Using Simulations to Derive the Gas Laws

Using Simulations to Derive the Gas Laws Time Two 40-50 minute class periods Level Physics or Chemistry, grades 9-10 Purpose Students use computer simulations to gain a deeper understanding of the gas laws. Overview Gas laws have an impact on several aspects of our lives. We may have ideas about what happens when we leave a soccer ball outside on a cold night and wake up to find it shrunken and dew- covered, but can we describe it in terms of variables, graphs, and relationships? In this lesson, students gain a deeper understanding of the gas laws by running experiments within a computer simulation interface and determining the mathematical form of the data they generate. Students explore the relationships between macroscopic properties of gasses pressure (P), volume (V) and temperature (T) and start to understand how these properties arise out of microscopic behavior (i.e., the motion of the gas particles and the interaction with the walls of the container). Student Outcomes Learner objectives 1. Students will be able to conduct controlled simulations to test their prediction(s). 2. Students will be able to collect data from a computer simulation, input them into a spreadsheet program, and then sort, plot, and analyze the data 3. Students will be able to determine the mathematical functional form of their data using a spreadsheet program 4. Students will be able to describe the relationship between pressure, volume, temperature and density in a gas, i.e., the gas laws. 5. Students will be able to distinguish between the microscopic and macroscopic properties of a gas system, and explain how they are related. 6. Students will be able to explain the qualitative behavior observed in real systems that involve a gas and changing properties 1

CT- STEM skills: 1. Data & Information a. Collecting/generating data d. Analyzing data 3. Computational Modeling a. Using Computational Models to Understand a Concept c. Assessing a model 4. Systemic Thinking b. Understanding relationships within a system d. Visualizing a system Next Generation Science Standards: HS.PS- CR.h. Construct explanations using data from system models or simulation to support the claim that systems with many molecules have predictable behavior, but that the behavior of individual molecules is unpredictable Science and Engineering Practices: Analyzing and Interpreting Data - Use tools and models to generate, gather and analyze data Developing and Using Models - Use / construct models to predict / explain relationships between systems and their components Crosscutting Concepts Systems and System Models Cause and Effect Common Core Standards: RST.9-10.7 - Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. - Interact with computer models of a microscopic situation - Gather data based on computer simulations - Use spreadsheet program to sort, compile, and graph data - Students are introduced to gas laws. Illinois State Science Standards: 11.A.4a Formulate hypotheses referencing prior research and knowledge. 11.A.4b Conduct controlled experiments or simulations to test hypotheses. 11.A.4c Collect, organize and analyze data accurately and precisely. 11.A.4f Using available technology, report, display and defend to an audience conclusions drawn from investigations. 2

Prerequisites Students should be familiar with what a gas is, and have been introduced to the concepts of temperature, pressure and volume. Students should be familiar with using Microsoft Excel for entering data, sorting, and plotting. Teaching Notes The introduction gives students a chance to think about what they already know (or think they know) about gasses and the properties that we ascribe to them. They can do this alone or with a partner. Part 1 is the hook the teacher plays you tube videos that show everyday examples that involve gasses with changing properties. Students make observations about what is happening in each system which quantities (P, V, T, N) are most important, and what is changing in the system over time. This will make the point that the topic is connected to everyday phenomenon, and get them excited about the activities that follow. Students should work in pairs or groups for the rest of the activity. 3In Part 2, students begin exploring the PhET Gas Properties simulation on their own. This gives them a time to try to understand what the simulation is modeling and how they can interact with the system. Students are curious and enjoy playing with technology this gives them time to do so. During this time, they should determine what variables they can vary and measure and how to do so. It is helpful to give them some suggestions to guide their exploration; they can ignore the gravity feature and the different types of species of gas (heavy and light) particles neither of these will be addressed in this lesson. While the students are exploring, the teacher can check- in with groups to see what they are learning. Find students/groups who have discovered important features of the simulation and how to control and/or measure them. Make a note of which groups have discovered what. After students have had about 5 minutes to explore, call up different students to demonstrate for the class how to control different aspects of the simulation. It is also important to note that when you change one variable, the system will respond in a certain way, depending on which variable is held constant. Make sure students are comfortable using the model, and are capable of varying and measuring the relevant quantities (P, V, T, N) before moving on. In Part 3, students perform controlled experiments with the model. They are given the goal of learning how P, V, T, and N are related, but are asked to design and run their own experiments. Different groups will choose to run different experiments. This is fine, as the groups can share their results later. Students can take note of the results of experiments that they did not do. Depending on how comfortable your students are with doing controlled experimentation, you may want to provide more guidance than is provided in this lesson. An example of an experiment that can be done is to keep the volume and number of particles constant, and see how temperature affects pressure. They can add or remove heat from the system to 3

change the temperature, and they will see the particles speed up or slow down as T changes, and P will adjust accordingly. There are many other combinations of pairs of variables that can be explored. If your students are familiar with Excel, you can have them enter and plot their data there. Alternatively, the data can be collected on paper and plotted by hand. In this lesson, there is no need to do any computationally challenging calculations or analysis (like making a best- fit line for the data). The main goal is to understand the qualitative relationships between the gas properties more- so than the quantitative. For these reasons, either option (Excel or pencil and paper) is appropriate. They are provided with a table to organize the main results of their three experiments, and there is also room to enter results of their classmates experiments. In Part 4, the goal is to begin to explore how the macroscopic properties of the system, such as P, V and T, are produced by the microscopic behavior of the system that is, the motion of the particles. Depending on abilities of students, the teacher may need to provide more or less guidance. After giving students time to ponder over these ideas, a group discussion will probably be needed to facilitate understanding of these deeper concepts. In Part 5, students think more deeply about the simulation itself, and how it compares to actual tabletop experiments. It is important for the students to realize that, in a real tabletop experiment, they would not have actually been able to observe the motion of the particles; this will hopefully lead to an appreciation of the some of the pros of using computer simulations to learn about STEM concepts. It can also lead into a discussion of the limitations of computer simulations. Extensions - Students can explore other features not addressed in this lesson, such as including gravity to the simulation or comparing results using heavy and light particles. - The PhET simulation can be used to do a more in depth study of the kinetic theory of gasses, including looking at speed distributions and average speeds of one or two types of particles. You can display Species information and Energy histograms under the Measurement tools. Pre- class Preparation The teacher should be familiar with the simulation and know how to control all properties of the system. Pressure (P) and Temperature (T) are displayed at all times in standard units (atm and K, respectively). To add or remove heat, thereby changing T, use the Heat Control button. Click and hold the mouse on the blue marker and slide upward to add heat, or downward to remove heat (cool) the 4

system. When you release the mouse button, you will stop adding/removing heat. You will see T change accordingly. To add gas particles to the box, you can pump the handle using the mouse click and drag the pump lever up, then press it down, and a set of particles will enter the box. In the panel at the right, you can see the number of particles in the box, and add or remove particles using the up/down arrows, or by simply entering a number in the box. Note that there are two kinds of particles heavy and light. This lesson does not discuss this at all, so you might want to suggest that they just stick with heavy particles, which are the default type of particle that will be added using the pump. To obtain the volume (V), you will have to measure the length of the box. Click on Measurement Tools to display a set of tools, including a ruler. Unfortunately, the ruler can only be used horizontally, so it cannot be used to measure the height. You may have to discuss the concept of volume with the students, in relation to the simulation. Of course, the computer screen can only display a 2D box, while volume is a 3D quantity. You can tell them to imagine that the box extends behind the screen to some depth. It turns out, the numerical value of the height and depth is not needed to understand how changing volume affects the system. The only dimension of the box that can be varied is the horizontal length of the box. You can change the length of the box by clicking to the left of the left wall, by the stick figure, and dragging in either direction. Since you can only change this length, it is sufficient to just measure the length, and assume the other dimensions (height and depth) remain constant. Therefore the volume will be V = length x height x depth. If students find it easier, they can choose values for the height and depth of the box, and assume them to be fixed throughout the experiment. Note that when you make a change to the system, it takes a bit of time to adjust. For example, if you change the volume of the box, the pressure will start to change as the particles adjust their motion in the new configuration. The pressure will always fluctuate a little bit this is due to the nature of pressure and how it is measured. Pressure is the net force of the particles on the walls of the box divided by the area. If you watch the simulation for a while, you will notice that the particles hit the walls randomly and at different speeds and angles. Due to this realistic feature, the measured pressure will fluctuate accordingly. Students may find this disturbing, but it actually represents the true nature of the system appropriately. They will have to choose the best value of pressure that the system seems to hover around. One of the variables P, V or T can be held constant in each experiment. You can do this by clicking on one of the variable names at the top of the panel on the right. Materials and Tools Access to computers with internet (pairs or groups is fine) Videos: 5

1. Whale: http://www.youtube.com/watch?v=uw0yyyj3b0m 2. Tire explosion: http://www.youtube.com/watch?v=_3_pmhba_- c&feature=related 3. Tire burnout: http://www.youtube.com/watch?v=x0cgurelknc 4. Steel Drum: http://www.youtube.com/watch?feature=fvwp&v=n- 3cu_Q119s&NR=1 PhET Gas Properties simulation: http://phet.colorado.edu/en/simulation/gas- properties Overhead projector to demo usage of simulation Assessment Completed spreadsheet and handout A nice way to test their understanding of gas properties is to have students create a narration for a physical event or experiment. The simplest idea is to provide them with a video, such as the steel drum video above, that shows how a gas system responds to changes in its properties (like the videos at the start of the activity). Students can create a screencast with the video is playing on their computer (without audio!), while they narrate the video based on what they have learned using the simulations. The teacher can play each groups narration for the class, or view and assess them privately. Screencast- O- matic provides free software for creating screencasts (http://www.screencast- o- matic.com/). Acknowledgements The Gas Properties simulation is available from PhET (http://phet.colorado.edu/). Parts of the lesson are adapted from the Gas Properties Modular Homework Activity available on the PhET website (authors: Julia Chamberlain and Ingrid Ulbrich) Student handouts start on next page. 6

Using Simulations to Derive the Gas Laws Introduction In this activity, you will explore the relationships between properties of gasses: pressure (P), volume (V), temperature (T), and number of particles (N). These relationships make up what we call the gas laws. You will learn how a gas responds when properties of the system are changed how microscopic* properties affect observable macroscopic* properties of the system, such as P, V, T *microscopic properties refers to very small scales - things we cannot see or measure with our eyes, like particles and atoms macroscopic refers to larger scale properties that we can observe and measure, like temperature Answer the following questions based on what you already know. It is ok if you do not know all the answers just write what you think! a. What is a gas? Name some gasses that you are familiar with. b. What is volume? How do you measure the volume of a square box? c. What is temperature? d. What is pressure? 7

Part 1: Observing real systems Watch each video and make observations based on what you see. What quantities (P, V, T, N) do you think are most important in each video? What are the experimenters changing, and what affect does it have on the system? 1. Whale: http://www.youtube.com/watch?v=uw0yyyj3b0m 2. Tire explosion: http://www.youtube.com/watch?v=_3_pmhba_- c&feature=related 3. Tire burnout: http://www.youtube.com/watch?v=x0cgurelknc 8

Part 2: Explore the Simulation Go to the website below and click on the Run Now! button: http://phet.colorado.edu/en/simulation/gas- properties Take 5 minutes to explore the simulation. Things to think about: Which variables can you change and how? How do you read/measure properties of the system (for example, pressure)? How can you hold certain variables constant? Now answer these questions: (1) Describe the system that is being modeled by the simulation (2) Why would you want to hold certain variables constant? (3) Write down at least two observations that are interesting to you. 9

Part 3: Understanding the Gas Laws Your goal is to learn about how pressure (P), volume (V), temperature (T), and number of particles (N) are related. You must design and perform at least 3 controlled experiments that can be done with the simulation to investigate the relationships between P, V, T, and N. (a) Review: what is a controlled experiment? (b) Briefly describe the three controlled experiments you will perform. Be sure to decide which variable(s) will be held constant. (c) How many trials or measurements will you do in each experiment? Why does this matter? 10

Perform your experiments and enter your data into an excel spreadsheet. Graph each data set in excel. When you are done with your experiments and analysis, put your results into the table below by using these 5 questions as a guide: (1) What are the independent and dependent variables? (2) Which variables are held constant? (3) As X increases, Y (increases / decreases). (replace X and Y with your variables) (4) X is (directly / inversely) proportional to Y. *Hint: A pair of variables is directly proportional when they vary in the same way (one increases and the other also increases). A pair of variables is inversely proportional when they vary in opposite ways (one increases and the other decreases). (5) Express the mathematical relationship between the two variables in this form: X1/Y1 = X2/Y2 OR X1 Y1 = X2 Y2, where X1 and Y1 represent the initial values of the variables, and X2 and Y2 represent the values of the same variables, but after you changed your independent variable. Only one of these relationships will match the observed behavior. Exp. Variables Constant Parameters As X increases, Y Increases, decreases, stays the same Independent/ dependent Relationship Proportionality Mathematical relationship directly proportional OR inversely proportional X1/Y1 = X2/Y2 OR X1 Y1 = X2 Y2 1 2 3 4 5 6 11

Part 4: Relating Microscopic to Macroscopic properties (a) The simulation shows gas particles moving around in the box. How does the behavior of the particles change when you change properties of the system? Give specific examples. *hints: think about speed of the particles, how they interact with each other, how they interact with the walls of the box. (b) Based on your observations from (a), try writing new definitions for temperature and pressure. Your definitions should include something about the behavior of the particles. Temperature: Pressure: (c) In this simulation, what are the microscopic properties of the system? What are the macroscopic properties of the system? How are they related? Microscopic: Macroscopic: Relationship: 12

Part 5: Using Computer simulations Imagine doing a real- life table- top experiment similar to what you did in the computer simulation. Imagine the materials you might use, and how you would measure properties of the system. (a) What would be different about using the simulation and doing an actual real- life experiment? (b) Did the computer simulation help you learn or visualize anything that you would not have with a real- life experiment? (c) Are there things about the simulation that are unrealistic or different from the real world? 13