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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. ©Modeling Instruction – AMTA 2013 1 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 2 U1-Matter v3.1 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/ ©Modeling Instruction – AMTA 2013 3 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 4 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 5 U1-Matter v3.1 ©Modeling Instruction – AMTA 2013 6 U1-Matter v3.1 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 ©Modeling Instruction – AMTA 2013 7 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 8 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 9 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 10 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 11 U1-Matter v3.1 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 ©Modeling Instruction – AMTA 2013 12 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 13 U1-Matter v3.1 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. ©Modeling Instruction – AMTA 2013 14 U1-Matter v3.1 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 15 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