PLACE THE ARRHENIUS THEORY IN PROPER PERSPECTIVE1 CONRAD E. RONNEBERG Denison University, Granville, Ohio
INTEE area of the social sciences there is frequent use end with a more or less complete diseusson of the of the expression "cultural lag" in referring to differ- Debye-Hiickel theory of interionic attraetion. An ences in cultures between nations, between regions unfortunate result of this approach is that often most within a country, or between different social strata. of the time devoted to the study of electrolytes is in It is one function of the social sciences to devise social terms of discarded coueept,s and not enough time is and governmental machinery to reduce this time lag. devoted to the modern interionic attraetion theory. But scientists also recognize that there is a lag in the Furthermore, the student is puzzled as to why so mueh general adoption of the advances continuously being time is spent on a theory, only to be told later that it is made in physical sciences. Undoubtedly the time lag unimportant. He then often adopts the erroneous is shortest in our centers of pure research where any conclusion that the Arrhenius theory has been entirely advance in knowledge is almost immediately carried discarded. into general practice. This is possible because of the 2. Texts which refer to the Arrhenius theory in its great effectiveness of our scientific journals and pro- chronological order of appearance but quickly point fessional societies in diffusing scientific knowledge. , out that "it no longer explains all the facts'' pertaining Ironically, the greatest time lag in adopting scientific to solutions, and then proceed to present an essentially advances is in the teaching profession. It is easy to see modern treatment of solutions. This approach, while why there must he a time lag in this area, but it is very quite common, often leaves the student disoriented questionable if it should be as great as it often is. The regarding our eoneepts of the properties of solutions delay in bringing scientific advances into the classroom since he frequently does not realize that the Arrhenius necessitates doing a continual job of "unteaehing," theory is still the accepted theory of solutions of weak where of course, all the time and energy of science electrolytes. 3. A third type of text, with reference to the t ~ a e teachers should he spent teaching subject matter. A glaring example of great differences in the pres- ment of solutions, is the type that uses the modern conentation of a l a ~ g esegment of the course in general cepts of solutions entirely. The author of one text in chemistry is the treatment of the modern eoneepts of this group, for example, goes so f i r as to avoid all referthe properties of solutions. One recent text in college ences to the theories of Arrhenius and Dehye-Huckel general chemistry, for example, presents the properties and to speak of ionization as fact. I n this group of of solutions of electrolytes in essentially the same man- texts there is a full discussion of the eolligative propner as texts published forty years ago. There is the erties of solutions of covalent and electrovalent subusual emphasis on the historical material leading to the stances-their similarities and their dissimilaritieswork of Arrhenius, and also mueh emphasis on the in terms of modern concepts of solutions. In a reconsideration of the entire subject of the treatso-called "abnormalities" in the colligathe properties of solutions of electrolytes. Then follows a listing of the ment of solutions with beginning students, att,ention is assumptions of the first ionization theory and the re- called to the fact that it is nearly universal practice to mainimg arguments of Arrhenius. In the entire dis- present very early in the course in general chemistry cussion about electrolytes, for example, nothing is said the electronic structures and the crystal lattices of about our modem understanding of covalent and elee- covalent and electrovalent substanees. This follows trovalent substances, even though they have been pre- a rather comprehensive study of the atom, its structure and behavior. Reference has already been made to sented in earlier chapters in the same volume. These observations led to an examination of ten certain texts which present the arguments of Arrhenius extensively used texts in general chemistry in regard in great detail. And yet it is to be noted that these to the treatment of solutions of covalent and eleetro- same texts specify that the crystals of electrovalent valent substances (1). These texts can he divided substances consist of lattiees of ions in contrast to lattices of molecules or atoms in covalent substances. into three general groups as follows: 1. Texts which largely follow the traditional Ar- With such a "build-up," there seems to be little reason rhenius approach and which in varying degrees call to return to the arguments of Arrhenius in the area of attention to the inadequacies of the theory and finally strong electrolytes which date back to 1887. To repeat the classical arguments is a time consuming and 'Presented befor? the Division of Chemical Education a t the 116th ,neetine of the American Chemical Society ~n Sari Fran- needless operation which inevitably results in placing the Arrhenius t>heorpout of proper perspective, with cisro, Ma.rrh 50.1940. 400
AUGUST, 1949
the unfortunate result that many students never realize that the Arrhenius concepts are entirely valid and are used in discussing the colligative properties of solutions of weak electrolytes. Students find no difficulty in relathg the properties of water as a solvent to its covalent and polar structure. The process of solution of methyl alcohol, a polar covalent substance, or of salt, in water is easily withim their comprehension. Both solutions are the result of the polar character of the water molecules. The end results are a dispersion in solution of hydrated methyl alcohol molecules in the one case and of a dispersion of hydrated ions in the case of the salt (See Figure 1). All experimental data indicate that the colligative properties are essentially identical in all solutions of these substances of the same concentrations of molecules or ions if sufficiently dilute and if all the ions are "free." A modern treatment of solutions demands that this observation be stressed. If the teacher still thimks it is necessary to present experimental proof that solutions of electrovalent substances consist only of ions in dilute water solutions, there is much additional evidence to be cited and even shown with simple lecture demonstrations. (1) The additivity of ionic properties such as color, viscosity, heat capacity, and refractive index. It is well known that the properties of a solution of a strong electrolyte, or of a mixture of strong electrolytes, are the sum of the properties of the individual ions. For example, the color of a dilute solution of copper dichromate is due to a solution containing the blue of the hydrated cupric ion, Cu(HzO)r++ and the orange color of the dichromate ion, Cr,O,= (See Figure 2). (2) The absence of a heat effect when solutions of strona electrolytes are mixed is evidence of complete ionization (2). (3) The constancy of the heat of neutralization of strong acids and strong bases (5). (4) The inability of proving the existence of undissociated molecules in solutions of strong electrolytes is further proof of complete ionization. Thys solutions of
Fig,,* 2. Prinoiplo of Additiety (Reproduced from "General Inorganio Chemistry," by M. C . Sneed end J. L. Maynard. D. V a n Nostrand Cn., New York, 1942.)
dilute hydrochloric acid are odorless, showing the absence of hydrogen chloride molecules. Similarly, benzene is unable to extract any silver perchlorate from its water solution even though silver perchlorate is readily soluble in benzene. Hence the water solution must consist of only silver and perchlorate ions. The historical approach of Arrhenius emphasized the "abnormalities" in the colligative properties of solutions of electrolytes. The modern approach above outlimed indicates that the colligative properties of solutions of' electrolytes are in no wise "abnormal." In reality the values for these properties should be considered normal. In other words, the following generalization for solutions of either covalent or elect,rovalent solutions can be shown to be valid. For true solutions, the change in: Freeaing point, AFP = n, X -1.86T./mo1/1000 g arator
Boilingpoint, ABP = n, X 0.52"C./mo1/1000g. water Osmotic pressure OP = nn X 22.4i%ms./mo1/1000 g wat,er (at, O'CI./
Note: ne is the number of mok of molerules or ions in 1000 grams ( n mols) ~ of water.
The experimental basis for this generalization is admittedly involved requiring a comprehensive knowledge of the thermodynamics of solutions. But as to its acceptance as a limiting law in dilute solutions, there can be no doubt (4). Instructors can justifiably present the matter as experimental fact to their students just as they present the gram-molecular-volume of a gas (22.41 liters) as experimental fact, seldom mentioning the fact that this value is actually only the limiting value as the pressure on the gas approaches zero. TABLE 1 Substance
Fi-
Sdution of an Electrodent Suhstanca in a Polo. so1ve.nt (Reproduced from "General College Chemistry." b y L. B. Riohardson and A. J. Soarlett, Henry E o l t B. Co.. New York. 1947.)
Observed freezing point
F. P./Mol
F. P . calc.
Osmoti,: Coefldent n
1.
Note: Concentrations 0.100 forrnula/weights of solute 1000 grams water.
ye[.
402
JOURNAL OF CHEMICAL EDUCATION
A modem treatment of solutions demands that departures in the values of colligative properties from the values calculated from total ion concentrations should not be ignored. The freezing-point data for some common substances is given in Table I. Using the modern approach the above outlmed study of the colligative properties of solutions of electrolytes should be done on the basis of complete dissociation. This leads logically to the concept of the osmotic coefficient "g" introduced by Bjerrum as long ago as 1907 (5). This is conveniently defined as the ratio of the apparent number of mols of ions present to that expected on the basis of complete dissociation. It can be further defined as
Data such as that presented in Table I lead directly to the concept of interionic attraction. Thus, when the concentrations of solutions of electrolytes become appreciable, the ions cannot behave as "free ions" but because of electrostatic attraction form ionic atmospheres or aggregates which result in an apparent ionization of less than 100 per cent. This leads also to a reduced electrical conductivity and gives reduced values for the colligative properties. This lays the foundation for the discussion of apparent degrees of ionization and the concept of activity. It is the purpose of this paper to point out that modern knowledge in regard to solutions of covalent and electrovalent substances requires a modern interpretation. This means a presentation in terms of the Ratio observed eolligative property = structure of covalent and ion lattices, the polar charTheoretical value if 100% ionized acter of water, and the theory of interionic attraction When g is unity, the measured and the calculated value where the concentration is such that the ions cannot for any colligative property are identical. In other words, g is a measure of the ideality of any solution act as "free ions." This modern treatment largely and (1-g) is a measure of its abnormality. Many by-passes the work of Arrhenius as related to strong experimental studies show that the value of g depends eleqtrolytes and thus avoids the possibility of students both upon the nature of the solute and upon the con- getting the impression that the Arrhenius theory is something thoroughly discredited and therefore abancentration. The data represented in Figure 3 reveal clearly that doned. The Arrhenius theory, however, should be the value of the osmotic coefficient decreases with taught only in connection with weak electrolytes where increase in the concentration of all the ions present experimental facts and the theory are fully in accord ( i . e., (1-g) increases) but that it also decreases with with each other. an increase in the charge on the ions. Thus ir! Table I the value of g decreases from a value of 0.93 for a LITERATURE CITED 1:1 salt to 0.61 for a 2 : 2 salt. This is evidence, of J. H.,"Principles of Chemistry," The Maecourse, that the value of the osmotic coefficient de- ( I ) HILDEBRAND. millan Comoanv. N e r York. 1947. creases with increase in the charge on the ions. SNEED.M.'C., AND J. L. MAYNARD, "General Inorganic Chemistry," D. Van Nostrand Co., New York, 1942. A. J., .wn A. ROSE, "General Inorganic ChemCURRIER, istry," MoGraw-Hill Book Company, Inc., New York, l.7 Ode T",
ELDER,A. L., SCOTT, E. C., AND, F. A. KANDA,"Textbook ~. - - ~ New , Ynrk 1948 of Charnistrv " Hsrner and Brothers 7 - --EARET,W. ~ . " , ' " ~ m i t college 6~s Chemistry," D. ~ ~ ~ l e t ~ ; Century Co., Inc., New York, 1946. JR.,"Essentid~of General HOPKINS. B. S., AND J. C. BAILAR, Chemistry, "D. C. Heath and Co., Boston, 1946. H. N.. "General Chemistrv." HOLMES. - . The Mscrnillan Comp a n y . ' ~ e wYork, 1941. L. B., AND -4. J. S C A R L E"General ~, College RICHARDSON, Chemistrv." Henrv Holt a'nd Co.. New Yark. 1947. . PAULING, L.. "General Chemistry," W. H. Freeman and Co., San Francisco, 1947. "General Inorganic SNEED.M. C., AND J. L. MAYNARD, Chemistry," D, van Nostrand Co., New York, 1942. Ibid., p. 404. GLASSTONE. S., 'iTherm~dynxnicsfor Chemists," D. Van Nostrand Co., Inc., New Yark, 1947, p. 417, BJERRUM, N., 2. Elektroehern., 24,259 (1907). ~
".
,rC Figu* 3. change in Osmotic coemcient with Chsng. i n Concentration and Type of Electrolyte (Reproduced from"Phydcs1 Chemiatry." by C. F. Prutton and 6. 8. Maron. The Maomillan Co.. New York. 1944.)
