A Reappraisal of Arrhenius' Theory of Partial Dissociation of Electrolytes

Chapter 6

A Reappraisal of Arrhenius' Theory of Partial Dissociation of Electrolytes

Downloaded by UNIV LAVAL on November 24, 2015 | http://pubs.acs.org Publication Date: January 1, 1989 | doi: 10.1021/bk-1989-0390.ch006

R. Heyrovska Na Stahlavce 6, 160 00 Praha 6, Czechoslovakia The actual 'ionic concentrations' and hydration numbers of over fifty univalent and multivalent strong electrolytes have been presented (for the first time). The degrees of dissociation and hydration numbers calculated from vapor pressures correlate quantitatively with the properties of dilute as well as concentrated solutions of strong electrolytes. Simple mathematical relations have been provided for the concentration dependences of vapor pressure, e.m.f. of concentration cells, solution density, equivalent conductivity and diffusion coefficient. Non-ideality has thus been shown to be mainly due to solvation and incomplete dissociation. The activity coefficient corrections are, therefore, no longer necessary in physico-chemical thermodynamics and analytical chemistry. A century ago, van't Hoff's (1) pioneering work on the gassolution analogy was followed by Arrhenius' (2) theory of partial dissociation of electrolytes in solutions. Later, electrolytes came to be classified as weak or strong with the supposition that the former are partially dissociated whereas the latter are completely dissociated in the given solvent (3,4). However, with the advance of experimental and theoretical knowledge, it has become increasingly evident that many multivalent and even some univalent strong electrolytes (especially those with bulky anions or cations) are incompletely dissociated not only in solvents of low dielectric constant but also in water. On the other hand, association of ions of simple strong electrolytes like NaCl in water is considered negligible (3-7). This report, which summarizes several years' research work (8,9) shows that all electrolytes including alkali halides and halogen acids are in association/dissociation equilibrium with their ions in aqueous solutions, thereby confirming Arrhenius' views. A short survey of the development of the ideas in the literature about the state of dissociation of electrolytes in solutions is as follows: 0097-6156/89/0390-0075$06.00/0 © 1989 American Chemical Society

In Electrochemistry, Past and Present; Stock, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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The basic analogy of the gas and solution ideal laws, established by van't Hoff (1), was found to be valid only for ve ry low gas pressures P and osmotic pressures π. Thus, at temperature T and molar volume V,

At higher P and π, the ratios (PV/RT) and (πV/RT) called, respec tively, the compression factor (10-12), z, and the van't Hoff factor (1,13), i, deviated from unity. Arrhenius (2) interpreted i as the total number of moles of solute actually present in the solution due to association/disso ciation of one mole of solute (B) dissolved in the given solvent (A) at the given concentration. Thus, for one mole of an elec trolyte B+- dissociating into V+ cations of charge z + and V- an ions of charge z- according to

where o is the degree of dissociation, V= V+ + v- and V+ z + = v-z-, i is given by

Thereby, an excess number, (V-1)o, of moles are created by the dissociation of B + - . At infinite dilution, an electrolyte is completely dissociated and therefore, o = 1 and i = V. For a non-associating/dissociating solute, like sucrose in aqueous solution, o = 0. The above idea gained a wide support for nearly three deca des, but was eventually given up mainly because there was no exact way of determining o from experiments like electrical con ductivity. The use of the Arrhenius conductivity ratio (^/^o), or other modifications, for the calculation of o , approximately satisfied the law of mass action or Ostwald's dilution law (2,14)

for weak acids. On the other hand, it gave neither the correct values of i nor the dissociation constant, o , independent of concentration for electrolytes like simple alkali halides. Stro ng electrolytes, by virtue of their 'anomalous' behavior (15), were assumed to be completely dissociated in water. This led to the introduction of the formal notations and conventions of 'ac tivity and activity coefficients for a unified representation of non-ideality (15). From then on, the deviations from ideality came to be expressed commonly by the molal osmotic coefficient, 0, and the mean molal ionic activity coefficient, V± (3,15,16). 0 is evaluated (3) usually from the vapor pressure measurements from the relation,


6. HEYROVSKA

Arrhenius' Theory of Partial Dissociation of Electrolytes


where pcΛ is the vapor pressure of water at temperature T, pA is that over the solution of molality m and aA is defined (3,15) as the activity of the solvent. 0 = 1 corresponds to complete dis sociation at infinite dilution. Φ can also be obtained from mea surements of osmotic pressure, changes in freezing and boiling points, etc.(3). V t is obtained directly from the e.m.f. measurements (3,1416), say, of concentration cells without transference, from the deficit free energy, AG(non-id), attributed to non-ideality,

where AG(id) is the supposed free energy due to complete disso ciation at any molality m. Vt is also evaluated from Φ through the Gibbs-Duhem relation by integration:

where (mVt) = aB is the activity of the solute B (3,15). Subsequent theories of non-ideality have been mainly concer ned with explaining the concentration and temperature dependences of V and Φ (3,16). For a comparison with various other theories for the non-ideal part of free energy of solutions, see (14). The interionic attraction theory (3,5,16-18) formulated on the assumption of complete dissociation of strong electrolytes, pre dicted the 1nV vs √m linear dependence and explained the √c dep endence of found empirically by Kohlrausch (3,14) for dilute so lutions. Since the square-root laws were found to hold for dilu te solutions of many electrolytes in different solvents, the in terionic attraction theory gained a wide acceptance. However, as the square root laws were found to be unsatisfactory for concen trations higher than about 0.01m, the equations were extended or modified by the successive additions of more terms, parameters and theories to fit the data for higher concentrations. See e.g., (3,16) for more details. At the same time, theories of ionic association were worked out by Bjerrum and others (3,5,14,16,19). According to these, free ions of opposite charge getting closer than a certain criti cal distance form separate associated entities. Thereby, the total number of moles of solute in the solution becomes lower th an that expected on the basis of complete dissociation. These theories show that ion pairs can be formed, although to a small extent, even in aqueous 1:1 electrolytes where the critical distance is 3.57Å at 25°C (3); for higher valent ions in solvents of lower dielectric constant, associated ions are more likely since the predicted critical distance is larger. In fact, the literature (3,5,16,20-32) provides growing evidence for ion association not only in aqueous and non-aqueous solutions of multivalent electrolytes and 1:1 strong electrolytes composed of bulky ions, but also in HC1 and NaOH (29). Thus, in cases where incomplete dissociation and formation of associated ions were evident, was incorporated (3,5,16,30-32) into the equations for Ø and v while retaining the Debye-Huckel-Onsager terms for the free ions .


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ELECTROCHEMISTRY, PAST A N D PRESENT


78

Solvation of the dissolved solutes as one of the important causes of non-ideality has long been recognized (14,33). Accordingly, there has been an increasing awareness of its influence on the properties of solutions (3,5,14,16,19,34,35). However, there is no concordance (19,36) in the reported values of the solvation numbers obtained by different methods, mostly due to the use of unsatisfactory theories of non-ideality. On the whole, one finds that the existing interpretations of the non-ideal behavior of solutions are fairly complicated and that there is no simple, meaningful and unified explanation of the properties of dilute and concentrated solutions. Therefore, the present author decided to interpret directly, without presupposed models, the actual experimental data as such rather than their deviations from 'ideality' (or complete dissociation) represented by formal coefficients like (Ø and v. Attention is paid here mainly to aqueous solutions of strong electrolytes, since these are considered anomalous (15). Extensive work on univalent and multivalent electrolytes has shown (8,9a-i) that when allowance is made for the solvation of solutes, Arrhenius' theory of partial dissociation of electrolytes explains the properties of dilute as well as concentrated solutions. This finding is in conformity with the increasing evidence for ion association of recent years mentioned above. The method of determination of the actual degree of dissociation, ck , and the hydration number, nh , from the existing data on vapor pressures is outlined below. This is then followed by the quantitative correlation of and nh with various properties of electrolyte solutions. and nh From Vapor Pressure The method of obtaining and nh is briefly thus: The vapor pressures of solutions were found (8,9g) to obey Raoult's (37) law, on correcting it for hydration (34,38) and incomplete dissociation (2,34) of the electrolyte. Thus, the vapor pressure ratio (data stored in the form of aA and Ø in ( 3 ) gives the mole fraction NA of 'free' water,

where nA = (55.51 - mnh) is the number of moles of 'free' water, 55.51 is the number of moles of water in one kg and n B = im is the total number of moles of solute. In Figure 1 are shown two examples of the general dependence of mpA/(p°A -pA ) on m found for over fifty electrolytes compared with that for sucrose for which = 0. It can be seen that the graphs are linear over a considerable range of concentrations, e.g., 0 - 2m sucrose, 1.8 - 4m NaCl and 1.8 - 4.5m KBr. This implies that i and nh are constant in these range of concentrations. From the slopes (=nh/im) and the intercepts (=55.51/im), the values of the constants, i m and nh were obtained. For sucrose, i m and nh were found to be 0.999 and 5.01 (lit: (14,38), n h =5) respectively. The values of n h and M [=(itn-1)/(V-1)] obtained for the electrolytes are given in Table I and Figures 2 and 3.



6. HEYROVSKA Arrhenius' Theory of Partial Dissociation of Electrolytes

Figure 1. P l o t s of mpA/(pA - p A ) v s . m for aqueous s o l u t i o n s at 25°C , 1) sucrose, 2) NaCl and 3) KBr (Reproduced with permission from Ref. 8. Copyright 1988 C o l l e c t i o n of Czechoslovak Chemical Communications.)


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ELECTROCHEMISTRY, PAST AND PRESENT

Table I. Degrees of Dissociation (ck) of Some Multivalent Electrolytes in Aqueous Solutions at 25°C Hydration Numbers (nh) are Given in the Last Row


m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4

MgCl2

CaCl2

SrCl2

BaCl 2 AlCl3

ScCl3 YCl3

CrCl3

0.759 0.749 0.741* 0.739 0.741 0.742 0.739 0.739 0.740 0.741*

0.753 0.736 0.728 0.724* 0.725 0.725 0.723 0.722 0.725 0.725 0.724*

0.750 0.731 0.720 0.717* 0.717 0.715 0.713 0.713 0.715 0.717 0.717 0.715*

0.747 0.720 0.711 0.707 0.704* 0.704 0.702 0.702 0.701 0.702 0.703 0.704*

0.705 0.678* 0.677 0.681 0.680 0.676*

0.682 0.671* 0.670 0.672 0.671 0.670*

0.675 0.657* 0.655 0.658 0.657 0.655*

0.698 0.675* 0.672 0.673 0.674 0.673*

—

—

—

—

-

—

0.740 0.724 0.715 0.703 0.678 0.671 0.656

0.673

15.30

27.17

±0.002 13.38

12.08 9.08

28.82

26.20

24.65

±0.02 * the upper and lower limits of m between which

=

m

Table I (continued)

m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

m n

h

LaCl3

CeCl3

PrCl3

NdCl3

SmCl3

EuCl3

ThNO34

0.679 0.655 0.655* 0.657 0.659 0.659 0.654 0.656*

0.670 0.660 0.655* 0.655 0.657 0.654 0.658 0.654*

0.674 0.656 0.651* 0.652 0.652 0.649 0.653 0.651*

0.671 0.654 0.651* 0.653 0.655 0.651 0.654 0.650*

0.678 0.663 0.659* 0.659 0.659 0.656 0.660 0.659*

0.684 0.664 0.657* 0.658 0.659 0.657 0.660 0.657*

0.562 0.542 0.532* 0.530 0.532 0.532 0.530*

—

0.657 0.656 0.651 0.652 0.659 0.658 0.531 21.92

22.24

21.87

22.38

22.79

23.25

22.37


Figure 2. Variation of degree of disssociation ( ) with concentration (m) for 1:1 strong electrolytes in aqueous solutions at 25°C.


6. HEYROVSKA Arrlienius' Theory of Partial Dissociation of Electrolytes


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ELECTROCHEMISTRY, PAST AND PRESENT

Figure 3. Variation of degree of dissociation ( ) with concentration (m) for multivalent electrolytes in aqueous solutions at 25°C.



6. HEYROVSKA Arrhenius' Theory of Partial Dissociation of Electrolytes

83

Assuming n h to be the constant (maximum) hydration number in the concentration range from m = 0 to m corresponding to the end of linearity in Figure 1, as in (3), the values of i and hence of [=(i-1)/(v—1)] were then calculated from Equation 9 using the vapor pressure data in (3). Figures 2 and 3 show the variation of with m for thirty five 1:1 electrolytes and some 2:1, 3:1, and 4:1 electrolytes. The actual values of at various m for the electrolytes of Figure 2 are tabulated in Table I of (8). Table I here gives the data for multivalent salts. The general observations from the above results are: 1) As m increases, decreases steeply from unity at infinite dilution to a constsnt minimum value m over a large range of concentra tions (the smaller the nh , the larger this range). The maximum degree of association, (1 - m ) , increases as n h decreases, as can be expected. The existing theories do not predict the attainment of a constant degree of association, or dissociation, in the given solvent. The equilibrium represented by Equation 3 can be characterized by the dissociation ratio (8), K, which becomes a constant Km when = m .

For a detailed treatment of the electrolytic association/disso ciation equilibrium in terms of Lange's inner potentials of the ions, see (9e). 2) The degree of association, 1- , is higher for multivalent electrolytes, in agreement with accepted views. 3) n h decreases, in general, for the halides in the order, H+ >...>Cs+ ,Cl-

A Reappraisal of Arrhenius' Theory of Partial Dissociation of Electrolytes

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