T H E IONIZATION OF STRONG ELECTROLYTES* BY WORTH H.RODEBUSH
In a recent paper1 the condition of highly polar substances in solution was discussed, and it was pointed out that this condition was in general quite different from the state which has usually been pictured for a salt that is completely ionized. It was predicted that the greatest departure from a state where the ions are actually free would be found a t concentrations in the neighborhood of molal. This prediction has received a striking confirmation in the work of Lewis and Randall2 who have found a minimum to exist in the activity of the strong electrolytes in the neighborhood of molal concentrations, and that the activity coefficient rises to very high values in concentrated solutions. The case of the very dilute solution still offers an opportunity for some very interesting observations. It is probable that no such thing as a completely polar electrolyte exists just as there are no perfect gases, but helium is very nearly a perfect gas and potassium chlorid must be very nearly a completely polar substance, and as in the case of the gas laws, we shall find it profitable to discuss the ideal case. A completely polar salt when in dilute solution would then be completely ionized in the sense that none or comparatively few of the positive and negative ions would be joined together in the position and orientation of the crystal lattice. That molecules of sodium chlorid exist in solution in a manner analogous to molecules in sodium chlorid vapor seems very doubtful. Recent calculations by Latimer3 show that a molecule of sodium chlorid in the vapor state is much more likely to dissociate into sodium and chlorine atoms than it is into the ions. The case is certainly far different in solution and analogies between solution and vapor are rather far fetched. It has been generally recognized that ions are hydrated in solution but it has not been recognized to what an extent this must be true. There is no reason to suppose that a salt like potassium chlorid would dissolve a t all were it not that the water molecules possess the power of neutralizing the electrical fields surrounding the potassium and chlorine ions. It seems probable that all ions are surrounded in solution by an envelope of water molecules. In the case of the chlorine ion with a negative charge and an outer shell of negative electrons the water molecules would be oriented with the hydrogens attached to the chlorine. In the case of the potassium ion the positive charge of the ion would counteract the negative external electron shell and the orientation of the water molecules would be problematical. Certainly they would be *Contribution from the Chemical Laboratory of the University of Illinois. Latimer and Rodebush: J. Am. Chem. SOC.42, 1419 (1920). *Lewis and Randall: J. Am. Chem. SOC.43, I 125, (1921). a Latimer: J. Am. Chem. SOC.45, 2803 (1923).
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WORTH H. RODEBUSH
held more loosely and this agrees with the common conception that potassium is one of the least hydrated ions. This solvation of the ions would tend to cause a positive deviation from Raoult's law since the amount of free solvent would be actually less than the calculated amount. At 0.01molal this effect would be negligible and since the ions are enveloped in water molecules, the solute now resembles the solvent and we have a condition where we should expect Raoult's law to hold were it not for the electrical forces. These are far from negligible. In a 0.01molal solution of potassium chlorid on the assumption of regular distribution the average distance between ions is of the order IO-^ ems. The force exerted by one ion upon another a t this distance is given by Coulombs law ele2 f.= - - IO-^ dynes kr2 which is about the same force as would be exerted by a potential drop of 600 volts per cm. in vacuo. The applied potential is obviously not likely to affect the degree of ionization of an electrolyte appreciably. Since a system tends to take on a configuration of minimum potential energy the ions will not be arranged in a regular distribution but there will be a tendency for ions of unlike sign to approach each other. Opposed to this will be the effect of the thermal agitation of the molecules. The problem of the distribution of the ions in a dilute solution is therefore a statistical one and attempts have been made by a number of investigators to solve it. Milner' approached the problem from a rigorous mathematical basis but he was not able to obtain a complete and satisfactory solution. The chief fault in Ghosh's wark2 was his failure to postulate a consistent clear picture . of the actual distribution of the ions in solution. The first apparently successful attempt in this direction has been made by Debye3 who, by a straight forward application of the theory of electrostatic potential together with the Maxwell-Boltzman distribution law, has arrived a t an expression for the free energy of a completely polar electrolyte in solution. Debye has derived a general expression for solutions of any concentration but the effective diameters of the ions enter into the expression in all except very dilute solutions where the diameter of the ions may be neglected. Since we have no data for the effective diameter of any ion, we can only hope to verify Debye's expression in dilute solution. The expression obtained by Debye for the partial molal free energy of a completely polar electrolyte in dilute solution is
Here m is the stoichometric molality, No is Avogadro's number, E is the charge of the electron, D is the dielectric constant of the solvent, Vo is the volume of the solution, (1000cc) C is a constant and kThas its usual significance. 2 u i ; is the number of ions per molecule and ZuizF is the sum of the products Milner: Phil. Mag. 25, 742
* Ghosh: J. Chem. Poc..
(1913).
113. ;go (1918). Dcbyc and Huckel: Physik. 2. 24, 185 (1923).
IONIZATION O F STRONG ELECTROLYTES
1115
of the number of each kind of ion per molecule multiplied by the square of its charge, and is directly proportional to the quantity Lewis has termed the ionic strengt,h. The second term in the equation above would give the free energy of an ideal solute and the third term shows that the free energy of an electrolyte in dilute solution is always less than that for an ideal solute. It is seen tliat even in the most dilute solution that we can study, the attraction between ions causes a negative deviation from Raoult's law. While it appears doubtful if Debye's calculations can give us a very exact account of irreversible phenomena such as conductivity, they should be capable of withstanding a rigorous check against activity measurements in dilute solution. On account of the errors entering into activity measurements in dilute solution we can not put too much dependence in the data for any individual salt. Fortunately we do not need to. G. N. Lewis with Linhart and Randall has obtained from a careful scrutiny of all available data, two empirical generalizations regarding the activity of strong electrolytes in dilute solution. If we can derive these empirical rules from Debye's theory then we shall have the most rigorous experimental check of Debye's theory possible. The first of these rules is the freezing point law of Lewis and Linhart' which may be written
e
I . 86Zqm
= 1-pm"
(2)
Here 8 is the actual freezing point lowering of a solution of molality m, and and /3 are constants. Let US see to what form of freezing point equation the Debye expression will lead. From thermodynamics we have the fundamental [equation for aqueous solutions. a
Substituting the value from
(I)
6 F, of 6m
Integrating with respect to "Ye and am and rearranging, we have for very dilute solutions
e I . 862qm
=I-
Z (vizi2)3'z No2e3(4r)1/Z milZ 9 ZQ (DRT)3/z
or
Lewis and Linhart: J. Am. Chem. SOC. 41, 1951 (1919).
(5)
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WORTH H. RODEBUSH
This is exactly the Lewis-Linhart equat,ion. It remains to compare the values of the constants. The value for CY from the Debye expression is, of course, for all types of electrolytes. Upon substituting the values of the constants in the last term of equation ( 5 ) we obtain‘ Z(UjZi2)3’*
P=0.205
2Ui
as the general expression for P. For uni-univalent electrolytes, we obtain P=0.290
CY=O.~OO
While Lewis and Randall obtained for potassium and sodium chlorides P’0.329
CY=O.535
For other types of electrolytes, we have the following comparison. Calculated
P uni-bivalen t Bi-bivalent
1.00
2.32
CY
0.500 0.500
Experimental
P
CY
04.72
0.374
1.44
0.38
I n the case of the uni-univalent salts where the data are most accurate the agreement is most satisfactory. In the case of the other types of salts the freezing point data in dilute solution are so uncertain that no better agreement is to be expected. The second empirical rule of Lewis and Randall relates to activity coefficients as obtained from solubility data in mixed electrolytes. It amounts to a more exact statement of the relation which was vaguely formulated as the isohydric principle. It is as follows: In dilute solutions the activity coefficient of a given electrolyte is the same jn all solutions of the same ionic strength2. The application of Equation ( I ) to activity of a slightly soluble salt in the presence of other electrolytes requires a careful consideration of the way in which ( I ) depends (a) upon the concentration of the ions of the slightly soluble salt, (b) upon the total ion concentration. Inspection of the derivation of ( I ) shows that it may be written in the form Fs=2ui RT In m+P z (uizi2) m’+C (8) where 2(uiz?)%mMrefers to the total ion concentration. The remainder of the constants of the third term of ( I ) were represented by p. The value of /3 will therefore vary when the valence type of the slightly soluble salt varies since it contains the term Z(uiz:) Since psmust be equal to the free energy of the solid salt C will be different for different salts. Salts whose ions are able to combine in crystal lattice in such a way as to neutralize effectively their electrical fields will be slightly soluble. The solubility of highly polar salts thus depends largely on what Born has called the grating energy. If we write F, = 2ui R T In (Y where CY is the mean activity of the ions of the slightly soluble salt then (8) may be transformed into the following equation 1
The value used for D is 80. For pure water it is usually taken Lewis and Randall: J. Am. Chem. SOC.43, 1141(1921).
RS 87.
IONIZATION OF STRONG ELECTROLYTES
1117
a
In m - = p1 Z(uiz?)%mU+C1
(9)
(Y E(ujzi2)m Here - is the mean activity coefficient and is the ionic strength m 2 as defined by Lewis. The above equation shows that a linear relation exists between the logarithm of the activity coefficient and the square root of the ionic strength in dilute solutions. This relation was shown by Lewis to hold for such data as are available'. The foregoing results justify the prediction that the equation of Debye for the free energy of strong electrolytes will be found to hold with great exactness for all types of strong electrolytes in dilute solution. In order to obtain further verification, it is necessary that more exact data be obtained for activities in dilute solution. Work along this line is in progress in this laboratory.
Actually Lewis plotted a / m instead of In a / m but the above conclusion holds a6 may be readily seen by replotting Lewis' data.
Urbana, Illinois.
