IONIC ACTIVITY VS. COXCENTRATION I N T H E INTERPRETATION OF EQUILIBRIA BETWEEN AMALGAMS AND AQUEOUS SODIUM AND POTASSIUM HALIDE MIXTURES BY GEORGE McPHAIL SMITH
In a recent examination by Bjerrum and Ebertl of a series of investigations carried out during a number of years by the writer and his students,2 the former advocate the use of ionic activities rather than concentrations, for the interpretation of’equilibrium data. This affords the writer an occasion for the presentation of his own views on this subject. To him it has long seemed that so-called activities have too often been made use of merely as quantities with which to force constant values from tentative equilibrium expressions; that while the conception of activity might perhaps be a very useful one in connection with the application of thermodynamics to certain chemical processes, its usefulness would seem often to be very questionable in connection with the interpretation of chemical reactions from the kinetic molecular point of view. It is the object of Bjerrum and Ebert to show that the data contained in the papers cited are in harmony with a recent hypothesis of the complete ionization of the strong electrolytes. They present their examination under the headings : “Transference Kumbers and Conductivity,” “Amalgam Equilibria,” and “Some Other Properties of Mixed Salt Solutions”; but the last they dispose of in the space of less than a page. The present paper will be limited to a consideration of Bjerrum and Ebert’s interpretation of the data on amalgam equilibria. With the discussion confined to data obtained by Wells and Smith in experiments with sodium and potassium alone, and numbered into sections in order to facilitate the critical examination that is t o follow, Bjerrum and Ebert’s argument is as follows.3
A. Bjerrum and Ebert’s Argument I . “In a series of papers Smith with various co-workers has carried out a number of excellent experimental investigations of the heterogeneous equilibria between amalgams containing two light metals (Na, K) and aqueous solutions of salts of these metals. 1 On Some Recent Investigations concerning Mixtures of Strong Electrolytes (Transference Numbrrs and Amalgam Equilibria) : Kgl. Danske Videnskab. Selskab, Math.-fys. Medd., 6, N o . 9, pp. 3-20 (1925). * G. McP. Smith: J. Am. Chem. Soc., 35, 39 (1913);Smith and Ball: 39, 179 (1917); Smith and Braley: 39, 1j4j (1917); 40, 197 (1918);Smith and Rees: 40, 1802 (1918); Stearn and Smith: 42, 18 (1920);Smith, Stearn and Schneider: 42,32 (1920);Wells and Braley and Hall: 42, 770 (1920);Stearn: 44, 670 (1922);Schneider Smith: 42, 185 (1920); and Braley: 45, 1121 (1923). 8 The numbering of tables and equations corresponds to that employed in Bjerrum and Ebert‘s paper.
8.50
GEORGE McPHAIL SMITH
“The results of these experiments are conveniently expressed in tables containing the values of the following equilibrium constant:
where [KHg], [NaKg]denote molal concentrations in the amalgams and [KX], [KaX] molal salt concentrations in the aqueous phase. 2. “From the many experiments made by Smith and his co-workers me are able to see how K varies with the amalgam concentration, with the ratio between the salt concentrations, and with the total salt concentration. “The variations of K caused by changes in the amalgam concentration do not here concern us. The values for K given in Table VI correspond to very nearly the same amalgam concentration. The salt-concentration ratio alters K to no great extent. The values for K given in the table always correspond to solutions in which the two metal salts possess the same normality. “From Table VI it may be seen how K changes with the total salt concentration for the different salt pairs. These changes in K Smith ascribes to the existence of complexes in the salt solutions.
TABLE VI‘ The Equilibrium Constant K at 25’ K and Na possess the same normality inthe solution. 0.15-0.20 Milliequiv. of metals per I O g. Hg. Ion Normality SaC1-KC1
NaC1-KI
NaBr-KBr
SaBr-KI
NaI-KI
0.453
0.461
0.457
0.4j6
--
2.0
0.402
0.453 0.445 0.425 0.39j
0.452
I .o
0.454 0.439 0.427
4.0
0.342
0.330
0.449 0.437 0.412 0.367 0.299
-0.448 0.433 0.406 0.360 0.276
0.I
0.2 0.5
NaC1-KBr
0.430 0.409 0,365 0.295
0.448 0.430 0.398 0.350 0.262
3. “In the following we shall show how the changes in the K values can be explained by the hypothesis of the complete ionization of the strong electrolytes without assuming the existence of complexes. “The lack of constancy in K is due t o the use of concentration instead of activity. In applying activity in the mass-action expression we get a true constant, designated KO. “We have Ko=K. FNJFx. (13) Here Fs denotes the apparent activity coefficient for the ion 8, i. e., the ratio between the activity of the non-aqueous ion (a,) and the concentration in the solution (c,) : F, =&S/CS. (16) 4. “If we suppose complete dissociation we can assume that the deviation of the activity coefficient from I is due partly to the electric forces between Wells and Smith: LOC.cit., Cf. Tables V-X, incl.
851
IONIC ACTIVITY VERSUS CONCENTRATION
the electric charges of the ions and partly to the hydration of the ions. Then the following relation will hold good :
Here f, denotes the decrease in the activity of the ion S , due to the electric forces, m, the hydration number of the same ion, po the vapor pressure of water and p the vapor pressure of the solution. “By introducing in (13) expressions from formula ( I 7 ) and by logarithmic transformation we obtain: log Ko/K=log fr;,-log fK+(mN,-md log (po/p). (18) j. “In order to explain the experimental data of TableVIbymeans of (IS), we may put f N a = f K , since the electric forces show approximately the same effect on the activity of ions of the same valency. For K O we may put the value to which K approaches with decreasing salt concentration (log KO= -0.34) and for log (po/p) the value from log (po/p) =0.00421.t =0.00421 (3.4.c,,,) = o . o I ~ ~ . c , , , . ( 2 1) Here t denotes the lowering of the freezing point of the solution, elon is the salt normality of the solution, and 3.4 is a value for the molecular lowering of the freezing point which can be employed with sufficient accuracy both for the sodium and potassium salts within the range of concentrations here employed. We thus obtain: log ( K o / K )= (mNa-mK) 0.0143 elon. (22) “In Table VI11 are given the values of mN,-mK, i. e., the difference in the sodium- and potassium-ion hydration, obtained from equation ( 2 2 ) , for the salt pairs: KC1-NaC1 and KI-NaI.
TABLE VI11 NaI-KI
NaC1-KCl Salt Normality -log K 0.I 0.344
log (K,/K)
mNa-mg
0.004
-
0.2
0.343
0.5
0.357
I .o
0.370
0.003 0.017 0.030
2.0
0.396 0.466
0.056 0.126
4.0
log KO= - 0.34
-log K ~
log (K,/K) mNa -mg -
0.349
0.009
-
2.4
0.366
0.026
3.5
2.1
0.060
4.2
2.0
0.400 0.450
0.110
2.2
0.582
0.242
3.8 4.2
lOgK0=-0.34
“For each salt pair the hydration-numbers found are sufficiently constant, but whilst the experiments with the chloride pair can be explained by the fact that sodium-ion combines with 2 . 2 more than potassium-ion, the experiments demand a difference of 3.9 in the hydration of the ions in the case of the iodide pair. For the other salt pairs in Table VI the changes in log K correspond t o hydration differences varying between 2 . 2 and 3.9. Since, according to our hypothesis the hydration difference should have been the same in all
852
GEORGE MCPHAIL SMITH
cases, the variation in the hydration numbers found for the various salt pairs shows that the change of K with salt concentration cannot be ascribed exclusively to hydration. In order to explain the results of the experiments, we must assume that the various anions have specific effects on the activity of the sodium and potassium ions, 6. “From investigations on non-electrolytes we know something about the effect of such forces and hence may draw certain conclusions as to their effect on electrolytes. “Solubility experiments with non-electrolytes have shown that the activity of these substances in solution is affected by the presence of foreign substances, both ions and non-electrolytes. These effects which have been called the salting-out effects ordinarily vary linearly with the concentration of the foreign substances. They may be explained partly by the hydration and partly by the dipole and quadrupole forces between the molecules. “Whilst the hydration effect only depends on the depressing effect of the foreign substances on the vapor pressure of the solvent (hence mainly on the number of their molecules), the effect of the dipole and quadrupole forces is specific for the different foreign substances. “When dealing with the activity of the ions we may, besides the effectsof the hydration of the ion and of its gross charge, also expect to find effects from possible dipole or quadrupole forces. From the experience gained from the salting out of non-electrolytes we may expect that these effects will be proportional to the concentration of the reacting substance. For any definite salt pair these effects will then be proportional to the concentration, like the hydration effect. If then, as above, the hydration numbers are calculated without taking into account the effect of these forces, we get constant hydration numbers for each salt pair, but on account of the specificness of the forces, the hydration numbers calculated for the various salt pairs may differ. In order to explain the experimental results of Smith and his co-workers we must assume that the dipole and quadrupole forces between halogen-ion and alkali metal-ion vary in such a degree with the nature of the halogen that activity differences corresponding to a hydration of one or two molecules of water may appear. This is what might be expected from experiments on the salting out of non-electrolytes. “TOcomplete the discussion we may add that the typical ion forces, i. e., the forces between the gross charge of the ions, may also lead to specific activity differences between the ions when we take into account the nonnegligible dimensions of the ions.”
7 . According to Bjerrum and Ebert, in their summary, it has thus been shown “how the careful experiments of Smith and his co-workers, on equilibria between amalgams and aqueous solutions of salt mixtures, might likewise be interpreted without the necessity of assuming complex formation when taking into account the more recent views on the nature of electrolytes.”
IONIC ACTIVITY VERSUS CONCENTRATION
853
B. Critical Examination of Bjerrum and Ebert’s Argument The following critical discussion of Bjerrum and Ebert’s study of the data obtained by the writer and his co-workers, on equilibria between amalgams and mixed sodium and potassium salt solutions, will, it is believed, suffice to show that Bjerrum and Ebert have not been fortunate in their attempt to interpret the experimental data.
[NaX1 = K is not, as Bjerrum and Ebert desig[KXI nate it, an equilibrium constant; although in the case of the equivalently I.
The expression
“Id
mixed salt pair KaC1-KCl, for example, its value should no doubt remain very nearly constant with increasing total salt concentration, if the salts really were completely ionized into simple and hydrated ions, as Bjerrum and Ebert suppose, and if in reality the excess hydration of sodium-ion over the hydration of potassium-ion remained constant, in accordance with their calculations. In the case of a specific salt pair, they have in no way accounted for a change in value of the ratio between the activities of the two cations with increasing salt concentration, so that it is hard to see how they can consider themselves to have explained the steady decrease in the value of K with increasing salt concentration. Wells and Smith,l on the other hand, developed the formula (KHg)(Na+)/ (nTaH,)(K+) = k , in which (Me& are mol-fractions and (Me+) are ionfractions, as a theoretical equilibrium constant for the system, and pointed out that, since in any individual case (KaX)/(KX) =n(Na+)/(K+), therefore (KHg)(NaX)/(n’aHg)(KX) =n.k = c,,-i. e . , that c, =n.k under specific experimental conditions, and that if C, is found to vary with the conditions, so must n also vary. C, was referred to in this paper as an “equilibrium expression”; since it (or B. and E’s. K ) varies in value with the changing total salt concentration, under otherwise identical conditions, reference to it as an equilibrium constant cannot be justified.2 2 . The first column in Table 1‘1, headed “ion concentration” by Bjerrum and Ebert, should be headed “total salt concentration”, since the table is an assemblage of experimental data; its contents should be confined to experimental facts and not involve any theoretical views whatsoever. Neither should the table itself be headed “The Equilibrium Constant K at 2 5 ” ’ ; the K values in the table are not constant for the different salt concentrations.
3. In the opinion of the writer, activities are too often made use of as quantities with which to force tentative equilibrium expressions to give constant values, regardless of whether anything is to be gained thereby or not. Bjerrum and Ebert, for example, state that the lack of constancy in the K values is due to the use of concentration instead of activity, and that the LOC.cit., p. 185 f .
* I n numerical va!ue,
our C, is identical with R. and E’s. K in the case of equilibria involving only univalent metals.
854
GEORGE M CPHAIL SMITH
application of activity in the mass-law expression yields a true constant, K O 1 : K o = K Fwa/FK; Cf. our expression n.k= C, (or, in their terms, n.K,=K). They are more concerned a t this point than we were with the nature of the variable n ; not satisfied with n in its simple, non-committal form, they which they then substitute for it the ratio of two unknown activities, FK/FN&, proceed to analyze ;further into
e,
etc. Even if correct they would
aNe/cNa
still have nothing but a more complex expression for n itself. They do later, under 5 , have to assume a value for KO, just as we had to assume a tentative value for our k . 4. Next, they assume complete dissociation and ascribe the deviation of the activity coefficient from I partly to the electric forces between the electric charges of the ions and partly to the hydration of the ions. On the other hand, but without any idea cf comple Le ionization, we ascribed the deviation of n from unity in value t o the existence in the solutions of hydrated or other complex ions, or both (see under 6). We are therefore agreed, concerning the possible existence and influence of hydrates. j . Finally,they attempt to explain the data of Table VI on the basis of compIete ionization and some other very questionable assumptions. For example, they set f N a = f K , the validity of which they themselves later seem to question in their concluding remarks, under 6 ; and they assume 3.4 as a value for the molecular lowering of the freezing point which can be employed with sufficient accuracy both for the sodium and potassium salts within the range of concentrations employed (namely, 0.1-4.0total normality.) Thus they develop a formula for obtaining the excess hydration of sodium-ion over the hydration of potassium-ion for the various salt pairs. The excess hydration values calculated for sodium-ion, while probably without any significance in fact, as Bjerrum and Ebert themselves tacitly admit later under 6, are fairly constant for different concentrations in the case of a given salt pair, but they differ from one salt pair to another. Therefore Bjerrum and Ebert conclude that in addition to the hydration differences between the cations, the various anions must also have specific effects upon the activities of the sodium and potassium ions. Since Bjerrum and Ebert assume complete ionization, since they also assume fNa =fx, and since in the case of a given salt pair their calculated excess hydration values for sodium-ion are the same at all concentrations, it is hard to understand the basis of their claim that they have accounted for the steady decrease in value of K , in the case of a given salt pair, with the increasing total salt concentration. Complete ionization, together with equal changes in the activities of the cations (fN,=fK; see 4, under A), and a constant difference 1 How could anybody apply the individual cation activities, though, without actually knowing their values?
IONIC ACTIVITY VERSUS CONCENTRATION
855
in the hydration of the cations, would rather point to a more nearly constant activity ratio of the cations in the case of a given sodium and potassium halide pair, and therefore to a more nearly constant value of K . 6. A very indefinite, hypothetical discussion of the specific effects of the anions upon the activities of the cations follows, in which, in their statement that certain effects on the cations vary linearly with the concentration of the foreign substances (in this case, the anions), Bjerrum and Ebert seem to have overlooked the fact that the anions increase in concentration, as well as the cations, with increasing total salt concentration. The impression produced upon the writer at this point is that of “anything rather than admit the existence of complexes (other than hydrates) in the solutions,”-an admission, of course, which would at once concede the inadequacy of the hypothesis of complete i0nization.l
7 . At this point it will perhaps not be out of place to give a short r6sum6 of our own interpretation of the data which Bjerrum and Ebert have assembled in their Table VI. Smith and for example, have pointed out that if, in the expression
(KHg) (Na+) = k , the value of IC were known, the ion fractions of the metals (NaHc) (K+) in t h e individual mixtures might then be calculated by means of the formulas, (K+) = (KHg)
(KHR) and (Xa+) = I - (K+); +k (KaHg)
and that, although we are unable to ascertain the actual value of k , if we assume for k a value equal to that of C, (or K ) a t o.2N concentration, we can then with the use of this tentative value at least, determine the direction and relative degree of the ion-fraction changes which accompany salt-concentration changes in the aqueous phase.a This was done, and it was found that the K+-ion fraction decreases while the Na+-ion fraction correspondingly increases, with increasing total salt concentration; and that these changes take place the more rapidly, the higher the average atomic weight of the halogens in the salt pair. These results are shown in Table XII, which is here reproduced. 1 Bjerrum and Ebert in their discussion have disregarded certain solubility determinations which were made in this connection by Smith and Ball (Loc. cit., p. 2 1 7 f.)! who, in a discussion of the effects of concentration changes upon the value of CO (or K ) in the case of equivalent mixtures of sodium and potassium sulfates, pointed out that the experimental data seemed to indicate the existence in such solutions of equilibria of the following nature, Sa2S04+K2S04=2NaKS04=2 (Me‘)++z (Me”S04)-, in which the intermediate ion KSOd-, being more stable, exists a t a higher concentration than the intermediate ion SaSOd-; and that upon this basis K,SOc should be more. soluble in Ka2S04solutions than in pure water, and that its solubility should increase with increasing concentration of the SazSOc solution. Upon investigation, this predicted behavior was definitely observed. Loc. cit., pp. 18j-7. 3 If there were any advantage to be gained by so doing, we might even claim this as a means of determining the changes in the “activity ratio” of the cations with increasing total salt concentration in solutions of the various salt pairs.
856
GEORGE McPHAIL SMITH
TABLE XII1 Ion Fraction Changes which accompany Salt-Concentration Changes in Equivalent Aqueous Mixtures of Sodium and Potassium Chlorides, Bromides and Iodides, at 25’. Total Normal Concentration of Equivalent Salt Mixture 0.1000 0 . 2 0 0 0 0.5000 1.000 2 . 0 0 0
4.000
Potassium-ion NaC1-KC1 0.499 0 . 5 0 0 0.493 0,485 0.470 0.430 Fractions Cal- NaC1-KBr 0.504 0 . 5 0 0 0.49j 0.484 0.466 0.421 culated a t 0.2 NaC1-KI 0.503 0 . 5 0 0 0.487 0.475 0.447 0.395 milliequivs. of NaBr-KBr 0.504 0 . 5 0 0 0.493 0.479 0.450 0.400 metals per I O g. NaBr-HI -- 0 . 5 0 0 0.491 0.474 0.44j 0.381 Hg, upon the NaI-KI -- 0 . 5 0 0 0.490 0.470 0.439 0.370 assumption that n is here equal to unity. These ion-fraction changes we have ascribed in our paper to the existence of hydrated, intermediate and or other complex ions, We did this deliberately, on the basis of the known existence of such ions; for example, we may cite the analogous silver complexes, [Ag(OH2)2]+, [Ag(KH3)2]+,[AgC12]-, [Ag(CN)21-. It is of course a well known fact that compounds such as Kz[PtC16], Na[AuCl,].nHzO, KMgC13.6 HzO, etc. may readily be obtained from aqueous solutions; and even the alkali halides are capable of forming addition compounds with one another, as well as with other substances,2 and these may ionize to give complex ions, especially in concentrated solutions. Certain alkali halides also show a tendency to p~lymerize,~ and in recent years evidence (based upon absorption-spectra data) has been adduced to indicate that the alkali metals, through the agency of residual valency, are capable of effecting closed-ring structures, with the formation of inner-complex salts.4 Through conductance studies of the alkali salts of certain organic acids, Lifschitzs has arrived at a similar conclusion. Evidently, then, since we may have the possibility of hydrated ions and molecules, addition and polymerized compounds, and many complexes capable of furnishing ions of various species, speculation as to just what specific Wells and Smith: loc. cit. p. 203. Joannis: Compt. rend., 112, 338 (1891); Ahegg and Riesenfeld: Z. physik. Chem., 40, 84 (1902). 3Zanno~ich-Tessarin:Z. physik. Chem., 19, 251 (1896); Andrews and Ende: 17, 136 (1895’1;E. W. Washburn: Trans. Am. Electrochem. SOC.,21, 137 (1912). 4Hantzsch: Ber., 43,3049 (1910); Hantzsch and Voigt: 45, 85 (1912). 6 Z. physik. Chem., 87, j67 (1914). 1
2
I O N I C ACTIVITY VERSUS CONCENTRATION
857
complex do exist in these solutions,’ and how they behave, is more or less futile. Nevertheless, owing to the greater tendency of potassium than of sodium, and of iodine than bromine or chlorine to form complexes, we should not be surprised to find, as we do in the equivalent aqueous salt mixtures under discussion, that the potassium-ion fraction decreases with increasing total salt concentration, and the more rapidly the higher the average atomic weight of the halogens is in the mixture. And, as a matter of fact, in the case of changes in concentration, and of changes from one salt pair to another, does not this interpretation account in a most satisfactory manner for the variations in value of the so-called cation “activity ratio” of Bjerrum and Ebert? When an ion loses in concentration, as compared with another ion in the same solution, it naturally must lose in “activity” also. In conclusion, we may again be permitted to point out that ionization is too often discussed as if it were a simple dissociation alone, and that perhaps too much faith is placed in the supposition that the mass-law (a law which applies even in atomic disintegrations) is non-applicable to the dissociation of strong electrolytes; that perhaps the mass-law is less at fault than we ourselves, in our inability to determine just what molecular species are present in such solutions, and their individual chemical properties and concentrations. At appreciable concentrations, especially in the case of mixtures, it would seem that the possible existence of complexes in solutions of (strong) electrolytes could not, without a flagrant disregard of known facts,* be set aside in favor of any theory whatsoever,-not even with the help of activities. Seattle, Washington, March, 1926. 1 We
may however assume, as a simple case, the following:
These addition compounds might ionize, as indicated, in either or both of two Tq-ays: (a) into metallic cations and complex anions, and ( b j into chloride anions and complex cations; the complex ions map he regarded as alkali-metal or chloride ions, as the case may be, which carry alkali halide instead of (or in addition to) water. Both types of complexes are Cr(0H2j4]Cl3.Concerning (h), see A. known to exist: e.g., (a) Kz[PtCle]and ( b ) [(CSCL)~ Werner: Bet-., 34, 1602 (1901); “Neuere Anschauungen, pp. 226, 208 (1913). 2For an interesting example of complex formation in the ease of aqueous nitric acid, see Hantzsch: Ber., 58 B, 941 (1924).
