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 at- mosphere, being a net result of the Coulomb at-

traction 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 at 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 be- havior 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-uni- valent strong electrolytes a t O°C. may,*in the concen- tration range here studied, be represented by the fol- lowing equations

1 - f u = j = 0 . 3 7 4 X c t + B c X c (1)

1 - f* = (0.219 + 29.5111.) X c* + B, X c (2)

where f. = 6 / ( v X 1.859 X m) and f, = A/Aa are the well-known osmotic and conductivity coefficients. The first term on the right side gives in either equation the limiting law, and the second term represents the individual properties of the electrolyte.

The alkali halides have coefficients B, = B, =

-0.6 + 0.2. as has been ~ointed out bv Lanze (5).

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-

SODIUM DIPICRYLAMINATE IN WATER AT ODC. DBTERMI- NATION OP B-CONSTANTS PROM OSMOT~C AND CONDUCTO- METRIC MEASUREMENTS

. . ciation of ions of equal as well as of opposite sign. The

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 the electrostatic effects are so dominant as to forces between ions of like sign were much stronger than the specific, individual properties a t these concentra- between those of opposite sign (examples, sodium pic- tinn. rate and dinitro~henolate). - We have studied a strong electrolyte, sodium dipic- ' Research Chemist.

'Compare for instance RIELLAND, J. CEEM. EDUC., 14, 412 r'laminate, which was found to have a very high and (1937). positive coefficient B, (+9.5), together with a coeffi-

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-coefficients were calculated from our measure- ments (3) by the procedure of Lange and Herre (6), by plotting (Figure 1) against c the functions

A . = l - f . - A , x c t (3)

A , = 1 - f , - A , X d (4)

The formal degrees of association were also computed as done by these authors, taking into consideration

TABLE 1

A S ~ E I A T ~ O N OP STRONG ELBCTROLYTBS AT 10-1 MOLAB SOLUTION IN WATBR AT OD. DUB TO VAN DBB W&&LI FL)xCBB

The non-ideal f"rr cnw8y

Per ccnl. d m m r r , nssocinlion of co1. 9rr male

ions with ElccVo- aon dcr Ent~al OPeosiU dnlir Wools

Elr~lraly t~ BS U P sign sign rffeclrl cffus*

LiCl Lil KF KC1 KI crci CSI HI08 Kl01 Kc101 KCIO.

- -

a Equal to L605 X mt + 1080 X m X Bo (.r..taaj] 'Equal to [I080 X m X (Be - Bo(i..,~.))l

Lange's empirical equation B, = B, for the electro- static forces. Instead of Lange's B,(d.n,li,l = -0.6 * 0.2, we have used values from -0.5 to -0.9 in order to take into consideration the small differences caused by the probable ionic diameter (11) of the ions in ques- tion. The formulas for the degrees of association finally become, for ions with like sign (double ions)

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 at O°C., giving the transference number t- = 0.332 of the sodium salt.

The function q6 at O°C. was computed equal to 0.46 at 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 mag- nitudes of the two principal sources of interionic forces, we have also calculated6 the non-ideal free energy due to electrostatic forces as well as to the individual van der Waals forces, and the results are seen from Table 1, columns 6 and 7.

Strong van der Wads forces (molecule-molecule ef- fect7) are characterized by the empirical fact that the relative heat content change in this case has the same sign as the free energy change, and is equal to i t in mag- nitude or larger, corresponding to the old rule that all dissociations increase with increasing temperature. The electrostatic forces (churge-charge effect), however, have free energy and beat content changes with oppo- site signs in the limiting law, while the heat content change of the churge-molecule effect is almost zero.

These facts furnish a convenient and rapid method of detecting such pronounced van der Wads effects whicb renders the pure electrostatic theory of electrolytes in- sufficient. Thus, in the case of dipicrylaminate, our measurements (3) indicate a t 0.05 molar about -0.5 - kcal. per mole, for 6 - E0 as well as for z2 - 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 com- mon strong el&ctrolytes do 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 they are (2) commonly based upon Br@nsted's principle of snecific ion interaction. whicb takes into account forces between ions with opposite sign only.

Much remains, however. to be done regarding the quantitative and theoretical treatment of dilute solu- tions of electrolytes. Thus we know at present very little about the distribution ofihe van der Waals forces within the three following groups: Keesom's orienta- tion.effect, Debye's induction effect, and London's dis- persion effect. -

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 therrna- dynamic r&ns the following equation fo; the-mean stoichio- metric 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 ) .

REFERENCES

(1) DEBYE AND HUCREL, PhyGk. Z., 24, 185, 305 (1923).

(2) GU~GENREIM, Phil. Mag., 19, 588 (1935). 42,287 (1936).

(5) LANCE. Z. b h ~ s Chem., 168, 147 (1934): ibid., 177, 193 (9) ON~AGER, Physik. Z., 27, 388 (1926): ibid.. 28. 277 (1927). . . . . ~. . . (1936). - ' (10) SCATCHARD. Chem. Rm'&s. 13; 7 (1933).

(6) LANCE AND HERRE, ibid., 181, 329 (1938). (11) ULICH, Z. Elektrochem., 36, 497 (1930); BRULL, Gam. chim. (7) LONDON, Trans. Faraday SOL, 33, 8 (1937). ital., 64, 624 (1934); KIELLAND, J. A m . Chem. Soc., 59, (8) MCBAIN AND BET& 3. A m . Chem. SOL, 57, 1905 (1935) 1675 (1937).