As an example, you are presented with how our students discover stoichiometry and per cent composition early in the second quarter. In step 1, students are given directions for heating a hydrate, sodium carbonate monohydrate to sodium carbonate by driving off the water.

Step 1. Read the general lab procedure below, which will be used for each of the three hydrate labs 2d1, 2d2, and/or 2d3

A major concern is the breakage of crucibles and covers. Take whatever precautions are necessary to insure that breakage is at a minimum. In addition, keep the crucibles dry. When not in use, store them in desiccators. After use, gently scrape out contents but do not wash. It is not necessary that you remove all of the anhydrate from the crucible before beginning a new experiment. Heat the crucible to dryness (some moisture from the atmosphere will have to be driven off), then let cool and weigh with cover to two decimal places. Add a few grams of hydrate (2.00 to 5.00 grams), then weigh the crucible, cover, and hydrate. Set the crucible on a clay triangle, on a ring attached to a ring stand.

Heat the crucible with the cover slightly ajar to drive off the water from the hydrate. Heat moderately at first to break water out of the crystal, then more strongly for a few minutes until the water appears to be gone. Then heat very strongly for about two minutes to drive traces of water from the center of the mass of hydrate. Let the crucible cool, then weigh the crucible, cover and anhydrous salt. Scrape out contents of the crucible and discard into crocks. Return the crucible to the desiccator. Calculate the masses of hydrate, anhydrous salt, and water.

Then in step 2, they are asked to perform the experiments. They have been given no advice whatever about analysis, except they have been guided to conclude that, from the experimental masses, they will be able to determine the masses of hydrate, anhydrate, and water. But the project comes abruptly to a halt near the end of step 2 when they are asked to do the following: “Determine what the experimental masses have to do with the relative atomic masses on the periodic table.”

Step 2: Perform (2d1) the Sodium Carbonate Lab (Na2CO3·H2O), 1 trial for each group member and answer the question posed. Use the above procedure with the sodium carbonate hydrate. Note that there is one water molecule in each hydrate molecule. Determine what the experimental masses have to do with the atomic masses on the periodic table.

Bewildered students come up seeking help and the teacher usually asks the student to explain what the question means. After a brief discussion, the teacher may ask the student, is there any information on the periodic table about these substances in the experiment? Since the class has recently discovered molecular weight from a unit on mass spectrometry, they are off to determine the molecular masses of hydrate, anhydrate, and water. Surprisingly, many are disappointed to find that the experimental masses are different from the theoretical or relative masses from the periodic table.

Some groups are able, at this point, to find some measure of success, but usually the organization of masses on the page is so poor that no patterns or relationships could possibly be discovered. The teacher might then further advise students that the teacher would also be unable to see any relationships from the organization of results. “Have you never seen a results table?” Most students who get an idea will ask first before they calculate the ratio, “Will this work?” The response from the teacher will be “Seems like you have an idea. Why not try it out and see if it leads anywhere.” This is such an obvious approach for anyone who has done any science, but apparently our students are still fearful of taking even the slightest risk.

Pretty soon, lots of groups have discoveries, and although they are usually unable to put them into these words, some have shown that the theoretical and experimental ratios of the mass of hydrate to anhydrate are the same. Or hydrate to water. Or anhydrate to water. Or the inverse of those three. Others are showing that the per cent of water in the hydrate is as predicted by the periodic table. Still others have found that the numbers of hydrate and anhydrate and water molecules are the same (m/MW) although they are not aware that the calculation gives the number of moles of each species. Generally, students will appear triumphantly after analysis of one trial and will make no effort to analyze the second trial unless encouraged to do so. Apparently, they do not get the notion of reproducibility yet so this a good opportunity to teach the concept. “Well maybe this ratio just happened, by luck, to work once. How do you know it’s valid? I mean you are six feet tall and you have six letters in your first name. I guess, once you were named, that pretty much determined your height.” … a long pause… “You disagree? Well I just gave you the evidence. How would you refute my evidence?” …and so on.

To the several students who have gotten nowhere and are growing desperate, but who have, now, well organized results tables, the teacher will probably say the following, “Hmm, look how much more sodium carbonate you wound up with than water. Just look at those masses. Yet you are making equal numbers of each. Does that look right?” The typical response after a very long pause is, “But look how big the sodium carbonate molecule is and how little the water molecule is.” To which the teacher might respond, “Are you suggesting the sodium carbonate should have a larger mass than water?” And then, “Have you any evidence that it should?” The student will direct the teacher to the molecular weights. If not, a glance at the periodic table usually does the trick. Upon which the teacher will exclaim, “You mean this is larger than this (experimental masses) because this is larger than this (theoretical masses)?” And finally, “Seems like you see a relationship. Let’s see what you come up with.” The class, many of whom have already gotten well established ideas, is then instructed that “I, who understand this principle, did not even have to do the experiment.” Knowing the mass of hydrate, and having the periodic table, I could have calculated the masses of water and anhydrate that would have been formed. If you have a solution, then you can also. Be sure to show this to me (step 3) before you are approved to go on with step 4.

Step 3: Write up your answer formally and get this solution approved by your teacher before continuing. You may not go on to parts 2d2 or 2d3 until your teacher has approved your solution to 2d1. When you have solved this problem, show your teacher your well organized data and results, and explain your conclusions. While this is a group project, each individual must get the teacher’s approval, in the grade book, before continuing with parts 2d2 and 2d3. Write up a short but formal lab report and submit it.

Step 4. Enter your experimental data from the sodium carbonate hydrate into the hydrate lab spreadsheet.

The students can then use whatever principle they discovered in step 2 to solve the problem in step 5. The teacher has accepted the students’ work but has not agreed that it is correct.

Step 5. Perform either 2d2 Sodium Sulfate Lab (Na2SO4·yH2O) or 2d3 Copper Sulfate Lab (CuSO4·xH2O) to determine the number of water molecules in each hydrate molecule. You may not begin this lab until you have your written conclusion to part 2d1 approved, in writing, by your teacher. Each of the above hydrates has an unknown number of water molecules attached to the anhydrous salt. However, by performing the hydrate experiments, and using the conclusion from part 2d1, you should be able to determine the values of “x” and “y” in the formulas. There are many methods of solution, probably the least satisfying of which is a trial and error method, in which you guess a value for x, calculate what should be the results and then compare them with your experimental results. Write up formal lab reports for either 2d2 or 2d3, clearly explaining the reasoning used in your calculation section. Your teacher should have advised you of special precautions and color changes involved in the copper sulfate lab.

Step 6. If time permits, perform both experiments for 2d2 and 2d3. You will receive extra credit if you do both.

Step 7. Enter this data into the hydrate lab spreadsheet.

Step 8. Turn in the two or three, short, but formal lab reports.

Following this, a class discussion ensues in which students describe all of the different methods they came up with and how they used these discoveries to solve the second problem. Of course, students will be teaching students stoichiometry and per cent composition in an atmosphere of discovery without the words “stoichiometry” or “per cent composition” being mentioned.

One of the premises of this course is that if students are unable to discover a concept on their own, of course with some appropriate guidance, as above, then it is too early for students to be studying this subject, and a subject they can discover should replace it in the curriculum. In this way, our students should not learn that chemistry is confusing and esoteric, but rather common-sensical and reasonable. And our students should find a personal relationship to the subject matter satisfying, as discovering mathematical puzzles hidden deeply in nature is exhilarating stuff.

If we consider the model that reality is outside, and each subject area or discipline has its own window with which it looks out at this same reality, then the chemistry window has, for far too many years been just like the windows described in Poe’s The Fall of the House of Usher:

“The room in which I found myself was very large and lofty. The windows were long, narrow, and pointed, and at so vast a distance from the black oaken floor as to be altogether inaccessible from within. Feeble gleams of encrimsoned light made their way through the trellised panes, and served to render sufficiently distinct the more prominent objects around; the eye however struggled in vain to reach the remoter angles of the chamber, or the recesses of the vaulted and fretted ceiling.”

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