THE DISSOCIATION O F STROSG ELECTROLYTES* IV. Miscellaneous Properties BY MORRIS B. JACOBS ASD CECIL 1’. K I S G
It is really remarkable that no known property of electrolytes is unquestionably connected with the concentration of the undissociated molecules in such a way that it can be used as a completely satisfactory test for the presence of these in solutions of strong electrolytes. Conductivity measurements have admittedly failed to give a measure of the concentration of ions; there seem to be no absorption bands characteristic of the undissociated molecules; vapor pressure measurements, valuable in the case of volatile weak electrolytes fail for strong electrolytes because they are non-volatile (salts) or because they are probably highly hydrated (hydrogen halides) in which case the vapor pressure could give little idea of the actual concentration of undissociated molecules or of ion-pairs. I t will be remembered that solutions of hydrochloric acid do have a very small, but appreciable, vapor pressure down to a concentration of 0.3X; but whether the extreme smallness of this vapor pressure and the lack of measurable vapor pressure at higher dilutions mean practically complete dissociation or not, is problematical. The absence of properties undisputably assignable to undissociated molecules is one of the chief arguments of the supporters of complete dissociation, who feel that while perhaps no single piece of evidence is conclusive for the theory, the entire mass of data is best explained by this theory. The writers feel that it is unfair to neglect the possibility of incomplete dissociation; just as unfair as it would be to neglect the possibility of compound formation in studying the deviations from the ideal laws in the case of non-electrolytes. The best evidence for complete dissociation is probably agreement with the Debye-Huckel and related laws; but at, present exact comparison of these with the experimental is possible only for highly dilute solutions. On the other hand, the best argument of those who do not accept complete dissociation except as a limiting law, seems to be the lack of evidence of any quantitative distinction between strong and weak electrolytes. I t apparently behooves the latter to find some property which belongs undisputedly to the undissociated molecule or to show convincingly that the deviations from the Debye-Huckel theory or other theories based on inter-ionic attraction and complete dissociation are caused by incomplete dissociation. I n the meantime, there remain a few more points commonly adduced in favor of complete dissociation whose evidence in this direction seems to the writers to be greatly over-rated. In this paper we wish to discuss critically the evidence offered by: ( I ) crystal structure data; ( 2 ) transference number * Contribution from the Department of Chemistry of Washington Square College, New
York University.
THE DISSOCIATION OF STRONG ELECTROLYTES
1923
and conductance; (3) certain electrical cells; (4) some of the experimental data which have been compared with the Debye-Huckel theory; and ( 5 ) the additivity of some properties not mentioned before. First we should again raise the question of the exact meaning of ionization and dissociatzon and the distinction, if any, between the two terms. By an ion we understand, according to the picture of the atomic physicist (if he can be said to have any picture) an atom or group of atoms in which one or more electrons are completely missing, or which have full possession of one or more extra electrons. Two such ions of opposite charge might “associate” to form an “electrical molecule” as suggested by Noyes in 1904 (an idea treated in detail by Bjerrum’ in 1026) or more than two such ions might form a group; in fact, such grouping, to a limited degree, in the sense that any ion will have more ions of the opposite charge near it, on the average, than ions of like charge, is postulated in the Debye-Huckel theory. It is not clear to the writers whether or not close grouping cf two ions of opposite charge, perhaps to form “electrical molecules,” is actually taken into account in the DebyeHuckel theory. At any rate, there should be a quantum difference between a true molecule and even an ion-pair or “electrical molecule”; but perhaps there can be all stages between, in which the ions are deformed or the valence electrons are in distorted orbits or orbits of exceptional energy levels. It has been assumed, a t least as a simplifying picture, that in the case of weak electrolytes we deal with only two conditions-complete ionization and complete molecule formation*-although this is not necessarily correct.3 1.
Crystal Structure Data
The X-ray evidence that the atoms of several salts exist as ions in the crystal has seemed to fit in perfectly with the complete dissociation theory. For instance, La;\Ier4 says: “The studies of the Braggs and others on the structure of crystals by means of X-rays furnishes more conclusive evidence for the new point of view. They find that no molecules of NaCl are present in the solid salt; instead the crystal structure consists of sodium and chlorine ions arranged in a cubic lattice, such that each sodium ion is surrounded a t equal distances by six chloride ions and similarly each chlorine ion by six sodium ions. That the forces holding a crystal of salt together are due to electrostatic forces between the charged ions, has since been established by the calculations of Born, Debye and Schemer, Fajans, lladelung and others upon the magnitude of the so-called space lattice energy.” I t should be noted that X-ray spectra can be used to fix the positions of the atoms in the crystal lattice (for instance the cubic lattice of NaCl), but do not themselves indicate with certainty whether the atoms are charged or uncharged. The intensity of the X-ray lines depends on the number of Det. Kgl. Danske Vidensk. Selskab., Math.-fys.Medd., 7, KO.9 (1926). Dissertation, Univ. of Copenhagen (1925). Also, other work on activity coefficients of slightly soluble weak electrolytes. 3 See Falans, Fowler: Trans. Faraday SOC.,23, 410,411 (1927). Trans. Am. Electrochem. Soc., 51, 507 (1927).
* Rordam:
MORRIS B. JACOBS A N D CECIL V. KING
I924
external electrons, it is true; and, theoretically, intensity measurements should indicate whether a crystal consists of charged or uncharged atoms. Practically, however, such intensity measurements cannot be made with the necessary accuracy. For this reason, the argument that simple crystals as h’aC1 and KCl consist of equally spaced ions depends on the calculations mentioned above, which show that the electrostatic forces of such charged ions are of the correct order of magnitude to hold the crystal structure together. However, it is obvious that many other substances form stable crystal lattices, with symmetrical spacing of the various atoms or groups of atoms involved, without such forces to stabilize the lattices. Also, all salts of symmetrical valence types each of whose radicals consists of a single atom, should crystallize in a cubic lattice, if held together by electrostatic forces alone. It is hard to reconcile the apparently molecular form of gaseous sodium chloride with a completely non-molecular form in the crystal. I t seems possible that in the crystal, the electron from each sodium atom, instead of being possessed by a single chlorine atom, might be equally shared by all the six nearest chlorine atoms. h’ow consider the solution of a crystal of sodium chloride; it must be admitted that we can have absolutely no idea of what happens in this process. Partington’ says that “in solution such a crystal would simply fall apart into its ions.” On the next page, however, Partington questions such a process of ionization for molecules. Such a picture is undoubtedly too simple. When a salt is melted it might be supposed that the ions would simply remain as such, with the added freedom of motion other than vibration. That this is not the case is well known. The conductivity of molten salts indicates a high “association factor” but the interpretation of this factor is not altogether clear. Great dilution with water should, of course, tend to break up any groups formed in concentrated solutions. It is evident that the structure of the crystal gives no indication of what is to happen when the crystal is dissolved in some solvent. The enormous difference between such substances as the hydrogen halides and the common salts, all of which take equal places in the complete dissociation theory, make it quite evident that the previous history of the electrolyte is of questionable significance with respect to its dissociation in water. 2.
Transference Number and Conductance Data
The conductance of an electrolyte a t a given dilution is, according to the law of Kohlrausch X, = n F cy (I: T) (1)
+
where U and T’ are the mobilities of the anion and cation. A t infinite dilution the conductivity is A, = n F (V T’) (2)
+
1
Taylor: “Treatise on Physical Chemistry,” and Edition, 634 (1931).
THE DISSOCIATION OF STRONG ELECTROLYTES
I925
since CY = I . Dividing ( I ) by (2) we get a = XX /, , the classical expression for the degree of ionization. This obviously depends on the assumption that the mobilities of the ions do not change with the dilution. This we now know is erroneous. It is probable that the mobilities change with the viscosity of the solution, with the electrostatic environment and perhaps with other factors, as changing hydration of the ions. However, the effect of these factors is difficult, if not impossible, to calculate; and the simplest way out seems to be to follow MacInnes:’ “So far as conductivity and transference data are concerned it appears, therefore, that the assumption of complete dissociation results in a simplification of the theory of monovalent strong electrolytes, since one variable, ion mobility, is substituted for two, i.e., the number and mobilities of the ions. The phenomena can otherwise only be explained by more or less indefinite distribution of the effects observed between these two variables.” MacInnes thus states the problem very clearly, and proceeds to attack the problem from the standpoint of the old rule of Kohlrausch, the additivity of ion conductances. He shows that in a number of univalent metal chlorides, the chloride ion has, a t any one dilution, nearly the same equivalent conductance (TX, transport number of the chloride ion multiplied by the equivalent conductance of the salt.). TX is not satisfactorily constant unless multiplied by an empirical viscosity correction (the relative viscosity raised to the 0 . 7 power) but with this correction the rule holds well a t concentrations as high as IM. MacInnes was inclined to interpret this as indicating that all these chlorides were completely dissociated. However, McBain and Rysselberge* have shown that this constancy fails for bi-valent metal chlorides. MacInnes and Cowperthwaitea later found no such constancy for nitrates of the univalent metals, and McBain and Rysselberge showed that the values of TX vary enormously for metallic sulfates. If constancy of TX is any indication of complete dissociation, most salts are not completely dissociated even a t rather low concentrations. Obviously, a satisfactory explanation is not available a t present. All the alkali halides seem to show additivity in several properties as we shall show later in this paper; but if this indicates complete dissociation, other salts are not completely dissociated. It is not quite clear to the writers whether electroendosmosis has been adequately considered in connection with conductivity and transference number experiments. Conductance through a membrane is usually abnormal, the water moving through the membrane in a direction determined by the sign of the charge between the membrane and the water. The effect is usually pronounced in very dilute solutions. The conductivity of very thin surface films has been shown to be highly abnormal. It is possible that there is more movement of water in the usual transport number apparatus than has been expected, due to a difference in charge of the glass and the solution. J. Am. Chem. SOC., 43, 1217 (1921).
* J. Am. Chem.
SOC., 50, 3009 (1928). Trans. Faraday SOC., 23, 400 (1927).
1926
MORRIS B. JACOBS AND CECIL V. KING
The high mobilities of hydrogen and hydroxyl ions have sometimes been explained as being due to a sort of “Grotthuss conductivity”; i.e., a single ion may move until it collides with a water molecule, when it will stick and a corresponding ion leave the other side of the water molecule. The experiments of McBain and Rysselberge,’ showing that the transference number of almost any positive ion, in low concentration in the presence of a high concentration of another salt having a common anion, is abnormal, merit more investigation. Sata2 states that he can account for the conductivity of acetic acid in acetone only by assuming that undissociated molecules as well as ions conduct. Onsage? has pointed out that in addition to the Debye-Huckel interionic attraction and electrophoretic effects an ion moving under a potential difference will be influenced by its own Brownian movement. Onsager’s final conductivity equation has been used by some investigators as a criterion of complet’e dissociation (with proper regard to its limitations). Davies4 has shown that, by assuming deviations from Onsager’s equation (in quite dilute solution) to be due 50 incomplete dissociation, a mass-action (activity) constant can be calculated for some bi-bivalent salts as well as some strong uniunivalent acids. Another method of attacking the problem of degree of dissociation has been discussed by Davies.5 W e n has measured the conductivity of solutions of electrolytes a t such high voltages that the migration speed of ions is of the order of several meters per second. The equivalent conductance rises above the normal and at sufficiently high voltages seems to reach a maximum. If we can assume that a t such high migration velocities interionic attraction and electrophoretic effects are negligible, this maximum conductivity should give ah, ; in fact, for salts which may be considered completely dissociated W e n considers the maximum value to be equal t o A,. Davies shows that for 0.001M MgSOa, for which he has calculated a dissociation of 92.4% from the deviations from Onsager’s equation, the maximum conductance increase should be II%, which agrees well with Wen’s value of 9% for o.ooog3M MgSO,. Objections to this interpretation of Wen’s experiments have been raised by Gyemant. The multitude of factors which may influence ion mobilities and transference numbers, and the diversity of opinion in interpreting experimental results with respect to complex ion formation6 and with respect to the true mobilities when the moving boundary method is used7leave much to be desired in the use of this type of data in support of complete dissociation. J. Am. Chem. Soc., 50, 3009 (1928); 52, 2336 (1930). Bull. Chem. SOC.Japan, 1, 245 (1926). 3 Trans. Faraday SOC.,23, 341 (1927). Davies: “The Conductivity of Solutions,” Chapters V I 1 and I S (1930). 5 “The Conductivity of Solutions,” Chapter SI. See Schneider and Braley: J. Am. Chem. SOC.,45, 1121 (1923); MacInnes:’47, 1922 (1925); Dewey: 47, 1927 (1925); Bjerrum and Ehert: Det Kgl. Danske Vidensk.fSelskab, MathAys. Medd., 6 , S o . 9 (1925). ’See hfukherjee: Kature, 122, 608 (1928).
THE DISSOCIATION OF STRONG ELECTROLYTES
1927
3. The Concentration Cells of Bronsted
I n 1919-1920 Bronstedl published measurements on the electromotive force of cells which have often been quoted in support of complete dissociation. With two cadmium amalgam electrodes in solutions containing M/I O to M/320 and M/20 to M / 6 4 0 cadmium sulfate, respectively, with the ratio always 3, both solutions made up to 2 M with magnesium sulfate, the electromotive force ratio was in agreement with that calculated from the Yernst equation, using the total cadmium concentrations. With two silver chloride electrodes in solutions containing 0.0032 M and 0.1M magnesium chloride and made up to 4 M with magnesium sulfate, the e.m.f. ratio was nearly in agreement with the Nernst equation. Considering the 0.0032 M magnesium chloride completely dissociated, the 0.1 pul magnesium chloride would be 99.3q7 dissociated. At first glance it seems that the simplest explanation of bhese results is that the cadmium sulfate and magnesium chloride are completely, or nearly completely, dissociated a t all concentrations. However, this need not be the case. The experiments simply prove that the activity coescienls of these salts are the same, or nearly the same, in the two solutions in the presence of the large excess of magnesium sulfate. Bronsted has demonstrated that this is true in general, in showing that the velocity of reaction of ions a t low concentrations in solutions of high ionic strength follows the classical reaction velocity laws. These experiments do not involve the degree of dissociation of the salts in question, It seems probable that even on the basis of the Arrhenius theory, in the presence of a constant ionic environment (high concentration of inert salt) the percent ionization of a salt present in comparatively low concentrations would remain appreciably constant over a considerable concentration range. One of the weak points in the application of sonductivity to the study of salts with respect to the ionization theory has always been that the conductivity of one salt cannot be measured independently of other salts present. Kevertheless, it is evident that the experiments of Bronsted are suitable to determine activity ratios but not degrees of ionization, or dissociation. 4. The Debye-Huckel Theory
This theory has without doubt come very close to explaining the behavior of electrolytes in rather dilute aqueous solutions. It assumes, in its simplest forms, that all deviations from the ideal behavior are due to interionic forces. Thus it neglects any lack of complete dissociation and also any specific peculiarities of ions no matter what their cause. Experimental agreement with the theory substantiates the underlying assumptions. Unfortunately, there is reasonably good agreement of experiment and theory only in solutions sufficiently dilute so that any reasonable modern theory of ionization must postulate nearly complete dissociation. It is in the region of deviation from the simpler form of the theory that we must- look €or incomplete dissociation. 1Medd. Vetenskapeakad. Nobelinst., 5, No. 2 5 , r (1919);Kgl. Danske Vidensk. Selskab., Math.-fys. Medd., 3, No. 9 (1920);Trans. Faraday SOC.,24, 727 (1928).
1928
MORRIS B. JACOBS AND CECIL V. KING
Very few non-electrolytes follow the ideal laws closely. The deviations have not in every case been satifactorily explained; there are some very clearcut reasons for non-ideality, such as association of the solute, compound formation with the solvent, etc., while others are difficult to measure quantitatively, such as chemical dissimilarity of solvent acd solute, differences in internal pressure, polarity, and other factors. In the case of electrolytes we should expect deviations from some of these causes to persist to very high dilutions, compound formation between the two parts of the solute (the two ions) being pronounced because of the high electrostatic attraction. The simple form of the Debye-Huekel theory would seem to bear to the “ideal” theory of the behavior of ions the same relation as the van’t Hoff equations for dilute solutions to the ideal equations derived from Ra.oult’s law or the van’t Hoff isochore. The simple theory ascribes all deviations of the ions from Raoult’s law to inter-ionic attraction; and even in doing this makes simplifying assumptions which invalidate it except for high dilutions. Some progress has been made in extending it; Debye and Huekel themselves added a factor necessary to account for a finite size of the ions. Gronnall, LaMer and Sandved’ have improved the mathematical treatment for ions of higher valence types. Otherwise the chief modifications have been in the addition of empirical terms which have some qualitative justification but are of a type which cannot be submitted to quantitative treatment.
A weak link in any form of the Debye-Huckel theory is in the manner in which the dielectric constant of the medium is used. Bjerrum? concludes that anomalies in heats of dilution, partition coefficients, Soret effect, and other properties are due to variations in the dielectric constant. Fowler3 says “the introduction of the dielectric constant makes use of a process of averaging in steps, which is illegitimate though probably not seriously in error, and should be replaced if possible by a deeper investigation, including a study of saturation effects in the polarization of the medium.” Hucke14has attempted to take into account the variation of the dielectric constant with salt concentration. He concluded that the dielectric constant should show a linear decrease with concentration, which seems probable a t low concentrations but is contrary to experiment at high concentrations. Walden and his co-workers5 have found indications that the dielectric constant first decreases, goes through a minimum and then increases. This effect has been found correct in general, although experiments are not checked6 exactly. Physik. Z., 29, 358 (1928).
* Trans. Faraday SOC., 23, 44j (1927). 3Trans. Faraday SOC.,23, 43j (1927). Physik. Z.,26, 93 (192j). Z. physik. Chem., 110, 43 (1918). Walden, Ulick and Werner: Z. physik. Chem., 116, 261 (r92j); Schmidt: Phys. Rev., ( 2 ) 30, 925 (192 ), Hellman and Zahn: Z. physik. Chem., 132, 399 (1928); Carman and Schmidt: Phys. &e;., ( 2 ) 31, 157 (1928). 4
THE DISSOCIATIOX O F STRONG ELECTROLYTES
1929
Gronwall and LaMerl outline a theory for the variation of the dielectric constant with concentration which is in substantial agreement with the experimental results of Walden. On the whole, the original Debye-Huckel theory or the extended forms seem satisfactory a t low concentrations, especially for uni-univalent salts, although even here small specific variations for individual salts may persist t o very high dilutions.* Bronsted? even before the original papers of Debyeand Huckel appeared ( 1 9 2 3 ) published papers on “the specific interaction of ions.” I n these papers he showed that the solubility effects of un-univalent salts have marked individual characteristics even in 0.I M solution and presented a simple method of dealing with these specific effects. The theory has been well e~tablished.~Whether “specific interaction” is connected with molecule or ion-pair formation is not known and is not necessary to the theory. The agreement with the Debye-Huckel theory in non-aqueous solution is far from being as good. Water happens t o be an excellent solvent for the theory in that its polarity and dielectric constant are such that the valence of ions plays a predominating role and specific salt effects are Data on solubilities and ion mobilities in solvents of low dielectric constant do not agree so well with the theory. Part of this may bc due to lack of correct dielectric constants; some writers6 are inclined to favor incomplete dissociation as one reason. The Debye-Huckel theory thus seems to be obeyed as a limiting law over a small range of concentration of strong electrolytes in solvents with a small range of dielectric constants and ionizing powers. In this range its validity is of utmost importance. Too little is known of the deviations at present to say what role lack of complete dissociation plays. 5.
Additivity of Properties
I n the preceding papers of this series we have pointed out that a number of properties of strong electrolytes which from the older experimental work were thought by the exponents of complete dissociation to be additive for positive and negative ions, have been shown on careful investigation to deviate from this rule. The deviations have been interpreted variously in favor of incomplete dissociation and otherwise. We shall point out some other deviations from additivity which make the interpretation of such data in favor of complete dissociation questionable.
’ Science, 64, 122 (1926). LaMer, King and Mason: J. Am. Chem. SOC.,49, 363 (1927). SDet Kgl. Danske Vidensk. Selskab, Math.-fys. Medd., 4, No. 4 (1922); J. Am. Chem. Soc., 44,877 (1922); 45, 2898 (1923). See Giintleberg: Z. physik. Chem., 123, 199 (1926); LaMer and Cook: J. Am. Chem. h C . , 51, 2622 (1929). 6 See Hammett and Diete: J. Am. Chem. SOC.,52, 4795 (1930). 6 Robinson: J. Phys. Chem., 32, 1089 (1928); Ulich and Birr: Z. angew. Chem., 41, 1075 (1928); Hartley and Bell: Trans. Faraday SOC.,23, 396 (1927); Fraeer and Hartley: Proc. Roy. SOC.,l W A , 351 (1925); Woolcock and Hartley: Phil. Mag., (7) 5, I 133 (1928); Kraus and Seward: Trans. Faraday SOC.,23, 488 (1927).
I930
MORRIS B . JACOBS AND CECIL V. XING
We have already mentioned the usual close additivity of properties for the alkali halides and the usual deviation for other electrolytes. We have discussed the “additivity” of ion conductances. LaMer and Gronwall’ have calculated the partial molal volumes of most of the alkali halides in water solution and their data show good agreement with the additivity principle even a t rather high concentrations. Data for other salts are probably too meager to be of much use, but it is unlikely that the same additivity will be found. Haeseler,2 working with LaMer, investigated carefully the additivity of the effect of ions on the solubility of benzoic acid in water. For the nine alkali halides (Li, Xa, K - C1, Br, I) the results indicate independence of the effect of individual ions within experimental error up to a concentration of 131, aside from minor deviations a t low concentrations probably due to the ionization of benzoic acid. Above this concentration there is a regular deviation which presumably persists to a very slight extent even to low concentrations. Experiments with other salts, however, showed pronounced deviations a t lower concentrations. The mechanism of such a salting-out effect is, of course, problematical; as before, the alkali halides seem to be a limiting case, but whether we should consider them completely dissociated and the nitrates and sulfates not depends on a more complete interpretation of the data. The experimental data on other properties such as partial volumes, specific heats, etc., are so meager that it is doubtful if they offer any convincing evidence for or against the theory. In concluding this series let us point out again that we are not trying to discourage legitimate use of the complete dissociation theory. The chemist should keep an open mind, accepting such a theory when it seems valuable, trying to find its limitations and the reasons for these limitations. I n the present situation it would seem very important to try to find some property unquestionably due to undissociated molecules, and then look for this property in solutions of strong electrolytes in aqueous and other solutions. I n addition, deviations from the limiting laws based on the assumption of complete dissociation should be systematically studied and the attempt made to learn if any or all of them are unquestionably caused by incomplete dissociation. .Veto York, A’. Y .
J. Phys. Chem., 31, 393 (1927). Dissertation, Columbia University (1929).
