We believe that it is appropriate to teach chemistry with an emphasis on ambiguity. Measurements are not exact and must be understood as approximations. Words are not exact, are often arbitrary, and must be understood as approximations with assumptions. Probably, much of our students’ education prior to chemistry has emphasized the concrete and the certain, and so it should have. But now that the student is comfortable with 9th grade biology (and 10th grade physical science, perhaps), we believe that it is time to learn to struggle with ambiguities.

We believe that this is a major yet necessary next step in the progress of one’s education. We also believe that it is the ultimate defense against quackery. Multiple choice tests and fill in the blanks have that wonderful simplicity of sports.

The lines on the athletic field are clearly marked. The rules are clearly defined. Right and wrong are defined, perhaps, by the position of the ball and the goal. We believe that our students are ready to move beyond this oversimplified version of learning into a very much messier world of uncertainty.

This section describes a technique used in generating 36 computer graded quizzes, each with three variables: x, y, z

Working in the background all second quarter is a quick basic program which solves the problems on 36 quizzes (4 different versions, each, of the 9 mole quizzes). An example of such a quiz might be:

Given the reaction of x grams of CyHz and given the equation: CyHz + O2 => CO2 + H2O

(the teacher pencils in the values of x, y, and z, which appear as blanks on the quiz)

1. How many grams of oxygen react?

2. How many moles of water are formed?

3. How many grams of water are formed?

4. How many grams of carbon dioxide are formed?

5. How many moles of oxygen molecules react?

Step 1: Balance the equation in terms of the variables y and z.

CyHz + (Y+Z/4) O2 => Y CO2 + (Z/2) H2O

Step 2: Determine the mole and gram ratios for the reaction

CyHz (Y+Z/4) O2 Y CO2 (Z/2) H2O

mole ratio 1 (Y+Z/4) Y Z/2

mass ratio 12Y +Z 32(Y+Z/4) 44Y 9Z

Step 3: Insert x grams of CyHz for the actual mass of CyHz. Set up the appropriate ratios to determine the actual moles and actual masses reacted for all of the reactants and products.

CyHz (Y+Z/4) O2 Y CO2 (Z/2) H2O

mole ratio 1 (Y+Z/4) Y Z/2

mass ratio 12Y +Z 32(Y+Z/4) 44Y 9Z

actual moles X/(12Y + Z) (Y+Z/4)[X/(12Y + Z)] YX/(12Y + Z) (Z/2)X/(12Y + Z)

actual mass X 32{(Y+Z/4)[X/(12Y + Z)]} 44[YX/(12Y + Z)] 18[(Z/2)X/(12Y + Z)]

Step 4: making the substitutions A = X/(12+Z) and B = Y + Z/4, the above table greatly simplifies:

CyHz (Y+Z/4) O2 Y CO2 (Z/2) H2O

mole ratio 1 (Y+Z/4) Y Z/2

mass ratio 12Y +Z 32(Y+Z/4) 44Y 9Z

actual moles A BA YA AZ/2

actual mass X 32BA 44YA 9AZ

Step 5: The answers to the quiz questions above are

1. 32*B*A

2. A*Z/2

3. 9*A*Z

4. 44*Y*A

5. B*A

Step 6: Write the program:

INPUT “Enter x, y, z”; X: INPUT Y: INPUT Z: A = X/(12+Z) : B = Y + Z/4: PRINT “1.”, 32*B*A : PRINT “2″, A*Z/2 : PRINT “3.” 9*A*Z : PRINT “4.” 44*Y*A : PRINT “5.” B*A

Unfortunately, I wrote this on the fly and didn’t bother to uncompile my quick basic program or test this one out so I hope no careless mistakes or typos crept into this. One day soon I will get around to testing this after which I will remove this message.

Step 7: Repeat steps 1-6 for the other 35 quizzes and link them with a menu.

Step 8: Give the student a quiz after penciling in the values of x, y, z.

Step 9: When the student submits the quiz, select the quiz number from the menu, enter the values of x, y, and z, which you penciled into the quiz, and the program will instantly output the answers. Naturally, a statement telling the computer to return to the menu (sorry, I used goto 10, since my menu is at 10; even though line numbers are from the age of the dinosaurs) after hitting enter (INPUT W) will ready the computer for the next quiz to be graded.

In this manner, one program will take care of grading individualized quizzes for the entire quarter. Unless you are preoccupied with other classroom matters, you will be able to give virtually instantaneous feedback to your students.

An example of a quiz sheet which is given to the student upon request follows:

Quiz 2 Mass Ratio Quiz:

Given the hydrate Na2SO4· 10H2O and given that x =___ :

1. Write the balanced equation for its decomposition into anhydrate and water.

2. Write the theoretical gram ratio

3. How many grams of Na2SO4 are in x grams of Na2SO4· 10H2O?

4. How many grams of water are in x grams of Na2SO4· 10H2O?

5. How many grams of Na2SO4· 10H2O are needed to contain x grams of Na2SO4?

Quiz 6 Per Cent Composition Quiz

Given the molecule: C__ H__ O__ : and given that x =__ :

.

1. What is the per cent of C in the molecule?

2. What is the per cent of O in the molecule?

3. How many grams of C are in x grams of the molecule?

4. How many grams of the H are in x grams of the molecule?

5. How many grams of the molecule contain x grams of O?

Quiz 10 Mole Quiz:

Given ___ moles of C__ H__ :

:1. How many moles of carbon atoms are there?

2. How many moles of hydrogen atoms are there?

3. How many hydrogen atoms are there?

4. How many carbon atoms are there?

5. How many molecules are there?

Quiz 14 Moles and Mass

Given ___ grams of C___ H___ :

:1. How many moles of carbon atoms are there?

2. How many molecules are there?

3. How many grams of hydrogen atoms are there?

4. How many hydrogen atoms are there?

5. How many grams of carbon atoms are there?

As quizzes are taken, they are torn off and the remainder of the quiz sheet is used for other students.

You may be confused by the fact that the quiz numbers jump by 4. This is because there are four different versions of each quiz. So quizzes 1, 2, 3, and 4 each are versions of the first mole quiz, while quizzes 5, 6, 7, and 8 are each versions of the second mole quiz.

In a little back street in Wilton, we find chemistry teachers Ebeneezer Jacobs, Ebeneezer Blizman, Ebeneezer Karas and Ebeneezer Gregory licking their tungstens with mercurial delight as they count their gold and silver collections from their students’ fees for broken glassware. “Praise, O Dimium!” the Ebeneezers shout. “Poor Marie Osmium, usually warm and iridium, has collapsed and is lying phlatinum from our titanium final examination, yet we am not dysprosium to become good samariums. “Did you see the way she lanthanum on the floor after seeing our test?,” asked an Ebeneezer! “Gadolinium!” exclaimed another Ebeneezer. Call a student government copper to lead her to her study hall.”

And in the prep room, Rubidium Cratchett Mola, local philosopher and lab technetium, a graduate of Berkelium Collegium in Californium, washes glassware in cold water while reading Kafka’s “Investigations of a Dog”. Rub is no Einsteinium, but he’s not sodium either, and he does tend right to bismuth all the time. It’s Christmas Eve and Rub asks to go holmium early. “You’ve got a lot of gallium,” replies an Ebeneezer. I’ll be frankium but firmium. Half a day’s work, halfnium a day’s pay.” “That’s all right,” the mystic, Rub reflects, “I’m anti-money anyway.”

Late that night, the Ebeneezers awake to see the ghastly and palladium face of their departed colleague, Gregor Mendel, who ironically looked worse in real life. With Mendel leaving him, an Ebeneezer heard the ghost say ” Iodide neon to a hundred and twenty years ago and since then I’ve gone out each night, trudgin around with those arsenine genetics tests that are as heavy and promethium as the rock problem. Long and protactinium is my argony. Mend your way, Ebeneezers!” Thus spake the genetic ghost this abromination and departed.

“That was very strange and ytterbium,” thought the Ebeneezers as they dozed off. But another ghost who looked a carbon copy of St. Nickelous came to wake the Ebeneezers. Growling good-bye to their starving dog, Plutonium, the Ebeneezers grabbed the ghost by the sleeve, and rhodium off into the Christmas past.

They flew all over Europium (to research Romium, Italium, then on to Polonium, making a raid on old girl friends that an Ebeneezer knew while he was in the Americium armed forces. There were Fluorine and Ruthenium, and a couple of great Scandium blondes. How he loved to pinch Lorine! What a foxy generation! They dined on stuffed boar – on corn on the cob, although garnished with herbiums from Indium. For dessert, they munched on tiny berrylliums from Germanium. Very tantalum. As they were feasting and flirting and fooling around as only the young and silicon, it occurred to the Ebeneezers that being mean old chemistry teachers isn’t the magnesium of occupations. But the jolly old ghost scolded the proud and vanadium Ebeneezers for actinium up and took them holmium again.

Then, just as their dreams were becoming mildly pleasant, the most prephosphorous apparition of all appeared and carried them off to view all sorts of ugly things which might come to pass. First, they saw Molly B. Denim coming out of that scavengering undertaking firm, Cesium and Barium , with Ebeneezer’s favorite jigsaw puzzle tests in her dungaree pocket. Then on to Rubidium Cratchett’s hovel where poor tiny Tin lay crippled; with his legs thorium and no way to helium. He was sulfuring and zincing into greater agony. “Oh what a cad me am!” declared an Ebeneezer, who wasn’t much of a grammaratarian either. And with that they awoke new and nobelium men. With radium smiles, they swore to Xenon never to give so cerium a chemistry tast ta tiney Tin again. Agile and lithium, and with a manganous heart, an Ebeneezer sprang from bed, took out a new dimium and called the doctor to come over and curium Tiny Tin’s leg. Tin was tellurium with joy and said, “Bless everyone, even mean old chemistry teachers.

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To complete this contest, find as many elements as you can (full names with slight errors in spelling allowed but no symbols, please!). Turn in a list of the atomic numbers of the elements found in order of increasing atomic number. One person in each class, the one with the most elements, number correct – number incorrect, will win a five point bonus.