Bring Back Equivalent Weight-If You Want the Kids To "Think"!

In the Classroom

Bring Back Equivalent Weight—If You Want the Kids To “Think”! Michael Laing Department of Chemistry, University of Natal, Durban, South Africa

We are constantly being told that our students cannot “think” and that they are unable to solve problems. Others tell us that we need to teach “skills and process” rather than “content”, but it is certainly not clear how this should be done (1). Some propose bubble balloon and string concept-mapping as a solution (including ways of assessing and grading the artistic efforts of the pupils!). Yet others propose the epistemological Vee heuristic device of Gowin (“guided by a dittoed work sheet”) as a panacea (2). The reality is simple: you cannot be successful at solving problems if you have not practiced solving problems! George Bodner puts it thus: “Problem solving is what you do when you don’t know what to do, otherwise it is not a problem” (3). To Solve a Problem Our students are seldom faced with a problem the solving of which requires a mental struggle followed by either insight or a flash of inspiration. What they do is carry out many exercises of the plug-and-chug variety: PV/T = PV/T; given five, find the sixth. To quote my friend Ray Commaille: “Last year’s problem is this year’s exercise” (4). Almost never do the pupils collect step by illogical step, random facts, all (unbeknown to them) related to the problem at hand—yet without seeing the tenuous threads that connect the facts and which will lead to a new concept that will bring understanding. Students need the experience of struggling with a collection of disconnected ideas and information and from this to finally hit upon the answer—to solve the problem. Typical chemistry and physics courses are not taught this way. We present perfection: modern derived knowledge to be learned and then applied to exercises— a facade of ideality, the details of which shall be memorized with little thought about how this construct was deduced. A fine example is electron configuration and its supposed relation to the reactions of an element and its position in the periodic table. It is not so. The Aufbau is not regular. There are plenty of exceptions: these we ignore and carry on propagating the myth of rational buildup of s, p, d, f, etc. electrons in their budgie boxes. Our modern chemistry textbooks avoid the issue. There is no debate or discussion of failure or philosophy. It is so much more “important” to present the ultimate sanitized result and then cover more “good stuff”. These books never tell of the struggle to get there. The students have lost something; it’s all too glib. “Learn the principles, and all else will be predictable” is the line. Sorry, the real world is not this way. Out there it’s the knowledge of simple facts and plenty of experience that count when you are confronted by a real problem, something new that has not been met before. I must repeat: a problem is something new that has not been

met before. We regularly give the students the answers before we ask the question. It might be unconscious, but we do it, and it is wrong. And the students naively and innocently believe that they are solving “problems”. Approach by the Scientific Method What we can do is to look at the process of problem solving as an exercise in the scientific method: • Experience difficulties • Identify the problem • Make observations • Look for patterns • Propose a hypothesis • Look for exceptions • Replace previous theory with a better one • Make predictions • Observe shortcomings • Repeat the cycle If this is done properly against a historical background and in a social context with information about the personalities involved, our students might begin to appreciate why one gets bogged down, how one’s own mind-set can hinder the breakthrough, and how the attitude of others can block our own progress. It is well for students to understand that too often advances occur only in the face of great opposition. The correct solution to a problem can often be blocked on purely personal grounds. Is There a Problem? Of course, before we can solve a problem, we must first recognize that there is a problem! and then identify exactly what it is. There may be too little information. What’s worse, sometimes we have too much information. Much of it may be simply white noise: too many concept balloons linked by sloppy macaroni. Quite often we don’t even know there is a problem: or worse still, sometimes we will not admit that a problem exists. Chemistry’s Most Important Problem There is one simple way to face problems. You must learn to struggle through them to eventually get the answer, by working through the material in the historical order of discovery. It is worth recalling the old Russian saying: “the past must inspire the future”. And, I believe, the best (and most important) example is the titanic battle to get from a vague concept of “element” to a correct understanding of atomic weight and valence, which was critical for the development of chemistry (5). And success turns entirely upon the concept of Equivalent Weight, an idea beautiful in its simplicity, yet formidable in its interpretation. But where to start?

Vol. 73 No. 11 November 1996 • Journal of Chemical Education

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In the Classroom

Two Hundred Years Ago Between 1750 and 1800, mankind’s understanding of materials advanced from the alchemy of Bergman to a proper conception of elements by Antoine-Laurent Lavoisier, who clearly understood the difference between metal and metal oxide. In a cyclic series of reactions the material of minimum mass was the element (often a metal). In 1789 Lavoisier published a Table of Elements – – (Figure 1), including radicals Cl and F , and oxides CaO and MgO, knowing that these were not the elements but recognizing that they were derived from elements as yet not isolated (5a). This was all made possible by the development of balances capable of weighing accurately. Stoichiometry and Equivalences In 1792 a German engineer, Jeremias Benjamin Richter, published a book called Stoichiometry, in which he listed the masses of various bases that were needed to neutralize 1000 parts by weight of acid. In 1802 another German, Ernst Fischer, published an improved table (Figure 2) (5b). For the first time we have “Equivalent Weights”. These tables were developed because they were useful to people in industry. They helped to solve problems in the plant. The concept “equivalent weight” was needed. “I have 1000 tons of sulfuric acid. Last time I needed 793 tons of lime to neutralize it. But there’s none left. How much soda, or potash, or magnesia do I need to do the job? More, or less, or the same weight?” You looked up the answer in the table of equivalents. A problem had now become a “look-up exercise”! No one quite understood why this should occur, but it was clear that different compounds (and elements) had associated with them a fixed weight linked to their reactivity. Around 1799 Joseph Louis Proust demonstrated that any compound had only one composition: “The cinnabar of Japan is the same as that of Almaden in Spain. The silver chloride of Peru is not different from that of Siberia.” Suddenly compounds and elements became entities for which weight was a very important characteristic (5c).

Figure 1. Lavoisier’s Table of the Elements ( Substances simples), 1789. At the top he places: Light, Heat; then Oxygen, Nitrogen, Hydrogen. Radical muriatique is of course chloride: no one had yet isolated chlorine gas. At the bottom are the intractable oxides: Chaux (CaO); Silice (SiO2).

Ideal Gases and Atomic Theory At this time, quite separately, scientists were studying the physical and chemical properties of gases. The standard relationships had been found: PV = constant (at a fixed T); Boyle, 1660 P/T = constant (at a fixed V); Amonton and Lambert, 1779 V/T = constant (at a fixed P); Charles, 1780

and it was these facts together with the behavior of mixtures of gases (viz., air and water vapor) that prompted John Dalton first to propose his atomic theory in 1803 and to enlarge upon it in 1808 (5d). 1. All material is made up of atoms. 2. An atom is the smallest particle of an element that can take part in a reaction. 3. The atoms of an element are identical. 4. The atoms of different elements are different. 5. A compound is made up of atoms of different elements in a fixed small whole number ratio.

He had linked the critical concepts: atom and element. 1008

Figure 2. Richter’s Equivalents, as revised by Fischer, 1802.

Journal of Chemical Education • Vol. 73 No. 11 November 1996

In the Classroom

And now he makes two assumptions that will cause a problem of such magnitude that it takes all of Europe’s chemists 50 years and the Karlsruhe Conference (6) before they finally agree on what is correct. Dalton makes the assumptions without sufficient factual information on which to base them. He assumes (without foundation) that the elemental gases are monatomic; and he assumes that water is a diatomic molecule HO (because this is the simplest formula) (see Figure 3). He also proposes that the hydrogen atom has a relative weight of 1 and that equal volumes of gases have the same number of atoms. There was a further confusing factor: Dalton used the term “atom” for both atom and for what we now call “molecule”. Other chemists used the reverse terminology, calling everything “molecule” (5f, 7a)! Integer Volumes of Gases Meanwhile, in France, Joseph Louis Gay-Lussac was experimenting with reactions between gases (hydrogen/ oxygen, hydrogen/chlorine, and many others), and in 1808 he found that the volumes of gases always reacted in simple whole number ratios (1:1, 1:2, etc.) to give an integer volume of gaseous product: 2 volumes of hydrogen react with 1 volume of oxygen to give 2 volumes of water 1 volume of hydrogen reacts with 1 volume of chlorine to give 2 volumes of hydrogen chloride (5e)

These simple experimental results cannot be explained if the “atoms” of gaseous elements are monatomic, as assumed by Dalton. In 1811 Amadeo Avogadro published his famous hypothesis, equal volumes of different gases contain equal numbers of “molecules”, from which it follows that the elemental fixed gases hydrogen, oxygen, nitrogen, and chlorine cannot be monatomic but must be diatomic (H2, O2, N2, Cl2) because without this postulate none of GayLussac’s experimental results can be explained (see Figure 4): Observation: 1 vol chlorine + 1 vol hydrogen gives 2 vol HCl With single atoms: 1 atom Cl + 1 atom H → 1 compound atom HCl. This does not fit! With diatomic molecules: joined pair of 2 atoms Cl + joined pair of 2 atoms H → 2 compound atoms HCl. This fits (5f).

Yet the chemical fraternity ignored Avogadro. Why? This question is worth discussing at length. Why would chemists not accept a diatomic molecule of an elemental gas? Because Berzelius had said that it was not possible to form such a bond between two identical atoms. According to Berzelius, bonds could only be formed between different atoms. Berzelius was a giant in chemistry so everyone believed his statement. No one thought laterally; they advanced blinkered. Surely dia-

(a)

(b)

(c)

Figure 3. Dalton’s Table of the Elements, with “Atomic Weights” 1808. Note how some are correct while others are half the correct value (due to oxygen’s being assigned its equivalent weight as its atomic weight).

Figure 4. Gay Lussac’s Experiments and Avogadro’s Explanation: (a) 1 volume of hydrogen + 1 volume of chlorine gives two volumes of hydrogen chloride gas. (b) 2 volumes of hydrogen + 1 volume of oxygen gives 2 volumes of water. Note the important assumption: equal volumes of gases contain equal numbers of molecules. (c) If water really had the formula HO, then 1 volume of hydrogen (H2) plus 1 volume of oxygen (O 2) would give 2 volumes of water (HO). This is not true; therefore the formula of water cannot be HO.


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mond consisted of only one type of atom—carbon. A diamond was an element. Lavoisier had shown this thirty years before. And diamond is very hard; therefore the identical carbon atoms must be strongly bonded to each other! Ergo: Berzelius is clearly wrong. But no one had the courage to say so nor the strength to stand up to the giant.

(he used the word atomicity) when he clearly stated that methane is CH4, and hence carbon has a valence of 4, from which follow the formula for CO2 and myriad others (5f, 9).

Electricity = Chemistry

The relationship between equivalent weight and atomic weight of an element (an integer ratio) was its “valence”, a concept quite difficult to grasp. Nowadays we seem to talk of “oxidation state” and “oxidation number” rather than “valence”. Ask yourself: what is (are) the valence(s) of carbon in CCl 4; CO2; CH4; CH3OH; OCH2; HCOOH; CH2F2? And then: what is (are) the oxidation state(s) of carbon in CCl4; CO2; CH 4; CH3OH; OCH2; HCOOH; CH2F2? Are they the same or different? Does it matter?

Michael Faraday, in London, showed that when water was electrolyzed, 2 volumes of hydrogen gas were obtained for every one volume of oxygen gas, and if these two-plus-one volumes of gas were mixed and sparked, exactly 2 volumes of water vapor were obtained. This observation was perfectly explained by Avogadro’s hypothesis (if water had the formula H2O): 2H2 + O2 → 2H2O Still, many scientists ignored the implication. Now Faraday made the most important discovery of all: that electricity was chemistry! He found in 1833 that a fixed amount of electricity always deposited the same mass of an element and that these masses were “equivalent”. One amp for five minutes had the same effect as 5 amps for one minute. Deposition of one gram of hydrogen gas required 96,000 amp-seconds (coulombs); the same charge gave 8 grams of oxygen, 32.5 grams of copper, 107 grams of silver—in each case, the equivalent weight. Despite all of this information, we find chemists listing two different types of “atomic” weights (one real, one the equivalent weight) in the same list. Here was compromise that inevitably led to contradiction and conflict (which is implicit if facts are ignored). As Shakespeare put it: “Oh, what a tangled web we weave, when first we practice to deceive!” Dalton deceived himself by assuming water was HO, and thereby created a terribly tangled web for all chemists. He blocked out from his mind GayLussac’s laws; he would not accept Avogadro’s hypothesis (8). And of course, the beautiful illustrations in his tables of compounds clearly showed the water molecule as two atoms joined (Figure 5). Chemists saw the diatomic water molecule, and therefore unconsciously believed it all the more.

Valence vs. Oxidation State

First Comes True Atomic Weight, Then the Periodic Table Yet still there remained no consensus about the term atomic weight—it was often wrongly used where equivalent weight was meant (Figure 6) (6). Ultimately the problem was seen to be so important that the greatest chemists of Europe called the Karlsruhe Conference of 1860, and only after 3 days of debate did Cannizzaro give

Water Must Be H2O! Here is the key to understanding the concepts of atomic weight (of the atom), which cannot be measured directly, and of equivalent weight, which can be measured by a chemical reaction—for example, by dissolution of zinc in hydrochloric acid to give hydrogen gas or ignition of magnesium ribbon to give MgO. The formula of water must be H2O; hence the atomic weight of oxygen must be 16, twice its equivalent weight of 8 (because 8 units of mass are equivalent to 1 unit of hydrogen). It is the ratio of 2:1 for the volumes of gas that is critical. The problem is solved if we accept the fact that hydrogen and oxygen are diatomic. The question is: How do we arrive at the “diatomic” gas molecule? This was elegantly described by Avogadro in 1811. But what seems to be so beautifully logical and self-evident was yet again ignored; it was not accepted by the chemists. Once more we must ask Why? Why? Why? Carbon Has a Valence of 4 By 1857 Kekulé had grasped the concept of “Valence” 1010

Figure 5. Drawings of the molecules of water, hydrogen sulfide (marked by arrow heads), presented by Dalton in 1835. It is quite clear that the molecules of different compounds had different sizes and shapes. By this date both Faraday and Berzelius had demonstrated that water was H2O. A further 25 years would pass before the Karlsruhe Conference and Cannizzaro’s important contribution.


In the Classroom

his presentation that clearly explained the difference between equivalent weight and atomic weight—and that understanding was possible only if the elemental gases were diatomic molecules (6). It took a further 10 years before there were a sufficient number of elements with correct atomic weights to allow the periodic table to be constructed by Meyer and Mendeleev between 1869 and 1871. Note carefully how Dalton’s atomic theory beautifully explained the concept “Element”, yet could not contribute at all to the construction of the periodic table. Even the discovery of the electron by Stoney in 1881 and the subsequent measurement of the ratio e/m in 1897 by Thomson did not help. Only after the discovery of X-rays by Röntgen in 1895 and the deduction of atomic number from characteristic monochromatic X-rays by Moseley in 1913 was the structure of the periodic table explained.

cess is neither simple nor straightforward. Despite knowing that the formula of water was H2O, Berzelius was a dedicated opponent of Avogadro’s hypothesis (7b). Moreover, there was the complication of the use of the word “atom” to mean, in today’s terminology, atom or group or molecule (7c). Forty years ago we typically did quantitative gravimetric exercises in the freshman lab: ignition of magnesium to give MgO; displacement of hydrogen by zinc. Both gave the equivalent weight of the metal. To get the atomic weight required the assumption that the hydrogen gas consists of diatomic H 2 molecules and that water is H2O. The importance of these assumptions is seldom made clear in current books, yet it was a lack of the idea of the “diatomic molecule of hydrogen” that led to the dreadful delay. Cannizzaro’s trick was not to worry about what forces held together the diatomic molecule.

Why the Delays?

Where Was the Problem?

We should debate with our students the reasons for these delays: 50 years from Avogadro to Karlsruhe! To appreciate the causes is far more valuable than memorizing the electron configuration of element Number 20. A rambling debate of this kind could even give some hints about how to go about solving a problem. The pro-

Equivalent weight is far more basic in a practical sense—it relies solely on measurement of mass of solids or volumes of gases. The problem seemed to be to understand the relationship between equivalent weight and atomic weight. One might say that equivalent weight plus intellect should yield atomic weight. But it didn’t (not for 50 years). It is often hard to come to grips with the difficulty. So often everything is woolly, like wrestling with a cloud of feathers. The key to success is to identify the real problem that, when solved, will open the way to everything else. In this historic case the real problem is the relationship between hydrogen, oxygen, and water. The huge intellectual step is to see that the critically important gases must be diatomic from the reaction of the volumes of these gases; and that water, the most important compound of all, is H2O. Until the formula H2O is accepted, there can be no consistency, no understanding, only contradiction. Dalton’s assumption of the 1:1 formula for water crippled chemistry for nearly 60 years! Worse still, chemists clung to two contradictory ideas in the face of so much evidence. Why? Is it possible that because Dalton’s simple atomic theory seemed so beautiful (8) and because it explained so much, they assumed that everything he postulated was true? A great error, so it turned out! Do our students understand all of this? Do we, the teachers, understand that most textbooks cover these important topics in the reverse order in which they were discovered? A perilous decision. We should always remember that first came Boyle’s Law, then 50 years later came atoms, molecules, and atomic weight, with s, p, d, f, etc. following after yet another 50 years. Doubtless there will be those who consider that the reintroduction of a discussion of “equivalent weight” would be a retrograde step because (i) it is not SI-approved; (ii) it is “hard” to understand; and (iii) worst of all, it is old fashioned. I disagree, but I shall leave the last word to Joel Hildebrand: “If the use of equivalents seems harder to the student than the use of moles or grams, he should psychoanalyze himself (10).” Now that is fighting talk! Acknowledgment

Figure 6. A Table of “Equivalent Weights” from the book, A Manual of Elementary Chemistry by George Fownes, published in London, 1856. The author omits any discussion of Avogadro’s hypothesis, yet he includes water as HO, without any critical discussion.

I thank my friend Don Hamilton, who believes that equivalents and normality are “good”, for our many discussions over coffee.


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Literature Cited 1. Wellington, J., Ed. Skills and Processes in Science Education; Routledge: London, 1989; pp 145–146. 2. Novak, J. D.; Gowin, D. B. Learning How to Learn; Cambridge: New York, 1984; p 36 and p 58 especially. 3. Bodner, G. M. J. Chem. Educ. 1986, 63, 873–877. 4. Commaille, R. Subject advisor for physical science and examination moderator. Personal lunch-time communication during discussion of the 1993 Natal Senior Certificate Higher Grade Physical Science examination paper. 5. Ihde, A. J. The Development of Modern Chemistry; Dover: New York, 1984; (a) p 78; (b) p 96; (c) p 100; (d) p 106; (e) pp 117, 119; (f) p 120. 6. Laing, M. Spectrum 1992, 30(2), 57–64. 7. Mierzecki, R. The Historical Development of Chemical Concepts; Kluwer: Doordrecht, The Netherlands, 1991; (a) pp 117, 118; (b) p 132; (c) p 134. 8. Brock, W. H. Educ. Chem. 1994, 31, 95–102. Here too the question is asked: Why did Dalton not accept Gay-Lussac’s results? 9. Benfey, O. T. From Vital Force to Structural Formulas; Beckman Center: Philadelphia, 1992; p 74. 10. Hildebrand, J. Principles of Chemistry; Macmillan: New York, 1940; quoted in Chem. Eng. News, Nov. 22, 1993, p 52.

Exercise As an exercise in reasoning (problem solving?) ask students whether the results of the following experiments are self-consistent, and what the atomic weight of zinc must be. 1. 6.5 g of zinc powder dissolved in copper sulfate solution to give 6.3 g of copper (it always gave slightly less than its own weight).

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2. 0.65 g of zinc powder dissolved in dilute hydrochloric acid to give 240 mL of hydrogen gas. The same result was obtained from dilute sulfuric acid. 3. Dilute sodium hydroxide solution was added to the solution from experiment 2. A white solid precipitated, and this was then filtered and heated to constant mass. It weighed 0.80 g. 4. 0.24 g of magnesium metal was ignited to form a white solid. Its weight was 0.40 g. 5. 0.24 g of magnesium was dissolved in acid (as in experiment 2) and 230 mL of hydrogen was collected. 6. As in experiment 3, sodium hydroxide solution was added and the precipitate was found to weigh 0.39 g. 7. An electric current was passed in series through a solution of copper sulfate and a solution of dilute sulfuric acid. After 30 min, 0.32 g of copper had been deposited and 57 mL of oxygen and 115 mL of hydrogen had been collected. 8. 2.42 g of black copper oxide was reduced by hydrogen gas until a constant weight of 1.93 g of copper metal remained.

If something is wrong, ask the students where is the error. CAVEAT: They may not use the concept of Mole, nor the numerical value of the Faraday, nor any known valences, nor any atomic weights other than 1 for the H atom.


Bring Back Equivalent Weight-If You Want the Kids To "Think"!

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