SOLUTIONS of ELECTROLYTES* ARTHUR W. DAVIDSON The University of Kansas, Lawrence, Kansas
General recognition of the fact that the degree of dissociation of typiGal strong electrolytes can be neither experimentally determined nor accupately defined, has made it desirable that the traditional presentation of electrolytic dissociation in the general chemistry course be drastically raised. Strong electrolytes in dilute aqueous solution may be regarded as practically completely dissociated, whereas the ions of weak electrolytes combine to form molecules according to the laws of chemical equilibrium. The decrease in osmotic effects and in equiwalent conductivity of strong electrolytes with increasing concentration may be attributed to the electrostatic constraints to which the ions are subject&; the actiwity coeficient of a strong electrolyte may be regarded as a factor by which the concentration must be multiplied to correct for such electrical effects.
+ + + + + +
W
HEN it was .first suggested by Sutherland, Noyes, Bjerrum, and others, about t h i i y years ago, that our views on electrolytes might be in need of radical revision, it was not to be expected that their tentative theories would be reflected immediately in the teaching of general chemistry,. nor, indeed, would such a change have been desirable a t that time. During the past ten years, however, the new theories of electrolytic solutions have established themselves on such firm ground, and have so greatly contributed to our understanding of the subject, that if confusion is to be avoided, a corresponding revision of the general chemistry course can no longer be delayed. It is natural that this departure from well-worn paths should not be without its painful aspects, but such minor hardships have been of frequent occurrence in the development of our science aqd have never been allowed to constitute a permanent impediment. I t may enable us to attain a better perspective on our own problems if we consider the plight of our predecessors of fifty years ago, when the revolutionary theory of Arrhenius suddenly burst in their midst. At that time, of course, the idea of the spontaneous separation of a stable compound into two simpler substances constituted a most radical and startling innovation. It seems probable that the English chemist Pickering voiced the bewilderment of many of his contemporaries in 1890 when he said ( I ) , "The theory of dissociation into ions is altogether unintelligible to the majority of chemists. It seems to be quite irreconcilable with our ideas of the relative stability of various bodies, and with the principle of conservation of enerm. -. How can we -
* Contribution to the Symposium on Modernizing the Course in General Chemistry, held under the auspices of the Division of Chemical Education at the 88th meeting of the A. C. S. at Cleveland. Ohio, Sept. 12. 1934.
24
regard it probable that compounds of such stability as sulfuric or hydrochloric acid should be thus entirely dissociated by water, while less stable ones such as hydrocyanic acid should remain intact? How can we admit that the more stable a body is, the more prone i t is to be dissociated?" He was concerned, too, about the charges which the ions were supposed to carry, and inquired of his audience, somewhat plaintively, we may imagine, "Whence come these electric charges, and by what agency are they brought into play?" These objections were not unreasonable, for, it must be remembered, Pickering knew nothing of electrons or of atomic structure, and was therefore unable to conceive a plausible mechanism of dissociation. We are no longer troubled by these particular questions, because we are able to picture a typical polar compound as one in which one or more electrons have passed from each atom of the metallic element to an atom of the nonmetal, the charged particles so formed being held together by electrostatic forces only; indeed it seems to us inevitable that such a compound would dissociate on going into solution. Hence that part of the theory of Arrhenius which maintains that ions exist in dissolved electrolytes, even in the absence of any external electrical forces, has not been seriously questioned in recent years; every new development in this field has, in fact, served to give it additional support, and the genius of its author now.stands out more clearly than ever. The classical theory, however, included also a second hypothesis, namely, that in all electrolytic solutions there are two clearly distinguishable portions of the electrolyte, ions and undissociated molecules, their relative proportions varying with the total concentration in accordance with the laws of chemical equilibrium. It is this portion of the theory which has been subjected to an increasing tide of criticism during the past thirty years, and which, at least in so far as it applies to strong electrolytes, is no longer generally accepted; and it is the discarding of this hypothesis that has necessitated the changes in the general chemistry course which are to be discussed. Since opinion on this point is as yet by no means unanimous, it may be well, before considering teaching problems, to state the case against the hypothesis just referred to. The objections to its retention are but very inadequately conveyed by the familiar statement that the dissociation of strong electrolytes does not conform to the law of mass action; the diiculty is far more fundamental than that. In its simplest terms, it may be expressed in this way: no experimental method is k n m by which the degree of dissociation of a strong electrolyte can be reliably determined, and i t i s therefore very doubtful that the concept of degree of dissociation has
any clear significance in such a case. The traditional methods of determining the degree of dissociation are based upon assumptions which, while approximately true for weak electrolytes (where sonic concentrations are small), are so far in error when applied to strong electrolytes as completely to invalidate the results obtained by their use. Thus the determination of degree of dissociation from conductivity data by means of the equation a = A/Ao, where n is the degree of dissociation, A the equivalent conductivity a t the given concentration, and A. the equivalent conductivity a t infinite dilution, rests upon the premise that ionic mobilities are independent of concentration, which has been proved to be untrue. The determination of the same quantity from freezing-point data (or from any other of the colligative properties of dilute solutions) i - 1 by means of the equation a = -- where i is the so-
v - l' called v& Hoff factor* and v the number of ions produced by the dissociation of one molecule of the electrolyte, is based upon the assumption that ions in dilute solution behave like perfect solutes, which is nndoubtedly false also. Both of these methods, for reasons which will be discussed later, give values for n which are certainly far too low. It happens, curiously enough, that the erroneous values calculated for a given salt in these two ways often agree fairly well with each other, especially in the case of uni-univalent electrolytes. Thus for potassium chloride in 0.1 normal aqueous solution both methods give a degree of dissociation of 0.86, while for hydrogen chloride a t the same concentration the conductivity ratio and the freezingpoint depression give values of 0.925 and 0.915, respectively. Since neither method is valid, the occasional agreement between the figures obtained in the two ways is of no intrinsic importance, but is to be regarded merely as a coincidence (2), (3); this accidental agreement, however, by lending apparent support to the Arrhenius hypothesis which we are discussing, has undoubtedly played an important part in delaying the rejection of this hypothesis. For ele$rolytes of higher valence types, no such close agreement is found; thus for magnesium sulfate in 0.1 normal solution, we find a to he 0.43 according to the conductivity ratio and 0.32 from freezing-point data. Further, if we tun to the field of non-aqueous solutions, it is a well-known fact that different methods of measurement of degrees of dissociation yield still more widely divergent values. Now one of the most important results of modem trends of thought in physics has been to emphasize the necessity of defining our concepts in experimental terms. This point of view was discussed by Dr. Langmuir (4) in his striking presidential address to the American Chemical Society a t Minneapolis in 1929; he gave especial emphasis to the point that if there are no conceivable operations that can be performed in order to arrive a t an answer to a question, then that question is That is, the ratio between thr ohaerwd mold freezing-point lowering and the theoretical mulal Itwcring on thearcurnption of no disw&tion.
meaningless. Applying this principle to the prohlem in hand, since there are no experimental means by which the degree of dissociation of a strong electrolyte can be satisfactorily measured, we are forced to the conclusion that our concept of degree of dissociation must a t least he somewhat lacking in clarity; and closer consideration reveals that, as far as strong electrolytes are concerned, it is indeed impossible to define this quantity in an unambiguous manner. With weak electrolytes, consisting, in the undissociated state, of actual molecules in which the atoms are held together by electron pair bonds, this difficulty does not arise. In the case of true salts, however, no such bonds exist, and the ions are united in any case merely by electrostatic forces; we may readily agree that the electrolyte is completely ionized a t all concentrations, but how far apart must a pair of ions be before we are to regard the molecule (if we may so designate it) as being truly dissociated? Or, conversely, how closely must a pair of ions approach each other before we are to regard them as constituting an undissociated molecule? It is not surprising, when the prohlem of degree of dissociation rests upon so insecure a theoretical foundation, that it cannot be solved experimentally (5). Even when the foregoing difficultiesare clearly recognized, however, most teachers of general chemistry have been reluctant to abandon the traditional viewpoint, partly because it has seemed desirable that the Arrhenius theory be studied for its historical interest (6), partly because the alternative has seemed to them to be altogether too formidable. How, for instance, could the interionic attraction theory, with all its mathematical intricacies, he explained to freshmen whose mastery of elementary.~lgehrais none too secure? Or, leaving this theory out of consideration, surely the student is not to he persuaded to accept the concept of activity as a substitute for concentration, in view of the fact that the former quantity can be rigor-
-F L F O
ously defined only by means of.the equation a = e RT .t Is there anything to he gained e k n by the somewhat simpler process of substituting for the degree of dissociation, whose significance is a t least easily grasped by the student, the vague concept of activity coefficient, which, though capable of being precisely defined and determined, can scarcely he explained in terms of any sort of concrete picture? m i l e these objections are certainly not without validity, they are nevertheless outweighed by the fact that if the student who intends to continue in chemistry is taught the classical theory in the general course, he will inevitably have to be told later that a considerable portion of it is not to he taken literally* process that will tend neither to increase his respect for his early training nor to facilitate his acquisition of the newer point of view. In fact, the necessity of uprooting the old theory in order to make room for the new
-
7 Where a is the activity, F and Fa the partial mold free energies in the given and the standard states, respectively. R the gas constant, and T the ahsolute temperature.
has undoubtedly been an important factor in creating the diiculties which the latter, a t first encounter, presents to many of us. Without this handicap, the newer theory is in some respects actually simpler than the traditional one, and it is possible to approach it by a path which offers no serious obstacles to the befiner. Such a line of approach will now be briefly indicated. In --- introducing. -~~ ',the snbiect of electrolvtic dissociation. the first sten natnrallv. .is to Dresent the three mourn of facts concerning aids, ba&, and salts which theory of electrolytes must explain: namely, additivity of chemical properties of the solute, abnormal effects upon vapor pressure and freezing point of the solvent, and electrical properties of the solution, including conductivity, migration, and electrode phenomena. In seeking to formulate a theory which will account for all of these facts, we still follow Arrhenius in our fundamental assumption that the electrolyte, on going into solution, dissociates into two new substances, the particles of which cany electrical charges. Now, in the closer consideration of this hypothesis, let us limit our discussion for the present to true salts, in the narrow sense, which constitute the largest and most typical group of electrolytes. The student presumably already has some acquaintance, which may well be renewed a t this point, with the rudiments of atomic structure and with the type of chemical union resulting from the transfer of an electron from one element to another. He should have learned to think of common salt, for example, as a compound in which each Sodium atom has lost an electron and each chlorine atom has gained one, and the resulting oppositely charged particles attract each other to form sodium chloride molecules, if in the gaseous state, or a lattice of alternating positive sodium and negative chlorine atoms in the salt crystal. It may now be pointed out that when such a crystal comes in contact with water, the forces holding together the charged particles or ions are weakened, so that when these ions wander off into the solution they are able to move about almost independently of each other. The oppositely char&d particles still exert electrical forces upon each other, it is true, but these forces are of much smaller magnitude than those which prevailed in the crystal. Under their influence, a sodium and a chlorine ion may, occasionally, even approach each other so closely as to constitute for a time what may be termed an ion-pair; the concentration of such ion-pairs cannot be determined, nor can even their existence be proved. But the number of pairs or clusters present in a dilute solution a t any time must in any case be very small compared to the total number of ions, so that the salt, for all practical purposes, may be considered to be completely dissociated. The dissociation of strong acids presents a somewhat different picture from that of true salts (7). In the case of hvdropen chloride, for instance, the bond between the atoms is probably of the covalent rather than of the ionic type, so that there is little ionization in the undissolved state; but the compound presumably re~
~
any
- -
acts with water to give a salt-like substance in solution, according to the equation HCI f H2O = &Of
+ CI-
This aspect of the problem of electrolytes, however, will not be further considered here, since it is to be treated in detail in the following paper of this symposium. It is evident that all w e e groups of characteristic properties of electrolytes can be accounted for, qualitatively a t least, in terms of the hypotheses which have been outlined above, just as they were by the traditional theory; quantitative relationships will require further consideration later. But it may be pointed out here that, having developed the newer viewpoint, with its emphasis on the fact that the properties of a strong electrolyte in dilute solution are the properties of the ions only, we shall be in a more favorable position to interpret chemical reactions between su'ch electrolytes in the simplest possible manner. As Dr. Wildman pointed out a t a previous meeting of this Division (a), if a student prefers the equation NaCl
+ AgNO* = AgCl + NaNOa
to the simpler As+
+ Cl-
=
AgCl
it must be only because he learned the former first and is reluctant to change his habits. If he can be trained in the general chemistry course to write the simple and appropriate ionic equations for such cases, he will be much better prepared for the reactions of qualitative analysis. With the newer theory as a background, it should not, for instance, be so diicult a task as it often is at present to persua.de the student in the latter course that ecinations such as NHXI
+ NaNOz = NH4NOs + NaCl
are meaningless, so far as dilute solutions are concerned, or to convince him that oppositely charged ions in solution do not combine to form compounds merely by virtue of their charges, but remain apart unless there is some special reason to the contrary. When we come to the consideration of weak electrolytes (water itself, weak acids and bases, and possibly a few salts of heavy metals),* we are concerned with substances which in the undissolved state are probably made up of molecules rather than of ions. Here the original theory of Arrhenius is valid almost in its entirety, and the method of presentation need not greatly depart from the traditional one. In this case only a small fraction of the dissolved molecules are, a t any instant, dissociated into ions; or to state it in another way, the ions in solution combine, to a considerable extent, to form molecules. This reversible reaction is subject to the usual laws of chemical equilibrium. Further, in dilute solutions of weak electrolytes,
* The number of electrolytes which are borderline cases between those generally classified as "strong" and "weak" is so small that they need scarcely be considered in the general &emistry course.
the concentration of ions is so small that their mobility does not vary greatly with concentration, nor does their osmotic behavior deviate widely from the laws of the dilute solution. These solutions, then, are almost free from the disturbing influences which invalidate both of the conventional methods of determining the quantity a for strong electrolytes. Hence the degree of dissociation of a weak electrolyte, a t any concentration up to about 1 molar, may be determined with a fair degree of accuracy from the conductivity ratio, A/&, and, in dilute solutions, from freezing-point data also; the two methods, moreover, give concordant results. The dissociation constant of such electrolytes can therefore also be determined with considerable accuracy, a fact which strongly supports the hypothesis that an equilibrium between ions and un-ionized molecules actually exists.* Up to this point, our discussion of strong electrolytes having been altogether qualitative, the newer viewpoint has been simpler than the old, as well as more nearly correct. But we have as yet left two important questions unanswered. If strong electrolytes are practically completely dissociated in dilute solutions, why does their equivalent conductivity nevertheless decrease so markedly with increasing concentration; and why are the effects of the solute on the physical properties of the solution so much smaller than would be expected according to the assumption that the ions act as independent solutes? Answers to both of these questions may be found in terms of the hypothesis of interionic attraction, firstsuggested by Milner in 1912. According to this hypothesis, the ions, even in dilute solution, are not distributed entirely a t random, as neutral molecules would be, nor are the movements of a given ion undected by its neighbors; but each ion has in its immediate neighborhood more ions of opposite sign than of the same sign, and is attracted by this oppositely cbarged "ion-atmosphere." without being definitely attached to any particular oppositely cbarged ion. Thus all the ions are subjected to electrical forces which exert a certain restraint upon themvharnper their freedom of motion, that is, and reduce their activity. From this point of view, the decrease in equivalent conductivity of strong electrolytes with increasing concentration is to be attributed to a decrease in the speed of migration of the ions rather than to a decrease in their number. A charged particle acted upon by an electrical field could not be expected to migrate so rapidly through a medium crowded with other charged particles as i t would if it were alone among the solvent molecules, and the high= the concentration of ions (the greater the degree of crowding), the greater would be this retarding effect. It would be expected, also, that this falling off in migration velocity would depend more npon the charges of the ions concerned than npon their
* It is probable, however, that in the case of most weak electrolytes we have to do not with a simple dissociation into ions, but with a reaction into which the solvent enters also, and in which a proton shifts from one molecule to another.
chemical nature. This hypothesis is in exact accord with the well-known fact that, for strong electrolytes, the conductivity ratio at a given concentration varies with the valence type of the compound. Thus, in 0.1 normal solution, A/& for most uni-univalent salts is about 0.85, for uni-bivalent salts about 0.73, and for bi-bivalent salts about 0.40. If the decrease in conductivity were due to chemical reaction between oppositely charged ions, we should expect to find wide variations among specific salts, even of the same valence type; the fact that the concentration and the charges on the ions are the determining factors is more easily accounted for on the basis of electrostatic forces. Debye and Huckel, and more recently Onsager, have calculated on a theoretical basis the effects of these electrical restraints upon conductivity, and have obtained equations which account very well for the observed conductivities of strong electrolytes in very dilute solution. These equations, of course, cannot be considered in detail in the general chemistry course; it may be mentioned, however, that they are of the general form A = A. - A
