Lesson 5. V - Volume and Pressure

Umit Aslan, Nick LaGrassa
Chemistry
45 minutes
High School
v3

Overview

This lesson introduces a computer model that allows them to change the location of one of the walls of the container, hence experiment with different volumes. They use this model to examine the relationships between container volume and pressure. Students use CODAP to collect data and then find a mathematical equation of the relationship between volume and pressure. They use the equation to make predictions about what the pressure will be for different volumes.

Standards

Next Generation Science Standards
  • Physical Science
    • [HS-PS2] Motion and Stability: Forces and Interactions
  • NGSS Crosscutting Concept
    • Patterns
    • Systems
    • Structure and Function
  • NGSS Practice
    • Analyzing Data
    • Constructing Explanations, Designing Solutions
    • Asking Questions, Defining Problems
    • Using Models
    • Arguing from Evidence
    • Conducting Investigations
Computational Thinking in STEM
  • Data Practices
    • Analyzing Data
    • Collecting Data
    • Creating Data
    • Manipulating Data
    • Visualizing Data
  • Modeling and Simulation Practices
    • Assessing Computational Models
    • Designing Computational Models
    • Using Computational Models to Find and Test Solutions
    • Using Computational Models to Understand a Concept
  • Computational Problem Solving Practices
    • Assessing Different Approaches/Solutions to a Problem
    • Computer Programming
    • Troubleshooting and Debugging
  • Systems Thinking Practices
    • Investigating a Complex System as a Whole
    • Thinking in Levels
    • Understanding the Relationships within a System

Credits

The 2019 version of this unit is developed by Umit Aslan (umitaslan@u.northwestern.edu) and Nicholas LaGrassa (nicholaslagrassa2023@u.northwestern.edu).

Acknowledgement

A majority of this unit is adopted from the earlier Connected Chemistry units developed by Uri Wilensky, Mike Stieff, Sharona Levy, and Michael Novak (see http://ccl.northwestern.edu/rp/mac/index.shtml for more details). Some elements are also taken from the Particulate Nature of the Matter unit developed by Corey Brady, Michael Novak, Nathan Holbert, and Firat Soylu (see http://ccl.northwestern.edu/rp/modelsim/index.shtml for more details).

We also thank undergraduate research assistants Aimee Moses, Carson Rogge, Sumit Chandra, and Mitchell Estberg for their contributions.

Activities

  • 1. Why does the marshmallow expand?
  • 2. Our experimental setup: the virtual syringe model
  • 3. It's CODAP Time!
  • 4. Testing the validity of our mathematical model

Student Directions and Resources


In Lesson 3, we explored the relationship between the number of gas particles in a container and pressure. We kept other factors (temperature and volume) constant.

In Lesson 4, we explored the relationship between gas temperature and pressure. We kept other factors (number of particles and volume) constant.

   

In this lesson, we are going to explore the relationship between volume and pressure.

The goals of this lesson are:

  • Analyzing the relationship between container volume (independent variable) and gas pressure (dependent variable).
  • Developing a mathematical model to express the relationship between container volume and gas pressure.

1. Why does the marshmallow expand?


Once again, before moving on to our computational explorations, let us consider the experiment on the right:

  1. The experimenter places a marshmallow inside an unsealed syringe.
  2. He pushes the plunger all the way until the marshmallow.
  3. He seals the syringe with his fingers.
  4. He pulls the plunger all the way
  5. The marshmallow expands.

 

Why does the marshmallow expand? Let's hypothesize.

Note: If your teacher has syringes (and maybe even marshmallows), you should try to conduct this experiment yourselves.


Question 1.1

What is the difference when the plunger is pushed all the way and when it is pulled all the way? Draw a sketch for each condition. (please spend no more than 6 minutes on this task).

Note: please use colors other than black to differentiate with the balloon outline.

Note: Draw your sketch in the sketchpad below


Question 1.2

Please explain your sketch verbally (min. 3 sentences)



Question 1.3

Did "gas pressure" factor into your thinking? If yes, please elaborate. If no, why? (min. 2 sentences)



Question 1.4

Why do you think a marshmallow is used in this experiment? What would happen if we used a piece of wood instead?

2. Our experimental setup: the virtual syringe model


The models we used in the previous activities did not let us change the volume of the container. However, many gas containers, like balloons and syringes, grow and shrink. In this lesson, we are going to explore the relationship between container volume and pressure. To do so, we will use another slightly different model. This model will allow us to simulate a syringe; it will allow us to chance the position of a wall, so that we can increase and decrease the volume.

Begin experimenting with your model and explore the relationship between your dependent variable (pressure) and your independent variable (volume). Conduct a preliminary experiment as follows:

  1. Run the model with the default parameters (initial wall position = 30).
  2. Wait for pressure to stabilize. Take note. Also note the volume of the container.
  3. Move the wall to the right at least 10 units above 30 (higher volume).
  4. Wait for pressure to stabilize. Take note. Also note the volume of the container.
  5. Move the wall to the left at least 10 units below 30 (lower volume).
  6. Wait for pressure to stabilize. Take note. Also note the volume of the container.

Record the changes in the data table below.

Note: We already know that increasing the number of particles increase pressure. So, do not change the number of particles in your trials. Otherwise, your data may mislead you.


Question 2.1

Record the results of your preliminary experiment below.



Question 2.2

Mark your data points in the plot below.

Note: Draw your sketch in the sketchpad below


Question 2.3

What kind of a relationship between volume-pressure do you observe from these three data points? Is it similar to our previous explorations (number-pressure, temperature-pressure)? Is it different? Please elaborate. (min 3. sentences).



Question 2.4

In the next page, you will conduct your last experiment in CODAP in this unit. Design your experiment using the table below:

Dependent variable: (P)ressure
Independent variable: (V) olume
Research question:

Is there any relationship between these two variables?

If yes, what is the mathematical nature of this relationship?

Note: Once again, we cannot directly set the volume of the container. Instead, determine values for the "wall position" parameter.

3. It's CODAP Time!


Now let's go ahead and conduct our final computational experiment within CODAP!!!

Note: If you do not remember the exact details, you can see your initial experimental design below the CODAP window. If you are not sure about your experimental design, consult your teacher before starting. 

  1. Run each experiment long enough so that pressure stabilizes before your model reports the data.
  2. Keep non-involved parameters (e.g., number of particles, ticks-to-run) fixed at all experiments.
  3. Run at least 3 trials (repetitions) for each combination.
  4. Try at least 5 different values for the independent variable (volume/wall-position).
  5. Speed up the model to conduct the experiments as fast as possible.
     


Question 3.1

First and foremost, save your CODAP experiment and upload it using the "Browse" button below. You can do it as follows:

  1. Click the hamburger menu () icon on he top-left corner of the CODAP window.
  2. Click Save ().
  3. Choose the Local File option ()
  4. Click Download ().
Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 3.2

Also, upload a screenshot of your plot.

You can export a plot in CODAP as an image:

  1. Click anywhere on the plot.
  2. From the side menu, click the camera icon.
  3. Click the "Export Image" item.
  4. A pop-up window will open. Choose the "Local File" option and then click "Download"

 

 

Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 3.3

At this point, if you collected enough data, you must have noticed that:

  • pressure decreases as volume increases
  • resulting plot looks more like an arc than a straight line

Both of these findings are different than our previous two explorations.

Why do you think we observe this arc-like plot? (min. 2 sentences).



Question 3.4

Unfortunately, using the "movable line" tool would not help us in this situation because our data does not show a linear relationship. What we observe is a non-linear relationship.

The specific type of relationship we are observing can be expressed through a mathematical form as follows: y = m / x, where m is a constant coefficient.

 

On the other hand, we can use CODAP's "Plotted Function" tool to approximate a mathematical function that fits our data:

  1. Click anywhere on the plot.
  2. In the opening window, click the "Plotted Function" option.
  3. A bar with caption f() will appear on the top of the plot. 
  4. Click the function bar and write "10000 / volume" as your plotted function. This means your function is P = 10000 / V.
  5. Repeat this step until you find a coefficient value that 

What was the coefficient that fit your data the best?



Question 3.5

What is your mathematical model (equation) that explains your data the best?

Write it as: Pressure = coefficient / Volume 

4. Testing the validity of our mathematical model


As usual, let's put our mathematical model to a test and if our inverse plotted function approach paid-off!

 


Question 4.1

According to your mathematical model, if we observe a pressure of 250, what would our volume be (approximately)?



Question 4.2

Were you able to validate your prediction within the model? Explain. (min 2. sentences)



Question 4.3

According to your mathematical model, what would pressure be if our container's volume is 5500?



Question 4.4

If you tried to validate your prediction with the model, you must have noticed that the largest volume allowed is 2970. Hence, we cannot test our prediction with the current version of the model.

Still, how confident are you in your prediction? Do you think your model would still be useful in situations that are not easily testable? Elaborate. (min. 3 sentences)



Question 4.5

Before finishing this lesson, let's return to our "marshmallow in the syringe" experiment. 

Now that you completed your computational experiment and developed a mathematical model of Pressure-Volume in a gas container, did your thinking about this phenomenon change?

Please explain your final understanding verbally. But more importantly, please elaborate how your understanding is informed by your mathematical model? (min 3 sentences).