George S. Morrison 214 North Austin Blvd. Oak Park, Illinois 60302
Cannizzaro's Atom-Free Stoichiometry
The following separate hut sequential statements from Cannizzaro's well-publicized 1858 paper1 effectively explain the basis for our current stoichiometry [(I)]On the basis of the hypothesis cited above [is., Avogadro's], the weights of the molecules [for which Cannizzaro chose the hydrogen molecule at 2 as the standard] are proportional to the densities of the substances in the gaseous state.. . . [(2)]The different quantities [masses]of the some element contained in different molecules are all whole multiples of one and the sane quontity [mass], whieh, always being entire, has the right to be called an atom . . . . [(3)]In order, then, to find the atomic weight of each element, it is necessary first of all to know the weights of all or of the greater part of the molecules in whieh it is contained and their composition.. . . [(4)Through the process afl expressing by svmhals the different atomic weiehts of the various elements. it is pwitde 11, express by menns o1"iormdne the n,mporitmn(s] of their 1r.e.. the 'free elements'] molrculcs and or those 1i.e.. the compositions of the molecules] of their compounds, Although historical tradition gives Avogadro the major credit for developing our stoichiometric reasoning, only the first of the above four statements is in fact hased on Avogadro's 1811 paper.2 To he sure, early in his paper Cannizzaro does acknowledge influence by Avogadro's postulation of diatomic and oolvatomic molecules of the easeous elements. hut he does not Hc&ally use this idea in statement (2). Instead, he first calculates the relative mass of the element present in each gaseous molecule of an entire set, and then in effect defines the atomic weight as the highest common divisor (giving integers) for the resulting set of experimentally hased masses. Statement (3) stresses the necessitv of a laree set of data. thereby indicating the inductiue hature OF~annizzaro'i atomic weight determinations. Conversely, Avogadro deduced the number of his hypothetically inferred atoms per elemental molecule from the comhining volume data of one or possibly two reactions, resting the validity of each of his atomic weights entirely upon the singular molecular weight of the element. statement (4) explains the meaning of the symbols and subscripts in molecular formulas, which Avogadro of course did notemploy, In an argument presented between statements (3) and (4), Cannizzaro demonstrates that his method of determining atomic weights is a valid approach even for those skeptical of all particle theories
.I(3a)l. If it should aooear .. to snv one that this method of lstoichi-
ometry, ahich requires] finding the aci~htsof the mnl~culea].]is roo hypothetiral. then iet him compare the composition of 1l.e.. rnlc~llnrethe mass u l a specilied element i n ] equal vdumes of substances in the gaseous state under the same conditions. He will not he able to escape the following law: [(3h)] The various quantities of the some element contained in equal uolumes either of the free element or of its compounds are whole multiples of one and the same quantity [mass per unit of volume]; [(3c)]
that is, each element has a special numerical value [the "one and the same quantity" of statement (3b), hereinafter entitled the "minimum density"] by means of which [i.e.,by assigning a symbol to designate this"minimum density"] and with the help of integral coefficients [subscripts]the composition by weight of equal volumes of the different substances in which it is contained may he expressed. In statement (3c), the formula, instead of designating the mass of a molecule, now designates the density of the gaseous substance. Each symbol, instead of designating the mass of an atom, now designates the "minimum density" of an element. The s u h s c r i ~now t desienates that oarticular multiole of the "minimumhensity" w k c h is the actual density contributed by the element to the density of the gaseous suhstance. From these strictly empirical designations, we can see that statement (3h) is in fact a universal empirical law in the sense that both Gay-Lussac's law of comhining volumes and the law of simde multiule orooortions can be derived from it without aio& o; molecules. If one adopts the same relative standard for both the atomic weight scale (2) and the "minimum density" scale (3h) (for example, by setting hydrogen gas a t 21, the two will obviously have the same numerical values. Emphasizing this equivalence by italicizing both statements, Cannizzaro considers (3b) to be a "direct deduction from the facts [more precisely, an inductively formulated law1 . . . ."But in his desire "to brine into harmony all branches ofchemistry [i.e., to go beyond stoichiometric problems] . . . ,"he "prefer[s] to substitute in the expression of the law [(3h)l the word molecule instead of volume [in effect obtaining (2) as a law1 . . . ."It thus becomes clear that Cannizzaro brings ~ v o g a d r b ' shypothesis into his stoichiometric reasoning as a matter of deliberate chemical judgment and not as a matter of stoichiometric necessity. Even in earlier times of more limited data, the inductive power of either statement (2) or (3b) would have enabled the establishment of the atomic weights more directly and with greater verification than did the deductive method of Avogadro's 1811 paper. If we are to accept Cannizzaro's own words, we must admit that his inductively based, essentially hypothesis-free stoichiometry is fundamentally different from Avogadro's deductive approach.
Presented at the Chemical Education Session, ACS Ninth Great Lakes Regional Meeting, St. Paul, Minn., June 5,1975. 'Cannizzaro, S., Nuouo Cimento, 7,321 (1858).Quotations are from Alembic Club Reprints, No. 18,The Alembic Club, Edinburgh, 1910, pp. 5-13; also in Leicester, H. M., and Klickstein, H. S., "A Source Book in Chemistry, 1400-1900," Harvard University Press, Cambridge, Mass., 1952, pp. 410-415. 2Avoeadro.A,. J de Phvs.. 73.58 (1811). See Alembic Club Reprints, h o . d , ' ~ &~lembie~cl'ub, ~ d i n b u r ~1899,p. h, 28; or Leicester and Kliekstein,p. 232.
Volume 53, Number 11, November 1976 / 723
