Chemistry Everyday for Everyone edited by
Resources for Student Assessment
John Alexander University of Cincinnati Cincinnati, OH 45221
Puzzles in Chemistry and Logic Carlos Mauricio Castro-Acuña and Ramiro E. Dominguez-Danache Departmento de Fisicoquimica, Facultad de Quimica, UNAM, 04510 D.F. Mexico Paul B. Kelter* and Julie Grundman Department of Chemistry, University of Nebraska–Lincoln, Lincoln, NE 68588-0304
For many years, we have recognized the importance of developing “reasoning skills” in our students. The literature contains many examples of instructional and assessment strategies to enhance and assess reasoning ability in chemistry. The importance of problem solving has long been an area of active research, as discussed below. Two of us (RDD and CMC-A) have been coaches and judges at Mexican and International Chemistry Olympiads. In this work with very formidable chemistry student-scholars, and in the work of all of the authors in the mainstream chemistry classroom, we have seen the benefits of developing students’ thinking skills through chemistry content questions that also use their reasoning ability. We have designed questions that require chemistry knowledge and the capacity to use data as part of a logical approach to finding answers. We call these questions “puzzles in chemistry and logic”. In this paper, we present puzzles that have proven challenging and popular in the Mexican Chemistry Olympiad. In addition, in view of our long-standing research collaboration at our two institutions and our recognition of the applicability of these puzzles to the first-year college chemistry audience, we also present data showing that mainstream general chemistry students at the University of Nebraska–Lincoln (UNL) enjoyed the problems and were challenged by them. Different Kinds of “Problems” Student understanding of a concept can be assessed in several ways, depending upon the depth in which the concept is covered, the teacher, and the assessment environment (timed exam, take-home problem set, etc.). An excellent set of papers on problem solving in chemistry can be found in the June 1987 issue of this Journal. Among these are a discussion by Middlecamp and Kean on the recognition of various types of problems (1), Zoller’s work on the development of questionasking skills by students (2), and Nurrenbern and Pickering’s study on solving problems as a measure of understanding at the molecular level (3). The relationship between problem solving and true understanding of chemistry is further explored by Sawrey (4 ) and Pickering (5). A broad range of problems covering all areas of the mainstream general chemistry curriculum is given by Barouch (6 ). A set of puzzle-based experiments for use in the organic laboratory recently appeared in this Journal (7). The puzzles in chemistry and logic that we present are not intended to be used in a detailed assessment of student understanding. Rather, they have been enjoyed by a wide
variety of students internationally and should be taken simply as challenging and interesting exercises. The first puzzle requires some basic chemistry knowledge and a little reasoning ability. The others require more chemistry and somewhat more thought. We hope that you will enjoy trying to solve these puzzles. The answers to the first three are given below. Measure your time and compare it with the time needed by our student sample and by your students. Example Puzzles
Problem 1. Pick the Temperature At 40 °C, compound “X” is a liquid, compound “Y” is a gas, and compound “Z” is a solid. The single set of melting points (in kelvins) of these compounds could be:
496
Y
Z
303
323
373
B
323
298
273
C
273
298
323
D
313
323
473
E
303
198
298
Problem 2. Sort Out the Substances An absent-minded student prepared five different solutions and placed them in five flasks numbered 1 through 5, but forgot to label the flasks. The prepared solutions are 0.5 M aqueous potassium chloride, 1 M sulfuric acid, 1 M acetic acid, 1 M aqueous sodium sulfate, and 1 M aqueous sodium hydroxide. After some experiments, we found the following information: • • •
Flask 3 contains a solution with a pH higher than 4.9. If H2SO4 is added to the solution in flask 4, the product is the same as that present in flask 2. In flask 5, there is not an organic compound.
With these data, indicate the name and chemical formula of the solution contained in each flask.
Problem 3. Which Sample Goes Where? In an old storeroom, we found six gas samples placed at random into six tanks of different capacities (1, 2, 3, 4, 5, and 6 L). Also at random, one identification label with a letter (A, B, C, D, E, or F) is placed on each tank. The gas samples are helium, nitrogen, chlorine, argon, air, and oxygen. On the basis of the following clues, match the sample and label that go with each tank. •
*Corresponding author. Email:
[email protected].
X A
Tanks A and D have capacities larger than 3 L but only A contains a pure gas with diatomic molecules.
Journal of Chemical Education • Vol. 76 No. 4 April 1999 • JChemEd.chem.wisc.edu
Chemistry Everyday for Everyone • • • • •
The biggest tank is labeled with a vowel and contains a noble gas. The 2-L tank contains mostly molecules of N2. The smallest tank does not have the label B or F. The main component of air is in tank B and the halogen is in a flask smaller than 4 L. The 5-L tank is not labeled with a vowel and contains an element first discovered in the sun.
Problem 4. What Is in Each Container? In this problem, you will have to assist the manager of our Quality Control Lab. She needs to organize some glassware and reactants and we have the following data. There are six pieces of commonly used glassware in a chemistry lab; a volumetric flask, a flat-bottom flask, a roundbottom flask, two Erlenmeyer flasks, and a graduated cylinder. Among these containers, two have a capacity of 100 mL, two can contain 500 mL, one has a 250-mL capacity, and one has a one-liter capacity. Each contains a different one of the following substances: gaseous nitrogen, gaseous oxygen, 1.0 M NaCl (aqueous), ethyl alcohol, distilled water, and 1.0 M NaOH (aqueous). On the basis of the following clues, match each container with its volume and the substance contained in it. • •
• • • •
The graduated cylinder is not used to contain gases and its capacity is less than 500 mL. The round-bottom flask contains a gas; its volume is bigger than 250 mL and also bigger than the flatbottom flask. The volumetric flask contains an electrolyte and has a capacity of 100 mL. The organic liquid is in an Erlenmeyer flask that has the same capacity of the flat-bottom flask. 200 mL of a solution with a pH higher than 7 is in an Erlenmeyer flask. At one atmosphere of pressure and T equal to 0 °C, the biggest flask contains about 1.43 g of gas.
You may use PV = nRT, where R = 0.0821 L-atm/mol-K. The chemistry-related possibilities are endless and we can enhance the chemical knowledge required to solve each puzzle as much as we want. For instance, we are now working on logical puzzles in which all substances involved are organic molecules and the clues are related to topics such as isomerism, secondary or tertiary carbons, and functional groups. Student Response to the Logic Puzzles A total of 250 students in the second semester of the two-semester (Chemistry 109 and 110) mainstream first-year chemistry course at the University of Nebraska–Lincoln completed the first three logic puzzles as a single extra-credit take-home assignment. The group included 97 men and 153 women. The mean first-semester (Chem 109) grade point average (GPA) of the students who took Chem 110 was 3.2, whereas the typical mean GPA in Chem 109 was about 2.3. Thus (and not surprisingly) the better students take the secondsemester course. The students were instructed to work either on their own or in groups and to spend as much time as necessary to answer each question. They were asked to record the amount of time spent on each logic puzzle and how much
Table 1. Results of the Logic Puzzle Assignment Puzzle
Correct Answers a
(Time ± SD)/min
Enjoyment b ± SD
Number
%
1
143
57
10.1 ± 7.8
2.67 ± 1.15
2
145
58
15.3 ± 12.0
2.67 ± 1.15
3
165
66
22.4 ± 16.5
3.06 ± 1.08
72
32
47.8 ± 21.8
–
All 3 an
= 250. bOn a scale of 1 (worst) to 4 (best).
they enjoyed each one. Finally, they were asked the context in which these kinds of puzzles should be used in the curriculum: for examples in class, on examinations, or as takehome assignments. The assignment was quite challenging to our students. As shown in Table 1, 57% of the students came up with the correct answer to puzzle 1, 58% correctly determined the answer for number 2, and 66% found the right answer for number 3. Only 32% of the students figured out the answers to all 3 logic puzzles. We expected puzzles 2 and 3 to require more time than puzzle 1, and as the table shows, that was the case. The table also summarizes data showing that the students modestly enjoyed doing the first two puzzles and really enjoyed puzzle 3. They found puzzle 3 to be, according to one student, “challenging, yet exciting”. Another student said, “Even though this one took the longest, it was the most fun…took a lot of brain power.” Students overwhelmingly thought that the puzzles should be used as take-home assignments rather than as part of timed in-class exams. Students required a wide spread of times to finish the puzzles. Puzzle number 2, for example, required an average of 15.2 ± 12.0 minutes to complete, far too wide a spread for a timed test. We determined the relationships between many variables such as time, correct response, enjoyment of the logic puzzles, and GPA via the Pearson correlation coefficient and found no significant correlations. This is not troubling because our main goal was merely to determine if these are interesting and well-received kinds of problems that you might consider using as part of your own curriculum. The one interesting correlation, as measured by a point biserial correlation coefficient (good for relating gender to other variables), is that women generally chose to work in groups of two or three whereas men generally chose to work alone (rpb = .58). The bottom line regarding the logic puzzles was cited above: students find them enjoyable and challenging as take-home exercises. That, combined with the teacher’s freedom to tailor the problems to the course, makes them of value in the mainstream general chemistry curriculum. The logic puzzles are well received in the Mexican Chemistry Olympiad competition and the mainstream college course at UNL. Could they be used in the U.S. Science Olympiad (SO) competition? One of us (PK) has been the Wisconsin State SO director (1986–1993) and Nebraska State SO co-director (1994–1998). In his opinion, such puzzles would be a fascinating departure from the current style of events that rely to a great extent on memory-level recall and design skills that are well practiced before the event. It is worthy of consideration at the state and national levels.
JChemEd.chem.wisc.edu • Vol. 76 No. 4 April 1999 • Journal of Chemical Education
497
Chemistry Everyday for Everyone
Literature Cited 1. 2. 3. 4. 5. 6.
Middlecamp, C.; Kean, E. J. Chem. Educ. 1987, 64, 1123. Zoller, U. J. Chem. Educ. 1987, 64, 510. Nurrenbern, S.C.; Pickering, M. J. Chem. Educ. 1987, 64, 508. Sawrey, B. A. J. Chem. Educ. 1990, 67, 253. Pickering, M. J. Chem. Educ., 1990, 67, 254. Barouch, D. H. Voyages in Conceptual Chemistry; Jones and Bartlett: Sudbury, MA, 1997. 7. McGowens, S. I.; Silversmith, E. F. J. Chem. Educ. 1998, 75, 1293.
498
$ 1. 2.
Answers to the First Three Puzzles C Flask 1: Flask 2: Flask 3: Flask 4: Flask 5:
3. CH3COOH Na2SO4 KCl NaOH H2SO4
Journal of Chemical Education • Vol. 76 No. 4 April 1999 • JChemEd.chem.wisc.edu
Beaker A: Beaker B: Beaker C: Beaker D: Beaker E: Beaker F:
$ 4 L, O2 3 L, N2 1 L, Cl2 5 L, He 6 L, Ar 2 L, air
