The PRESENT STATE offhe PROBLEM of ELECTROLYTIC SOLUTIONS* CHARLES A. KRAUS Brown University, Providence, Rhode Island INTRODUCTORY AND HISTORICAL
A
S THE topic of my discussion, I have selected the problem of electrolytic solutions. This topic seemed all the more appropriate since the first great contribution to the solution of this important problem was made fifty-two years ago by Svante Arrhenius ( I ) , the first recipient of the Willard Gibbs Medal of the Chicago Section of the American Chemical Society. Accordmg to the theory of Arrhenius, electrolytes, on dissolving i n a medium, undergo dissociation into positioely and negatiwely charged molecules or ions, which ions are i n eguilibrium with undissociated molecules of the electrolyte and are subject to the same thermodynamic and kinetic laws as are ordinary neutral molecules. The theory met with immediate and striking success in the case of weak electrolytes (acids and bases) but failed in the case of strong electrolytes (salts). Actually, the problem of strong electrolytes was not finally solved until forty years later (1923) when Dehye and Huckd (2) showed that by taking into account the effect of Coulomb forces on the distribution of ions in a medium, the properties of strong electrolytes could be accounted for a t low concentrations. To bring the original theory of Arrhenius into harmony with our present conceptions, it is only necessary to substitute for ions acting independently of one another (like neutral molecules) the more accurate model of ions interacting with one another according to the Coulomb force law. It is interesting to note that while the Debye-HuckelOnsager theory, which I will simply call the "ionatmosphere theory," greatly modifies the original theory of Arrhenius so far as strong elecfrolytes are concerned, it leads only to a correction term (or factor) in the case of weak electrolytes. For more than forty years, the attention of physical chemists was focused on the problem of strong electrolytes, while the equally important problem of weak electrolytes was neglected. It was generally assumed that only the acids and bases may appear as weak electrolytes and that the salts are essentially strong electrolytes. Physical chemists, with few exceptions, looked a t the problem of electrolytes from the narrow and somewhat distorted point of view of aqueous solutions. Water was the typical solvent for electrolytes and, if electrolytes were soluble in media other than water, this was in itself exceptional and the properties of such solutions might he expected to he "abnormal." * Scientific address delivered by the recipient of the Willard Gibbs Medal Award, 1935 (Kent Chemical Laboratory, The University of Chicago. May 25th).
I t is known, today, .. that all liauid media. with the DOSsible exception of the light hGdrocarbons, possess'the power of dissolving electrolytes and that such solutions exhibit characteristic properties due to the presence of ions, dipoles, and more complex aggregates of electrolytes. A complete understanding of electrolytic phenomena will be arrived a t only when it is known how the properties of electrolytes vary with (and depend upon) the fundamental constants of the media in which they are dissolved. As early as 1900, Franklin and Kraus (3) showed that solutions of the ordinary salts in liquid ammonia approximate the law of mass action a t lower concentrations. In 1913, Kraus and Bray (4) reviewed the existing data relating to non-aqueous solutions and concluded that the law of mass action applies generally to binary electrolytes dissolved in solvents of lower dielectric constant, provided that the concentration of the electrolyte be not too high. In 1926, Bjerrum (5) proposed the ion association theory to account for the properties of aqueous solutions a t higher concentrations and derived an expression for the ion association constant in terms of ion diameters, dielectric constant, and temperature. I n solvents of very low dielectricconstant, reliable data have been lacking. m i l e it was known that electrolytes dissolved in solvents of very low dielectric constant are capable of conducting the electric current, it was not known whether the equivalent conductance of electrolytes in such media approaches a limiting value differing from zero. It was a t this point that a thoroughgoing investigation of solutions of electrolytes was undertaken a t Brown University with a view to determining the generality of the phenomena and, in particular, to determining how the properties of a solution depend upon the dielectric constant of the solvent medium on the one hand, and the size and configuration of the ions on the other. MATHEMATICAL
In to present the results of our investigations concisely, it is necessary to resort to graphical methods; a brief mathematical introduction will make the interpretation of the graphs clear, The original theory of predicated kinetic equilibrium between ions and un-ionized molecules of a electrolyte (this discussion will be restricted to binary electrolytes), according to the equation M + f X- S MX. This leads to the mass action equation:
where K is the dissociation constant of the electrolyte and the symbols in parentheses signify concentrations of the molecular or ionic species in question. If c is the total concentration of electrolyte and y is the fraction of electrolyte that exists in the form of ions, we have the obvious relations: (M+) = (X-)
= cy;
whence
(MX)
= c(1
-
~yP/(l y) = K.
-
y),
(2)
Equations (1) and (2) hold for ideal solutions. For non-ideal solutions, that is, solutions where forces act between the molecules or, in this case, ions, the concentrations of equation (1) must be replaced by activities and. since the activitv a = fc.,where f is the activitv coefficient of the ionic species in question, equation (2) takes the form:
media. If the theory as above outlined is correct, the experimental points will lie on a straight line. If the dissociation constant is large, the lines will lie near the cA axis; as the dissociation constant diminishes, the lines become steeper and approach the l/A axis. DISSOCIATION CONSTANT AND DIELECTRIC CONSTANT
Before proceeding to a comparison of the conductance data, we need to consider how the properties of an electrolyte depend on the dielectric constant of the solvent medium. The ion-association theory of Bjerrum yields an equation relating the dissociation constant of the electrolyte with the dielectric constant of the medium. This theory has since been extended by Fuoss (7) and extensively tested in the Brown laboratories. In
.
cyYl(1
- Y) = K,
(3)
it being assumed that the un-ionized molecules MX behave normally. This equation may be written in the form: 1/7.- c 7 7 / K f 1.
(3')
According to Debye and Hiickel, f is given by the equation: -1og.f = B
CY
(4)
and, according to the Debye-Hiickel-Onsager theory, the conductance of an electrolyte is given by the equation: where A, is the equivalent conductance of the electrolyte present in the form of ions whose concentration is cy, A, is the limiting equivalent conductance approached as the concenGation approaches zero, and-a is the Onsager coefficient, vhich may be computed from known properties of the solvent and of the electrolyte. The degree of dissociatiofi y of the electrolyte a t the concentration G is given by the equation:
0.5 log D 1.0 1.5 morns 1.-DIISOCIATION CONSTANT AS A FUNCTION OE' DIELECTRIC CONSTANT
Figure 1, negative logarithms of dissociation constants (-log X),are plotted as ordinates against the logaIn this equation, A and c are experimental values and A, rithms of dielectric constants of the media (log D) as may be approximated; the equation may be solved for abscissas. At a dielectric constant of about 40, the y and its value substituted in (3'). We then have curve crosses the axis of log D; the dissociation constant is large and the electrolyte is, in effect, completely dissociated. As the dielectric constant decreases below 40, tbe value of K decreases, the decrease being the more This equation is linear in terms of F/A and - as F rapid, the lower the dielectric constant of the medium. variables, and a plot of these variables yields the value For a dielectric constant of 2.4, the dissociation conof l/A, as intercept on tbe axis of l/A; the slope of the stant is of the order of 1 X The points on the curve yields the value of the dissociation constant K. plot represent dissociation constants computed from F is a correction factor for the ion-atmosphere effect, conductance data for solutions of tetraisoamylammonwhich is readily calculated from the experimental data ium nitrate in mixtures of dioxane and water (8). according to the method of Fuoss (6). These results go to show that the dissociation of an Equation (7) affords a convenient means of graphi- electrolyte into ions is, in the main, controlled by the cally comparing the behavior of electrolytes in various dielectric constant of the solvent medium and that in
solvents of high dielectric constant, electrolytes are and that, irrespective of strength, the experimental completely dissociated. It should he added, however, data yield a linear plot according to equation (7). that the properties of solutions of an electrolyte are likewise dependent upon the size and configuration of the ions. Time will not permit a detailed discussion of IN LIOUD M ( m 4 this interesting question; suffice it to say, that as the ions become larger, the curve shown in the figure is displaced to the left, that is, toward lower dielectric constants, while as the ions become smaller, the curve is displaced toward higher dielectric constants. Those electrolytes which have the largest ions are the most highly dissociated in a given solvent. COMPARISON OF ELECTROLYTES I N DIFFERENT MEDIA
In Figure 2 are shown plots of equation (7), for a number of electrolytes in water a t 25'. The curves in
In Figure 3 are shown plots of equation (7) for potassium iodide, bromide, and chloride in liquid ammonia (9) a t -34' (dielectric constant, 22). If similar plots were made for these salts in aqueous solution, their graphs would coincide with that of hydrochloric acid. In liquid ammonia, with its lower dielectric constant, the curves for the three salts T i e r markedly. All three are inclined to the cA axis, the inclination increasing from iodide to chloride in accordance with their dissociation constants, which decrease in the order: iodide, bromide, chloride. Potassium iodide is approximately five times as strong an electrolyte as potassium chloride. This result is in accord with ion dimensions deduced from lattice distances in, crystals. It is iuterestmg to note that, although'the three halide ions differ in size in the undissociated molecules, or ion pairs, as freely moving ions they have the same dimensions, since the three salts have the same value of FIG-
O r CONDUCTANCE FUNCTION FOR AQUEOUSSo~rrrro~s f
2.-PLOT
4
/
CONDUCTANCE FUNCTION
..w
BPg
the lower figure relate to hydrochloric acid and iodic acid. It will he noted that the points for hydrochloric acid lie upon a horizontal straight line, correspondmg to a very large dissociation constant or, in other words, to complete dissociation of the electrolyte. The points for iodic acid lie upon a straight line which is inclined to the horizontal axis, the inclination being determined by the dissociation constant of this acid, which is 0.17. In the upper figure, the vertical scale has been contracted 100 times over that of the lower figure. On this scale, the inclination of the curve for iodic acid is scarcely perceptible, the curve for monochloroacetic acid is markedly inclined, and that for acetic acid is almost vertical. The slopes in all cases correspond inIn Figure 4 are shown plots for a number of electroversely to the dissociation constants of the acids in lvtes in ethvlene chloride (10) constant, 10.2). . . (dielectric . quest& that is, the smaller the constant, the greater the slope. It is evident, from this figure, that in aque- The slopes of the plots on one fipre must not be comous solutious we have eiectrolytes of varying strength pared with the slopes on another, since different scales
are employed. In ethylene chloride, as in other solvents, the experimentally determined values yield straight-line plots, indicating the adequacy of equation (7). The values of the dissociation constants in ethylene chloride are distinctly lower than in liquid ammonia. It will be noted that within fairly narrow limits the strongest electrolytes are those with the largest ions. Thus, tetrabutylammonium salts are stronger electrolytes than tetramethylammonium salts. Of the electrolytes shown in Figure 3, tetrabutylammonium hydroxytriphenylboron is the strongest and the tetramethylammonium salt of the same anion is the weakest electrolyte. Tetrabutylammonium nitrate is of intermediate strength; the nitrate ion is smaller than the hydroxytriphenylboron ion. Ion dimensions, as computed from dissociation constants, are not independent of the second ion of the binary electrolyte. This is particularly true of ions that have a highly complex structure. Thus, tetramethylammonium picrate is a stronger electrolyte than tetramethylammonium hydroxytriphenylboron, but in the case of the tetrabutylammonium salts, the picrate is slightly weaker than the boron derivative (10). Constants of a number of electrolytes in ammonia and in ethylene chloride are summarized in Table 1. TABLE 1 CONSTANTS OF SOX=
ELBCTROLYTEB IN S ~ V B R SDLYBKIS AL
~~~~~i~ at -340 SDIUIC
NaBr KC1 KBr KI
AO 315.5 347.8 346.0 344.4
K
x
28.7 8.7 20.3 41.9
10'
A*
x
10'
4.27 3.03 3.76 5.13
''A'' may be interpreted ar the distance between centers of charge in the ;"",,sirs
FIGURE 5.-CONDUCTANCE OR SOLUTIONS I N DIOXANE-WATER MIXTURES (Numbers in figure are dielectric constants)
of the conductance curve changes. Below a dielectric constant of about 8, the conductance curve has a minimum. This minimum becomes more pronounced and moves toward lower concentration as the dielectric constant diminishes. In pure dioxane, the minimum lies in the neighborhood of 1 X 10-W. It will be noted that at. concentrations below the minimum, the curves at,the bottom of the figure aopreach linearity, corresponding to a slope of -I/?. This form of the curve is characteristic of a weakly dissociated binary electrolyte. For such an electrolyte, we have cAa/A, (A, -'A) = K
-
and since A is negligible in comparison with Ao, we have LAS = KA.' SOLVENTS OF VERY LOW DIELECTRIC CONSTANT
Thus far we have considered only dilute solutions of electrolytes in solvent media having dielectric constants lower than 10. It remains to determine experimentally the form of the conductance curve as the dielectric constant of the solvent is gradually lowered to that of a non-polar medium. In Figure 5 are shown conductance curves for tetraisoamylammonium nitrate in various dioxane-water mixtures (ll), the dielectric constants of which range from 78, that of water, to 2.2, that of dioxane. In order to be able to represent all these conductance values on a single figure, logarithms of equivalent conductance are plotted. as ordinates against logarithms of concentration as abscissas. It is seen thatj as the dielectric constant of the medium diminishes, -the conductance diminishes and the form
d log A/d log c =
- 'I2
It remains to account for the conductance minimum in solvent media of low dielectric constant. This may be done by taking account of the tendency of ions to associate with ion pairs to form what are called "triple ions" (12) according to the equations: MX f M + = MXMf
and MX
+ X- = XMX-
If we take into account the formation of triple ions, the conductance equation a t lower concentrations assumes the simple form:
which may be written
