Avogadro's Concept of Equivalents for Teaching Cation Exchange Capacity

Avogadro’sconcept of equivalentsfor teachingcation exchange1 capacity

Steve2 J. Thien

ABSTRACT

A thoroughunderstanding of cation exchange will have probably learned their chemistry under capacity, whichrequires mastery of manychemical the aforementioned definition, their students will conceptsin an introductorysoils course,is crucialto fully comprehendingthe nature of soils. Student come with another concept in mind. The role of performancein this area hadbeen especially low on chemistry is so basic to agronomic education that courseobjectives requiring working knowledge of the the resultant information gap needs to be recon- conceptof chemicalequivalents. Four specific dif- ciled. The basic simplicity of using Avogadro’s con- ficulties associatedwith understandingand using cept, plus its ability to organize and clarify many equivalentsare examined.Avogadro’s concept of an equivalentas 6.02 X 1023charges is outlinedas an previously difficult concepts to quantitative chemis- alternative pedagogicalapproach. The advantages of try make the new approach educationally attractive. simplicity and readily apparentstoichiometry are This paper uses cation exchange as the agronomic offered in someexamples. The approachhas sig- format for illuminating the advantages of teaching nificantly increasedstudent performance on related agronomic chemistry based on pedagogical use of courseobjectives. Avogadro’s number. Additionalindex words: Soil chemistry,Pedagogi- cal approach. DIFFICULTIES IN LEARNINGEQUIVALENT CHEMISTRY

MEDEOAvogadro, a 19th century Italian Cation exchange is a fundamental chemical concept used in understanding soil science. Its im- A physicist, is perhaps best remembered for his portance to comprehending the nature of soils is hypothesis that laid the framework for our under- frequently considered parallel to the impact of standing of molecular weights. In addition to dis- photosynthesis in studying crop science. Yet, the tinguishing between molecules and atoms, his work necessity of defining and explaining this theory by established that equal reacting units (moles) must have the same number of molecules. The number using difficult chemical terminology and concepts bears his name, is customarily denoted by the sym- frequently presents a block to learning. Soils in- structors, especially those in introductory courses X bol N, and has a value of 6.02 1023 (8). Instead where students are initially exposed to cation ex- of expanding on the concept of a mole as a finite change, must recognize the challenge of such a number of reacting units, chemical educators in the learning situation. A thorough understanding of past have favored a combining ratio approach. But now, Hawthorne (6) has reported on a growing this concept is so fundamental and crucial to full comprehension of the properties of soils that every tendency in chemistry education to abandon the definition of a mole as a mass of material that hap- teacher’s effort should reflect the requisite amounts pens to react with 16 g oxygen (or 1 g hydrogen, of time, talent, resources, and pedagogical ap- or 12 g carbon), and, instead, to teach students that proaches to insure maximumunderstanding. the mole is Avogadro’s number, N, of molecules, a The high degree of difficulty students exhibit in clearly defined number of particles. An extension comprehending the nature of cation exchange has of using this definition, shows an equivalent to sim- been repeatedly acknowledged in informal discus- ply be Avogadro’s number, N, of charges. While in sions on agronomic teaching. My own discussions no way representing a new chemical theory, the about this problem with students and their per- change signifies a different reasoning scheme needed by its learners and users. IContribution No. 1, College of Agriculture, Kansas Implications of this pedagogical change will State Univ., Manhattan, KS66506. quickly spread to related chemical education in 2Associate professor of agronomy,Kansas State Univ., agronomic courses. While most agronomic teachers Manhattan. 35 36 JOURNAL OF AGRONOMIC EDUCATION

formance in meeting specific course objectives on cal relationship, which is also embedded in the the various components of cation exchange have previous two examples, contributes considerable focused on some specific difficulties. It seems the confusion. definition, cation-anion attraction, utility, and Students who may grasp the previous three cause present little difficulty compared with master- points point out an additional difficulty. They ing a working use of the term "equivalent" to ex- ponder how an equivalent of base, something being press relationships. While there seems to be no comprehended and defined in terms of so many suitable alternative to using this terminology, the grams, reacts in the soil not with grams of anything, shift in basic chemical education to using a concept but with negatively charged sites that have no ap- of molecular chemistry originally explained by parent weight parameter--more confusion about Avogadro offers some solutions to making the con- what an equivalent really represents. cept of chemical equivalents more easily learned. Those who have mastered the concept of an Four areas of difficulty frequently mentioned by equivalent find no real obstacles to comprehending students lend insights to their problem. First, the above examples. Frustration on the teacher’s agronomy students are quick to acknowledge a dif- part maybe forthcoming, however, when struggling ficulty in understanding the conceptual definition with a student, or many students, who simply "do of equivalency. Through non-Avogadron general not see" the relationship. An "examplish" defini- chemistry texts, they have learned that the equiva- tion, ghost units, lack of obvious stoichiometry, lent is a mass of material that combines with 1 g of and disimilar reacting units offer little help in such hydrogen (or I6 g oxygen, or 12 g carbon). Most a situation. students seem able to recite that relationship from From a pedagogical viewpoint, describing equiva- memory, or at least acknowledge an exposure to it. lents as a weight of material seems to be the basis Why the difficulty then? The difficulty seems to of the difficulties described. Hawthorne’s (6) re- be not in understanding what is said, but in under- search shows that about one-third of the most re- standing the basis for saying it. In other words, it cent chemistry texts give pedagogical approaches comes across more as an example than a definition. using N, not just merely mentioning its value. Six Another problem is encountered because some recently published introductory soils texts (1,2, 3, agronomic texts suggest that an equivalent weight 4, 5, 7) give no treatment of equivalents as Avoga- can be arrived at by dividing an ion’s atomic weight dro’s number of reacting charges. One (4) mentions by its valence. If a student fails to comprehend the the value of N, so a conceptual gap already exists textbook definition above, examining this relation- between educational approaches used in chemistry ship strains the logic of the concept even more--as and agronomic texts. follows. Both dimensions, atomic weight and valence, are essentially unitless relations representing MEETINGTHE DIFFICULTIES ratios of combining weights (or numbers of atoms) and ionic charges. Hence, the quotient should also Avogadro’s concept directly addresses the four be unitless, but it isn’t because an equivalent is student-acknowledged problem areas with clarity given the units of grams. Assuring the student that and logic. A mole is conveniently explained as a the atomic weight can be assigned the units of finite number, Avogadro’s number, N of molecules grams, and now can be called the gram atomic (def. 1), weight, strains logic further. And it is no time to tell a puzzled student that it "just works out that A mole equals 6.02 X 10 23 molecules [1] way", or to freshen up on beginning chemistry. A more nearly logical approach is needed to build a and an equivalent is likewise simply explained as knowledge base from which to learn more about Avogadro’s number, N, of chemical charges (def. 2) soils. If you do not, you later have to point out that the formula (atomic weight + valence) does An equivalent equals 6.02 X 1023 charges [2] not necessarily work for oxidation-reduction reactions. This definition is for a nonredox reaction. In a A third difficulty in understanding and using the redox reaction, an equivalent refers to Avogadro’s equivalent-as-a-mass concept is its lack of apparent number, N, of electrons given off or taken up. stoichiometry. After all, why should 9 g aluminum, Since cation exchange reactions represent nonredox 20 g calcium, and 23 g sodium all be chemically reactions, discussion here is confined to that part equivalent to 1 g hydrogen? That apparent whimsi- of the definition. THIEN: AVOGADRO'S CONCEPT IN TEACHING 37

Those two definitions greatly simplify the concept of moles and equivalents and rule out ghost Two basic computations involving equivalents are needed when working with cation exchange situations; either equivalents are converted to grams, units. As will be seen later, all units agree with the or vice versa. After the conversions are made, further mathematical manipulations may be required to solve a problem, but they usually repre- basic rules of unit cancellation, lending the needed sent simpler numerical logic. Examples of each conversion using the con- logic and self-checking capability to problem setup. cept of an equivalent as Avogadro's number (N = 6.02 X 10") of charges are given here. For easier calculation, leave all exponents of 10 as the 23rd Perhaps the greatest single advantage associated power. with Avogadro's concept of equivalents is the I. Converting equivalents to grams Example A. How many grams of sodium are in 2.1 equivalents of stoichiometry it contributes to problems. Because sodium? of the readily apparent stoichiometry, enormous Step 1. Determine the number of charges in 2.1 equivalents. areas of quantitative chemistry can be organized (#equivalents)(charges/equivalentl* = #charges (2.11(6.02 X 10") = 12.6 X 10" charges and clarified for students by using the concept of Step 2. Convert number of charges to number of ions. an equivalent as a standard number of reacting (# charges) ^ (— charges/ion)! = ~ ions (12.6 X 10") -Ml) = 12.6 X 10" ions units. For example, in an exchange reaction an Step 3. Convert number of ions to weight of ions. equivalent of material contains 6.02 X 1023 positive (^ ions)(grams/ion}§ = grams (12.6 X 10")(3.8 X 10~"g/Na'ions) = 48.3glMa' charges and replaces only that amount of other ma- II. Converting grams to equivalents terial from exchange sites that also possess 6.02 X Example B. How many equivalents of calcium are in 2 grams of 23 calcium? 10 charges. This approach has the logic missing Step 1. Convert grams of ions to number of ions. 2+ when one explains that 20 gCa occupies the same (gram) ^ (gram/ion) § = #ions amount of the cation exchange capacity as 39 g K+. (2) + (6.6 X 10""l = 0.3 X 10" ions Step 2. Convert number of ions to number of charges. In the same manner, a soil with 20 me/100 g (#ions)(#charges/ionlt = #charges exchange capactiy becomes a soil with (20/1000) (0.3 X 10" ions)(2) = 0.6 X 10" charges Step 3. Convert number of charges to equivalents. 23 (6.02 X 10 ) charged sites per 100 g. It is easy to (•# charges) "^ (# charges/equivalent)* = #equivalents comprehend how that much soil holds an amount (0.6 X 102-')^(6.02 X 10" 1 = 0.1 equivalents Ca2+ of ions whose charges also sum to (20/1000) (6.02 23 * by definition from Avogadro's number, X 10 ). If the ions were all monovalent, then t obtained from the Periodic Table, i.e., the valence. 23 there also would be (20/1000) (6.02 X 10 ) ions. § obtained by dividing the weight of one mole of the ion (obtained from 21 If the ions were divalent, only (1/2) (20/1000) the Periodic Table) by the number of ions in one mole; i.e., 6.02 X 10 . 23 (6.02 X 10 ) ions would be necessary to occupy Fig. 1. Using equivalents in cation exchange applications. the same number of sites. Critics of the pedagogical use of Avogadro's taught another way in this chemistry course, virtually all students will use the method outlined in Fig. number say it is too large to be fully comprehended and is bulky to use in equations. Whether large 1 on exams. Switching to the Avogadron concept of equiva- numbers or combining weight ratios are more easily understood and used depends on an individual's lents has smoothed out a previously rough portion pre-conditioning. When chemistry texts do the pre- of an introductory soils course, both from an in- conditioning needed to work with exponential structor's and student's viewpoint. terms, then it is advantageous to adapt this stoichio- metric scheme to teaching cation exchange. SUMMARY Complete comprehension of cation exchange CLASSROOM APPLICATION theory in soils is virtually impossible without a working knowledge of chemical equivalents. Basic A switch to Avogadro's concept of equivalent chemistry education trends toward teaching a more chemistry has resulted in dramatic improvement of simplified explanation of the equivalent. This student performance on related course objectives. training method has merit because it adds order and Before changing, less than 20% of a large introduc- clarification to a complicated concept. This paper tory soils class handled cation exchange problems is to alert readers to the change with the hope that on exams satisfactorily. One semester of college interest in effective instruction will generate a chemistry is a prerequisite for this class, but a non- follow-through evaluation of its usefulness in agro- Avogadron approach was being taught. For the nomic teaching situations. past three semesters, a class handout (Fig. 1) has been used in conjunction with a problem set, virtually identical in content under both systems. Satisfactory student performance on related test items is now approaching 70 to 80%. Even though 38 JOURNAL OF AGRONOMIC EDUCATION