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Shaking Dice to Model Equilibrium Principles Mark as Favorite (22 Favorites)

ACTIVITY in Establishing Equilibrium, Equilibrium Constants, Reaction Quotient, Graphing. Last updated July 26, 2021.


In this activity, students work together in small groups using a variety of multi-sided dice to model the dynamic character of a chemical equilibrium. Students will collect, share and analyze data in order to understand that the rate of a chemical reaction depends on the concentration of reactants (and products) as modelled by the different sided dice.

Grade Level

High School (AP Chemistry)

AP Chemistry Curriculum Framework

This activity supports the following unit, topics and learning objectives:

  • Unit 7: Equilibrium
    • Topic 7.1: Introduction to Equilibrium
      • TRA-6.A: Explain the relationship between the occurrence of a reversible chemical or physical process, and the establishment of equilibrium, to experimental observations.
    • Topic 7.2Direction of Reversible Reactions
      • TRA-6.B: Explain the relationship between the direction in which a reversible reaction proceeds and the relative rates of the forward and reverse reactions.

NGSS Alignment

This activity will help prepare your students to meet the performance expectations in the following standards:

  • HS-PS1-5: Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs.
  • HS-PS1-6: Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium.
  • Scientific and Engineering Practices:
    • Using Mathematics and Computational Thinking
    • Developing and Using Models
    • Analyzing and Interpreting Data


By the end of this activity, students should be able to:

  • Qualitatively explain that the amount of products and reactants stays constant when equilibrium has established.
  • Qualitatively explain that an equilibrium consists of a forward and reverse reaction and that both these reactions actively take place even though the amount of reactants and products remains constant.
  • Notice that the rate of a chemical reaction depends on the concentration of reactants (and products) as modelled by the different sided dice.
  • Understand that the rate of the forward and reverse reactions moves toward a constant value.
  • Calculate the reaction quotient Qc for the modelled equilibrium.
  • Use a spreadsheet to calculate the average of a series of numbers and present data in a scatter plot.
  • Analyze a scatter plot graph.

Chemistry Topics

This activity supports students’ understanding of:

  • Chemical Equilibrium
  • Equilibrium Constant
  • Establishing Equilibrium
  • Reaction Quotient
  • Data Analysis
  • Graphing


Teacher Preparation: 20 minutes
Lesson: 30-60 minutes


  • Set of multi-sided/polyhedral dice
    • suggested to have 20 dice per group
  • 2 Plastic cups per student group
    • label 1 cup as “R” (reactants) and the other as “P” (products)
  • Access to Google Slides or another collaborative spreadsheet program


  • No specific safety precautions need to be observed for this activity.

Teacher Notes

  • This activity works well at the beginning of a unit on chemical equilibrium.
  • The inspiration for this activity came from a 1999 article in the Journal of Chemical Education called “Equilibrium Principles” in which a similar game is introduced, using sugar cubes.  Sugar cubes have become harder to find recently and they make for a messy activity since they crumble. Using dice does not just allow for a cleaner and reusable solution, it also allows for modelling additional features of chemical reactions (for example, use fewer sides as a model for higher collision chance, or higher concentration) especially when multiple sided dice are used by different groups.
  • Some important features of a chemical equilibrium are that it is dynamic, and that within a closed system, it moves to a point where the concentrations of products and reactants do not change. This last feature easily ‘hides’ the dynamic aspect of a chemical equilibrium from students. Using a large enough collection of dice makes both features of an equilibrium visible again.
  • The activity itself is deceptively simple: student groups shake a set of (20) dice 8 times. Upon each shake, certain numbers are designated to move from the reactant cup to the product cup or vice versa. I suggested the numbers 1 and 3 so the activity works for D4 as well as higher-sided dice. After each time they record the number of dice in each cup in a spreadsheet. The entire experiment is repeated at least 5 times so that a somewhat reliable mean is generated. Students then graph the number of dice in each cup versus the number of throws. A typical graph of establishing equilibrium is the result.
  • An example graph is shown below:
  • Comparing graphs from different groups can lead to rich discussions about topics such as:
    • The time it takes for the equilibrium to establish itself and the connection to kinetics.
    • What elements of a chemical reaction are modelled adequately by the different sided dice.
    • The dynamic aspect of a chemical equilibrium. Even though the number of dice in each cup roughly stays the same when the equilibrium is established, after each shake dice still move between cups.
  • Steps to lead the activity in the classroom:
    • Create a shared spreadsheet with a separate tab for each student group. Each group will record their data in the tab assigned to them.
    • Divide the class into groups of 2-3 students. Provide each group with a Reactant cup (labeled as “R”) with 20 dice. All dice in the cup should have the same number of sides. Also provide an empty Product cup (labeled as “P”).
    • Assign roles within the groups:
      • Dice need to be shaken (model running the reaction)
      • Outcome needs to be measured (analyzing products and measuring data)
      • Data needs to be collected, and entered in the spreadsheet
    • Prepare for some noise and start shaking!
    • Share student results on a large screen as they are recorded.
    • When all data is collected, students need to plot the average amount of dice in each cup against the number of throws. You can either have students calculate the mean themselves, or you can add the formula to the spreadsheet so it automatically populates once students start entering their data.
  • Extension idea: Increase the amount of agreed upon numbers that will move between cups and/or increase the number of dice in a set to model changes applied to an equilibrium.
  • Note: additional time may be needed if the data analysis is done by students rather than through a template created by the teacher.

For the Student


In this activity, you will learn about chemical equilibrium by simulating a chemical reaction that proceeds to equilibrium.


In your group, assign the following roles:

  1. Lab Tech: You will shake the dice on each throw. Each throw simulates a chemical reaction being set in motion with each die being a molecule.
  2. Recorder: You will count the number of dice in each cup after each throw.
  3. Data analyst: You will enter the data in the collaborative spreadsheet and create a graph. A scatter plot works best for this activity.


  1. Prepare your spreadsheet to record the following data:
  1. Put all 20 dice in the Reactants “R” cup. This cup represents your reactants.
  2. Shake the cup and empty it on your desk. Transfer all dice with number 1 or 3 to the Products “P” cup. That cup represents the products.
  3. Count the number of dice in each cup and record in your data table under ‘Throw 1’.
  4. Shake both cups and empty them on your desk. Make sure the dice from cup R don’t get mixed up with the ones from cup P.
    1. R-cup throw: Transfer all dice with number 1 or 3 to the P cup.
    2. P-cup throw: Transfer all dice with number 3 back to the R cup.
  5. Count the number of dice in each cup and record in your data table on the next line.
  6. Repeat steps 5-6 six more times so you have a total of 8-10 throws.
  7. Repeat the entire process 4 more times so you have a total of 5 experiments.
  8. Create a scatter plot with the throw number on the x-axis and the mean in each cup on the y-axis. Provide each axis with an appropriate title and provide your graph with an appropriate title too.

Reflection Questions

Discuss the following questions in your group and be ready to share your thoughts with the class.

  1. Is the graph in any way a surprise? If so, discuss why.
  2. Sketch what the graph would look like if no numbers would ever go from the Product cup back to the Reactant cup. 
  3. After how many throws did the number of dice in each cup not change anymore?
    1. Does this mean that individual die stay in their cup after each throw? (Does it mean that no 1 or 3 are rolled anymore?)
    2. Did you answer the previous question with ‘no’? Then what does it mean?
    3. Other groups have dice with a different number of sides. How do you think that will affect your answer for the previous question?
    4. Browse through the scatter plots from other groups. Does the evidence support your answer? Discuss any discrepancies and try to formulate an explanation.
  4. Calculate the ratio between the number of dice in the Product cup and the number of dice in the Reactant cup when your graph does not change anymore.
  5. Imagine your group's goal was to increase the number of dice in the Product cup. Identify at least 2 different ways in which you could achieve this. How does this relate to an actual chemical reaction?