JCE Classroom Activity: #77
Instructor Information
Modeling Dynamic Equilibrium with Coins
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Martin Bartholow Shawnee Mission North High School, Overland Park, KS 66202;
[email protected] This Activity explores factors that influence dynamic equilibrium, including how long it takes two populations to equilibrate, and the relative amounts of reactants and products present at equilibrium. Students first use concrete objects (coins), then progress to mathematical calculations of equilibrium without physically manipulating the objects.
This Activity can be used as an initial introduction to dynamic equilibrium. It can be used as a concrete example when discussing forward–reverse reaction rates and Keq calculations. This Activity can also tie in to Le Châtelier’s principle. In the second suggestion under More Things to Try, students add an additional quantity to either the reactants or products midway through the process and observe its effect on the data.
About the Activity Wilson (1) has used this type of activity, and others (2–5) have used variations to help students explore equilibrium. The physical movement of objects, followed by numerical analysis, allows students to simulate reaction populations macroscopically. For the rate constants given in steps 1–9, students should generate the data shown in the table below. Note that the dynamic part of the equilibrium in this model occurs only when students are actually moving the coins; movement would continue even after dynamic equilibrium was Number Number reached if this were a chemical reaction. Instructors may wish Round # Starting A Starting B of A to of B to to discuss this limitation of the model with students. move move Students are usually surprised that a larger rate constant gives a 1 48 0 24 0 smaller equilibrium concentration, and that the ratio of the rate constants matches the final Keq. For steps 1–9, the rate constant 2 24 24 12 6 ratio of 0.5:0.25 gives a Keq of 2:1. 3 18 30 9 7 The optional analysis in More Things To Try automates the process using a spreadsheet or programmable calculator. Online 4 16 32 8 8 materialsW contain examples of student data and graphs for More 5 16 32 8 8 Things to Try and data tables for the student Questions.
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Answers to Questions 1. In Try This, the two piles equilibrate at 16 in pile A and 32 in pile B, Keq of 2. The second case gives the same results, but equilibrates in fewer rounds. 2. Rate constants a → b = 0.3 per round and b → a = 0.5 per round would give a 3/5 ratio for pile A and pile B. Final sizes would be pile A: 18 coins, pile B: 30 coins. Note that a round in the Activity is equivalent to a unit of time for a real rate constant. 3. The size of the initial population has no effect on Keq. The number of rounds changes slightly, because of the rounding effect. 4. The size of the rate constants, especially the forward rate when the reaction is starting with all of the material in pile A, determines the time to reach equilibrium. Some students may suggest a significantly smaller rate to test their hypothesis. If rates of 0.05 and 0.025 are substituted for the first series of rates, then the final equilibrium is the same, but the number of rounds increases by an order of magnitude. 5. If the 48 coins are initially split between the two piles, or all of them are placed in pile B, the final equilibrium distribution remains the same.
This Classroom Activity may be reproduced for use in the subscriber’s classroom.
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Integrating the Activity into Your Curriculum
References, Additional Related Activities, and Demonstrations 1. Wilson, Audrey H. Equilibrium: A Teaching/Learning Activity. J. Chem. Educ. 1998, 75, 1176–1177. 2. Silverstein, Todd P. Equilibrium: A Teaching/Learning Activity (Letter to the Editor). J. Chem. Educ. 2000, 77, 1410; see also author response: Wilson, Audrey H. J. Chem. Educ. 2000, 77, 1410. 3. Huddle, Penelope A.; White, Margaret D.; Rodgers, Fiona. Simulations for Teaching Chemical Equilibrium. J. Chem. Educ. 2000, 77, 920–926. 4. Paiva, João C. M.; Gil, Victor M. S.; Correia, António F. Le Chat: Simulation in Chemical Equilibrium. J. Chem. Educ. 2003, 80, 111. 5. Moog, R. S.; Farrell, J. J. Chemistry—A Guided Inquiry, 2nd ed.; John Wiley and Sons: New York, NY, 2002; p 192. JCE Classroom Activities are edited by Erica K. Jacobsen and Julie Cunningham
www.JCE.DivCHED.org
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Vol. 83 No. 1 January 2006
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Journal of Chemical Education
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JCE Classroom Activity: #77
Student Activity
Modeling Dynamic Equilibrium with Coins When there is a continuous exchange of items between one population and another, the system will reach dynamic equilibrium. In chemical reactions an equilibrium state can be recognized when the number or particles or concentration of each of the two populations (reactants and products) remains constant, but there is evidence that individual atoms or molecules are still exchanging between the two populations. This Activity explores factors that influence dynamic equilibrium, including how long it takes two populations to reach equilibrium, and the relative amounts of reactants and products present at equilibrium.
Try This You will need: 48 coins (or small objects such as paper clips or Legos), pencil, paper, and calculator. During each “round”, you will move coins from pile A (reactants) to pile B (products) and from pile B to pile A. You can stop collecting data when the piles reach dynamic equilibrium. What data will you observe when this happens? Since coins cannot be divided, if you perform a calculation that results in a fraction of a coin, round the answer down. __1. Label a sheet of paper: Equilibrium for rate constant: a → b = 1/2 per round and rate constant: b → a = 1/4 per round. Construct a table with five column headings: Round #, Starting A, Starting B, Number of A to move, and Number of B to move. __2. Begin with 48 coins in pile A. For round one, calculate how many coins to move from pile A to pile B using the appropriate rate constant from step 1. Record this number in the table under “Number of A to move”. __3. Determine the number of coins to be moved from pile B to pile A using the appropriate rate constant from step 1. Calculate this number before moving any coins from A to B; record it under “Number of B to move”. __4. Complete round one by moving the numbers of coins you determined in steps 2 and 3 (and entered in columns 4 and 5) to the appropriate piles. __5. How many coins are now in each pile? Begin the next round by recording the appropriate numbers of coins under “Starting A” and “Starting B”. __6. Determine the number of coins to move from A to B and B to A using the new starting numbers and appropriate rate constants. Record the numbers under “Number of A to move” and “Number of B to move”. Complete the round by moving the coins. __7. Repeat steps 5 and 6 until the piles reach dynamic equilibrium. __8. Calculate the equilibrium constant, Keq. The equilibrium constant measures how far a reaction proceeds before reaching equilibrium. For this Activity, this can be calculated using: Keq = final # of coins in pile B兾final # of coins in pile A. __9. Rounds can be performed mathematically without coins. Based on the rate constants and starting numbers above, write two equations that would allow you to calculate the numbers in piles A and B for each round.
More Things To Try Calculations can also be done using a calculator or a spreadsheet. __1. Devise a program that uses the same data columns from step 1 above and determine data for an initial population of A = 10,000 and B = 0 for 40 rounds. Graph “Starting A” and “Starting B” versus the number of rounds. __2. Modify the program to determine the effect of adding 5000 more items to the A or B pile at round 20. Graph the results. How does adding to one population affect both groups?
Questions 1. Predict the effect on Keq if the rate constants change to: a → b = 2/3 per round and b → a = 1/3 per round. Test your prediction. How does this compare to Keq and the number of rounds needed to reach equilibrium using the rates in step 1? 2. What is the relationship between Keq and the rate constants? Calculate the final size of the piles for a → b = 0.3 per round and b → a = 0.5 per round, with 48 coins. 3. What effect does the size of the initial population have on Keq and the number of rounds needed to reach equilibrium? Using the rate constants from step 1, try an initial population of 480. 4. The number of rounds to reach equilibrium in this Activity is very small. Predict what determines the number of rounds needed to reach equilibrium. Carry out the necessary procedure to test your prediction. 5. Use the rate constants from Try This step 1 to predict the final sizes of the piles when starting with: (1) 24 coins in pile A and 24 coins in pile B, and (2) 48 coins in pile B. Test your prediction.
Information from the World Wide Web (accessed Nov 2005) Chemical Equilibrium. http://www.geocities.com/CapeCanaveral/Launchpad/5226/equilib.html This Classroom Activity may be reproduced for use in the subscriber’s classroom.
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Journal of Chemical Education
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Vol. 83 No. 1 January 2006
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www.JCE.DivCHED.org
