Pattern Recognition in Descriptions of Cation/Anion Reactions for Solving an bottle Puzzle A Freshman Laboratory Experiment Scott Stiegl Harvey Mudd College, Claremont, CA 9171 1 One of the most enduring freshman lab experiments is the one that explores reactions between aqueous solutions of binary ionic compounds. At its simplest, the experiment is pouring solutions together and writing down what happens, an exercise in observation; a t a more advanced level, unknowns are classified into the groups of the classical cation and anion "qual. scheme" (1-10). Often, a set of known "trainine reactions'' are done with a "trainine set" of solutions. Wken the training reactions show what Lappens when each cation and each anion are mixed toeether. the trainina set solutions are usually aqueous (cation, NOS-) solutions and aqueous (Naf, anion) solutions. In many such cation1 anion experiments, each cation's name is placed in the first row of an array-like table and each anion's name is placed in the first column. The observed results of the training set reactions fill the array which can then be called the "training set results array". In the simplest experiment, an unknown is one of the (cation. NO1-) or one of the (Na+. anion) trainine set solutions. A listof the results of the reactions of theuunknown with either the cation or anion training set is matched to a row or column in the training set results array, identifying the unknown as one of the trainine set solutions. Althouah the whole training set results arrayis needed, it is used oily one row or column a t a time. A more challenging way of using the array is to give an unknown that is not a training set solution but a solution of any two ions which do not react. The unknown is mixed with all the training set solutions to give two lists, a list of the unknown/cati& results, and a fist of the unknownlanion reaction results. Then, a row and a column in the array are matched with the two lists, identifying both the cation and the anion of the unknown. The above ways of using the training set results array are, in two respects, very forgiving of student error. First, for every wrong observation, only one element in the array will be wrong. Since the student matches a whole row or column, one or even several wrong elements still enable a partial, best match; there is alot of redundant information. If toomuchof this kind of error occurs, only a few or even only one reaction result may be used to identify the unknown. The purpose of the array is thus defeated; the array is supposed to he a large universe of results, all useful. Second, the training set solutions are used twice, once to make the array, and once to react with and identifv the unknown: more redundancv. While it is fine to design error-forgiving experiments, one would sometimes like to reduce the redundancy in an experiment to the point where the student must do almost every reaction correctly and observe results accurately in order to identify even one unknown. This is the purpose of the cationlanion experiment known variously as the "n-bottle" or "zeta-bottle" puzzle, in which several (n) unknown solutions, each containing two nonreacting ions from the training set, are mixed only with each other and not with the training set solutions (11).
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Journal of Chemical Education
In a typical implementation of the n-bottle puzzle, the student makes the training set results array, makes a results array for the n bottles' reaction results, is given a list of oossible identities of the n bottles' contents, and is wished well. Since the same cations and anions are present in both the training set and t h e n bottles, there must be a relationship between the training set results array and the n-bottle results. But what is it? This experiment shows a way for students to recognize such a relationship. Experimental
The Training Set 0.1 M solutions of sodium fluoride. sodium chloride. sodium carbonate, sodium chromate, sodium phosphate, ammonium nitrate, silver nitrate, calcium nitrate, copper(I1) nitrate, aluminum nitrate, and iron(II1) nitrate are prepared. l M solutions of sodium hydroxide and nitric acid are prepared. A 0.01 M solution of sodium sulfide is prepared. All reagents are reagent grade. These solutions are the training set. They are put into 750-mL wash bottles (Nalgene Unitary 2402-0750), which makes them easy to dispense and restricts the volumes used; a second's hard squeeze delivers about 2 mL. Each student is given only one 20-mL beaker in which to doallreactions. Thestudent squeezes about 2 mL of a cation solution into the beaker, then 2 mL of an anion solution. The sharp stream of solution mixes the two solutions well. The student then immediately describes the reaction results in his or her notebook in prose form. These results need not be arranged in array form; in fact, they are best not since the little boxes of an array discourage a complete written ohservation. The reaction is then washed down the drain, the beaker rinsed with deionized water, and another reaction is done in this beaker. Using.only. one beaker avoids three sources of error in this type of experiment: the myriad of unlabelled test tubes prone to misidentification, contamination from dried-on substances often found on used test tubes, and slow reactions which give time-dependent results. If a student is not sure of a reaction result, she or he is encouraged to repeat it as often as needed. Reaction Scores, The Results Array The student uses prose to describe the reaction, but then derives a "score" from the description. These 49 scores are entered in a 7 X 7 training set results array. The cations fill the first row: H30+ (from HNOs), NHa+, Agf, CA2+,Cu2+, A13+, and Fe3+. The anions fill the first column: OH-, F-, C1-, C0a2-, CrOqZ-, SZ-, and Pod3-. Scoring is done this way: if no reaction is apparent, the score is "-". If the solution or supernatant either changes color upon reaction or just has the color of one of the reactant solutions, the resultant color gives the score, a lower case "y" for yellow or orange, "g" for green, "b" for blue or violet. Two gases are produced, NH3 and H2S. If the gases are smelled, the results are scored "n" and "s". As many students do not know what these smell like, one might point this out during the lab period. Finally, if a precipitate forms,
the score of the reaction result of (NHd2Cr04and A1F3: going counter-clockwise, "y" "Yy" "-" "-"= "Yy"; a yellow precipitate with a yellow supernatant. Same-row or same-column reactions give a line instead of a rectangle, and only two scores to combine; for example, the reaction of (NH4)2Cr04and (NHJ2S give "y" "s" = "ys". Starting with the identified nth bottle, the object is to find a set of n-bottle scores such that all rectangular or linear score combinations predict all the actual scores of the nbottle reaction results. T o some students' dismay, using the array does not give an algorithm for solving the n-bottle puzzle. The puzzle is solved by guessing. The array organizes the training set data, the predictions for n-bottle reactions, and the actual n-bottle reaction results so that the student can show that there is a set of n-bottle identities that are consistent with this information. For example, the reaction of (NH4)zCrOa with n-bottle solution 2 gives a red precipitate with a yellow supernatant, scored "Ry". Glancing through the array, one seesan "Ry7'at (Agf, C104~-).Boxing the score a t (Ag+, F-) with the score at (NH4+,Cr042-), one "-" "-"= "Ry". So, gets a combination "y" "Ry" AgF is a possible solution for n-bottle solution 2. Guessing similarly, with the score a t (Ag+,F-) as a comer, leads to other self-consistent n-hottle solutions' reaction scores and identities. Every n-bottle set will have an interesting set of interactions. In our six-bottle problem, most students correctly identify (NH4),Cr04, AgF, A1C13, and HCI. The (NH4l2S gives them trouhle because they must detectthe odor of NH3 in the presence of the odor of H2S. This is possible, hut only if the training set has given them a memorable whiff of NH3 at (NH4+,OH-). T o make sure, the NaOH is made 1M to ensure a basic enough solution to give NH3(g) and a score of " ,* n , not "-". Interestingly, H2C03 (H30+,C032~) and Ca(OH)2, quite different compounds, are indistinguishable under the six-bottle interactions; the scores of the two are the same. All reaction scores must be reliable in order to identifv even one n-bottle solution. If the scoring and analysis is done in the lab, some students will realize this and want to repeat key reactions to make sure of their scores. This is desirable asit shows them how dataaualitvis increased bvredication. Since the array is a toil, n i t an algorithm, much still depends on the student's imagination. The training set has been selected to give "discriminating information" in the score array by~-giving- dissimilar rows and dissimilar columns. There are enough "-"and lower-case scores in the array to allow up to 24 n-bottle solutions. If the student is also asked to write chemical eauations for. sav. all the reactions scorine "W", then he or shk will see dksc;iptive chemistry in three forms: the urose notebook description of a reaction which allows for a wide range of expression, the score description which narrows the ranee of ex~ressionconsiderahlv but allows patterns to be formed andrecognized in a ~ a r g ~ a m o u n t of data, and the chemical formula description of the reaction which relates the reactions' results with familiar models of chemical bonding.
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Training set resuR anay wlth s m e s . Shown in an example of predicting the reaction which resuns fmm mixing two six-bonk solutions, (NH4hCr04and AIFo.
its color is scoredusing the upper-case letters "W" for white, "R" for red. "Y" for vellow or oranee. " G for -ereen,. and "BL", "BR';, "BK' fo; blue, brown, and black, respectively. Areaction has one or two scores. For examde, the reactionof AgNO? with N a E r 0 4 gives a red precipitate of Ag2Cr04and a vellow C r O A a a ) suuernalsnt and is scored "Kv". but the reaction of ~ g ~ 0 ~ ~NaCl k i gives t h white AgCl witha colorless supernatant and is scored " W . The n-Bottle Solutions Anv number of solutions in) can be used that have cations and &ions from the training Let. We used six (n = 6): sat'd Ca(0HLin 1M NaOH. filtered before usine. 0.1 M solutions o f ~ g ~ AlC13 , ' ~ ahio ~ ~ ion: , dissolving is very exothermic), (NH4)2Cr04,and (NH4)2S, all reagent grade. The last was prepared from a 20% solution of "ammonium polysulfide", S These are also put into 750aqueous ( N H 4 ) ~ (Matheson). mL wash bottles and placed away from the training set solutions. n - 1 bottles are labelled bv letters or numbers that can be permuted togive many unknown identifications. The nth bottle is labelled with its identitv: (KH1)7Cr0, is our sixth. T h e n bottles are reacted pairwise to give-(n - 1) (n - 2) . . . 1 reactions, 15 for n = 6. These reaction results are recorded and scored, but the scores are not put into an array. The student must not react the n-bottle solutions with the training set.
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In the array (see figure), a reaction result with a score of "-"or a lower-case letter means this (cation. anion) solution is a possible n-bottle solution; e.g., (NH4)2Cr04scores as "y", Ca(OH)%scores as "-". The chief use of the array is to predict the results of the reaction of any two possible nbottle solutions. Two examples show this use. T o predict the reaction of (NHM!rOa, score "y", and AIF3, score "-", first find the position of these scores in the array. Then imagine or draw a rectanele which has these two scores as diaeonal corners (see figure).Kow, when t he four scores at the corners ofthis rectangleare combinrd (+), the resulting wore will be u
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1. Mowan, W. 0.;Lyman, J. A. Chemirtry, An Elementary Textbook;MscMillao: New York. 1913:p 138. 2. Weleher, F. J.;Hahn,R. B. S~mimicraQuolitotiva Anolyzis: Vao Nmttand: No. VorL,
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7. B m o b , D. W.; Holtzclaw. H.F.. Jr.;Lewis, J. D. J. Cham. Educ. lW5,52,581. 8. Lambert, J. L.: Meloan, C. E. J. Cham. Educ. 1977,54,249. 9. Manroe,M.B.:Abrsms.K. J.A CouraoinE*perimentolChemiafry.BrakII;hohoma": Ssn Francisco, 193%pp 283-308. lo. Mmller, T.; Beilar, d. C.. Jr.; Kleinbcg, J.; Goaa, C. D.; Caatellion. M. E.; Metz, C. Chemistry, with Inorganic Quolifofivo Anolysir. 2nd ed.; Academic: Orlando, FL. ,OM. " L. 9'. .""., -.."y"". 11. MacWwd,G.E.;Laeaetfre,E.N.:Brpcn,G.J. Chem.Edue. 1940.17.520.
Volume 65 Number 4
April 1988
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