Expressing cation exchange capacity in milliequivalents per 100 grams and in SI units 1

Many students in introductory soil science and soil chemistry courses have difficulty understanding the chemical concepts that are associated with expressing cation exchange capacity in either equivalent units or the International System of Units (SI). This paper is intended as a handout o help beginning soils students understand these chemical concepts using a step-by-step review of chemical units. The handout incorporates Avogadro’s concept into the definitions of equivalent and gram-equivalent-weight in order to give the student a logical basis for understanding equivalents and their application to cation exchange. It also clarifies the use of SI units in expressing cation exchange capacity. Sample problems and solutions are provided to give students practice in this application. Although cation exchange capacity is expressed in milliequivalents per 100 grams (units which are still used in practically all introductory soil science texts), conversion of cation exchange capacity values in milliequivalents per 100 grams to SI units is relatively easy for the student once the concept of equivalent is learned. Additional index words: Equivalent, Gram-equivalent-weight, Soil chemistry. WEt HAVE found that students in introducmany ory soil science and in soil chemistry courses have difficulty understanding the concept of equivalent and applying it to express cation exchange capacity in milliequivalents per 100 grams. Seven recently published introductory soil texts (1, 4, 5, 6, 7, 10, 14) and two soil chemistry texts (2, 3) do not explain this concept and these units in terms that many beginning soils students can easily comprehend. Brady (4) eschews equivalent units in favor of the current International System of Units (SI); his book is the only introductory soils text thus far that uses SI units. Some of these texts use the conventional definition of equivalent in terms of acid/ base and redox reactions which are not particularly relevant to cation exchange reactions. Although university chemistry is required prior to taking introductory soils at Washington State University, these chemistry classes also use definitions foreign to what is needed to define cation exchange capacity in soils classes. For acid/base and redox reactions, one equivalent is defined as the amount of substance that will react with Avogadro’s number of hydrogen ions or with Avogadro’s number of electrons, respectively, in a given chemical reaction. As a result, the definition of equivalent depends not only on the type of reaction 84 (acid/base or redox) but on the specific reactants and products (2). For example, one mole of Hg can be considered to be either one or two equivalents of Hg depending on whether it is oxidized to Hg* or Hg~÷, respectively. The inherent ambiguity in this treatment of the term causes general confusion among freshman chemistry students, and several recent introductory chemistry texts have dropped the term altogether (G. Crosby, personal communication, Dep. of Chemistry, Washington State University). No such ambiguity exists in the use of equivalents in cation exchange reactions if the definition is based on Avogadro’s number (one mole) of charge without reference to hydrogen ions or electrons. We have, thus, developed a handout which teaches the student to understand and use equivalents to define cation exchange capacity (CEC) independent of what the student may have learned from freshman chemistry. We have used the handout in the introductory soils class at Washington State University for the past two semesters. The students have responded well to the handout, and most of them could adequately answer similar CEC problems (to those on the handout) semester’s end as well as general questions on the important topic of cation exchange and cation exchange capacity. No comparison of the students’ understanding of such CEC problems between the last two semesters (academic year 1983-1984) and any semester that preceded these last two was made because (i) a different instructor taught the course pre-academic year 1983-1984 and (ii) such CEC problems as on the handout were not asked of the students before the academic year 1983-1984. However, we have documented the usefulness of the handout through a student questionnaire and included the results of the questionnaire at the end of this paper. The handout serves two purposes. First, it is intended to help the student understand conceptually why cation exchange capacity is measured in units of equivalents per unit mass, and then in SI units. Secondly, it provides a method for calculating the number of equivalents of an ion from the mass of a mole of the ion (gram-atomicweight) and its ionic valence. Avogadro’s number is used to develop the conceptual framework, but its use is avoided in the calculations because it is unnecessarily cumbersome. ’ Contribution from the Dep. of Agronomy and Soil Science, Washington State Univ., Pullman, WA 99164-6420. Scientific Paper No.: SP 6728. 2 Assistant professors of soil science, Washington State Univ., Pullman. REGANOLD & HARSH: EXPRESSING CATION EXCHANGE CAPACITY 85 An argument for using Avogadro’s concept to teach students how and why equivalents are used to define cation exchange capacity was developed by Thien (12). The success of this method was indicated by the students’ dramatic improvement in handling cation exchange problems during examinations (12). Thien’s method involves defining an equivalent as Avogadro’s number (6.023 x 1053) of charges. Conversions from equivalents to grams are then made by multiplying equivalents by 6.023 x 1023, dividing the result by the number of charges per ion, and, finally, multiplying by the mass (in grams) per ion. Thien avoids the use of equivalent weight, present in many introductory soil science textbooks, because obtaining equivalent weight in grams involves dividing atomic weight by valence, two "essentially unitless" relations. And yet, he presumably obtains his "charge per ion" term from the ionic valence and his "gram per ion" term by dividing atomic weight by Avogadro’s number, two essentially unitless relations. Furthermore, he argues that the use of equivalent weight is confusing because it must be explained to the student that ionic valence can only be used in its calculation if there are no redox reactions. Yet, this disclaimer is also required in his definition of equivalent. As a result, Thien (12) has not avoided the conceptual problems he set out to eliminate. It is the purpose of this paper to suggest an alternative method to Thien’s using the following definitions: 1. A mole of atoms, ions, molecules, or charges is 6.023 x 102~ atoms, ions, molecules, or charges. 2. Gram-atomic-weight is the mass in grams of a mole of atoms. 3. An equivalent is the amount of an ion containing a mole of charges. 4. Gram-equivalent-weight is the mass in grams of an equivalent of ions. The term gram-equivalent-weight can then be used to convert from grams to equivalents without recourse to Avogadro’s number. Since most students are already familiar with, for example, converting from grams to moles using gram-atomic-weight, this presents a logical analogy. No conceptual difficulty arises since the use of unitless terms has been avoided by defining gramequivalent-weight and gram-atomic-weight in terms of the mass of a mole of ions or atoms (8). The suggestion by Thien (12) that Avogadro’s concept be used to explain equivalents to students grappling with the units and stoichiometry of cation exchange is an excellent one. The student handout below uses the concept repeatedly in taking the student through the chemical definitions to arrive at a simple formula for expressing cation exchange capacity and in explaining the value of the equivalent unit. This approach is offered as an alternative to requiring students to make all calculations on a per ion basis as suggested by Thien (12). To summarize, our definitions and method of calculating CEC improve on those from traditional chemistry and soil science textbooks by: 1. Eliminating definitions from traditional chemistry based on electrons or protons which are relevant primarily to redox and acid-base reactions, respectively; 2. Eschewing unitless terms used by Thien (8) by employing gram-atomicand gram-equivalent-weight definitions; and 3. Using a formula for calculating CEC which is based conceptually on Avogadro’s number, but does not employ 6.023 x 102~ in the actual calculation. One may argue whether "equivalent" should be used at all in an introductory soils course, given that some journals (e.g. Soil Science Society of America Journal) now permit only SI units in submitted papers and that the current trend in general chemistry is away from the unit. We would argue that as long as the term is in common usage in soil science, it should be taught at the introductory level. There are still journals which allow and even encourage the use of equivalents in defining CEC (e.g. Clays and Clay Minerals), and the term is incorporated into some of the most widely used cation selectivity coefficient expressions (11). We also feel that once students have mastered the expression of CEC in meq/100 g, teaching them to become equally conversive in SI units is relatively easy (12). STUDENT RESPONSE TO THE HANDOUT We documented the usefulness of the handout in Introductory Soil Science at Washington State University through a student questionnaire, which gave us an idea of the students’ chemistry background and response to the handout. We found that although 8307o of the 96 students that responded had taken introductory chemistry, 3507o of them had been given a traditional chemistry definition of equivalent (i.e., based on acid-base or redox reactions), and 5107o of them did not remember if they had been given a definition. Of the 3507o of the students who had been given the traditional chemistry definition, 84°7o found the definition on our handout to be "far easier" or "somewhat easier" to understand. Ninety percent of all the students (including those who had not had introductory chemistry) rated the handout as being "very helpful" or "somewhat helpful" with regard to understanding CEC; only 10070 found it "not helpful" or "confusing." Four of the 27 students in upper division Soil Chemistry requested a copy of the handout to review their chemistry, so we also gave them the questionnaire. All four students had taken introductory chemistry, all found our definition on the handout "far easier" to understand tlaan the chemistry definition, and all rated the approach on the handout with regard to understanding CEC and related calculations as "very helpful." In view of the straightforward approach to defining and calculating CEC and the favorable student response, we recommend the use of this handout to our peers teaching introductory soils courses. The handout will also be useful to any students needing to strengthen their background in use of basic chemical units. 86 JOURNAL OF AGRONOMIC EDUCATION, Vol. 14, No. 2, Fall 1985 THE STUDENT HANDOUT Part 4: Charge and Ionic Valence Expressing Cation Exchange Capacity in Milliequivalents/lO0 Grams and in SI Units The cation exchange capacity (CEC) of a soil is measure of the negative charge of the solid phase of a soil balanced by exchangeable cations. This negative charge is usually expressed in milliequivalents per 100 grams (meq/100 g) of soil. The CEC of a silt loam soil, for example, might be 18 meq/100 g. To get a better understanding of how and why these units are used in expressing CEC, let’s review our chemical units.