On DILUTE SOLUTIONS of ELECTROLYTES JACOB KIELLAND' Porsgrurm, Norway
T
HE Debye-Hiickel-Onsager theory of strong electrolytes (1,9 ) , with its concept of the ion atmosphere, being a net result of the Coulomb attraction forces and the thermal vibrations, has given us an exact quantitative picture of the limiting law of reversible as well as of different irreversible properties of ionic solutions. The oroblem of the soecific. individual deviations from this law a t finite concentrations (say, a t 10W3 to about 5 X 10-2 molar in water), however, has not reached its final solution. In the case of relatively small inorganic univalent ions, the individualities may be accounted for by means of their different degrees of solvation, e. g., different ionic diameters (ll), which may be taken into consideration when computing the electrostatic forces according to Debye and Hiickel. In many other cases, however, this correction does not suffice. According to recent work by Lange (5),McBain (8), Kortum (4), and others,%one is forced to take into account also the van der Wads forces, especially the additive London dispersion forces (7). These have been shown to be of considerable importance for the behavior of certain ionic solutions, since they sometimes are as strong as to cause association even between ions of equal charge, in spite of the electrostatic repulsion. Let us consider the familiar conductance and osmotic properties. The experimental material for uni-univalent strong electrolytes a t O°C. may,*in the concentration range here studied, be represented by the following equations 1-fu=j=0.374Xct+BcXc 1
- f*
=
(0.219
+ 29.5111.)
X c*
+ B,
Lange also for the first time tried to estimate the London dispersion forces in ionic solutions, and was able to show that the order of magnitude was such as to account for the individualities observed in the osmotic behavior of the alkyl ammonium halides studied by himself. From the combination of osmotic and conductance studies, Lange and Herre (6) recently evaluated the observed van der Waals effects in terms of formal asso-
(1)
X c
(2)
where f. = 6 / ( v X 1.859 X m) and f, = A/Aa are the well-known osmotic and conductivity coefficients. SODIUM DIPICRYLAMINATE IN WATER AT ODC. DBTERMIThe first term on the right side gives in either equation NATION OP B-CONSTANTS PROM OSMOT~CAND CONDUCTOMETRIC MEASUREMENTS the limiting law, and the second term represents the individual properties of the electrolyte. The alkali halides have coefficients B, = B, = ciation of ions of equal as well as of opposite sign. The -0.6 + 0.2. as has been ~ o i n t e dout bv Lanze (5). . . These, and other electrolyies having about the same results were particularly interesting, as it could be coefficients, are regarded as ideal ones in the sense that definitely shown that in some cases the van der W a l s forces between ions of like sign were much stronger than the electrostatic effects are so dominant as to the specific, individual properties a t these concentra- between those of opposite sign (examples, sodium pictinn. rate and dinitro~henolate). We have studied a strong electrolyte, sodium dipic' Research Chemist. r'laminate, which was found to have a veryhigh and 'Compare for instance RIELLAND, J. CEEM.EDUC., 14, 412 positive coefficient B, (+9.5), together with a coeffi(1937).
146
cient B, (-2.5) still more negative than any electrolyte studied by Lange. Accordingly, very strong van der Wads forces must occur in this case, and particularly between the two univalent anions, which probably must possess quite large polarizabilities. The B-coefficientswere calculated from our measurements (3) by the procedure of Lange and Herre (6),by plotting (Figure 1) against c the functions
The function q6 a t O°C. was computed equal to 0.46 a t molar, from Lange's equation
The results obtained for sodium dipiaylamiuate as well as for electrolytes measured by Lange, are given in Table 1, columns 4 and 5 . In order to give a more complete picture of the magA.=l-f.-A,xct (3) nitudes of the two principal sources of interionic forces, we have also calculated6 the non-ideal free energy due A,=1-f,-A,Xd (4) The formal degrees of association were also computed to electrostatic forces as well as to the individual van as done by these authors, taking into consideration der Waals forces, and the results are seen from Table 1, columns 6 and 7. Strong van der Wads forces (molecule-molecule efTABLE 1 fect7) are characterized by the empirical fact that the AS~EIAT~O OPNSTRONG ELBCTROLYTBS AT 10-1 MOLAB SOLUTION IN WATBR AT OD. D U B TO VAN DBB W&&LIFL)xCBB relative heat content change in this case has the same The non-ideal sign as the free energy change, and is equal to i t in magf"rr cnw8y nitude or larger, corresponding to the old rule that all Per ccnl. dmmrr, nssocinlion of co1. 9rr male dissociations increase with increasing temperature. ions with ElccVo- aon dcr The electrostatic forces (churge-charge effect), however, Ent~al OPeosiU dnlir Wools Elr~lralyt~ BS UP sign sign rffeclrl c f f u s * have free energy and beat content changes with oppoLiCl site signs in the limiting law, while the heat content Lil change of the churge-molecule effect is almost zero. KF KC1 These facts furnish a convenient and rapid method of KI crci detecting such pronounced van der Wads effects whicb CSI renders the pure electrostatic theory of electrolytes inHI08 Kl01 sufficient. Thus, in the case of dipicrylaminate, our Kc101 measurements (3) indicate a t 0.05 molar about -0.5 KCIO. kcal. per mole, for as well as for - HsQ, hence, very strong forces of the molecule-molecule type must be p-esent. It is important to have in mind-that some of the common strong el&ctrolytesdo show large van der Waals forces between ions of equal sign even in dilute solution. This fact must for example influence the application of semi-empirical and theoretical equations to the thermo- dynamic properties of mixtures pf electrolytes, since a Equal to L605 X mt 1080 X m X Bo (.r..taaj] 'Equal to [I080 X m X (Be - Bo(i..,~.))l they are (2) commonly based upon Br@nsted'sprinciple of snecific ion interaction. whicb takes into account Lange's empirical equation B, = B, for the electro- forces between ions with opposite sign only. Much remains, however. to be done regarding the static forces. Instead of Lange's B,(d.n,li,l = -0.6 quantitative and theoretical treatment of dilute solu* 0.2, we have used values from -0.5 to -0.9 in order tions of electrolytes. Thus we know a t present very to take into consideration the small differences caused by the probable ionic diameter (11) of the ions in ques- little about the distribution ofihe van der Waals forces tion. The formulas for the degrees of association within the three following groups: Keesom's orientation.effect, Debye's induction effect, and London's disfinally become, for ions with like sign (double ions) persion effect.
z2
6 E0
+
1 q = the ratio between the equivalent conductivity of the double anion and that of the single ion. 6 Puttine m = c at small concentrations. we eet for therrnadynamic r&ns the following equation fo; the-mean stoichiometric activity coefficient of the solute: -2.303 X l o g ~ + f = 3 X 0.374 X mt 2 X B. X m which facilitates the energy computations (it is seen that for BO. .=,~O,we obtain the well-known limiting expression - In f , = s X 11. ' S e e pp. 22;( in the excellent review of Scatchard ( l o ) .
+
and opposite sign (ionic pairs) r
=
(Be
- B4~~t.a.)X
c
+6 4
(6)
The limiting conductivity of dipicrylarninate anion was determined by us to A. = 12.8 a t O°C., giving the transference number t- = 0.332 of the sodium salt.
+
REFERENCES
(1) DEBYE AND HUCREL, PhyGk. Z., 24, 185, 305 (1923). (2) GU~GENREIM, Phil.Mag., 19, 588 (1935).
42,287 (1936).
(5) ibid., 177, 193 . . LANCE.Z. b h ~ sChem., 168, 147 (1934): . . (1936). - ' (6) LANCEAND HERRE,ibid., 181, 329 (1938). (7) LONDON,Trans. Faraday SOL,33, 8 (1937). (8) MCBAINAND BET&3. A m . Chem. SOL,57, 1905 (1935)
(9) ON~AGER, Physik. Z., 27, 388 (1926): ibid..~.28. 277 (1927). . . (10) SCATCHARD. Chem. Rm'&s. 13; 7 (1933). (11) ULICH,Z. Elektrochem., 36, 497 (1930); BRULL,Gam. chim. ital., 64, 624 (1934); KIELLAND, J. A m . Chem. Soc., 59, 1675 (1937).
