Ohio
Shiu Lee1 Northern University
I
A Redefinition 01 "Mole"
A
term is a concise, symbolic representation of a concept. Just as individual concepts may be organized to form an idea, so terms may be combined to convey it. Sound terminology promotes effectiveness and colwenience in speech and writing and, through them, comprehensionof knowledge. Unmund terminology, on the other hand, impedes wmmunication. Therefore, it is desirable to investigate chemical t,erminology with the aim of seeking greater comprehension by students. This paper will deal with the invest,igation and the proposed improvement of a set of terms having the most fundamental significance in chemistrythe gram formula weights. The requirements of sound terminology may be set fort,h as follows:
as mole, g mole, gmw, g atom, g ion, g equivalent, g ep wt, gew, and simply equivalent. But there is lack of uniformity among authors. Their definitions are straightforward, but beginners nevertheless find them hard to grasp. The most difficult appears to be gram equivalent weight.$ But even in the case of the mole, the student's ability to use the term correctly may not mean full comprehension. An interesting fact is that the mole has frequently been applied to ions in addition to molecules, which shows a tendency to simplify the terminology. The widespread difficulty with, and the evolution in, the gram formula weights are the result of had terminology as can be shown below.
A term should have a name which is simple and distinctive; A term should represent a e m e p t which has basic significance
A gram formula weight is generally defined in textbooks as "the sum of the atomic weights of a formula, expressed in grams," or somewhat more completely, "the quantity of a substance having a weight in grams equal to the sum of its atomic weights" (italics mine). Objections may be raised as to (1) the inadequacy of the definition and (2) the lack of "basic" significance of the terms: (1) As defined, a gram formula weight is merely a weight or quantity, e.g., 1 mole of KO is 30.008 grams, 3 moles of it are 90.024 grams. Actually a gram formula weight is more than that: it is a unit of weight or quantity, as in 3 moles of NO, and 1.70 g atoms of C, where one mole and one g atom are the respective units. A definition which does not show this unit significance is inadequate; it would be analogous to the definition of meter simply as 39.37 inches long without showing its significance as a unit of length. (2) Again, as defined, 1 g atom of oxygen is 16 grams, 1 mole of water is 18.016 grams, and there are as many different gram formula weights as there are substances. Since each gram formula weight is also a unit, there are, then, as many different units as there are substances. The result is a multiplicity of units which does not appeal to the scientific mind. This multiplicity of units may be prevented if the definition of a gram formula weight is not based on weight, but on a common denominator among these units. Specifically, there is a number, Avogadro's number, which underlies all gram formula weights. Avogadro's number may well be used directly, rather than simply implied, as the basis for the definitions of the gram formula weights, so that all of them will have the same unit. Some authors, amone them Keenan and Wood.a
(SO that it may readily be combined with other terms t,o convey more complex concepts); A term should have a definition which covers fully the concept it represents.
Although the adjectives "simple," "distinctive," and "basic" in the above requirements cannot be exactly defined, their meanings are quite clear in practice. The human intellect which demands that knowledge be rational also requires that terminology be sound. Either consciously or subconsciously, man is constantly reevaluating the terms with which he is in contact-in common usage, teaching, and learning. Those terms that are unsound will be found unduly digcult to understand or inconvenient to use. In the inevitable evolution of language, they will sooner or later be revised or simply go out of use. The terms gram atomic weight, gram molecular weight, gram ionic weight, and gram equivale.ntweight-generally referred to as gram formula weights-are most essential to chemical calculations. They are practical, measurable quant,it,ieswhich bear the same proportion to the weight of t.heir respective unit particles. Their long names have given way to many abbreviated forms, such Present address: Yale University, New Haven, Connecticut.
rFditor's
note
Readers will recall the definitiue discussion q f the "mole" 38, 86 (1961). by Prqfessor Guggenheim i n THIS JOURNAL, The articles and letters here presented ( p p . 649-56)are r e p w sentalive of the communications submitted to the Editor's ofice since F e b m m l ~ . This collection i s not published with the int e n t i a of deciding any pedagogic issue or of e*tablishing uneq?hocal tenninolog?,. The purpose i s to urge teachers to take a ,fresh look at what they have been taking for granted. When skeptical reezaminalion replaces the habit of mere repcfition, teaching improves.
I
Reexamining Existing Terminology
'MELDRUM,WILLIAMB., J. CHEM.EDUC.,32,48-51
(1955). S K ~C. W., ~ AND ~ WOOD, ~ ~J. H., , "General College Chemistry," Znded., Harper & Brothers, Publishers, New York, 1961, p. 111. Volume 38, Number II,November 196 1
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have defined the mole as "the weight in grams of 6.02 X 1O28 molecules of any substance" (italics mine). Although the numerical significance is explicit, this mole is still a weight, which varies from substance to substance and does not solve the problem of the multiplicity of units. This problem, however, can be solved by defining the mole directly as a pure number. The apparently simple way in which the terms for the gram formula weights were coined has given rise to names which appear illogical and tend to mislead. Each of the gram formula weights consists of three words-"gram," the word for the species ("atomic," "molecular," . . .), and "weight." These three words, taken individually or as a group, may be criticized. First, the words in gram formula weight are completely separate and hyphens are seldom used; yet they are really dependent parts of a single term. A metric or English unit usually consists of one word (kilogram, gallon) or two words (square meter), but seldom more than two. A unit as simple and frequently used as the one in question should not he represented by three words. Second, since the word "gram" already implies weight, the presence of "weight" is redundant. Furthermore, no other weight unit carries the word "weight" in the unit ("hundredweight," which is one word, is not an exception). Most serious of all, one might logically ask: If "gram" and "weight" are present in a gram formula weight, why is it not always explicitly expressed in grams? The fact that the term is most frequently used as a unit is thus made obscure by its very name. Third, the presence of atom, molecule, or ion in a gram formula weight may also he objected to. They are as unnecessary as the presence of solid, l i p i d , and gas would be in gram or milliliter. Only when the type is omitted can a term have sufficient breadth to cover all types. There is a prevalent malpractice in t,he use of gram formula weight without clearly specifying whether (a) the weight in grams or (b) the number of the unit is meant. Following is an example of this ambiguous usage taken from a current, widely used text,hook: (a)vam epivalent weight = gram molecular weight/change in oxidation number, ( b ) gram eyuivalat weights = normality X liters of solution.
The lack of clear specification is a frequent source of confusion for the beginner. Some authors have adopted the practice of omitting weight for cases like (b), while retaining it for cases like (a). In similar manner, g atom and g ion are distinguished from g atmnic weight and g ionic weight. This practice of distinguishing between the complete and the abbreviated names is illogical and tends to confuse the terminology. Redefining "Mole''
Three conclusions may be d r a m from the above: The set of gram formula weights should not contain the three narts ("gram," the species, and "weight") and therefore should be abolished. The gram formula weights should be replaced by a single term which is applicable to all species. The new term should be defined on the basis of Avogadro's number (rather than on weight) and its significance as a unit should be clearly stated.
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For the name of this new term, a word derived from Count Arnadeo Avogadro's name, such as Aunola (Avogadro's no. of formulas) might be adopted; this would also give recognition to a great pioneer in chemistry. However, the use of the term mole (which has long been used to imply Avogadro's number of molecules and frequently charged particles) is preferable, for its name has none of the shortcomings of the complete name, and its adoption would prevent dislocations in usage. The writer proposes to redefine the mole as "a umit o f number equal lo Avogadro's number." I t may be applied to all chemical species (atoms, molecules, ions, radicals, electrons) as well as all physical species (unit cells, colloidal particles, etc.). Examples of correct uses are as follows: 2 moles of copper (or Cu), water (or H20), and iodide (or I-); 2 moles of copper atoms, water molecules, and iodide ions (meaning 2 X 6.024 X loz3of each kind). If the name of a substance can mean more than one form, as oxygen (02, 0, 0 1 6 , Ot7, etc.), the form should be specified; for example, 2 moles of oxygen molecules, atoms, Ole, 0°, etc. In the absence of an indication, however, the most common molecular form (or isotopic mixture) or the simplest formula should he assumed: 1mole of chlorine will mean 1 mole of the natural occurring isotopic mixture of CL. Note that it is preferable to say 1 mole of oxygen (6.024 X loz3) atoms weighs rather than is 16 grams. The mole as redefined is similar to the words hurul~ed and m i l l i a which are units of pure numbers. Recently, Guggenheim4 defined the mole as "the amount of substance containing the same number of molecules (or atoms or radicals or ions or electrons as the case may be) as there are atoms in 12 grams of '2C" (italics mine). (The actual value of Avogadro's number is not material to the discussion.) This definition recognizes the mole's use in connection with all chemical species, but it cannot be used in connection with a physical species. Another difference between Guggenheim's and the writer's moles lies in the fact that the former is a n amount of substance which carries with it physical significance, while the latter is entirely a n abstract number. The question arises, therefore, as to whether it is desirable to attach physical significance to the mole. Since the type of substance should always follow the mole (or should he implied), it does not seem necessary for the mole itself to carry any physical significance. "Molic" Weight The weight of a g atom, g mole, or g ion may be expressed as "the weight per mole" of the respective species; e.g., the weight of calcium is 40.06 grams per mole. The frequent use of the concept of per mole, however, requires a shorter term which the writer wishes to introduce as "molic." (Molic is distinguished from molar and molal which represent concentration.) Examples of its use are: the molic weight of aluminum is 26.98 grams; the molic volume of hydrogen gas (or any gas) is 22.4 liters under st,andard conditions. Xote that "molic," like "mole," refers to t,he most common molecular form (or isotopic mixture) or t,he simplest 'GUGGENKEIM, E. A,, J. C ~ MEDUC.: . 38. 86-87 (1961).
formula if the exact species is not shown. Other examples are: the molic atomic weight of nitrogen is 14.008 grams; the molic ionic weight of chloride is 35.457 grams; and the molic molendar weight of a suhst,ance equals the sum of its molic atomic weights. The new mole and molic weight are designed to replace gram atomic, gram molecular, and gram ionic weights in all their numeriral implications and weight uses. "Eq" and "Equic"
The related term gram equivalent weight should be renamed simply "eq" (t,o be pronounced as ek) which, similar to "mole," will be defined numerically. An eq of a species may be defined as "a unit of number of t,hat species capable of donating, accepting, or sharing one mole of electrons, protons, or electron pairs in a react,ion (depending on whet,her a reductant, oxidant, acid, or base, and whether the Lewis sense is referred t,o)." An eq should always be related to a mole so that it is convenient to use. For example: 1 mole of zinc is capable of donating 2 moles of electrons and, therefore, is equal to 3 eqs. It follows t,hat 1 eq of zinc weighs
one-half of the molic weight ('/2 X 65.38 = 32.69 grams). The weight of a substance per eq may he termed "equic weight." Since the capacity of a substance in donation, acceptance, or sharing may depend on the nature of the reaction, it may be necessary to specify the reaction so that an eq will be a definite number. In this connection, the terms "acid eq," "base eq," "oxidant eq," and "reductant eq" may he used. Thus, 1 mole of HICrOnis equal to 2 acid eqs or 3 oxidant eqs. The term "milli-eq" may he used to represent a number which is one one-thousandth of an eq. A solution has been worked out in this paper in simplifying and rationalizing the set of gram formula weights: the writer proposes that the new terms "mole," "eq," and their companion terms "molic" and "equic" weights he adopted to replace the existing set of gram formula ~veights. Mole and eq represent very large numbers which cannot be directly measured like the gram formula weights, but the replacement of a weight by a number-of the concrete by the conreptual-follows a well-traveled path in the evolution of t,erminology.
Volume 37, Number 1 I , November
1961
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