THE PRESENT STATE OF THE ELECTROLYTE PROBLEM CHARLES A. KRAUS Metcalf Research Laboratory, Brown University. Providence, Rhode Island
HISTORICAL BACKGROUND
ONEof the oldest, if not the oldest, problems inphysical chemistry is that of electrolytes (1). It goes back to the days of Alessandro Volta, more than 150 years ago. Volta's discovery of a method for generating electricity by means of chemical reaction constitutes one of the major developments in physical science during the eighteenth century. Prior to Volta, electricity was known only in the static form as generated by friction. It was available only in small quantity and at high potential. The current developed on discharge was very weak and transitory. By means of Volta's cells, it was possible to generate electricity under controllable conditions and at convenient potential and current. It thus became possible to measure both potential and current. This soon led Ohm to the discovery of the law which bears his name. With large and controllable currents available, it became possible to construct electromagnets and thus obtain strong magnetic fields. With such fields at their command, Faraday and Henry discovered electromagnetic induction. This, in turn, led to Maxwell's electromagnetic theory of light. It also led to the present-day electrical industry. Early in the nineteenth century, Sir Humphrey Davy, reversing the process that goes on in a Voltaic cell, isolated the elements sodium and potassium by electrolysis of their fused hydroxides. Some 25 years later, Faraday discovered the laws governing electrolysis. He showed that the reactions occurring at the electrodes for a given quantity of electricity are equivalent for all electrolytes. He devised the nomenclature presently employed in the electrolyte field, including the term ''.ion." In those days, our knowledge of atoms and molecules was very vague and it is likely that Faraday had no clear idea of what ions really were. However, he did clearly understand that the ions wandered through the solution toward one electrode or the other under the action of the applied electrical field. In the 1860Js, Hittorf showed that the ions of an electrolyte in solution transfer their charges in different amount. In other words, he showed that the two ions had different mobilities. In the 1870Js,Kohlrausch introduced the concept of molecular or equivalent conductance. He showed that, as the concentration decreased, the equivalent conductance increased and appeared to approach a definite value in the limit of infinite dilution. He also showed that the conductance of an ion under given conditions was independent of other ions that might be present.
For many years, chemists working in the electrolyte field were plagued by lack of knowledge as to the extent to which electrolytes exist in the form of ions. In the 1850's, Clausius suggested that electrolytes in solution might be dissociated into ions, perhaps t o the extent of a few per cent. Finally, about the mid-1880's, Arrhenius proposed his ionization theory. This theory was based on three underlying postulates: (1) Electrolytes are completely dissociated into their ions in the limit of infinite dilution. (2) The equivalent conductance of the free ions is independent of concentration. The decrease in conductance with increasing concentration is due to the association of the ions to neutral molecules. The degree of dissociation at any given concentration was thus equal to the ratio of the observed conductance to the limiting conductance at infinite dilution. (3) The equilibrium between the ions and the undissociated molecules conforms to the law of mass action. We now know that the second of these postulates is invalid. The mobility and, therefore, the conductance of the free ions decreases with increasing concentration and it is, therefore, not possible to derive the degree of dissociation of a strong electrolyte directly from conductance measurements. A few years prior to the announcement of the Arrhenius theory, Ostwald had measured the conductance of a considerable number of weak acids and bases. These results were found to be in accord with the theory and it was possible to determine the dissociation constants of these electrolytes. So, also, van't Hoff had measured the freezing point depression for solutions of a considerable number of salts in water. He found that the molal depression for 1-1 salts as greater than that of non-electrolytes by a factor greater than 1 which increased with increasing dilution approaching a value of 2. The freezing depression results appeared to be in substantial agreement with this early theory of Arrheuiui. T11~1l11.0rYa150 arroun~rdfor the phcnornenon of ha\ ~ i l "r d ~ m i . d; for the ~ M C Voi I ; l d t i on 1111, -(~lnlili~v of other salts. Thus, there was considerable evidence in support of the Arrhenius theory. However, when the theory was applied to strong electrolytes, the dissociation constant as calculated on the basis of the theory was found t o be anything but constant. The calculated value mas found to t e quite large at high concentrations and to decrease continuously with decreasing concentration without approaching any limit other than, perhaps, zero. JOURNAL OF CHEMICAL EDUCATION
It was obvious that strong electrolytes do not conform to the A r r h e ~ u stheory and many came to doubt that the ion concept had any validity whatever. A controversy arose which continued for almost forty years, when Debye and Hii~kelsupplied the solution of the problem. THE ION ATMOSPHERE THEORY
The theory of Debye and Hiickel (2) takes into account the interaction of an ion with an equal counter charge which is distributed throughout the solution; this constitutes the ion atmosphere, as it is appropriately called. The theory accounts rather success fully for the thermodynamic properties of electrolyt,e solutions. For the activity coefficient of the ions it leads to the simple limiting equation where (3 is a constant depending only on the dielectric constant of the solvent, the temperature and the numher of unit charges on each of the ions. The DehyeHuckel theory, in its general form, accounts satisfactorily for the thermodynamic properties of dilute solutions. It did not account satisfactorily for the conductance of the electrolyte solutions. However, the gap was filled by Lars Onsager (3) a few years later. According to Onsager's theory, the conductance of an electrolyte is given by the equation: where An is the limiting conductance and a and (3 are constants depending only on the dielectric constant and the viscosity of the solvent, the temperature and the numher of unit charges on each of the ions. The ahove equation is a limiting form. If values of A are plotted against values of dc,the points approach nearer and nearer to a straight line whose slope is equal to aAo (3. For salts of the same type, the slopes differ little, hut the slopes increase as the number of unit charges on the ions decreases. Equation (2) is a limiting form of a more general equation from which terms of higher order have been omitted. At the same time, it is based on the assumption that the ions may be treated as dimensionless point charges. Very recently, Fuoss and Onsager (30) have extended the Onsager theory to electrolyte solutions in which the ions have finite size and taking into account various terms of higher order. The equation to which this new theory leads contains only two adjustable constants which may be evaluated from conductance data and both of which have physical meaning. They are Aa, the limiting conductance, and a, the sum of the radii of the ions. I t is obvious that the constant An permits of but little adjustment and that the value of a must he consistent with known atomic and molecular dimensions. The theory accounts for the conductance of ordinary salts, such as ICCl, in aqueous solution up to a concentration of about 0.01 N. Thus, if we know AO and a, we are able t o predetermine the conductance of free ions as a function of concentration. This hecomes important when we are dealing with solutions in which ion association occurs. Ion Association. The association of ions is well illustrated by the measurements of Fuoss and Kraus
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VOLUME 35, NO. 7, JULY, 1958
(4) with solutions of i-Am,NNOa in dioxane-water mixtures. As the dielectric constant of the solvent mixture decreases with increasing dioxane content, there is a large and continuous decrease in the conductance at any one concentration. This decrease is due, mainly, to increasing ion association with decreasing dielectric constant. The dielectric constant8 of water and dioxane are, respectively, 78.6 and 2.20. At a concentration of 3 X N, the conductance of i-AmliTNOa in water at 25' is 89; in dioxane, it is 2.7 X 10". At this concentration, this electrolyte in dioxane is dissociated into its ions to the extent of three parts in 10 million. I n water, a t the same concentration, its ions are associated to ion pairs to the extent of six 'parts in one hundred thousand (8). It would appear that the dielectric constant is a controlling factor in the association process of ions. One result of interest in these early measurements of Fuoss and Kraus is the fact that, when values of log A are plotted against values of log C, the plot is very nearly linear for dilute solutions in mixtures of lower dielectric constant and the slope of the plots is equal to -I/*. In other words, the conductance values conform to the Ostwald dilution law. The constant of the ionion pair equilibrium may be evaluated fairly closely from conductance values. At low concentrations in solvents of very low dielectric constant, where the concentration of ions is extremely low, the ion atmosphere effect becomes negligible and the equivalent conductance serves as a direct measure of the degree of dissociation of the electrolyte. The value of Aa may always be approximated fairly closely by means of Walden's rule. When we come to solvents of higher dielectric constant, the conductance of the free ions changes with concentration due to the ion atmosphere effect This effect appears to he the greater the higher the concentration of ions and, therefore, the greater the degree of dissociation of the electrolyte. The dissociation constants as presently determined for electrolytes in solvents of intermediate dielectric constant are uncertain to an unknown extent. Some of these constants have been determined by the method of Fuoss and Kraus (5). I n this method the assumption is made that the conductance of the free ions conforms to the simple Onsager equation (2) ahove. In other cases, the method of Fuoss and Shedlovsky (6) has been employed. According to this method it is assumed that the conductance of free ions deviates positively and nearly linearly from equation (2) and the deviation is much the same for all salts of the same type. We have reason for believing that the deviations from equation (2) may differ markedly for different salts and that they may he greater than is implicitly assumed in the Fuoss-Shedlovsky method. If ion association occurs, the conductance of an electrolyte is given by the equation (8): Here, A d is the deviation of the conductance of the free ions from equation (2) and A.A is the conductance decrease due to ion association. The experimentally observed deviation from equation (2) is:
If A,A is known, A,A becomes known and the degree of
association of the electrolyte followsfrom the equation:
Here r is the degree of dissociation of the electrolyte. If 7 is known, the value of the dissociation constant is given by the equation:
where f is the activity coefficient of the ions. Assuming that the conductance of the free ions conforms to the conductance equation of Fuoss and Onsager (SO), Fuoss (91) has developed the theory underlying the formation of ion pairs and has devised graphical methods whereby the values of Ao, a, the sum of the ion radii, and K,, the association constant, may be evaluated. Using these methods, Fuoss and Kraus (52) have analyzed the conductance data of Martel (7) for solutions of several electrolytes in dioxane-wat,er mixtures.
I n Table 1 are given values of D and K, for NaBrO, in dioxane-water mixtures. Association Constants of NaBrOI i n Dioxane-Water Mixtures
%
%
Diozane
D
K.
Diozane
D
K,
0 10 20 30
78.48 70.33 61.86 53.28
0.50 0.68 0.90 1.33
35 40 50 55
48.91 44.54 35.85 31.53
2.10 2.73 6.87 11.8
As may be seen from the table, the association constant of NaBrOa in water is very small. At a concentration of 0.01 N, the degree of association is of the order of 0.4%. I t is apparent that to determine the association constant of electrolytes by means of conductance measurements, the data must he of high precision. The association constant increases markedly with decreasing dielectric constant. For a mixture of D = 31.5, the value of K. is more than 20 times that in water. The association constant may be expressed as a function of D by means of a simple exponential equation. The logarithm of K , is a linear function of the reciprocal of the dielectric constant, 1/D. In Figure 1 is shown a plot of log K. versus 100/D. It will be noted that the experimental K, values approximate a straight line very closely. The K. values of other electrolytes
that have been examined conform to the same t,ype of plot as does NaBrOa. If AQ, a and K , are known, the conductance of the electrolyte may be calculated for any concentration. For NaBrOa in dioxane-water mixtures of dielectric constant 48.91, the values of Ao, a, and K,, are, respectively, 61.785, 3.96 X and 2.10. I n Figure 2, are shovn values of A d , the observed deviation of Afrom equation (2), plotted against the concentration of the electrolyte. The continuous curve represents calculated values of AQA;the circles represent experimental values. As may be seen from the plot, the conductance values are reproduced within the limit of experimental error. The average value of the parameter a for XaBrOa was found to be 4.02 + 0.07 X over the range of dielectric constant studied. For i-AmpKNOa and Bu4NI, the a values determined were, respectively, 7.7 and 8.0 X lo+. The K. values for these electrolytes are larger than for NaBrOa. Azzarri and Kraus (8) have calculated association constants for a considerable number of salts in water. The values of K. which they obtained are from 30Yo to 70% larger than those of Fuoss and Kraus, yet, with these K. values, measured conductances are reproduced within the limit of experimental error. The reason for this seeming inconsistency is simple. Azzarri and Kraus assumed that the deviation of the conductance of the free ions from equation (2) is a linear function of concentration. According to the equation of Fuoss and Onsager, which Fuoss and Kraus employ, this deviation should include a C log C term. This corresponds t o a negative deviation from Onsager's equation for concentrations below 1 normal. In the method of Azzarri and Kraus, this term is included in the A.A term. A plot of C log C versus C closely parallels one of (1 - 7 ) versus C. Due to the presence of the C log C term in the deviation, as assumed by Azzarri and Kraus, their values for K. are too large. However, the sequence of K. values for different salts is the same as in the correct method of analysis by Fuoss and Kraus. From the sequence of the K. values, as found by Azzarri and Kraus, as well as by Fuoss and Kraus, it follows that the association constant K. is larger for salts of larger ions than for salts of smaller ions. So, for example, K., as we have seen, is larger for BulNI than for NaBrOa. So, also, NaBr03 is associated in water while NaCl is unassociated. In a variety of non-aqueous solvents, from benzene to nitrobenzene, association constants are the larger the smaller the ions, in conformity with Bjerrum's theory (9). In water and in dioxane-water mixtures of dielectric constant >31.5, association constants are
The ourve gives the calculated values; points.
the &&a
are erperitnental
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smaller as the lattice ions are smaller. It remains to account for these facts. The interaction between a pair of ions depends on the charge, size, structure, polarizability and, in some instances, the dipole moment of the ions. I t also depends on the interaction of the ions with the solvent molecules which, in turn, depends on the size, structure, dipole moment, and polarizahility of the solvent molecules. The interaction of the ions with each other is, therefore, dependent on their interaction with the solvent molecules. These two interactions are not independent, they are competitive; as the interaction of the ions with the solvent molecule is greater, that hetween the ions is weaker. The effect of the interaction of ions with solvent molecules on the value of K. is well illustrated by solutions of Me4NPi in different solvents. On the basis of Mercier's data (35),Fuoss and Kraus have shown (32) that in solutions of this electrolyte in dioxane-water mixtures, the ions are unassociated down to a dielectric constant of 19.07. In acetone (17b) (D = 20.3) the association constant calculated on the basis of the Fuoss-Onsager equation is approximately 75. On the basis of equation (2) the value is 89. In the free picrate ion, the charge is distributed over the phenolic oxygen atom and the three nitro groups. In water, the distributed charge interacts with the water dipoles and the charge distribution is little affected by the Me4N+ion. Thus, the interaction between the ions is not sufficiently strong to stabilize the ion pairs. In acetone, the solvent molecules are larger and their dipole moment is smaller than that of water. The interaction of the solvent molecules with the charge on the picrate ion is correspondingly weaker. On the other hand, the interaction of the charge on the MenN+ ion with the charge on the picrate ion is large and, due to this interaction, the charge on the picrate ion is displaced in the direction of the counter ions and ion association occurs. I t is unfortunate that we lack data for other ions of the picrate type which might he expected to exhibit similar behavior. The introduction of a dipole into one of the ions of an ion pair leads to increased association. Thus the association constants of ethyl-, hydroxyethyl-, and methoxyrnethyl-, trimethylammonium picrates in ethylene chloride (10) are, respectively, 2.0, 15, and 3.9 X lo4. I t will he noted that the last two of the ahove named ions are isomeric; the hydroxy compound doubtless has the larger dipole moment and it has much the larger association constant. As the size of the central atom of tetraalkylammonium ions is increased, the dissociation constant decreases slightly. Thus, the constants of the picrates (11) of Bu4N+, BupP+. and Bu4As+ are, respectively, 2.26,1.60, and 1.42 X If the positive ion contains an active hydrogen atom, the dissociation constant of the ion pair will be reduced TABLE 2 Dissociation Constants of Partially Substituted Alkylammonium Picrates i n Nitrobenzene
Ion
VOLUME 35, NO.
K X
lo4
1, JULY, 1958
I n
K
x lo4
further due to hydrogen bonding. Thus, the dissociation constant of i-Am4NPi in benzene is 2.18 X 10-18; that of Am3NHPi is 4 X 10-21. I n Table 2 are shown K values for partially substituted ammonium picrates in nitrobenzene (12). It will be noted that BuaNPi has a large dissociation constant, approximately 0.2. On replacing one hutyl group by a hydrogen atom, K falls to 1.90 X On further substitution of butyl groups by hydrogen, only a small further decrease occurs in the value of K, to only 1.46 X 10W4for NH4Pi. If the hydrogen atom is connected with nitrogen through an oxygen atom, as in the case of Me3NOHPi, the dissociation constant falls to the low value of 0.17 X lo-? Triple Ions. I t is a well established fact that, in solvents of dielectric constant less than about 12, the conductances at lower concentrations decrease with increasing concentration roughly in accordance with Ostwald's dilution law. At higher concentrations, the rate of decrease falls off and the conductance, A, passes through a minimum value. Thereafter, A increases with increasing concentration. With decreasing D, the minimum shifts toward lower concentrations. This phenomenon is well illustrated by the results of Fuoss and Kraus (46) with solutions of i-Am,NNOa in dioxane-water mixtures. For D = 12, A is approaching a minimum a little above 0.1 N; for D = 9.0, the minimum lies at 0.07 N. With decreasing D, the concentration at the minimum shifts regularly to reach a value of 2.5 X N in pure dioxane. The occurrence of the conductance minimum may he accounted for on the assumption that the simple ions interact with the ion pairs (4b) to form the triple ions, - and - -. At low concentrations, triple ions will he present in only negligible amounts but they will he found in increasing proportion as concentration increases. Since the formation of triple ions will not affect the concentration of simple ions appreciably, the conductance of the electrolyte will he greater than it would be if triple ions were not formed. Ultimately, the conductance due to the formation of triple ions just offsets the conductance decrease due to the association of simple ions and a minimum appears. At higher concentrations, the conductance increases with increasing concentration. If one assumes that the equilibrium constants for the two triple ions have the same value and one approximates the Aa values for the two ions, the equilibrium constant may be determined. It has been found that on this basis the conductance may he accounted for reasonably satisfactorily from low concentration through the minimum (IS). However, a t concentrations ahove the minimum, the conductance is greater than that calculated on the basis of triple ions only.
+ +
+
TERRA INCOGNITA: CONCENTRATED SOLUTIONS
Our knowledge of electrolytes today is much as was our knowledge of Africa prior t o the explorations of Livingston and Stanley; it is peripheral. We know something of dilute solutions in water up to, perhaps, 0.1 normal; in benzene, up to 1 X N, and we know a little something about fused salts. But we know very little about the vast area that lies between dilute solutions, on the one hand, and fused salts on the other. Some of the things we need to know are the following:
(1) The fraction of the electrolytes in solution that exists in the form of ions, the "ion fraction." ( 2 ) Nature of the ions and their interactions with one another. (3) Nature of the interaction of ions with solvent molecules. (4) The effect of ion-solvent interaction on ion association. (5) Effect of ions on the state of the solvent.
The Ion Fraction of Electrolytes
Dilute Solutions. About the only means we have for determining the fraction of an electrolyte that exists as free ions is to measure its conductance. In principle, if we know how the conductance of the free ions varies as a function of their concentration, the concentration of such ions in the solution may be found and the ion fraction becomes known. Unfortunately, the relation between conductance and concentration is not known except for very dilute solutions where the generalized equation of Fuoss and Onsager (30)is known to hold. If the association constant of the electrolyte is small, K , < 1000, and the conductance data have adequate precision, the value of K . and, therefore, the ion fraction, may he evaluated by the method of Fuoss (51). I n solvents of intermediate dielectric constant, if K. > 1000, the association constant of the electrolyte may be approximated fairly closely by the method of Fuoss and Shedlovsky (6) and the ion fraction becomes known. As of now, the only electrolyte solutions for which we can determine the ion fraction directly from conductance measurements are solutions in solvents of very low dielectric constant, such as benzene. For a strong electrolyte, such as Am4NSCN, the ion fraction, at 1 X N, is 1 X lo-=; the limiting conductance, Ao, is approximately 100 as determined on the basis of Walden's rule. The concentration of free ions is, therefore, 1 X lo-". At this low ion concentration, the ion atmosphere effect becomes negligible and the conductance serves as a direct measure of the degree of dissociation of the electrolyte. With one known exception, the conductance of electrolytes in water decreases continuously from dilute solutions to the limit of solubility. The exception is KI a t 0" ($9). For these KI solutions, the conductance passes through a minimum followed by a maximum. This peculiar behavior is due to the changing viscosity of the solution. For this salt, the viscosity decreases. passes through a minimum a t 3 normal and thereafter increases. The maximum and minimum of the conductance values are clearly due to the changing viscosity. A corrected conductance plot, in which observed A values are reduced in proportion to the viscosity decrease, is of a normal type. In solvents of low dielectric constant, where a minimum appears a t low concentrations, the conductance, beyond the minimum, increases continuously up to approximately 1 N, where a maximum appears. This maximum is due to the increasing viscosity of the solution. The viscosity of these solutions at low concentrations differs little from that of the solvent. There can be no doubt that the observed conductance increase is due to an increase in the ion fraction even though we may not know just what the nature of the ions may be. It needs to be borne in mind that the conductance increase may he very large. For i-Arn,NHPi in benzene between the
N and the maximum at. 1.06 N, minimum at 1 X the conductance increases 1.74 X lo5-fold. At the minimum, the conductance is 2.7 X lo-'; at the maximum it is 0.047. Assuming Ao to be approximately 100, the ion fraction increases from 2.7 X to 4.7 x Concentrated Solutions. When we come to more concentrated solutions, where the viscosity is often many times greater than that of the solvent, we can no longer estimate the ion fraction hy means of the experimental conductance values. The best we can do here is to assume the approximate validity of Walden's rnle. According to this rule, the condnctance of an electrolyte is inversely proportional to the riscoritg, so that their product, Aq, is a constant. This holds reasonably well for limiting conductances in different solvents. The rule probably holds equally well for viscosity changes due t o changing electrolyte concentration. Thus, by means of the change of Aq values, n.e can follow changes in the value of the ion fraction. In the limit, the most concentrated solution that we can obtain for any electrolyte is the fused salt. We can measure its equivalent condnctance and its viscosity and thus obtain a value for the Walden product, ~ ~ h i cweh shall designate as If, now, we add a solvent of low dielectric constant to a fused salt and measure the conductance and viscosity of the solution, we find that the conductance increases while t,he viscosity decreases. The product A7 also decreases. This decrease is due to an ion association and the degree of association, 1 - 7 , is approximately given by the equation:
where y is the ion fraction. We are postulating here that the fused salt is completely dissociated into its ions. At the present time, me have data for only one electrolyte whose conductance and viscosity have been measured over the complete concentration range from dilute solution to fused salt. These data relate to solutions of Bu&NPiin butanol at 91'. The measnrements were carried out by Dr. Ralph P. S e ~ n r d(14), of the Pennsylvania State University. The limiting conductance, Ao, of the salt is 71.5 and that of the fused salt, 0.778. The viscosity of the solvent is 6.09 X and that of the fused salt is 581 X lo-? Thus, the conductance-viscosity product,, Aoq, for the limiting dilute solution is 0.435 and for the fused salt = 0.452. The conductance-viscosity product for the fused salt is practically the same as that for the solution at infinite dilution. The agreement betv-een these two values is, perhaps, better than one might have expected. In any case, the agreement supplies evidence to support the view that the fused salt is completely dissociated into its ions. The dissociation constant of the electrolyte is 3.2 X lo-'. The salt is 50% dissociated at approxiN. The conductance decreases continmately 1 X uouslv with increasine concentration to that of the fused salt without the appearance of a minimum. This indicates that triple ions are not formed. The conductance-viscosity product falls off sharply in dilute solution primarily due to ion association. At a concentration of 0.083 N, the value of Aq passes through a pronounced minimum after which it increases con-
-
JOURNAL OF CHEMICAL EDUCATION
tinuously t o that of the fused salt. At the minimum, the value of A?/(A& = 0.18. At this concentration the electrolyte is associated to the extent of about 80%. The striking fact is that the ion-ion pair equilibrium, which conforms to the law of mass action in dilute solutions, in that the degree of association increases with concentration, goes into reverse at a concentration of 0.083 N a n d the degree of association decreases thereafter until the completely dissociated fused salt is reached. Similar results have been found for solutions of salts in bromine (15) although data are lacking for dilute solutions. Since the dielectric constant of bromine is only 3.09, salts are highly associated even in fairly dilute solutions. The conductance viscosity product increased with concentration for the more concentrated solutions and the fused salts gave about the same value as that obtained for other fused salts which range between 0.5 and 2.0. This phenomenon of the reversal of the ion-ion pair equilibrium is a very general one although we have but few cases where measurements extend over the whole concentration range from dilute solutions to fused salts, and we do not now know at what concentration the reversal occurs. It may, however, he confidently stated that zf the ions of any typical electrolyte are associated in any solvent at low concentration, the degree of association will reach a m i m u m ualw at some higher concentration and thereafter will decrease continuously until the fused salt i s reached. Nature of the Ions
Our present discussion will be limited to typical electrolytes, that is, electrolytes which exhibit an ionic structure in the crystalline state and which exist only as ions in the fused state as well as in highly dilute solutions (ionopheres) (36). This excludes such substances as the acids which form ions in solution only if a suitable reaction occurs with the solvent molecules (ionoaens) . - . (36). In solvents of higher dielectric constant and in dilute solution in solvents of low dielectric constant, we have to deal only with simple ions. Aside from the number and kind of atoms in these ions and the number and sign of the charges that they carry, our knowledge of simple ions is very limited. Because of the charges that the ions carry, they interact with the solvent molecules; particularly so, if these molecules have a large dipole moment. Soluation of Ions. We can gain some knowledge of ion solvation by studying solutions in suitable nonaqueous solvents. For example, there can be little doubt that sodium, lithium, and silver ions are solvated in pyridine (16). If ammonia is added to solutions of these ions, their conductance increases. The addition of NH, at a concentration of 0.23 N to a solution of LiPi in pyridine increases the limiting conductance of the Li+ ion 39%. At the same concentration of NH,, the conductance of the Na+ ion in NaPi and NaI is increased 45%. At a concentration of 0.37 N of NH3, the conductance of an Ag+ ion in AgN03 is increased 19%. Evidently, the smaller ammonia molecules displace the larger and less basic pyridine molecules with a consequent increase in the conductance of the ions. Similar effects are not found with the quaternary ammonium ions or the picrate ion. Studies along this line VOLUME 35, NO. 7, JULY, 1958
with other solvents might throw further light on the solvation of ions. The ions, as they exist in ion pairs, are not necessarily identical with the free ions in solution. Solvent molecules attached to the free ions may no longer retain their position under the action of the intense fields when the ions are in contact. An intercomparison of the dissociation constants of ion pairs in different solvents may throw some light on the problem. In Table 3 are shown values for the dissociation constants of picrates of Li+, Ka+, K+ and MepS+ions in three different solvents: pyridine, acetone, and nitrobenzene. The dielectric constants of these solvents are, respectively, 12.01, 20.47, and 34.8. All three of the solvents are of the aprotic type and two of them have basic properties. Values of K for Me4SPi are given for purposes of comparison. TABLE 3 Dissociation Constants of Pimates in Different Solvents
Me,NPi LiPi NaPi KPi
6.7 0.83 0.43 1.0
112. 10.3 13.5 34.3
400. 0.0006 0.28 6.86
I t will he noted that the K values for the alkali metal salts in acetone and pyridine are markedly lower than those for MepNPi. It is of interest also that, in pyridine, K is greater for LiPi than it is for SaPi. In nitrobenzene, the K values for the alkali metal picrates are strikingly lower than that of MeJPi. The value of K of 400 X 10W4is doubtless somewhat larger than the true value due to the assumption that the conductance of the free ion conforms to equation (2). However, the true value cannot differ greatly from the value given in the table. For KPi, K is many times lower than that of Meaxpi, in contrast to the values in acetone. The K value for KPi in nitrobenzene ( D = 34.8) is practically the same as that of Me4NPiin pyridine (D = 12.01). For NaPi, K in nitrohenzene is 40% less than that in pyridine, while K for LiPi in pyridine is 1400 times greater than that in nitrobenzene. It appears that in acetone the ions in the ion pairs do not differ greatly from the free ions. The low values of K for the alkali metal picrates in pyridine indicate that the ions in the ion pairs are smaller than the free ions; the solvent molecules are not completely retained in the ion pairs. The same is true for the same ions in nitrobenzene, particularly for NaPi; no solvent molecules can be present in the ion pairs. In the case of LiPi, one might suspect that not all the lithium is present in the ionic form in the ion pairs. I t is of interest to note that the conductance of the K + ions (17.8) in nitrobenzene is almost the same as that of the Me&+ ion (17.1). Earlier in this paper, it was pointed out that Me4NPi is unassociated in water and in dioxane-water mixtures down to a dielectric constant of 19.03. I t was suggested that the absence of ion association in the mixtures of lower dielectric constant might be due to the fact that the charge in the free picrate ion is distributed over the entire ion and that in the presence of water molecules, the charge distribution is not greatly changed due to the
Figure 3.
Type 1 ,
Auocietion Numb...
n 1.3,. Different Type. of Electro1ytea in Ben=.n.
i-AmsNHPi: type 8 , i-AmtNSCN;
lype 3, CAm4NPi.
presence of a Me4N+ ion. In organic solvents with larger molecules and smaller dipole moments, the charge on the picrate ion is localized, probably on the phenolic oxygen atom, due to the presence of the counter ion. This accounts, in part, for the otherwise unusually low K values of the picrates in pyridine and nitrobenzene. Association of Ions in Benzene. As the dielectric constant of the solvent medium decreases, the in tens it,^ of the fields surrounding the ions increases and new types of interaction products appear. I n solvents of high dielectric constant, only ion pairs are formed. I n solvents of somewhat lower dielectric constant, triple ions are formed. I n solvents of low dielectric constant, polyionic structures of higher order appear a t higher concentrations; some of these are neutral and others carry charges. Benzene is a solvent of low dielectric constant (D = 2.28) in which electrolyte solutions have been studied extensively. Here, we have conductance data (18) from 1 X N to above 1 N, cryoscopic data ($3') from 1 X loW3N to 0.75 molal and molecular polarization ($4) values down to concentrations approaching 1 X N. The properties of these solutions are very sensitive to the size and structure of the ions as was to be expected. The properties of electrolyte solutions in benzene are primarily determined by the size and structure of the ions and the dipole moment of the ion pairs. On the basis of their properties, the solutions fall into three well-defined types. I n Table 4 are given values of the dissociation constant, K; the dipole moment, p ; and the distance, d, between the centers of charge of theions in the ion pairs, for i-Am3NHPi, i-Am,NSCN, and iAm4NPi. These salts are, respectively, of types 1, 2, and 3. Type 1 electrolytes consist of two large ions which are hydrogen bonded; both K and the dipole moment are relatively small. Type 2 electrolytes consist of a large positive and a smaller negative ion; both K and p are TABLE 4 Constants of Electrolvtes in Benzene (lb)
relatively large. Type 3 electrolytes comprise two large ions; both K and fi are somewhat larger than for type 2. In Figure 3 are shown plots of the association number, n, (formula weights per mole) for each of the three salts of Table 4. On examining this figure, it will be noted that d-Am,NHPi, of type 1, is only slightly associated to quadrupoles (6%) at the lowest concentration (1 X 10W2 N). At the highest concentration, n = 2.75, association has not proceeded very far beyond the quadrupole state. The quaternary ammonium picrate, i-AmrNPi, is of type 3, and more highly associated than is the tertiary salt. At the highest concentration (3.8 X N), 40% is associated to quadrupoles. As may be seen from Figure 3, i-AmlNSCN, of type 2, is highly associated. Molecular polarization measurements indicate that association t o quadrupoles is appreciable a t 4 4 N , At 1 X10W3N, the association number has already reached a value of about 3.5. Association increases with concentration until n reaches a maximum of 26 at 0.14 N. Thereafter, n decreases rapidly t o a value of 11.5 a t 0.49 N. The behavior of this electrolyte is typical; other electrolytes of the same type exhibit the same behavior. Conductances in Benzene. The conductances of electrolytes in benzene also fall into three typical patterns, as shown in Figure 4, where values of log A are plotted against values of log C for the three salts of Table 4. Type 1 is characterized by a relatively high concentration at which the minimum appears, and a very large increase in conductance.between the conductance minimum and maximum. Thus, for i-Am&HPi, the conductance at the minimum (1 X loW3N) is 2.7 X lo-'; the maximum lies at 1.08 N and the conductance is
Figvrs 4.
Condustans. Plots for Electrolytes i n Benreno
0.048. Between the two concentrations the conductance increases 1.74 X lo5-fold. For type 2, the minimum lies at much lower concentrations than for type 1 and the conductance increase between minimum and maximum is markedly smaller. We do not have data for i-Am,NSCK through the maximum but we have such data for BuaNSCK(18). For this electrolyte, the minimum lies in the neighborhood of 1X N and the conductance is 0.8 X lo-" the maximum lies at 1.35 N and the conductance is 1.16. The conductance increase is 1.4 X lo4-fold, about onetenth that of the tertiary picrate. Characteristic of type 2 is the manner in which the conductance increases with concentration; it takes JOURNAL OF CHEMICAL EDUCATION
place in a series of steps. The tetraisoamylammonium halides all conform to type 2. To illustrate the effect of the different halide ions on the observed phenomenon, values of the concentration of the minimum are given in Table 5, along with the conductances at the minimum and at concentrations of 1 X N and 1 X N. TABLE 5 ~
Comparison of Conductances of Tetraisoamylammonium Halides in Benzene (13) X lo'----Cmi, C= C = Halide X 105 C 1 x 10-8 1 X lo-*
*
Chloride Fluoride
2.0 2.5
0.56
The dissociation constants of the halide salts of i-Am4N+decrease as we go from iodide to fluoride and the minimum shifts toward higher concentration. The conductances at the minimum decrease in the same order. Above the minimum, the conductance increases the more sharply the higher the concentration of the minimum. At the minimum, the conductances differ markedly, that of the bromide is three times that of the fluoride. For salts of the smaller ions, the conductance, above the minimum, increases more sharply than for the larger ions. Between 1 X l0W3 N and 1 X N, the i-Am,N+ halides have practically the same conductance. At concentrations above the minimum, the dissociation constant of the electrolyte is no longer a significant factor in the ionization process. As illustrating the greater conductance increase of salts of smaller ions beyond the minimum, it may be noted that between the minimum and C = 0.001 N, the conductance of the bromide, chloride, and fluoride increases, respectively, 3.8, 6.0, and 10-fold. Between C = 0.001 and C = 0.01, the conductance increase for these salts is practically the same, 2.8-fold. A lower limit is readily found for the ion fraction of salts in benzene by dividing the observed conductance by the limiting conductance, AQ. For benzene, AQ is roughly 100. At the minimum, the ion fraction of salts of type 1 is of the order of 3 X and of type 2, 1 X At the conductance maximum, the ion fraction for BurNSCN, on this basis, is 1.16%. However, at the conductance maximum (1.35 N), the viscosity of the solution is about 20 times that of benzene. The ion fraction must lie in the neighborhood of 20y0. At high concentrations, a large fraction of the electrolyte exists as ions in benzene. While it is possible t o approximate the fraction of electrolytes that exists in the form of ions in benzene solution, except a t very low concentrations, we do not know what the ions are. At concentrations well below the conductance minimum, the electrolyte exists as simple ions and ion pairs. In the neighborhood of the minimum, triple ions are also present. Quadrupoles may also be present but only in negligible amount. In the case of Am3NHPi, simple ions must be present in large proportion along with triple ions up to 0.01 N, where quadrupoles are present to the extent of 60y0. At high concentrations, ions of higher complexity may appear in considerable proportion since hexapoles are present in considerable amount. I t seems probable that VOLUME 35, NO. 7, lULY, 1958
simple ions are present in measurable proportion up to 1 N, the conductance maximum. If this is true, the equilibrium between the ions and ion pairs must go into reverse in the neighborhood of the minimum. With type 2 electrolytes, such as Am,NSCN, there is a sharp conductance increase a t the minimum, indicating that a new process of ion formation has set in which differsfrom that leading to triple ions. At 1 X low3N, the electrolyte contains on the average 3.5 formula weights of electrolyte per mole; there can be very few triple ions present. If we are to account for the large conductance increases at higher concentrations on the basis of simple ions, any ion pairs that might be present would have to be very highly dissociated. It is possible that the conductance increase above the minimum is due to the breaking up of the complex polyionic structures into charged fragments. Such a process might serve to account for the stepwise increase of the conductance of type 2 electrolytes. I t is to be noted that, while the dissociation of the electrolyte into ions increases continuously above the minimum, the association of the ion pairs increases up to a concentration of about 0.2 molal. I t would appear that, as the concentration of ions increases, the forces interacting betweeu the ions weakens. This leads, first, to an increase in dissociation of the electrolyte into ions a t concentrations above the minimum and, second, t o dissociation of the polyionic aggregates into simpler structures, at concentrations above about 0.2 molal. Ultimately, this leads to the completely dissociated fused salt which exists only as a collection of free ions. Type 3 electrolytes have only limited solubility and we have data for only one example of this type, i-Am4NPi, up to a concentration of 1.32 X 10-= N. At concentrations below the minimum, the conductance of AmNPi closely parallels that of i-Am4NSCN. However, the minimum for the thiocyanate lies a t 1.4 X N, while that of the picrate lies at 5 X N. As may be seen from Figure 4, the conductance of the thiocyanate rises sharply a t the minimum and thereafter increases stepwise. The conductance plot of the picrate is everywhere convex toward the C-axis. From the minimum to 2 X l0W3 N, the conductance of the picrate is much lower than that of the thiocyanate; above 2 X l0W3 N, the conductance of the picrate is much the higher. I t is apparent that the process of dissociation of the electrolyte to ions, as well as their association to complex polyionic aggregates, is highly sensitive to the size and structure of the ions. Interaction of Ions with Solvent Molecules
Since ions in solution are surrounded by strong electrical fields, we should expect that they would interact with the electrical dipoles of the solvent molecules. We should also expect the interaction to be the greater the more intense the field around the ions, the smaller the solvent molecules and the larger the dipole moment of the solvent molecules. Such interactions manifest themselves in various ways. They affect the motion of the ions through the solvent medium, they may lead t o the formation of definite solvates, and they may affect the interaction of the ions with one another. Ion Conductance and Solvation. I n the limit of infinitely dilute solutions, the conductance of ions is de-
termined by the nature of the ions, such as their size, and by the properties of the solvent, such as its viscosity. The state of the solvent, however, is unaffected by the ions as it may be in more concentrated solutions. We have values for the limiting conductance of a considerable number of different ions in water and some half dozen non-aqueous solvents. In water, the ion conductances have a fairly high precision but in other solvents the precision is usually much lower. So long as we are comparing the conductance of ions of the same sign, this lack of precision will not mislead us seriously in any conclusions that we may draw. We shall first consider monatomic ions, that is, ions consisting of a single atom carrying one unit charge. About the only ions of this type for which we have data are the halide ions, C1-, Br-, and I- and the alkali metal ions, Li+, Na+, and K+. In Figure 5 are shown the percentage differences between the conductances of the C1- and I- ions with re-
are almost identical while in acetone, Br- is considerably greater than Cl-.' What is particularly striking is the large difference for the halide ions in ethylene chloride; the conductance of the I- ion is 12% smaller than that of the Br- ion and that of the C1- ion is 16% greater. It appears that the iuteractions of ions with solvent molecules and, therefore, their conductances are greatly dependent on the nature of the solvent molecules. The only univalent positive ions for which we have data in a variety of solvents are the alkali metal ions KC, Na+, and Li+. However, our knowledge of these ions is much more limited than is that of the halide ions because of their limited solubility, particularly in organic solvents. In Table 6 are shown values of the ion conductances of K+, Na+, and Li+ ions in water, ammonia, pyridine, and nitrobenzene. The conductance value for Li+ is lacking in nitrobenzene because its picrate is so weak an electrolyte that its Ao value cannot be determined. For purposes of comparison, ion conductance values are also given for Me4N+, EtrN+, Bu4N+,and H4N+ions. TABLE 6 Conductance of Positive Ions in Different Solvents Ammonia Wale7
spect to that of the Br- ion. Let us first consider the conductance values in H20, NH,, and HCN (20). I n these solvents the differences are very small, amounting a t most to about 3%. The order of the conductance values differs in the three solvents. I n HzO, the order is Br- > I- > C1-. I n NHa the order is C1- > Br- > I-, and in HCN, it is I- > Br- > Cl-. It is obvious that the conductance of these ions is not determined by the lattice size of the atoms that carry the negative charge; the cause for their having the same conductance must he sought elsewhere. This must lie in the interaction of the ions with the solvent molecules. The intensity of the fields surroundimg the ions must increase greatly as we go from the relatively large I- ion to the much smaller Cl- ion. As the field intensity increases, the interaction with the solvent molecules increases and the conductance decreases with respect to that of larger ions. In solvents having large molecules, the order of conductance values is, in all cases hut one, Cl- > Br- > I-. Thus, the conductance of the Br- ion is markedly greater than that of the I-ion in pyridine, acetone, nitrobenzene, and ethylene chloride, while it is smaller than that of the C1- ion in nitrobenzene and ethylene chloride. In pyridine, Br- and C1- ion conductances
(dl
Pyidine (16)
Nitrobenzene (ld)
Inspection of Table 6 will show that the conductances of these alkali metal ions increase in the order K + > Na+ > Lif in all solvents. The differences are greatest in water and smallest in nitrobenzene. I n water, the differencesbetween the Kfion and the Na+ and Li+ions amount, respectively, to 32y0 and 46%. For the solvents, water, ammonia, pyridine, nitrohenzene, the diiferences between K+and Na+ions amount, respectively, to 32%, 20%, 18%, and 8%: I t seems probable that, with the exception of nitrobenzene, the Na+ and Li+ ions are solvated in all these solvents. In the case of pyridine, as was pointed out in an earlier section, we have independent evidence for solvation of the Na+ and Li+ ions. In water, the conductance of the K + and Na+ ions is much larger than that of the Me4N+ion, while that of the Li+ ion is intermediate between that of the Me4N+and EtPN+ions. In pyridine, the Li+ ion has nearly the same conductance as the BulN+ ion and onehalf that of the H4N+ion. In nitrobenzene, t,he conductance of the Na+ ion is 8yo less than that of the I Br- > I-. The conductance value for CI- ion as shown in Figure 5 is in error. The order of the conductances of the halide ions in acetone is the same as it is in the other three organic solvents and the differences between the three ions are very small.
JOURNAL OF CHEMICAL EDUCATION
little greater than that between the chloride and bromide ions (20.2 and 21.6). I t is reasonable to assume that the alkali metal ions are not solvated in nitrobensene in the same sense that they are in the other three solvents. Yet, the Na+ ion definitely has a lower conductance than the K+ ion. However, as in the case of the halide ions in water, the conductance is determined by the interaction of the ion with the solvent molecules rather than by the size of the ions. The H,N+ ion is of interest; in water, its conductance is almost the same as that of the K+ ion, in liquid ammonia, it is the same as that of the Na+ ion. I n pyridine, however, the conductance of the H4N+ ion is exceptionally high, being nearly 50% greater than that of the K + ion. This may indicate that the K + ion is solvated in pyridine. I n nitrobenzene, the conductance of the H4N+ion is only 3% greater than that of the K+ ion. It seems probable that the H4N+ ion may be solvated in ammonia but not in the other solvents. Although we have data for only a limited number of polyatomic negative ions in different solvents, we may draw some conclusions from those that we have. In Table 7 are shown conductance values for a number of negative ions in ethylene chloride and nitrobenzene. TABLE 7 Conductance of Negative Ions in Ethylene Chloride (19) and Nitrobenzene (12) Solvent
BF,
SCN-
NOs-
C1Q-
Cl-
C,&CIa CsHaNOz
42.7 22.1
42.4
40.1 22.6
39.2 20.9
39.1 22.2
..
It will be noted that, in ethylene chloride, the chloride ion has the lowest conductance of the five ions listed. Its conductance is 9% less than that of the BF4- ion and it is the same as that of the C104- ion. In nitrobenzene, the conductance of t,he C1- ion is the same as that of the BF4- ion and somewhat smaller than that of the NO8- ion. Obviously, the conductance of these negative ions is not. determined bv their size alone: some other factor must he involved: I t is to be looked for in the interaction of the ions with the solvent molecules. The smaller the ions, the greater is their interaction with the solvent molecules. Ion Conductanceand Ion Size. W i l e it is not possible to change the size of the negative ions in a systematic manner, this is readily accomplished in the case of positive ions by means of the quaternary ammonium ions. We have data for the conductance of quaternary ammonium ions from HIN+ to AmPN+in a variety of solvents, including water. I n studying the effect of ion size on conductance, it is advantageous to compare equivalent ion resistances (19) rather than conductances. I n comparing ion resistances in different solvents, it is necessary to take into account their different viscosities. Accordingly, we shall compare values of resistance-fluidity products, RY, or l/AVs. I n Figure 6, are shown values of R+f for ammonium ions from H4N+ to Am4N+ in water, pyridine and acetone (17b). Here, values of R+f are plotted as ordinates against the number of carbon atoms in the ions as abscissas. Let us first consider ion resistances in water. It will VOLUME 35, NO. 7, JULY, 1958
,
H ;
I
M.&
I
U,N+
I
W~N*
I
B",N+
I
B.~.N+ 20
NUMBER OF CARBON ATOMS
Figure 6.
Reciprocal AVOProducts for QuaternaryA m m o n i u m Ions in water. Acetone. and Pyridine
be noted that in water the resistances increase roughly as a linear function of the number of CHI groups in the ions, all the way from H,N+ to ArnpN+. The resistance change is greatest in going from Et4N+ to Pr4N+ and smallest in going from Bu4N+ t o Am,N+. I t would seem that the resistance which an ion experiences in drifting through the solution under the action of an impressed field is dependent on its cubical rather than its linear or quadratic dimensions. Perhaps it would be better to say that it is dependent on its volume. The resistance plots for pyridine and acetone are sirnilar to those for water for the larger ions, although the resistances are markedly smaller for these solvents than for water. On the other hand, the resistances for H4N+, Me&N+,and E 4 N +are much greater in organic solvents than in water. I n the former solvents, the reduced resistances, R+f, differ little for these ions, although they are somewhat larger in acetone than in pyridine. I t is of interest to note that in acetone the resistance of the H4N+ion is almost as great as for the Et4N+ion and greater than for the i\lenN+ion. The resistance plots for ethylene chloride and nitrobenzene are very similar t o those for pyridine and acetone. The reduced resistances, R+f, for the BUN+ ion have nearly the same value in the four organic solvents, showing that Walden's rule applies fairly well for this ion in such solvents. It is of interest to compare the conductances of negative ions with those of positive ions of about the same size and structure. I n Table 8 are shown ion conduetancesfor the C104- and the MePN+ions in a number of different non-aqueous solvents. TABLE 8 Conductance of C1O4- and M e s t in Different Solvents
CI0,-
MerN
+
A-/A+
Ethulae ehlkde ($2) 39.2 42.6 0.92
Pyridine (16)
47.6 43.0 1.11
Aeetne (171 115.3 97.8 1.18
Nztrobenzene
(la) 20.9 17.3 1.21
The two ions have the same symmetry and the MerN+ ion is the smaller on the basis of atomic dimensions. I n ethylene chloride, the conductance of the Me4N+ ion is 8y0 greater than that of the Clod- ion. In the other three solvents, the conductance of the
C10,- ion is from 10% t o 20% greater than that of the Me,N+ ion. This-goes t o show that the conductance of smaller ions in non-aqueous solutions is in large measure determined by the interact,ion of the ions with the solvent molecules rather than by their lattice size. Ion Conductance and Temperature. Except for the measurements of A. A. Noyes (83) and his associates, we have no data as to the conductance of ions at high temperatures. However, we know that if ion association does not occur, the conductance of electrolytes increases wit,h temperature, due to the decre~singviscosity of the solvent. If ion association occurs, the condnctance increases with temperature a t lower temperatures, where ion association is small, and passes through a maximum at a higher temperature as ion association increases due to the decreasing dielectric constant. The lower the concentration and the higher the dielectric constant of the solvent, the higher the temperature a t which this maximum appears. With 1-1 electrolytes in water, the maximum appears above 306°C.; with 2-2 electrolytes, it appears between 100" and 200". Already, Kohlrausch had pointed out that the temperature coefficient of ions of higher conductance is smaller than that of ions of lower conductance. I n other words, the transference numbers of ions approach each other with increasing temperature. On the basis of Noyes' data, Johnston (84) examined the relation between the conductance of ions and temperature in water up to 156'C. He found that the conductance could be expressed as afunction of fluidity by a simple exponential equation: AO =
kP
(8)
where f is the fluidity of the solvent and k and p are empirical constants. He found that, for ions of high conductance, p is less than unity but that for ions of very low conductance, p is equal t o unity. Thus he found p = 0.97 for the sodium ion and p = 1.008 for the acetate ion. For the potassium ion, p is equal to 0.89 and for the chloride ion to 0.88. The acetate ion h a s a low condnctance in water and its value off/Ao- is equal to 2.71 0.01 for eight different temperatures from 0' t o 156'. If we compare the conductance values of the different ions with those of the acetate ion, we find that the ratio Aaion/Aoacetate decreases with temperature and the decrease is the greater the higher the conductance of the ion. Thus, at On, the ratios for Na+, K+, and H+ to acetate ion a.re, respectively, 1.28, 1.99, and 11.8 (nearly twelve); a t 306", they are, respectively, 1.11, 1.18, and 1.82 (i.e., nearly equal). Since the conductance of the acetate ion varies directly as the fluidity of the solvent, the decrease in the ratios is not to be ascribed to a relative increase in the conductance of the acetate ion. We can only conclude that the mobility of the other ions is slowed down with respect to that of the acetate ion. Since its conductance is low, it seems probable that the acetate ion is hydrated. Seemingly, the degree of its hydration does not ohange greatly with temperature. Possibly thedegree of hydration of the other ions increases with temperature. Without doubt, the manner in which the conductance of the different ions changes with temperature is related to the great decrease of the dielectric
*
constant of the solvent with increasing t,emperature. We should expect the interaction of the ions with the water molecules to increase as the dielectric constant of water decreases and we should expect t,be effect of such interaction to be the great,er t,he smaller the ion. Ion-Solvent Interaction end Ion Association
The interaction between two ions of given charge a t short range depends on the size, structure, and polarizability of the ions, and, also, on the size, structure, dipole moment, and polarizability of the solvent molecules wit,h which the ions likewise interact. The situation here is analogous to that of two magnetic poles toward which an armahre is brought. As the armature approaches the poles, the force between the armature and t,he poles increases, while that between the two magnetic poles decreases. If the solvent molecules are small and have a large dipole moment, their interaction with small ions will be large and the interacting force between the ions will be correspondingly small. Thus, it may happen that the action between two large ions is greater than that acting between two small ions. In this way, one may account for the greater association of the halides of large quaternary ammonium ions in water as, also, the greater association of iodide8 with respect to that of bromides and chlorides. It needs to be emphasized that, while the interaction between ions at long range may be accounted for on the basis of a macroscopic dielectric constant, this cannot he so done when the ions are at short range. In this latter case, the specific constitutional factors of solvent molecules, as well as of ions, play a predominant role. The effectof small amounts of non-electrolytes on the conductance of fused salts throws some light on the role of the non-electrolytes in the a.ssociat.ion of ions. The viscosity of fused salts below 100°C. is high and, on adding a non-electrolyte of much lower viscosity, the conductance increases. To get some idea of the degree of association of the electrolyte, we arc forced to rely on the conductance-viscosity product. Cnfortunately, there are only a few instances in which we have data for systems in which non-electrclytes have been added to fused salts. I n brief, we may say that,, if the added non-electrolyte has a very high dielectric constant, ion association will not take place when it is added to the fused salt. If the added substance has an intermediate dielectric constant, ion association sets in with the init,ial addition and the association process continues until the minimum in the value of Aq is reached. On adding a substance of very low dielectric constant, ion association sets in and increases greatly with increasing concentration of the additive; the association process continues until the conductance minimum is reached a t a relatively low concentration. We have no data for the conductance and viscosity of fused salts on addition of water, but n e have such data for potassium formate in this solvent at 50.5' up t o a concentration of 15.5 N , where there are only 1.4 molecules of water per molecule of salt (85). The limiting value of the conductance-viscosity product in dilute solution, Anv, is 1.024. At a concentration of 3 N (16 H20/m. salt), AT = 0.742; at 7 N (5.5 H&), Aq passes through a. minimum value of 0.683; at 15.5 N (1.4 II2O),A? = 0.781. Above a concentration of 1.0 JOURNAL OF CHEMICAL EDUCATION
N , there is no great change in the value of Av; the increase above the minimum may well be due to an increase in the mobility of the formate ion as a result of decreasiug hydration. As was pointed out in an earlier section, when hutanol ( D = 10) is added to fused Bu;NPi a t 91°, the value of As falls off t,o about 20% that of the fused (14) salt at a concentration of 0.083 AT. So, also, when bromine ( D = 3.09) is added to a fused bromine complex of (CH,),NHBr at 25', the value of A7 falls off to a very small fraction of that of the fused salt (16) as the concentration of bromine increases. It seems that the association of a fused salt, at a given ratio of solvent to salt, is the greater the smaller the dielectric constant of the added non-electrolyte. But it has no meaning to speak of the dielectric constant of a solvent in a solution when the number of ions is comparable to that of solvent molecules. The governing factor in the association proceys is not the dielectric const.ant of the additive; rather! it is the dipole moment, polarizability, and size of the molecules of the non-electro1.yte. The interaction between the ions and the solvent molecules will be the greater the smaller the molecule^ and the greater their dipole moment. The greater the interaction of the ions with the solvent dipoles, the smaller will be the interaction of t,heions with each other. There is need for further investigation in t,his area of the electrolyte problem. Ions end the State of the Solvent: Negative Viscosity
meet
With the exception of water and glycerol, the viscosities of electrolyte solutions are greater than those of the pure solvents. I n general, the viscosities are the greater the larger the ions and they are great,er in nonaqueous solvents than in water. This may, in part, be due to ion association. Thus, the viscosity of a 1 N solution of potassium format,e in n-ater at 50.5" is 9% greater than tha.t of water and that of XI in !iquid ammonia at -33' is 40% greater than that of the solvent. The viscosity of a 1 N solution of i-Am&SCN in henzene at 25' is 9 times that of the solvent. Here, the high viscosity is in large measure due to the large polyionic aggregates that are formed by the salt in benzene. On the whole, the viscosities of salt solutions in water are relatively small. But what characterizes the viscosity of aqueous solutions is the fact that ~ h i l the e viscosities of some solutions are greater than that of water, of others they are smaller. These so-called negative viscosities are specific effects of the ions. Thus, the viscosity decrease is greater as me go frcm chloride to iodide and from lithium to potassium ions. In water at 25", at a concentration of 1 N , the viscosities of KC1 and KI are, respectively, 0.987 and 0.93. Under the same conditions, the viscosities of LiCI, NaCI, and KC1 are, respectively, 1.142, 1.097, and 0.987. The negative viscosity effects increase markedly with decreasing temperature and disappear a t about 50'. It is difficult to escape the conclusion that the lowering of the viscosity is due to a change in the state of the solvent resulting from the presence of the ions. While negative viscosity effects have been reported in glycerol, further data are not extensive. Indeed, data are not very extensive for aqueous solutions. We have conductance (96)and viscosity (27) data for VOLUME 35, NO. 7,
nnY,1958
LOG (CONCENTRATION) Figure 7. Fluidity and Conductance Plots of Ki in Water at O'C.
K I in water at 0" from 2 X 10-3 N to 5.66 N. A? illustrating the paucity of data in this field, it may be noted that the conductance data go back 50 years and the viscosity data 80 years. These data, while not of the highest precision, nevertheless afford a rather exceptional opportunity for determining the effect of viscosity on conductance. For the conductance in this case does not decreasecontinuously with increasing concentration; it passes through a flat minimum followed by a flat maximum. While the conductance of an electrolyte at higher concentrations cannot be predicted on a theoretical basis, observed conductance values are rather closely reproduced over a considerable concentration range by the equation of Storch (28) which may be written:
where n and D are empirical constants. For aqueous solutions, n has a value close to 1.5. Let us now correct the conductance in direct proportion to the viscosity change, writing A' = Av/m
where vo is the viscosity of water at 0 ° , 0.01797. Introducing this corrected value of A into equation (9), v e have (CA'). = C(Ao - A')DAOm-'
(10)
and, taking logarithms: n log (CA') = lag C(Ao
- A')
+ log DAon-I
(11)
If this equation holds and if the viscosity correction is valid, a plot of log C(& -A') versus log (CA') should be linear with a slope equal ton. The value of D may then be obtained by means of equation ( 9 ) . When such a plot is made for K I in water at 0 ° , it is found to be linear ($9). The value of Aa is found by extrapolation of the dilute solutions. The constants of equation (10) are thus found to be: D = 2.62, & = 81.12, andn = 1.51. Using these values for the constants, values of A' may
be calculated in accordance with equation (10). Curve A of Figure 7 (29) shows A' values as a function of log C. This curve represents the conductance of X I corrected for the fluidity change of the solution on the assumption that the mobility of the ions is proportional to the fluidity of the solution. If values of A' are multiplied by the value of the fluidity (curve C) a t diierent concentrations, one obtains A, the uncorrected conductance of XI, which may thus be compared with the measured values. The continuous curve B of the figure shows the results of such comparison; the circles represent experimental conductance values. The calculated values are in agreement with the experimental ones within the limit of experimental error. They also reproduce the maximum and minimum of the experimental values. It appears that the viscosity effect may be allowed for if the viscosity of the solution is lower than that of water which, a t 0°,is 0.01797. It should be pointed out that viscosity corrections, s' made above for KT, are inapplicable in the case of electrolytes whose solutions are more viscous than water. A plot of A7 versus log C does not enable one to visualize how Aq varies as a function of C. At the concentrations 0.0, 1.20, and 5.7, the values of A7 are, respectively, 1.46, 1.07, and 0.89. The A7 versus C plot levels off at higher concentrations and might be approaching a limiting value of 0.7 or 0.8. These values are not too different from those for potassium formate in water a t 50.5". For this salt a t concentrations of 0.0, 1.0,and 5.0, the values of Aq are, respectively, 1.024, 0.788,and 0.713. As we have aiready seen, the values of Aq for this salt pass through a flat minimum and thereafter increase somewhat; this occurs at a concentration greater bhan 5 N . It would seem that the factors that govern the conductance decrease a t low concentrations weaken a t high concentrations, and the conduct,ance of the electrolyte is mainly governed by the viscosity of the soluticn. When we examine salts the visc,osities of whose solutions are greater than t,hat of water, such as LiCI, for example, we find that if we correct A in direct proportion to lj'q, the conductances are over-corrected. The effect of viscosity on conductance for salt solutions where 7 > 70differs from that where q < 7,. IN CONCLUSION
Essentially the electrolyte problem is that of accounting for the properties of electrolyte solutions in terms of the interaction of ions with one another and with the solvent molecules. These interactions are not independent; they are competitive. As the interaction of the ions with the solvent molecules is stronger, that between the ions is weaker. Save in the limiting case of dilute solutions, the properties of electrolyte solutions cannot be adequately accounted for in terms of macroscopic concepts, such as dielectric constant and viscosity. I n a dilute solution of a completely dissociated electrolyte, the interaction of an ion with its distributed counter charge may be successfully described in terms of the dielectric constant and viscosity of the solvent. The recent theory of Fuoss and Onsager reproduces experimental conductance values in water a t 25' within the limit of experimental error up to about 0.01N. When, however, the frequency of close approach cf one ion to
another becomes appreciable, the description will no longer be quite accurate. To what extent the description may be in error a t any given higher concentration we do not know; we do know that at su5ciently high concentrations, the description fails completely. As the interaction bet.ween the ions and solvent molecules becomes weaker, t.he interaction between the ions becomefi s~ficientlyst,rong to produce stable ion pairs; ion association occurs. On further weakening of the interaction of the ions with solvent molecules, the ions intera,ct with ion pairs; triple ions are formed. When the interaction of ions with solvent molecules is very weak, as in a solvent of very low dielectric constant, the ion pairs int,eract to form quadrupoles and more complex charged and neutral polyionic structures. At lower concentrations, the equilibrium between ions and ion pairs conforms t o the law of mass action; ion association increases with increasing concentration. However, in all cases, there is a concentration where the equilibrium reaction goes into reverse. Thereafter afieociation decreases with increasing concentration until the completely dissociated fused electrolyte iu reached. The concentration a t which the equilibrium reaction goes into reverse has been established in only one case. However, there is ample evidence that goes to show that the phenomenon is a general one. When a solvent is added t o a fused electrolyte, ion association does not occur if the interaction of ions with solvent molecules is large, that is, if the solvent molecules have a large dipole moment, and are not too large. When solvents of lower dielectric constant are added, ion association sets in and increases with decreasing concentration of electrolytes. The lower the dielectric constant of the solvent, the greater is the association for a given addition. Association increases with increasing concentration of solvent until a concentration is reached where the equilibrium react,ion reverses. The conductance of ions is in large measure dependent on their size and the viscosity of the medium through which they move. However, their motion is also influenced by other factors, particularly in the case of small ions. Here specific interactions between the ions and the solvent molecules affect their conductance significantly. Interaction between the ions and the solvent dipoles is involved. As stated above, the properties of electrolyte solutions are, in the main, determined by the interaction of the ions with one another and with the solvent molecules. These interactions depend on the charge, size, structure, and polarizability of the ions and on the size, structure, dipole moment, and polarizability of the solvent molecules.
I n the preparation of this paper, I have had the able and generous assistance of my friend and colleague, Dr. Robert L. Kay. I wish, also, t o acknowledge my indebtedness to Miss Clara L. Harden, who deciphered and transcribed some reams of hieroglyphics, and to Mrs. V. Jane Maclachlan, who prepared the figures. LITERATURE CITED (1) Severd phases of the problem artre discussed in somewhat greater detail in two earlier papers: C. A. K R A U(a) ~ J. Phys. Chem., 58, 673 (1954); ( b ) 60, 129 (1956).
JOURNAL OF CHEMICAL EDUCATION
DEBYE,P., AND E. H i i C m ~ Physik. , Z.,24, 305 (1923). ONSAGER, L., ibid., 28, 277 (1927). ( a ) K R A U ~C., A., and R. M. Fuoss, J. Am. Chem. Soe., 55,21 (1933); ( b ) Fuoss, R. M., and C. A. KRAUS,ibid., 55.2387 11933). ~ ~ ~ ~ , ~ ( a ) FU&, R. M., and C. A. KRAUS,ibid., 55,1019 (1933); Fuoss, R. M., ibid., 57, 188 (1935). Fuoss, R. M., A N D T. SHEDLOVSKY, ibid., 71,1496 (1949). MARTEL,R. W., AND C. A. KRAUS, Proc.Na1. Acad. Sci.. 41, 9 (1955). AZZARRI, M., AND C. A. KRAUS,ibid., 42, 590 (1956). BJERRUM,N., K g 1 Danske Vidensk. Selskab, 7 , No. 9 (1926). MEAD,D. J., J. B. RAMSEY, D. A. ROTHROCK, JR., A N D C. A. Xnrns. .I. Am. Chem. Soe., 69,528 (1947). I., AND C. A. Knaus, ibid., 69, 814 (1947). , AND C:. A. KRAUS,ibid., 69, 2472 (1947). Fuoss, R. M., A N D C. A. KRAUS,ibid., 55, 3614 (1933). SEWARD, R. P., ihid., 73,515 (1951). MERCIER,P. L., A N D C. A. KRAUS,PTOC.Nat. A e d . Sei., 42,487 (1956). D. S., A N D C. A. KRAUS,J. Am. Chem. Soe., ( a ) BUROESS, C. J., AND C. A. KRAC'S, 70, 706 (1948); ( b ) CARIGNAN, ibid., 71,2983 (1949). M. B., AND C. A. KRAUS,ibid., 70, 1709 ( a ) REYNOLDS, M . J., A N D C. A. KRAUS,ibid., (1948); ( b ) MCDOWELL, 73,3293 (1951).
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L. E., AND C. A. KRAUS,ibid., 72,166 (1950). (18) STRONG, W . E., Ph.D. thesis, Brown University (1941). (19) THOMPSON, C. A., Ann. N . Y. Aead. Sci., 51,789 (1949). ( 2 0 ) KEAWS, (21) ( a ) KRAUS,C. A., AND W. C. BRAY,J. Am. Chem. Soe., 35, V . F., and C. A. KRAUS,ibid., 1315 (1913); ( b ) HNIZDA, 71, 1565 (1949). W . E., A N D KRAUS,C. A., ibid., 69, 1016 (1947). ( 2 2 ) THOMPSON, (23) NOYES,A. A,, ET AL., Carnegie Publication No. 63. J., J . Am. Chem. Soe., 31, 1010 (1909). (24) JOHNSTON, (25) RICE, M. J., JR., AND C. A. KRAUS,PTOC.Nat. Acad. Sci., 39, 802 (1953). W . H., J . Am. Chem. Soe., 32, 946 (1910); ( b ) (26) ( a ) SLOAN, KAHLENBERG, L., J . Phys. Chem., 5,339 (1901). A,, Wied. Ann., 1876, 1591. (27) SPRUNG, L., Z. physik. Chem., 19, 13 (1896). (28) STORCH, (29) KRAUS,C. A., J. Am. C h m . Soe., 36,35 (1914). J. Phys. Chem., 61, 668 (30) Fuoss, R. M., A N D L. ONSAGER, (19571. (33) COPENHAFER, D. T.,A N D C. A. KRAUS,ibid., 73, 4557 (1951). ~. (34) GEDDES, J. A., AND C. A. KRAUS,Trans. Faraday Soc., 32, 585 (1936). 13.5) MEECIER.P. L.. AND C. A. KRAUS.PTOC.Nat. Acad. Sci. 41, 1033 (1955). (36) Fuoss, R. M., J. CEEX.EDUC.,32, 527 (1955)
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