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Simulation of Reaction Orders

This simulation is designed for introductory chemistry students, who have never heard of this subject before in their lives. Proper pedagogy thus dictates that the instructor does NOT begin by pushing the students into the deep end of the pool of mathematical abstractions. A better starting point would be to help the students to QUALITATIVELY conceptualize what is happening before going into the quantitative realms. This may take an investment of a few minutes of class time, but it should preclude hours of later befuddlement. It is, afterall, a rather simple concept to experienced scientists, but too often "blows away" the novice.

The qualitative conceptualization might be enhanced by a simple simulation such as shown here. Two reactants are simulated by two unequally sized decks of differently colored index cards.* A "solution" is made when these reactants are mixed together in the form of the randomly shuffled decks. The mixed deck is then a simulation of the solution at some given point in time when one can then see where the various reactants lie in relationship to each other. In a simple A+B→AB reaction, you can determine whenever a product molecule "AB" (or "BA") has been formed by looking for every instance where an "A" card is next to a "B" card. Such pairs are noted by the brackets ABOVE the displayed cards to the right.

In the more complex 2A+B→ABA reaction, product "ABA"would result in products wherever a "B" card is sandwiched between two "A" cards. Such a triplet is noted in the above picture by the bracket BELOW the string of cards. For this the instructor could take a large deck of white index cards, representing reactant "B" and then add a few pink "A" cards. By merely fanning the deck, the class can easily see the "solution" at that moment in time, and can pick out any AB or ABA products - even from a distance. Thus, in mere seconds, the students have a mental image of what is happening in a solution.

Let's see what happens if we add 9 more pink cards to the "solution" (we double the number of pink cards). We see that for the simple reaction A+B→AB, we have doubled the number of AB pairs. Thus there is a linear correlation between substrate added and product produced - a "first order" relationship. However, for the more complicated 2A+B→ABA reaction, doubling the number of pinks results in a four-fold increase in ABA pairs. This is an exponential result. More specifically it is to the exponent of 2 (squaring), and is thus a "second order" relationship.

Therefore, this normally difficult subject of reaction orders should now be rather transparent to the students.

At this point, the class should be divided into groups and each group be given a large deck of whites and a smaller number of pinks (or whatever color your supplier has). The students should add 4 pinks to their deck of 100 whites, shuffle the deck well, and determine how many AB/BA and ABA products they get. Then add more pinks reshuffle and make another determination. They are recording the number of pinks to the number of whites for both product types. More pinks are added, and so on, over and over.

Thus some experimental data is accumulated which may be graphed and analyzed. Of course because we are not working with an Avogadro's number of cards, statistical variations will occur between groups. But that's good because it opens the door to using educated judgments when drawing lines and curves on the graph - "We don't connect the points, but rather draw smooth lines or curves."

In brief, this should quickly allow the students to conceptualize what is happening and why various reactions have first, and second order kinetics. (And higher orders are similarly conceivable.) This conceptualization is the most important thing for the student. Only then will the student have an appreciation of the math behind all of it . To do the math without the students' full conceptualization, is only a tedious exercise and understandable only by the more brilliant students. That tediousness is illogical since the conception part is so easy if presented correctly.

FROM SIMULATION TO REALITY

In order to experimentally ascertain the rate of a reaction one looks to measuring the "initial velocity" because that is the only point in time where the concentrations of all reactants are known with certainty - thereafter, their concentrations are being depleted as products are being formed. Experimentally, this is determined by measuring the amount of product as time elapses. That will give a line similar to the red one in the figure shown here. The blue line is drawn in with a straight-edge, and is called the initial velocity or V_o. Thus, in order to switch our mind-frames from the card deck simulations to real reactions, we must mix our reactants and take readings of product accumulation at timed intervals, do the graphing so as to determine the V_o of that particular reaction.

SIMULATION OF A ZERO-ORDER REACTION

For an attempt at simulating a zero-order reaction - one such as radioactive decay. Here concentration should have no effect.

Give groups of students different numbers of white cards. The instructions are that they are go keep track of the FRACTION of white cards relative to what they started with, N/N_o. All groups will thus start with 100% white.

Then all groups will be told to pretend that an hour has passed and they are instructed to discard 15% of their white cards. They will calculate their individual N/N_o ratios (all will get 85%). Then, after a second "hour" has gone by, they will be instructed to get rid of 15% of the white cards they have in hand and calculate the new N/N_o (72%), and then to rid another 15% and so on over and over again (61%, 52%, 44% and so on). When the instructor asks each group for their percentages, they class will see that the values are the same no matter what the initial concentration of white cards was.

GRAPHING THE DATA

Next is a lesson in using semi-log graph paper! Go to that webpage and learn about one of the handiest tricks ever in graphing.

If the students were to graph their zero-order, "decay" data, above, on this paper, they should get a straight line that descends downwards from the upper lefthand corner. Next they would be asked for how many "hours" were needed to have eliminated 50% of the white cards. The answer would be the half-life (T_1/2) of the reaction. Again all groups should get roughly the same T_1/2 values.

With regard to the first and second order work done earlier, the students can plot their data gained where more and more reds are added to the white deck and triplets are formed. Voila! a straight line! But this time one that rises from the lower lefthand corner. Straight lines on semilog paper indicate exponential functions. If the line is parallel to a line of 2^x it is a second order reaction, and if parallel to 3^x, then it is a third order reaction, and so on.

* Clean-up trick: Disassembly of the mixed decks into single color decks can be facilitated by a trick commonly used by magicians. Make one of the decks slightly narrower than the other (but keep the same length to facilitate good shuffling of a mxed deck by the students). Thus if a mixed deck is loosely held vertically by the long edges, you have two choices: (1) most of the narrower cards will slip out, or (2) you can lift out the wider cards.

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