Lawrence Suchow New Jersey Institute of Technology Newatk, New Jersey 07102
General chemistry textbooks nearly always point out carefully the limitations of the gas laws and the laws of Raoult, Henry, Dulong and Petit, etc. A large majority,' however, simply state with little or no qualification the concept of definite proportions or constant composition, despite the fact that i t has now long been known that there are a great many "exceptions" to this law (as well as to the related Law of Multiple Proportions). In 1967, Dingledy and Barnard ( I ) pointed out, quite correctly, that considerable deviation from simple stoichiometry occurs in copper sulfides, and they concluded that the common introductory laboratory experiment employing the preparation of copper sulfide to prove the Law of Definite Proportions was not a suitable one. .Recently, Wilhelm (2) agreed with this and suggested instead the preparation of CuI. Should, however, an experiment be chosen to yield the desired result of "proving" the Law of Definite Proportions when another could as well be employed to "prove" the opposite? Would it not be better to make i t clear that the Law of Definite Proportions, while sometimes accurate, is often less so, and in many cases is quite inaccurate? The Law of Definite Proportions does hold for all molecules in the gaseous state and for simple molecular compounds in all states of matter. It is not, however, valid for nolvmers: for even if the individual mers are identical ihr&~~ho;t,there is still considerable variation in polymer molecule leneth, branchinn, chain terminators, etc. Certainly, also, there is even less uniformity among molecules of copolymers. The best documentation for the arguments against the Law of Definite Proportions is provided by inorganic solids. All solid solutions may be considered to be nonstoichiometric because they exist within ranges of varying composition. For example, single-phase garnet-structure compositions are found continuously from Yb3Ga5012 to Yb3.8Ga4.2012 (3). The garnet structure is stable over so great a composition range in this case because of the ability of the ytterbium ion to occupy octahedral as well as dodecahedra1 sites in the lattice. Also often classified as solid solutions are the tungsten bronzes, an example of which is Na,W03, where x can range from just above zero to nearly one (4). Structure and physical properties vary with composition. At lower values of x , one finds two successive non-cubic structures which give way to the defect cubic perovskite type a t about x = 0.4. Electrically insulating WOa is converted Presented under a different title at the 168th National Meeting of the American Chemical Society, Atlantic City, New Jersey, September 9,1974. 'Noteworthy exceptions known to the author are "University Chemistry," by Mahan (71, and "Chemistry," by Sienko and Plane (81. 2Ranges of formulas of transition element and rare earth mmpounds are found to differ considerably in various sources checked. This in itself emphasizes the failure of the Law of Definite Proportions. Although Zn appears with the transition elements as the periodic table is usually depicted, it is really a representative element because its 3d and 4s shells are filled and reaction aeeun only via the 4s electrons.
The Failings of the Law of Definite Proportions first into a semiconductor by incorporation of small amounts of sodium and then into a metallic conductor (with accompanying metallic luster) on further addition of Na. The presence of Na also results in bright colors which shift from deep violet through red to golden yellow as x rises. Although one might argue that solid solutions are not inconsistent with the Law of Definite Proportions because. they melt incongruently and have disordered structures, the fact remains that these varying compositions do actually exist in the solid state and are usually rather easily prepared, often by solid state reaction. Furthermore, pedtectic compounds also melt incongruently, and a-AgzHgI4 is accepted as a compound even though its Ag+ and Hg2+ ions are completely disordered. A major area of nonstoichiometry is found among compounds of the transition and the inner transition (rare earth and actinide) elements because of the variability in their oxidation states and the ease with which different oxidation states can occur together in one solid phase. For example, iron sulfides, Fel_,S, are known in which x may vary from 0-0.2 (41. "FeO" is always deficient in iron, existing as Fel-,O with x values over the range 0.05-0.16 (4). There are many titanium-oxygen compositions in addition to TizO, TiO, Tiz03, Ti305, and TiO2; included are the ranges TiOo.60 to Ti01.35 and Ti01.m to T i O ~ s o(4). Lack of stoichiometry is so widespread among the oxides and chalcogenides of the various transition metals that the nonstoichiometric material in this group seems to be typical rather than exceptional. The electrically conducting character of materials such as those discussed here is, in fact, most often due directly to the nonstoichiometry. Extensive nonstoichiometry is also found among the praseodymium oxides (4, 5) over the range P r 0 1 . ~(or PrzOs) to Pro2 because of the close relationship between the C-Mz03 and fluorite structures. An especially common phase occurs a t Pr01.sa or P16011. which is the usual composition of commercially available praseodymium oxide.2 Although, as stated, the transition and inner transition elements are in their compounds a rich source of nonstoichiometric single phases with wide composition ranges, nonstoichiometry is also found in compounds of the representative elements, although their ranges of composition are much narrower. Examples3 are ZnSel-, and Znl_,Te, where x is of the order of only about 10-5. Such deficiencies are of a magnitude that would not he discovered by ordinary cbemicai analysis, which of course i$ what has the past been used to "prove" the Law of Definite Proportions. The vacancies which result (of selenium in theformer case and zinc in the latter) are sufficient, however, to make ZnSel_, an n-type and Znl_,Te a p-type semiconductor a t room temperature and even well below. Stoichiometric ZnSe and ZnTe can also be prepared and are found to be insulators. ZnO and ZnS behave similarly to ZnSe, and a large percentage of non-molecular inorganic solids exhibit a t least such low-level nonstoichiometry. Even CuI, the compound employed by Wilhelm (2) to prove the Law of Definite Proportions, is vulnerable, especially when subjected to varying 4 pressuresat elevated temperature, and Cu-deficient p-type CuI is known. (Cu Volume 52, Number 6, June 1975 / 367
is, of course, a transition element which can exist in both monovalent and divalent states so that CuI is especially vulnerable). Nonstoichiometry also exerts its influence on many additional physical properties of solids. Vacancies certainly affect mechanical properties. Introduction of nonstoichiometric quantities can change the colors of solids, as in the case of the already mentioned tungsten bronzes. As an additional example, heating NaCl in Na vapor yields a yellow material with a chloride deficiency of approximately 1in lo4. The color is caused by light absorption a t a socalled color (or F)-center, which is an electron (from the excess Na) trapped at a chloride ion vacancy. Similarly, KC1 becomes blue when heated in K vapor. Even ferromagnetism may be induced by nonstoichiometry. Consider gadolinium selenide (6J, for example. GdzSea is a paramagnetic insulator with a defect Th3P4 structure. One may therefore write its, chemical formula as Gdz.moo.aaSer. Contmuously varyrng quantities of additional Gd mav be inserted into the vacancies, amd this nonstoichiometry results in simultaneous onset of electrical condurtivit\ and ferwmagnetism. Small amounts of excess Gd-cause semiconductivity and larger quantities metallic conductivity. With increasing Gd, the Curie point rises gradually to 100°K with the maximum allowable excess. The ferromagnetic interaction apparently occurs via the conduction electrons.
368 / Journal of ChemicaIEducation
I t is clear, therefore, that many interesting and useful physical properties of solids actually derive from their nonstoichiometry. To continue to teach the Law of Definite Proportions as if it were immutable permits no intelligent discussion of the fascinating, technologically important materials which now strongly influence our lives. The Law of Definite Proportions should probably be presented to students for its historical significance in chemistry and can also be employed in the many cases where i t does 'apply, as well as in those cases where it appears valid within normal limits of analytical error. The student and his professor can then continue to solve stoichiometry problems where possible hut both should be aware of thelimitations of the assumptions made Literature Cited (11 Dingledy,D.,andBarnard, W. M.. J. CHEM. EDUC..44.242 119671. (21 Wilholm, 0 L..J. CHEM. EDUC., SO. 4 6 7 ( 1 9 7 3 1 . 131 Schneider. S. J.. Rnth. 8. S.. and Warine, J. L.. J R e 8 Nnt. Bur. Stand. SEA.
346-374 119611. Wells. A. F.. "Sfruetural
Inorganic Chemistry," 3rd Edition. Oxford Univerrity Press. London. England. 1962. (61 Eyring. L.. Wuatite~Related Oxide Phaars of the Rere Earth and Actinide Elsrnents." oo. '67-86 of "LanthanideiAcfinide Chemistry." ACS Advances in chem/stry Serles.=71. 1967. 161 Mefhfessd. S., and Martir. D. C., "Magnetic Semieonducton." in "Hondburh der Physik,"Volurne XVlII/l. Springer-Verlag. Bnlin, Gerrnsny, 1968. 17) Mahan. B. H.. "University Chemistry," 2nd Edition. Addi9on~WerloyPublishing C"..Reading, Mass.. 1%9. 181 Sionko. M. J., and Plane. R. A , "Chemistry." 4 t h Edition. MeCraw-Hill Boak Co.. New York. 1971.
(41
..
