J. H. Hildebrand
Un~vers~ty of Cal~fornta Berkeley, 94720
A View of Aqueous Electrolytes through a Watery Eye
Having agreed recently to try to explain to general readers the state of affairs existing in solutions of electrolytes in water, I began by opening the third edition of "Reference Book of Inorganic Chemistry," by Latimer and Hildebrand, to page 542, which contains a figure in which activities of alkali and hydrogen halides are plotted against square roots of molality. As I contemplated this plot I thought, how is it possible to explain to a reader ignorant of thermodynamics the physical meaning of such an artifact as the activity of a substance a t infinite dilution, where none of it is present? In 1913 I published a paper1 which correlated data I had obtained on vapor pressures of mercury over amalgams with data that had been obtained by Richards and Forbes and by Hulett and Crenshaw on the emf of concentration cells of base metal amalgams. It was necessary for my purpose to derive one of the equivalent forms of the "Gibhs-Duhem" equation, of which I had not then heard. I used it subsequently many times in order to calculate activities of one component of a solution from measured values of the other, always considering the pure liquid as the standard state. In 1923, Lewis and Randall, in their famous "Thermodynamics," used our data on thallium amalgams to illustrate the convention used for solutions of electrolytes by considering the activity of the thallium to be unity at the dilute end. That neither convention is' either right or wrong can be seen from the GibbsDuhem equation in the symmetircal form
contains curves for At/m against log m for electrolytes of various types. The lines in the figure permit the following interpretations of the state of affairs in each of the several solutions. (1) The nonelectrolytes, sucrose and hydrogen peroxide, by virtue of their capacity for hydrogen bonding, depress the freezing point by the theoretical amount, -1.86' per mole, up to molal concentration in the case of sucrose and even to 10 X molal in the case of hydrogen peroxide. (2) If the ions of KC1-the salt most often selected as "typicaln-were truly "ideal" in their behavior in water, one would expect the depression to be 3.72", but not only is it somewhat less hut it diverges from the horizontal well below 0.01 M. This is the divergence accounted for by the theory of Debye and Hiickel, according to which the ions surrounding any one ion are predominately of the opposite sign. Because of the long range of electrostatic attraction, this interaction is far from negligible, even in very dilute solutions. The electrostatic attraction between Mg2+and 502can he expected to be 4 times as large as that between
+
This says only that, since XI $2 = 1, al - XI, and& $2 slopes a t any value of x are equal in value hut opposite in sign. Since most of our knowledge of the state of dissolved electrolytes has been derived from their effects upon the solvent, especially from depression of the freezing point, let us examine the experimental data of depressions per mole of electrolyte per 1000 g of water instead of a derived function such as activity. What the water thus "sees" directly is the number and the degree of independence of the several species of particle in the solution. The good old "International Critical Tables" was compiled while people were still investigating aqueous electrolytes, and it contains extensive data on freezing point depressions, At, over wide ranges of molality, m, moles of solute per 1000 g of water. The figure Research supported by the National Science Foundstion. 'HILDEBRAND, J. H., Trans. Am. Electvoehem. Sm.,22, 335 (1913).
224
/ Journal of Chemical Edumfion
t
r -3
.
I
-2
-I log m
i
I
0
I
I
Depression of the freezing point of 100 g of water per mole of solute for various subrtancer.
K+ and C1- at the same dilution, and accordingly the line for MgSOa rises steeply between 0.001 M and 0.01 M. The line for uni-divalent K2S04is of intermediate steepness, and the line for K3Fe(CN)sis the steepest of all. (3) Sulfuric acid, as is well known, ionizes strongly into H + and HS04-, and the first H+, as concentration increases, opposes ionization of the second, so that in 0.1 mold concentration H&Oa is virtually a uni-univalent electrolyte. (4) The lines for AgN03, RC1, NaC1, KOH, and HC1 all diverge from one another when their concentrations have risen as far as 1 molal. The line for AeNO. is rising sharnlv to the level of a non-electrolyte. wiich-one may re&nably attribute to incornpieti ionization. (5) The downward plunges of the other lines above molal concentration seem clearly to be related to hydration. From a purely electrostatic point of view, the strength of hydration should increase with ionic charge and decrease with ionic radius; moreover, not only are cations in general smaller than anions, but also they attract the more polarizable part of water molecules. Such hydration can have two consequences, one, to diminish the attraction between anion and cation, the Debye-Hiickel effect, allowing them to be more effective in depressing the freezing point of water; the other is to reduce the amount of unbound, solvent water. Both of these effects can contribute to the diierence seen between the lines for KC1 and NaCl. The hydra-
tion of the OH- of KOH and the H + of HC1 have additional strength by reason of hydrogen bonding. The affinity of concentrated H2SOafor water is well known. The marked difference between KzSOd and MgCl,, each dissociating into 3 ions, accords with the differences between the charges of K + and MgZ+and their radii; 1.33 X cm and 0.65 X cm, respectively. (6) The fact that all of these electrolytes, as well as most others, fail to depress the freezing point to an even multiple of -1.86' was regarded in the early days as evidence of incomplete dissociation, as is the case with weak acids, but with developing theory of chemical bonding, and determinations of crystal structure, which showed no molecules of KC1 in its crystal, it has become the custom to speak instead of ion pairs. Such "pairing" reduces electric conductivity as well as freezing point depression in solutions of K2SOIand MgCL. Cations of the transition elements form strong hydrates of unquestionably covalent character, on the evidence of changes in color and slow hydration and dehydration. I t is not difficult, if one wishes, to proceed from data such as those plotted in the figure to calculate the activity of water a t O°C in each solution over the range of concentration covered, but experimental data, plotted as in the figure, seem to me to reveal far more about the physical states of these solutions than any artifact that can be calculated from them. The water itself has a clear view of the state of substances dissolved in it.
Volume 48, Number 4, April 1971
/
225
