Frank Brescia City College of New York
CUNY New York, 10031
Equivalents-A Winner or a Bead Horse
The object of this article is to review the history of the stoichiometric term "equivalent"l and examine its rele. vance over a centuryafter the international of 1860 was held a t the Technische Hochschule in Karlsruhe. T h e atomic theory acquired life when John Dalton ( I ) preceived its use as an instrument for obtaining the relative weights of atoms, the ultimate particles of elements, and of "compound atoms," the ultimate particles of compounds. His method was forthright hut naive: atoms of the same element, he assumed, repel each other while the atoms of different elements tend to attract each other. A "compound atom" of 1H and 10 would then tend to repel a second H or 0 atom, leading to the conclusion that a 1to 1combination of atoms is most probable. The smallest mass2 ratio, based on H = 1, found experimentally would then correspond to the relative weights of the atoms. Water, with a hydrogen: oxygen mass ratio of "1:7", and ammonia, mass ratio "1:5", naturally lead to the assignment of the atomic weights "1,7 and 5" and to the formulas 00,HO, "relative weight S", and 00,HN, "relative weight 6," the first record of atomic weights, symbols of elements, and formulas of compounds. T h e existence of only one compound of two elements signalled a compound atom composed of one atom of each element so that their atomic weights and the compound formula followed directly from the measured mass ratio. "When two combinations are observed, they must be presumed to he a binary, and a ternary3." The relative positions of atoms in compound particles were determined by the assumption that the atoms "of the same kind repel each other and therefore take their stations accordingly." These conclusions were supported by other evidence (2).
congress
Oxygen and hydrogen have never been made to combine in any other proportion than that in which they exist in water. Hence this proportion must be that which unites most readily, and with the greatest force. Now as the atoms of hydrogen repel each other, as is the case also with the atoms of oxygen; and as hydrogen is attracted hy oxygen; it is obvious that when they are mired equally, as is the ease when 200 measures of hydrogen gas, and 100 measures of oxygen gas, are put into a tube, and fired by electricity, they will most readily unite atom to atom. This, though not in itself deeipive, is a corroborating circumstance. It follows from this that a g~venbulk of hydrogen gas contains only one-half the number of atoms that exist in the same bulk of oxygen gas. Although Dalton's hypothesis was accepted by Jons Jacob Berzelius. this s i m ~ l eand attractive apvroach drew much fire. ~ u & h r ~~ a i refused y to acceptthe arbitrary assumption that water is composed of 1 atom of hydrogen and 1 atom of oxygen. And William Wollaston proposed the use of the term Equivalent Weight4 ( 3 )in place of Dalton's atomic weight. These weights were experimentally obtained directly from the mass of an element that combined with 10 g of oxygen. If an element has more than one equivalent weight, these different masses are in simple ratios. Accordine to this IDalton's) view. when we estimate the relative
sihle . . . to discover which of the compounds is to he regarded as 362 / Journal of Chemical Education
consisting of a pair of single atoms, and since the decision . . . is purely theoretical, . . . I have not been desirous of warping my numbers according to an atomic theory, but have endeavoured to make practical convenience guide. . ." The experimental concept of equivalent was extended to acid-base reactions "So that the same quantity of potash that is saturated by 100 sulphuric acid, requires of muriatic 66." Wollaston's suggestion that "equivalent" he used for "atom" only served to compound the confusion: For example, (using current data and nomenclature) the mass ratio of nitrogen oxide, 7:8, and dinitrogen oxide, 14:8, leads to the formulas NO and NzO, respectively, but equally valid we may write the mass ratios as 1416 and 1 4 8 leading to the formulas NO2 for nitrogen oxide and NO for dinitrogen oxide. Thus, although Wollaston believed he successfully divorced equivalent weights from atomic theory, enormous confusion and ambiguity persisted as chemists used atomic and equivalent weights as synonymous terms. This painful problem plagued chemistry and hindered progress through a half century because of the failure to accept Avogadro's hypothesis (5). Berzelius, for example, insisted that GayLussac's law of comhining volumes5 meant that equal volumes of elementary gases a t similar conditions contain the same number of atoms. His tahle of atomic weights (7) (recalculated for the standard I2C = 12 instead of 0 = 100, chosen to yield 000 for the mantissa) included A1 = 27.34, Ae = 215.95. C1 = 35.46. Na = 46.36. In mite of the high accuracy, he had no acceptable method of'determiningwhen his values represented the atomic weight or some multiple of it. In his texthook, Justus von Liebig discussed "atoms" and "eauivalents" without distinction: the book includes an unlahelled tahle of equivalent weights, relative to 8 parts of oxygen, with the special remark "that these relative numhers do not change" (81, states that chemists have agreed that the chemical svmbol of an element "signifies n i t merely the element hui neither more or less than its equivalent" (9), postulates that these equivalents are the atomic weights since "we possess no means of ascertaining the number of atoms," (10). discredits the use of formulas and advises "to banish all that is hypothetical from the symbolic language of chemistry" (10). The New Edition of Draper's textbook (11) index refers equivalent numhers, combining numhers, and atomic weights to the same tahle " the while ''~Lrner's Elements of ~ h e k i s t r ~contains statement, "The numhers thus obtained for the various substances are called their combining numbers, equiualent or atomic weights" (12).= 'Readers interested in the role of equivalence in the origin of the word "valency" are referred to reference (45). 2Mass and weight will be used synonymously. 8 1 atom of A + 1 atom of B and 1 atom of A 2 atoms of B. 'The term combining weight, used in the same sense as the term equivalent weight was introduced by Thomas Young ( 4 ) . The term, however, is not clearly defined and "Weight Combining" is included with density in a table of the properties of the elements. 5Berzelius,in a letter to Dalton, chided him for questioning the accuracv of Gav-Lussae's work: "I should have thoueht rather that
+
fault.. ." ( 6 )
The orohlem was finallv resolved with the acceotance of ~anniziaro's application-of Avogadro's ideas 'Powerful mental resistance to Avoaadro's invention of moleculesmolPcules intPgrantes (c&npound molecules), molPcules constituantes (elementary molecules) and mol6cules elementaires (atoms)-developed with Dalton's idea that like atoms experience repulsion, with Berzelius' electrochemical theory i n which likd atoms naturally repel each other, and with Jean Dumas' experimental work on vapor densities in which a constant moiecular weight is not obtained for certain elements (like sulfur) under different experimental conditions. The 1860 Congress was called with the hope that "many misunderstandings might be removed" . . . and agreement reached on "more precise definitions of the concept of atom, molecule, equivalent, atomicity," and formulas of compounds (13). The accuracy of Stanislao Cannizzaro's derivation of molecular and atomic weiehts and molecular formulas, without invoking equivalent weight data, is reflected in two statements in his "Summary of a Course in Chemical Philosophy" (14): Le uarie quantitd della stesso elemento contenute in diverse molecole son tutte multiole intere di una medesima quantitd, la quale, entranto semore intera. deue a rapione chiamarsi atomo" and "Le Larie quantitd dello s t k o elemento contentute in uolumi eouali sia del corm libero sia dei suoi comooste son tutte multiple intere di una medesima quantitd." Very curiously, the term molecular weight makes its first appearance in the Summary. Twenty six tables of data correctly establish molecular and atomic weights and molecular formulas of many substances from hy&ogen, Hz, to "beniacetate of ethylene," C ~ H ~ ( C ~ H ~ O ~ ) ( C Zthe H ~estahlished OZ); atomic weights of about 17 metallic elements are used to verify the validity of the Dulong and Petit rule (15). He clearly showed that the determination of an equivalent is purely empirical, independent of the concept of atoms and molecules, and that no known data contradicted Avogadro's ideas. In his Summaryg, Cannizzaro extended ample credit to other chemists who in one form or another accepted (although mainly misinterpreted) Avogadro's conception of atoms, molecules, and the determination of their relative n ~ m b e r s . ' ~ In his tribute to Cannizzaro, Tilden concluded that "There is, in fact, hut one science of chemistry and one set of atomic weights" (17) but confusion prevailed for several decades (18). Nevertheless, acceptance of the Cannizzaro method lead Lothar Meyer and Dmitrii Mendeleev to the periodic law and others to the development of the concepts of valence and structural dhemistry. Meyer declared that "It was as though scales fell from my eyes, doubt vanished, and was replaced by a feeling of peaceful certainty" while Mendeleev confessed that "without those atomic weights my generalization would not have been possible." In his 1905 textbook (191, Mendeleev reduced the subject of equivalents to smaller type, separated from the main text with the statement, "The doctrine of equivalents would be precise and simple did every metal only give one oxide or one salt." "College Chemistry'' by Ira Remsen (20) stressed that combining weights are "entirely independent of any speculations regarding the constitution of matter and the existence of atoms" and included the Cannizzaro method of calculating atomic weights and molecular formulas. The work of Jean Stas (21), Edward Morley (22) and William Noyes (23) inaugurated the kind of research that led to the accurate atomic weight determinations of Theodore Richards from equivalent weights and approximate atomic weights based on the ideal gas law or the Dulong and Petit law. For such purposes, the relation, atomic weight = equivalent weight X valence, made its appearance in Alexander Smith's "General Chemistry for Colleges", with a section, "Advantages of Atomic Weights over Equivalents" (24). In more recent times, other methods have displaced
stoichiometry for the determination of atomic weights. However, a proper and necessary use of equivalents only appears to remain in the comparison of the abilities of electrolytes to carry current. I t is a fact that the movement of one Ca2+ ion over the same distance as one Na+ ion transports twice as much charge, a built-in advantage discounted bv takina h ' mole Ca2+ to 1 mole of Na+ (25) and conductivity (formerly called defined (26) as "&trolytic specific conductance) divided bv the concentration (mole per liter) = molar conductivityof electrolyte or ion': &. The formula unit whose concentration is c must be specified." For example, a t 25'C, A(112 Mg2+) = 53.06 R-I cm2 mol-', A(Mg2+) = 106.12, A(MgC12) = 258.80, and A(112 MgC12)" = 129.40, so that 53.06 R ~ m mol-' - ~ may be referred to as the molar conductance of 112 Mg2+. Consistency is maintained in the calculation of the emf of cells and electrode potentials by defining zI2 as the numher of moles of electrons (faradays) involved in the cell or electrode reaction as written. In fact, to update Michael Faraday's concept of an equivalent, ". . . the atoms of bodies which are equivalent to each other in their ordinary chemical reactions, have equal quantities of electricity associated with them" (28), we need only to add: namely, one mole of electrons. As in the classic race, the "atom" finally placed first but the "hare" liveried in the new colors of the normality stable competes against the "mole" while Freshmen observe the race in "most admired disorder" (29). The system of normality was first introduced in 1860 by John J. Griffin (30) to standardize the comoosition of standard solutions for analytical purposes. ~ n h e the r heading of "Preoaration of Standard Solutions." the term normal solution is used in the sense that such solutions contain equivalent quantities, e.g. "0.01134 NH3/0.042 HN03/0.046 KzC03". Indeed it was an excellent idea for 1860, particularly since the available accurate atomic and molecular weights were not generally accepted. The word "normal" was also introduced into the language of chemistry during the studies of the colligative properties of solutions, especially while comparing the freezing point properties of a "gram-molecular normal solution of a completely undissociated compound" with "gram-molecular normal" "solutions of electrolytes" (31). The concentrations of both kinds of solutions were symholized.by n , e.g. "the dissociation of 0.001 n BaC12 is 94.2%". Gram-molecular normal "was employed instead of gram-equivalent normal because a molecule produces the same lowering of the freezing point whatever the equivalence of the acid or base may he". In current nomenclature, read 0.001 M BaC12 for 0.001 n, and normality for gram-equivalent normal solutions and today, as a century ago, 0.001 normal solution of phosphoric acid is perfect nonsense. Confusion persisted: the 1912 Table of International Atomic Weights is labelled "International Symbol Weights" with the warning that (32) 6Gmelin's "Handbook of Chemistry,'' Cavendish Society, 1, 42 (1848). in the same sense lists "Atomic Weight, Combining Weight, Chemical Weight, Chemical Equivalent, Combining Proportion, Equivalent Proportion, or Equivalent Number, Stoichiometrical Proportion,or Stoichiornetrical Number." 7The different quantities of the same element contained in different molecules are all multiples of the same quantity which is indeed the atomic weight of the element. 8The different quantities of the same element contained in equal volumes of the element or of its different compounds are all multiples of the same quantity. gPreparation far his students to simplify the presentation of chemical theory and avoid the chaotic status of atomic weights and formulas; "far him to teach was to live" (16). loAndre Ampere, Charles Gerhardt, Auguste Laurent, and Dumas. "Similar to the formula notations used by Friedrich Kohlrausch (27).
"Formerly symbolized by n Volume 53. Number 6.June 1976 / 363
these may be named atomic weights.. . but symbol weight is preferable"; and "normal solution" is an abbreviation for "molecular normal" meaning "a solution of such concentration that a molecular weight in grams of the solute is present in a liter of solution. By equivalent normal solution we mean" . . . "that an equivalent weight in grams of solute is present in a liter of solution. If equivalent normal is intended the term equivalent normal will be used. Harry Jones (33) avoided the use of the mole, preferring gram-molecular weight and normal solutions in terms of eatliter. Harold Fales (34), however, repeated the warning that "The scheme of normality a s a basis of definition is inadequate and should be abandoned. The great disadvantage . . . is the ambiguity to which it often leads hecause of the fact that the weight of reagent necessary to make a normal solution depends upon the purpose for which i t is used . . .." Consequently, all calculations in his textbook are hased on molarity. The term "mole" was introduced by Wilhelm Ostwald (35); officially recognized by IUPAC, i t is accepted as a Base Ilnit in the International System of Units to mean the amount of suhstances; 1 mole of Hgi2+ has a mass of 401.18 g. Its related quantity, "concentration of soiute substance B", is defined as moles of B divided by the volume of the solution (36). The ereat advantage of this unit is self-evident: freedom fromamhiguity, simplification of the stoichiometrv of analvtical (titration) data.. esneciallv oxidation. reduction and non-monohasic acid-base reactions, and it satisfies the criterion of an analysis: "An analysis is not completed until the results have been expressed in such manner that the person for whom the results are intended can unequivocally understand their significance.and relate them to the purposes for which the analytical data were requested" (37). A pefusal of current literature (38) reveals the consistent use of the molar system for electmlytes except for occasional lapses into the normal system for unequivocal monovalent acid-base exchanges involving NaOH, NH3, HC1, HOAc. T h e question of the need of the equivalent system for nursing and allied health students is often raised. Chernistry however is not a static science. In accord with the 1973 recommendations of IUPAC, "Quantities and Units in Clinical Chemistry" (39) nutritionists and laboratories all over the world are adopting S I Units-amount of substance. mole. substance concentration. mole oer liter. mass concentration, g per liter-in reporti& resuits obtained in hosoital laboratories (40). In a "New Chemistrv Program for 'Nursing and ~ l l i e d~ e a l t hStudents" (41), the topFc sequence includes only the mole concept and molarity. If the interest in a solution, 0.01 M Na+, 0.01 M Ca2+, and 0.01 M K+, involves the total cation charge per liter. the question, "Find the total cation charge con~e&ation'; is more meaningful than the same question asked in the equivalent system. Replacement or equivalent by the charge does not, of course, change the numerical result. Similiarly, if the interest in finding the mass of Fez+ in a solution by titration with 45.74 ml 0.02111 M KMn04 (5Fe2+ (eq) + KMn04 (aq) 8H+ (aq)),the answer is ohtainahle in the same stoichiometric framework taught in the first semester of the Freshmen Chemistry Course
+
45.74 ml X 0.02111
mmole KMnOd ml
From the Lecture Hall of the Chemical Institute, University of Roma, Cannizzaro's "remains were borne by a company of his students to their last resting place." Has the time arrived for us, the descendants of his teaching spirit, to depose the remains of "equivalents" from our lecture 364 / Journal of Chemical Education
halls? Or shall we wait for the future to close the circle on us with the epitaph. "Failure to clear away the confusion was due to no lack of clearness of thought, knowledge of facts, or cogency of reasoning hut rather 6the conserv&ve indisposition to change which often enchains the scientific world, in spite of the-precepts of the science which it professes" (42). Definitely, it serves no pulpose in Freshmen Chemistry courses (43). It may find some use in advanced courses for the analysis of samples whose composition cannot he specified in terms of a single reacting component of known stoichiometry, for example, a mixture of actinides and certain mixtures of oolvmers or biochemicals that can nevertheless he titrated'to-a reproducible endpoint. For such ourooses. new definitions of eauivalent (in terms of 3 . . grams of carhon-12 in '%HI) and normal solution are under consideration by IUPAC (44). For such mixtures, however, neither the mole or equivalent system permits conversion of titration results into a mass unit. ~
~
Literature Cited
J. W.. "Comprehensive Treatise of Lnowanie and Theoretical Chemirfry", vol~me 1, Longsman, Green and Co.. London. ,922. pp. 7b79, for earlier application of equivalency toadd-base Peadions. 14) '"An Lntroduetion U, Medical Literature, including s System of Practical Nnrology. ete", Underwood and Blaekr. London, 1813. p. 58. 151 Avogadro. Amedeo, il de Phvsiyus, de Chemis, d'Hisfoire Noturdlo d des Arts. 73.58 118111,78,131 (ISlO. 161 Read, J.. "The Development of Modern Chemktry". G. Bells and Sons. Lundon, " ,%> ."".,p I&
