# Simulating Simple Reaction Mechanisms

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1 Simulating Simple Reaction Mechanisms CHEM 4450/ Fall 2015 Simulating simple reaction mechanisms with dice rolling For this model, you will use 100 dice to model three simple reaction mechanisms under various conditions. You will assume that the reactions you model occur in 1cm 3 so that the concentrations are simple to calculate. For example, if 12 of your dice are considered species B, you would have a concentration of 12 cm -3 for B. In all of the simulations, you will use 100 dice, and assume that they are all species A when you begin. So, [A] 0 is 100 cm -3 for all simulations. Each time you roll the dice, you will simulate 1 second in the reaction. So, the first round of rolls will produce concentrations for the species at time=1s. After the second, you will have concentrations for time =2s, and so on. Once a die has been rolled, it is not to be rolled again during that second. Each die gets one chance to react per time interval. Instead of a traditional write-up, I just expect to get your data/calculations/and answers to the questions asked in the lab. Each portion of the lab requires a large plot with 6 traces on it. Three will be from the modeled concentration vs. time, and three from your data. I also want to see nice tables with the modeled data and the dice data for each mechanism.

2 Parallel Reactions A B k 1 A C k 2 Part 1: k1>k2 [A] = [A] 0 e k Tt [B] = k 1 k T [A] 0 (1 e k Tt ) [C] = k 2 k T [A] 0 (1 e k Tt ) = [A] 0 [A] [B] 1. Use excel to model the concentrations for all species as a function of time. a. Assume [A] 0=100, k 1=1/6 s -1, k 2= 2/6 s Roll the dice! a. First, all dice will be in area A. b. For t=1s, roll all dice in A. Those landing on 1 move to B, Those landing on 2 or 3, move to C. The rest remain in A. c. Continue until all dice are moved to B or C. Note that Dice in B or C will not be rolled again. d. We expect that the values of [B]/[C] equal k 1/k 2 at all times. Produce a column in excel that calculates this from your theoretical and your experimental values. Does it equal k 1/k 2? e. What are the branching ratios for B and C

3 Reversible Reactions A B k 1 B A k -1 Part 1: k1>k-1 [A] = [A] 0 k 1 + k 1 [k 1 + k 1 e (k 1+k 1 )t ] [B] = k 1[A] 0 k 1 + k 1 [1 e (k 1+k 1 )t ] = [A] 0 [A] 1. Begin by modeling the kinetics using k 1=2/6 s -1, and k -1=1/6s Roll! a. Time=0s. Begin with all dice in area A. b. Roll all dice in A. Move values 1-2 to area B. Count the dice in area A and B for t=1s. c. Roll all dice in areas A. If a 1 or a 2 is rolled, move the dice to area B. Roll all die in B (not the ones you just moved this round, but the ones already here.) If a 6 is rolled, that die moves back to A.

4 d. Continue rolling until the values are stable (+/- 3) for several turns. 3. Use your data to show that the value of K eq calculated from equilibrium concentrations is equal to k 1/k -1.

5 Consecutive reactions A B k 1 B C k 2 General: [A] = [A] 0 e k 1t [B] = k 1 k 2 k 1 [A] 0 (e k 1t e k 2t ) [C] = [A] 0 [1 k 1 (e k1t e k2t ) e k1t ] k 2 k 1 0 Part 1: Assume k1>k2 The equations above for the species simplify to: [A] = [A] 0 e k 1t [B] = [A] 0 (e k2t e k1t ) [C] = [A] 0 [A] [B] 1. Assume that the value of k 1 is 5/6 s -1, and the value of k 2 is 1/6 s -1. Use excel to model the concentrations of A, B, and C as a function of time. a. Set [A] 0 =100, k 1=5/6, and k 2=1/6 b. Make a column in excel for time values in units of seconds. You will need about 25 seconds to run this simulation. c. Make a column for the calculated value of concentration A using the values of [A] 0, and k 1. d. Make a calculated column for [B]. e. Use Mass conservation to calculate the value for [C]. 2. Now, roll your dice! a. It is best to partition the table into 3 areas one for dice that represent each species. b. Begin with all of your dice in area A. This represents time=0 s.

6 c. Now, roll all of the dice in A. If the value is between 1 and 5, move the dice to area B, if you roll a 6, the die stays in area A. When all of the dice have been rolled once, stop. Count each die and record the numbers of A and B for time= 1s. d. For time =2s, begin with your dice in area B. Roll all of these dice. If the value is a one, move the die to area C, if it is between 2 and 6, leave it in area B. Now roll the dice in area A and move all dice to area B that land on values 1-5. e. Count all the dice in each area and record the values for t=2s. f. Continue in this manner until all dice are moved to area C.

7 Part 2: Assume k1<k2 The equations above for the species simplify to: [A] = [A] 0 e k 1t [B] = k 1 k 2 [A] 0 (e k 1t e k 2t ) [C] = [A] 0 [A] [B] 1. Assume that the value of k 1 is 1/6 s -1, and the value of k 2 is 5/6 s -1. Use excel to model the concentrations of A, B, and C as a function of time. Note the difference in [B] from before! 2. Now begin rolling again. a. For t=0, all dice are in area A. b. For t=1, roll all dice, let only dice landing on 6 move to area B. Record your numbers for t=1s. c. Roll all dice in B. Any that land on values 1-5 move to C. Others stay in B. Now, roll all A s, only those landing on 6 may be moved to area B. Count the dice to finish t=2 s. d. Repeat, until all dice have been moved to area C. Note how both Part 1 and 2 took about the same number of seconds comment on the rate limiting step, and how this controls the overall rate of the reaction. 1. Show (mathematically) how the equations are simplified.

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