. The expansion of the
water during freezing can burst the can or bottle. So, it follows that a piece of ice will have a smaller
volume when it melts to water. The question is: does the mass also decrease?
Lab performance notes
Students should find the mass of the vial + a small piece of ice.
Because the ice takes a while to melt, they should set the vial aside and go on to part 3 rather than
wait for the process. They should periodically warm the vial in their hands to speed up the process.
Post-lab discussion
Students should do their calculations and post their class results as before. Unless students shake
their vial and allow water to leak out, they should find that the change in mass is very nearly zero.
Again, as homework, have the students represent the particles of water in the solid and then liquid
states.
Part 3 – Mass of a precipitate
Apparatus
Balance
Two small vials
0.1M solutions of Ca(NO3)2 (16.4 g per liter of solution) and Na2CO3 (10.6 g per liter
of solution). 300 mL of each should be sufficient for a class of 12 groups.
Pre-lab discussion
Show students that when some solutions are combined, a solid forms. The question they must
answer is: does the mass change when the solid is formed?
Lab performance notes
Students should fill each of the vials no more than 1/3 full of the solutions. They should cap the
vials and find the mass of both vials together. Then they should carefully pour the contents of one
vial into the other; then put both vials and caps back on the balance pan. Once they have found the
mass after the reaction, students should pour the solution and precipitate into the waste bottle
provided. Encourage the students to be careful, as they now realize that, if they spill a solution, the
mass will appear to decrease. No special precaution needs to be taken with the CaCO3, but the
students should discard the contents of the vial with the precipitate into a waste bottle on general
principles. At a later time you can wash the CaCO3 down the drain, or add some acid to the solid
before discarding the solution down the drain. The vials can be washed in soapy water and rinsed.
Post-lab discussion
Students should do their calculations and post their class results as before. Unless students spill
solution during the transfer, they should find that the change in mass is very nearly zero. Again, as
homework, have the students represent the particles of the substances in the solutions before mixing
and after the precipitate has formed.
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Part 4 – Mass of burning steel wool
Apparatus
Balance
Small tuft of steel wool
Crucible tongs
Bunsen burner
Evaporating dish
Pre-lab discussion
Ask students what happens when something burns. Their experience should lead them to conclude
that a flammable substance diminishes when it undergoes combustion. They might not think that a
metal can burn. Ask them to predict what will happen to the mass of the steel wool when it is
heated. Students will remember that pieces of steel wool dropped off in the first experiment; lead
them to propose ways of containing the dropped pieces, such as an evaporating dish.
Lab performance notes
Students should find the mass of the steel wool as they did before. They should light the burner, then
holding the steel wool by the tongs over the evaporating dish, heat the steel wool until it glows.
They should turn the steel wool around in the flame so that all sides are exposed. Any pieces of the
steel wool that break free during heating should fall into the dish and then be transferred to the
balance pan. Students should be asked to describe how the appearance of the steel wool changes
when it is heated strongly. Discard the steel wool when they have finished finding the mass.
Post-lab discussion
Students should do their calculations and post their class results as before. Most students will find
that the mass of the steel wool increases by a few hundredths of a gram. After the previous 3
experiments, they might be reluctant to accept that the mass should increase as some of the iron
combines with oxygen. Students might have difficulty representing this change with a particle
model. Students have been known to say that the steel wool gains mass by combining with particles
of the flame. During the whiteboarding session at the end of the set of experiments, there will be
time to discuss what happens when the steel wool is burned. At this point, do not just tell them that
the iron in the steel wool is reacting with oxygen in the air! Let them propose suggestions for what
made the mass increase, without correcting them.
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Part 5 – Mass of dissolved sugar
Apparatus
Balance
Vial with cap
Sugar
Pre-lab discussion
Ask students what happens when something dissolves. A soluble solid appears to disappear in
solution. Ask students to predict what will happen to the mass when sugar dissolves in water.
Lab performance notes
Students should fill a vial about 1/2 full of water, then put about a 1/4 tsp of sugar in the cap of the
vial. They should place the vial, water, cap and sugar on the pan of the balance. Then, students
should carefully pour the sugar into the vial, taking care not to spill any. They should gently swirl the
vial to get the sugar to dissolve. If they shake too vigorously, they risk solution leaking out of the
vial. When the sugar has completely dissolved, they should find the mass of the vial and contents
again.
Post-lab discussion
-
Have the students report any change in mass by doing the following calculation:
Mass vial, water & sugar after
Mass vial, water & sugar before
Change in mass
It is likely that there will be a few more losses than gains (due to spilling sugar or shaking so
vigorously that water leaked out). The reasons for the apparent loss in mass should come out in the
discussion. Again, have the students represent the particles of the substances in the sugar and water
before mixing and after the solution has formed.
Part 6 – Mass of dissolved Alka-Seltzer
Apparatus
Balance
Vial with cap
Small piece (1/4 tablet) of Alka-Seltzer
Pre-lab discussion
Remind students what happened in the previous experiment. A soluble solid appeared to disappear in
solution, yet the mass remained nearly constant. Ask students to repeat the experiment, but this time,
dissolving a piece of Alka-Seltzer in water.
Lab performance notes
Students should fill a vial about 1/2 full of water, then put the 1/4 tablet of Alka-Seltzer in the cap of
the vial. They should place the vial, water, cap and AS on the pan of the balance. Then, students
should put the piece of AS into the vial, and loosely cap the vial. They should observe what occurs
when the AS appears to dissolve. When the piece of tablet has completely dissolved, they should
find the mass of the vial and contents again.
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Post-lab discussion
-
Have the students report any change in mass by doing the following calculation:
Mass vial, water & AS after
Mass vial, water & AS before
Change in mass
All of the groups should find that the mass of the system appears to decrease. In fact, you might
want to adjust the scaling of the histogram to be able to display the results graphically. The reasons
for the apparent loss in mass should come out in the discussion.
Culminating board meeting
Assign different groups to the six experiments. Have each group sketch the histogram based on class
results and the particle representations of the system before and after the change. Have the groups
display their findings to the others, then ask members of each of the groups to explain what they
think has happened in each of the experiments. As you circulate through the class during
preparation, you should encourage students to make representations at the particle level that are
consistent with the findings of the class. For example, in the ice and water experiment, the
whiteboard should show that the volume of the ice is larger than that of the water, yet the number of
particles should be the same. If you find students making representations that reveal misconceptions
that are interesting, allow these to be resolved during the board meeting. For example, in the heating
steel wool experiment, students agree that something is added to the particles of iron in the steel
wool to explain the slight gain in mass. However, few are likely to suggest that it is oxygen from the
air that is the culprit. Students are more likely to suggest that particles of the burner gas (or carbon
from the methane) are sticking to the particles of iron.
In the final two experiments, students should be able to distinguish a loss in mass due to carelessness
(spilling sugar during the transfer) from the loss in mass due to the escape of a gas from the container
(during the dissolving of Alka-Seltzer).
Remind students that their results are evidence for the Law of Conservation of Mass. Students can
frequently state the law, “Matter can neither be created nor destroyed.” without seeing that it applies
to the experiments they have just performed. Perhaps a better statement of this important law is “If
nothing enters or leaves the system, the mass of the system remains the same, despite changes in its
appearance.”
3. Worksheet 1
This worksheet gives students the opportunity to review the concepts uncovered in the lab.
4. Activity: Comparing volume units
Apparatus
Containers with parallel sides and regular bases.5 This activity is most effective when containers of
different shapes and sizes are used.
250 mL or 500 mL graduated cylinders
rulers
5
As of 2/2013, these could be found at http://www.enasco.com/product/TB16963T for $67.
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Pre-lab discussion
Review the volume of a regular solid, emphasizing that the volume (in cm3) can be found by
multiplying the area of the base by the height, V  A h. They can measure the volume (in mL) by
using a graduated cylinder.
Lab performance notes

Explain to students that they will compare the volumes they measure and calculate (in cm3) with the
volumes they measure (in mL) in a graduated cylinder. Students should add water to a container,
measure the height of the water, calculate the volume in cm3, and then empty the water into the
graduated cylinder to measure the volume in milliliters. They will repeat this procedure for at least
five different heights.
This is an ideal time to introduce students to the use of the program or Logger Pro from Vernier
Software to prepare graphs from data collected in the lab. Students will plot volume (in mL) vs.
volume (in cm3) and obtain a best-fit line for their data.
Post-lab discussion
Students should find that the slope of the line is very nearly one. This is clear evidence that these
units of volume are equivalent. It will be informative to see if students can account for the fact that
the best-fit line is unlikely to pass through the origin. You can use this opportunity to discuss when
the intercept can be considered negligible.
5. Notes on measurement, precision and accuracy
Since students were unlikely to have obtained a value of 1.0 mL/cm3 for the slope of their line, this is
the ideal time to discuss limitations of measurement. Students need practice in learning how to read
scales and recognize that the way they report their measurements indicates the quality of the
instrument used to make the measurement. Fred Senese’s website on measurement6 has some nice
lecture slides on measurement as well as a tutorial on how uncertainty arises from the type of
instrument you are using to make the measurement.
5a. Optional activity on measurement, precision and
accuracy
In the unit folder is an activity that you can do with your students to help them see that the “rules”
regarding rounding of calculated answers are more like guidelines that arise from a sensible way to
judge how many digits to keep in a quantity that is derived from measurements.
6. Worksheet 2
This worksheet gives students the chance to read scales and report values with the appropriate
precision.
6
http://antoine.frostburg.edu/chem/senese/101/measurement/index
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7. Lab: Mass and volume
Apparatus
Sets of cylinders of iron and aluminum7 labeled A and B
Graduated cylinders large enough to accommodate the metal cylinders
Pre-lab discussion
Now that we have tools to measure the size (volume) and the amount of matter (mass) of a sample, it
would be useful to see what relationship exists between these two measures.
Lab performance notes
Elicit from the students a reasonable procedure for the experiment. It would make better sense to
find the mass of the cylinders before they found the volume; otherwise the moisture on the cylinders
would increase the reading they obtained for the mass. Review with the students how to determine
the volume of an object by water displacement. Students can generate plenty of data in short order if
each group measures the mass and volume of two cylinders and posts the data on the board for all to
use. Make sure that they record the data in the correct table for each set. Students should create two
data sets so that both sets show up on the same graph.
Post-lab discussion
Students should find that the data from the two sets produce two
distinct lines of best fit. They should write equations for each line,
deciding whether they should keep the y-intercept. Challenge the
students to think of what specific errors in technique might have
produced a non-negligible intercept.
Next, suggest that the slope has physical meaning. The name for
this quantity, density, should be reserved until after an operational
definition is established. Arnold Arons8 writes, “Teaching is
significantly strengthened, however, if one carefully abides by the
precept ‘Idea first and name afterwards,’ not just in this instance,
but in the introduction of every new concept.” You should find
g
ways of stating the value of 2.7
3 other than “2.7 g per cubic
cm
centimeter.” There is considerable evidence that students do not fully appreciate the meaning of the
word “per”. As an alternate, try “each cm3 of the substance has a mass of 2.7 g.”
Students commonly confound mass and density by using the word “heavier” to mean both “more
massive” and “more dense”. One way to address this problem is to pass around cylinders of iron and
aluminum such that the iron is less massive than the aluminum. We have found that students will
say that the iron is “heavier” than the aluminum, confusing greater density for greater mass. You
might consider requiring students to explain what they mean when they use the term “heavier”.
8. Worksheet 3
Students make comparisons of the mass, volume and density of pairs of objects based on particle
representations. They relate density to the graph of mass vs. volume.
7
These samples can be cut from 1/2” cylindrical rods of aluminum and iron. Pieces should range from 0.5” to 1.5” in
1/8” increments.
8 A. Arons, Teaching Introductory Physics, John Wiley & Sons, 1997.
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9. Worksheet 4
This worksheet gives students the opportunity to manually calculate the slope of a graph of mass vs.
volume to obtain the density of a substance. They then use density as a factor to convert mass to an
M
equivalent volume and vice-versa. This approach is encouraged over the use of the D 
equation
V
to solve for a missing quantity because it encourages dimensional analysis and the use of units. If
2.7g
1cm3
students view density as a factor relating mass and volume such that
are seen as
and
1cm3
2.7g
equivalent, then students can use either form to solve for the missing quantity. For example, the
1cm3
solution to question 3 is 70g 
 8.9 cm3 , rather than “I plugged it into my calculator.”
7.9g

10. Quiz

11. Activity: Density of a gas
Apparatus
25 x 150 mm test tube
pneumatic trough
balance
1/2 tablet of Alka-Seltzer
#4 stopper and delivery tube
250 or 500 mL bottle
100 mL (or 250 mL) graduated cylinder
Pre-lab discussion
Students already know that when Alka-Seltzer “dissolves” in water, a gas (carbon dioxide) is
released and that the gas has some mass. In this lab they are to determine the density of the gas.
Lab performance notes
Because the mass of the gas produced is very small, it is
best to determine its mass by the difference in the mass
of the test tube, water and Alka-Seltzer before and after
the reaction. If you wrap a rubber band around the
hanging support of the balance pan you can get the test
tube to stand upright on the pan of the balance. Fill the
tube no more than 1/4 full of water and find the mass of
the test tube, water + Alka-Seltzer. Students must be
careful not to spill any of the contents of the tube before
or after the gas is generated. It would be good to
demonstrate this reaction so that students see how to
collect the gas produced by displacement of water in the
bottle in the trough. Ask the students how they would
go about measuring the volume of the gas in the bottle. Some will suggest measuring the volume of
the water left in the bottle and subtracting that from the volume required to fill an empty bottle.
Others will suggest measuring the volume of water required to bring the water level back to the top.
Either way involves subtraction, so students need to record their values.
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Post-lab discussion
Have groups post values of mass, volume and density of the CO2 gas. If any of the solution in the
tube escapes during the generation of the gas, the mass after reaction will be too small, making the
calculated mass of gas too large. Since all the groups use roughly the same amount of Alka-Seltzer,
the values should be similar; outliers will be readily spotted. Students usually obtain values that are
g
close to the accepted value of 2.0  10 3
for the density of the carbon dioxide at room
cm 3
conditions. What is more important than obtaining the correct value is that students note that the
density is three orders of magnitude smaller than that of liquids or solids. They need to recognize
that a model that accounts for this fact must have the particles much farther apart than they are in the
liquid or solid state. 
12. Activity: Thickness of a thin layer
Apparatus
regular and heavy duty aluminum foil, cut into rectangles with sides ranging from 15 to 25 cm.
ruler
balance
Pre-lab discussion
Show the students a sheet of aluminum foil and inform them that they now have the tools to
accurately determine the thickness of the foil. Ask students if they think they could use their rulers
to directly measure the thickness; most will certainly agree they cannot. Remind the students that in
an earlier activity, we calculated the volume by the formula V  A h. Show that with
V
rearrangement, they can obtain the equation h  . Ask them what information they would need in
A
order to calculate the volume of a sheet of aluminum foil. Hopefully students will see that by

1cm 3
multiplying the mass of the foil by
, they can obtain the volume and that they can find the area
 2.7g
of the sheet of foil by measuring its length and width. This gives them the values they need to
calculate the thickness of the foil.

Lab performance notes
Student can measure the length and width of the foil to the nearest 0.1 cm, and then carefully fold the
foil so that they can place it on the pan of the balance. When finished, they can unfold the foil and
smooth it out for the next class to use.
Post-lab discussion
Have students record the values they obtain for the thickness of the regular and heavy-duty foil.
Students should obtain values of ~ 1.6 x 10–3 cm for the regular and 2.4 x 10–3 cm for the heavy-duty
foil. These values are consistent with the claim that heavy-duty foil is 50% thicker than regular.
Follow the discussion of class results by stating that they have just determined an upper limit for the
size of an atom. Certainly the foil must be at least one atom thick, so an atom can be no larger than
the thickness of the regular foil. Students will certainly agree, but are unlikely to reach consensus on
how many layers of atoms are present in a sheet of foil. Inform the students that the accepted value
for the diameter of an aluminum atom is 2.9 x 10–8 cm. From this they can calculate that there are
approximately 50,000 atoms of aluminum in the layer of regular foil.
©Modeling Instruction – AMTA 2013
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U1-Matter v3.1
In the resources folder are two clips from the episode “Atoms” from the Ring of Truth series
(WGBH). In the first, a goldworker shows how gold leaf is made; in the 2nd, rough measurements of
a thin layer of oil spreading out on a pond can be used to estimate the size of a molecule of oil. Also
in this folder is a short movie showing how one could perform the experiment to determine the
thickness of an oleic acid film on water.
13. Worksheet 5 – Size of Things
From the lab, students have an upper limit for the size of the aluminum particles. The Size of
Things9 website gives students practice in making estimates of the size of things at various scales.
Students should recognize that atoms are very tiny (~10-10 m), but not infinitesimally tiny.
14. Unit Review –The Model so Far . . .
The modeling approach requires students to create models to predict and explain the behavior of
matter. As more complex behaviors are observed, it stands to reason that changes in models must be
made. At the end of every unit, as a means of preparing for the test, students may review and refine
the model they used to explain events observed throughout the unit. This can be done as a
homework assignment that they discuss in small groups the next day. Small groups, then, can put
their ideas about the model (i.e., what it is, how it has changed) on whiteboards presented during a
board meeting. To keep them organized and to allow them to see the progression of the models used
in the class, the handout "The Model so Far . . ." may be used. This handout should be given to
students after the discussion of Unit 1's model and they should write a short paragraph (this may or
may not be accompanied by sketches) detailing the characteristics of the model. Students should
keep this handout and add to it as a means of reviewing for every unit.
For Unit 1 specifically, students should recognize that matter is comprised of particles that have
mass and take up space. These particles can "pack together" in different ways, giving different
substances and different states of matter different densities. Students should also develop the Law of
Conservation of Mass and the idea of "systems" and "surroundings" in their model.
15. Unit 1Test
9
http://www.vendian.org/howbig/
©Modeling Instruction – AMTA 2013
16
U1-Matter v3.1
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