Lesson Plan - Ideal Gas Model (AgentSheets)

Basic Model:

Description

The Ideal Gas Model simulates particles of gas randomly bouncing around in two different, connected containers. The particles move randomly, do not interact with each other, and diffuse from one container into another based on preset variables. This model attempts to convey how the particles will move towards equilibrium while the ratios of volume to number of particles in each flask remains the same. Users may change the volume of each flask and the amount of particles starting in each in order to study the effects that each change has on the migration of gas particles between the two containers.

Background Information

Gasses behave in set, mathematical ways when in ideal situations. More specifically, the pressure, temperature, volume, and number of moles of particles are all in a specific ratio. While this scenario does not happen in real-life situations, studying the ideal gas laws will provide a better understanding of what real-life situations are attempting to approach. With a constant pressure and temperature, the volume of the gas' container and the number of particles are equal to a constant. Since the constant is equal for any two containers, the ratio of volume to particles of one container will equal the ratio of volume to particles of another container. This model attempts to expand upon this idea by allowing users to study the effects of the change in volume and number of particles on the system's attempt to reach equilibrium. When one variable is changed, the two flasks return to equilibrium through random chance of moving particles, illustrating Avogadro's Law.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. As time progresses, the following events occur:

1. The gas molecules bounce randomly in a flask
2. Molecules change flasks according to their random trajectory
3. The density of each container increases or decreases
4. The pressure in each container increases or decreases
5. The number of molecules in each flask nears an equilibrium point
6. The ratio of volume to number of molecules in each flask nears an equilibrium point

CHANGE in this formula includes manipulating the variables affecting the volume of each flask and the number of particles in each. With a visual aid, students will be able to see the effects of specific changes qualitatively, and through the simulation properties they will be able to quantitatively understand the ratios of each variable.

Teaching Strategies

Teachers should begin by asking the students to think about what should happen in the model simply by intuition. The following questions will help start the students' thinking in the correct direction:

1. If more students were added to the classroom, how "stuffy" would the room be? Would people want to leave? If everyone were running around at once, would more people be knocked outside of the room?
2. This model deals with gas particles in a flask, which is much smaller than students in the classroom, but there are still similarities in each situation. What would happen if the pressure were to increase in one of two connected flasks containing gas particles?
3. How would a large container decrease the pressure within if the objects inside were moving around?
4. If more particles were added to the system, what would be the result? How do you know?
5. As an increasing number of particles are surveyed in the container, would the estimate of pressure become more or less accurate? Why?
6. Over time, what would the pattern of movement between the two containers become?

Implementation

How to use the Model

This model contains a couple of parameters that may be manipulated to produce different results:

1. The N1 and N2 simulation properties determine the amount of molecules in the first and second flask when the simulation begins
2. The V1 and V2 simulation properties determine the volume of the first and second flask when the simulation begins.

Editing the "Simulation Properties," located on the right hand side after clicking on the gray drop down arrow, will control these attributes. The Ratio attribute is calculated by dividing the ratio of the number of gas particles in each flask (Nratio) by the volume ratios of each flask (Vratio). These are unchangeable, as they are calculated as the simulation runs. Sliding the Slow/Fast slider at the bottom of the simulation will change the speed that the particles move around the container. Clicking the green play button in the bottom left corner of AgentSheets will run the simulation. Immediately, the particles will begin randomly bouncing around the first flask and eventually move into the second. The Simulation Properties will begin reflecting the changes within the system. The black button next to the play button will allow advancement through the simulation one tick at a time. Stepping through the simulation will allow for a better understanding of the random movement of molecules and elastic collisions.

Learning Objectives

1. Understand equilibrium and explore ideal ratios for gas
2. Understand how manipulation of any variable will eventually lead to equilibrium
3. Understand the law of large numbers, or how with more particles, the results of experimentation will likely lead to a closer approximation of ideal situations.

Objective 1

This objective is best accomplished by allowing students to run the simulation multiple times and survey the trends in the variable change. Students should focus on the number of molecules and the ratios presented to find the point at which each variable remains relatively constant. Ask the following questions:

1. What happens to the numbers and ratios over time in relation to their change?
2. Which flask has the most molecules after the numbers seem to stop moving as much? Why would this be?
3. How are the ratios of each variable related? What does this number imply?
4. The equation represented in this situation is N1/V2 = N2 /V2, where N1 is the number of molecules in the first flask and V¬2 is the volume of that flask and N2 is the number of molecules in the second flask and V2 is the volume of that flask. How does this provide a mathematical model for when one of the variables is changed?
5. Do molecules tend to move towards a high concentration or away from it? Why is that?

Objective2

Students should begin to manipulate the variables in order to study their effects on the equilibrium points and the movement of the molecules. Ask the following questions:

1. What effects did you notice when manipulating the variables in general? Were the effects short-lived or did they affect the end result of the simulation?
2. As the number of molecules increased in the system, what seemed to happen to the movement of the molecules? Thinking back to the mathematical equation or the classroom analogy, what do you think happened with the pressure?
3. When the volume of one flask is increased, is there a change in the number of molecules in that side of the system? In the pressure?
4. How would these changes be implemented in the classroom analogy? Can you think of any other systems that behave in similar manners?

Objective 3

The variable that students should be focused on for this objective is the number of molecules in the flask. With an increased amount of molecules in the system, they should be able to see a more accurate estimation of the equilibrium point. The following questions may help in guiding students to the correct ideas:

1. Do any of the ratios fluctuate? If so, by how much? If not, why does it not?
2. When the amount of particles in the system is increased, what happens to any fluctuating ratios?
3. Using what you know about equilibrium points, would an increase in particles relate to a more accurate prediction of any equilibrium point?

Extensions and Related Models

Extension 1

Students should have begun to understand the ideal gas laws through this model. Following the model, explain to students that the ideal gas laws are just that, "ideal," and they are not how the particles would behave in a real situation. Explain the idea of elastic versus inelastic collisions between molecules, the effect of mass on the interactions, and then ask these questions to further the students' understanding of actual gas interaction:

1. When gasses collide with each other in ideal situations, would the collisions be elastic or inelastic? How about in real world situations?
2. With ideal gas laws, it is assumed that the molecules are single points and take up no space. How would the mass of the particles have an effect on the interactions in real life?
3. Temperature may also have an effect on the interactions of the gas molecules in real life cases. Thinking back to the equation PV=nRT and the classroom analogy, how would temperature and the movement of the particles relate to a change in pressure?

Extension 2

Ask students to research the structure of the diaphragm and how it helps humans to breathe. Discuss the interaction of gas particles and the ideal gas laws-especially Boyle's Law-in relation to the organ. In a human diaphragm, the muscle contracts, allowing a larger volume for the lungs. The pressure in the lungs becomes much less than that of outside, which forces air into the lungs. Ask students the following questions in order to discuss ideal gas in relation to biology:

1. When the diaphragm contracts, what happens to the volume of the lungs? Based on the model previously studied, what will this do to the pressure of the lungs?
2. How will the air inside the lungs differ from the ideal gas model, since the lungs are encased inside the body?
3. When one says that the "wind was knocked out of them," what is actually happening? Whose law is not being allowed to function?

Related Models

Generic Chemical Dynamics

This model will allow students to further explore the topic of equilibrium. The chemical equations presented in the model may be manipulated in order to understand reactants, their intermediate stage, and the eventual products. How this may be tied into the Ideal Gas Model is through the reversal of the reaction. Since the equation is reversible, the reaction will eventually reach equilibrium with products and reactants at an appropriate ratio.

Dominant Recessive Sampling

The Dominant Recessive Sampling Model will allow students to further understand the Law of Large Numbers. With an increased number of trials or events, real world situations will present themselves more like the ideal. With genetics, if the recessive allele has a certain frequency, one can attempt to find this number by counting the number of individuals with the recessive alleles in a given population. As the number increases, the actual allelic frequency will begin to appear. By changing the population size in this model, students will be able to better understand the idea and application of the Law of Large Numbers.

Supplemental Materials:

• Dominant Recessive Sampling tutorial and background information

Pseudo Random Numbers

This model will present a way for students to understand flaws in the model in relation to its simulation of a real world, random event. The gas particles in the Ideal Gas Model bounce around randomly in the flask, but computer models cannot fully represent random chance. The Pseudo Random Numbers model explores this idea and shows how random chance is presented in the model through multipliers and shifts. Ask students how pseudo random numbers are related to the computer simulations, and specifically how they affect the results of the gas model.

Diffusion in a Box (Excel)

Diffusion in a Box will allow students to understand the movement of gas molecules in a container with the added variable of selective barriers. In the Ideal Gas Model, students were presented with two flasks between which the gas could flow freely; this model instead focuses on understanding gas movement within four different compartments of a box. Concepts of random movement of gas particles and pressure will be revisited, and additional topics of equilibrium will be introduced.