Yes Arrhenius, electrolytes are indeed partially dissociated in solutions at all concentrations

*R. Heyrovská

Symposium Svante Arrhenius

 

 

November 27 - 29, 2003, Uppsala, Sweden, commemorating

 the Centenary of the award of the

nobel prize to

svante arrhenius

 

*(J. Heyrovský Inst. of Phys. Chem., Academy of Sciences of the Czech Republic, Dolejškova 3, 182 23 Prague 8, Czech Republic.)

 

(photo: dbhs.wvusd.k12.ca.us/Gallery)

 

 

Contents

I: The theory of electrolytic dissociation due to Arrhenius, (p.3).
II: The anomaly of strong electrolytes, (p.4).    

III: The empirical theory of electrolytes, (p.5); 

Equations for properties of strong electrolytes based on complete dissociation, e.g., NaCl  ¢  Na+ + Cl-, (p.6). 

IV.1:  Arrhenius‘ theory of partial dissociation found valid from “0 to 3m“, (p.7). 

IV.2:  Arrhenius‘ theory of partial dissociation found valid from “0 to saturation“, (p.9);

Equations for properties of strong electrolytes based on partial dissociation, e.g., NaCl  D  Na+ + Cl-, (p.10).

IV.3:  Guldberg and Waage’s law found valid for 1:1 strong electrolytes, (p.12). 

IV.4:  Bjerrum’s theory found valid for 1:1 strong electrolytes, (p.13).      

V: Conclusion, (p.14). 

References, (pp. 15 – 26).

Figures (9) and Tables (3)

Photos, I: Arrhenius in Spitzbergen in 1896 and II: the same place, “Virgohamn“, in 1967 (photo by R. Heyrovská).

 

 

I: The theory of electrolytic dissociation due to  ARRHENIUS

 

    ARRHENIUS [1] made a major contribution to solution science when he discovered in 1883 that an electrolyte like NaCl dissociates in water partly into the “active (ions) form, the rest being the inactive (undissociated)“ form:

 

(1 - a)c NaCl  D (ac) Na+ + (ac) Cl-   

 

where a £ 1 is the degree of dissociation at concentration c. Arrhenius calculated a as the ratio, L/Lo, where L is the equivalent conductivity of the solution at concentration c and Lo is that at infinite dilution, when a = 1. The total number of moles of solute in the solution per mole of the dissolved electrolyte, is given by,

 

i = (1 - a) + 2a = (1 + a)  £ 2

 

This factor, i, appeared in van’t Hoff‘s [2] equation for the osmotic pressure, pos

 

posV = iRT

 

where V is the molar volume.

    Ostwald [3] found that Arrhenius theory confirmed Guldberg and Waage’s [4a,b] law for the dissociation constant K of a weak acid:

 

K = a2c/(1 - a) = (L/Lo)2c/[1 - (L/Lo)]

 

    The above successes brought Arrhenius, van’t Hoff and Ostwald, together as an “Ionist Trio“, who foresaw the great potentialities of the new theory. Ostwald’s laboratories soon became the “learning center“ for scientists from far and wide.

 

II. The anomaly of strong electrolytes  

 

    Subsequently, it was found that the use of the conductivity ratio for a was satisfactory only for dilute solutions, especially for highly dissociated electrolytes, a typical example being NaCl in aqueous solutions. Attempts were made at modifying the conductivity ratio and taking hydration of the solute into account.

    Bousfield [5] showed, although approximately, with the degrees of dissociation evaluated from freezing point depressions, that Raoult’s [6] law for the vapour pressure of solutions of non-electrolytes, is also valid for electrolytes, on allowing for their partial dissociation and hydration.

 

III. The empirical theory of electrolytes

 

    In the absence of any idea as to the concentration of the undissociated electrolyte“, Lewis and Randall (L & R) [7] proposed an empirical dissociation constant,

 

Ka = a+a-/aB = 1

 

where a+ = a- = aB1/2 = a± = mg± is the mean molal ionic activity in a solution of molal concentration m (m moles of solute per kg of solvent), aB is the molal activity of the undissociated electrolyte and g±  is the mean molal ionic activity coefficient.

    The observed linear dependence (approximate) of lng± and other solution properties on √m or √c for “very dilute solutions“, was explained by Debye and Hückel (D & H) [8a] as due to interionic interactions, by assuming complete dissociation of the electrolyte,

 

NaCl   ¢ Na+ + Cl-   

  

    The success of the D & H equations (which are for complete dissociation of the electrolyte) was taken as an endorsement of L & R’s definition of g±, although it involves the activity of the “undissociated“ electrolyte. L & R [7] stated that for (their) thermodynamics, it did not matter whether one considers the electrolyte as partially or completely dissociated.

    The D & H equations were subsequently extended, by adding more parameters and terms to fit the data for higher and higher concentrations.     

    Bjerrum [9] developed a theory of ionic association, but he too considered that ion pairs were unlikely in solutions of 1:1 electrolytes like NaCl(aq).

 

Equations for properties of strong electrolytes based on complete dissociation, NaCl   ¢ Na+ + Cl-

 

A:  Equivalent conductivity, L: (0 ~ 3m), [10]

Lo L  » (B1Lo + B2)Öc                                   c < 0.1m.

L = (h/hA)[ Lo ‑ B2Öc/(1+ BaÖc)][1‑ B1ÖcF/(1+ BaÖc)]

 

B:  Diffusion coefficient, D: (0 ~ 3m), [10]

D = (Do+D1+D2){1+0.036m[(D*/Do) - nh]} (1+mdlng±/dm)(hA/h)                                       

 

C:  Solvent activity, aA = (pA/pAo): (0 ~ 6m), [11]

= exp(-2mf/55.51); f : osmotic coefficient (non-ideality coefficient), (subscript A is for solvent)

posVA = -RTln aA = -RT(2mf/55.51)

f = 1- zMzXAfI1/2/(1+bI1/2) + m(2nMnX/n)(bMX(o) +bMX(1)exp(- aI1/2) + m2(4nM2nXzM /n)CMX    

 

D:  E.M.F. of concentration cells, DE: (0.01 ~ 6m), [11]

[= -(2RT/F)ln(mg±)];

g±: mean ionic activity coefficient (non ideality factor)

ln(g±) = - zMzXAf [(I1/2/(1+bI1/2)+(2/b)ln(1+bI1/2)] + m(2nMnX/n){2bMX(o)+(2bMX(1)/a2I)[1-(1+aI1/2-a2I/2) exp(- aI1/2)]} + m2(2nM2nX zM/n)(3CMX) 

 

E:  Molal volumes, Vm: (0 ~ saturation), [12]

Vf,MX = (Vm - VAo)/m = VMXo+Ao+A1bMX(o)V+A2bMX(1)V+A3bMX(2)V+A4CMXV  

 

IV.1: Arrhenius‘ theory of partial dissociation found valid from “0 to 3m“

 

    The author realized that the above theories had amounted to converting experimental data into ²catalogues² of best-fitting parameters, rather than “explaining“ the significance of the observed results. See [13] for similar opinions. Therefore, the author preferred to re-analyse the available data by a careful and systematic investigation (1980 -). It became gradually evident by 1984 that Arrhenius‘ idea of partial dissociation was indeed correct. The author obtained experimental support for the presence of ion pairs in the work (in 1992) on X-ray diffraction studies of saturated alkali halide solutions, by Ohtaki and Fukushima [14]. 

    Presented below are the main points of the author’s quantitative re-establishment of the theory of partial dissociation. Details can be found in articles [15] – [62].

    By systematic analyses of the existing experimental data, the author found [15], [16] that van’t Hoff’s gas-solution analogy was valid (for higher pressures of gases and) higher concentrations of solutions, with the van’t Hoff‘s factor i in Bousfield’s equation.

    Subsequently, [17] – [24], with the degrees of dissociation (a) and hydration numbers (constant, independent of m) evaluated from osmotic pressure (os.p.) using osmotic coefficient (f) data, the solution properties could be explained over a large concentration range, (0 to 3m), see Figs. 1 & 2.

    The Debye, Hückel and Onsager’s (D, H & O) [8a, b]  c“ law for conductivity, explaining Kohlrausch’s [8c] observation, was found to be an “asymptotic limiting law“ for complete dissociation at infinite dilution. For dilute solutions, L vs (1 - a) gave a linear dependence over a larger range of concentrations (0 - 0.1m) than the (D, H & O) law, e.g., see Fig. 1a.

    The quantitative correlations were further improved [25] – [39] by evaluating a and hydration numbers (ns) from the equation for vapour pressure using the data on osmotic coefficients (f).

 

IV.2: Arrhenius‘ theory of partial dissociation found valid from “0 to saturation“

 

    A re-examination of the results obtained so far, showed that the degrees of dissociation a obtained from osmotic pressure (os.p.) were nearly the same as that evaluated from vapour pressure (v.p.). On using the a values evaluated from v.p. into the equation for os.p., the latter (a bulk property) gave a lower hydration number than the former (an interfacial property) over the entire concentration range from “0 to saturation“.

    This finding enabled the author to evaluate values of a and hydration numbers (from the existing data on osmotic coefficients), which explained quantitatively the basic thermodynamic properties of NaCl(aq) from “zero to saturation“, for the first time. See Figs. 3 & 4, Tables 1 & 2 and [40] – [44].

    Thus, as the actual molalities of ions (2am) and ion pairs [(1 - a)m] became available since 1996, the non-ideality factors, g± and f (evaluated on the basis of complete dissociation) became un-necessary.  See Fig. 5.  

 

Equations for properties of strong electrolytes based on partial dissociation,

NaCl   D Na+ +  Cl-

 

(A): Equivalent conductivity (L):  [17, 22, 32]

Lo  L » L+‑(1 ‑ a)                     … (0 to 0.1m)

Lo  L = L+‑(1 ‑ a) + KL,p pos    (0 to ~ 3m)

where L+‑ and KL,p are constants, obtained as the slope and intercept of the linear plot of (Lo L)/pos vs (1 ‑ a)/pos. See Figs. 1a,b.

Note: The results have to be extended up to saturation, using the data in [43], [45], [48].

 

(B): Diffusion coefficient (D): [18, 32, 35]

D = (pos/c)[1/(hDNAv)]              (0 to ~ 3m)

Do = 2kT/hD                  … (at infinite dilution)                                       

where hD is the Stokes factor, NAv is the Avogadro number. The product Dhc increases linearly with pos. Since NAvD is the slope, one obtains D, for calculating Do. See Fig. 2.

Note: The results have to be extended up to saturation, using the data in [43], [45], [48].      

 

(C): Solvent activity, aA = (pA/pAo): [40 - 46, 48]

aA = NAfs = nAfs/(nAfs+im) [=exp(-2mf/55.51)] 

pos = iRT/VAfb = iRT(55.51m/nAfb)dAfb = 2RTmfdAfb

-aAlnaA/(1- aA) = nAfs/nAfb       ... “0 to saturation

where nAfs = (55.51 - mns), nAfb = (55.51- mnb) are the molalities of free water, ns and nb are surface and bulk hydration numbers, VAfb is the volume of free water per mole m, and dAfb is the density of free water. The values of ns, nb and i can be obtained by using the above relations and the available data on aA . See Figs. 3 - 5.

 

(D):  E.M.F. of concentration cells, DE : [40 - 46, 48, 55] [DE = -(2RT/F)ln(mg±)]; (DE from g±, data):

DE = - dA(2RT/F) ln[(am/nAfs)/rso]

                                                         ... (~ 0.001 to saturation)                                                                    

where nAfs = (55.51 - mns), (am/nAfs) = rs, and dA is the slope of DE vs ln rs straight line. See Fig. 6.

 

(E): Molal volumes, Vm: [43, 48, 53], “0 to saturation” 

Vm - VAo = m[(1- a)VBo+ afvo)];                  (m < ma,min)

Vm - VA = am(fvo + dVd) = am(VBo+ dVel); (m > ma,min)                                                                                                        

where VAo is the volume of 1kg of water in the pure state; VBo is the volume of one mole of the electrolyte; fvo = (V++ V- + dVel); V++ V- is the sum of the volumes per mole of the ions; dVel is the electrostriction, dVd  = VBo- (V++V-) and VA < VAo. See Fig. 7.

    The above interpretation was found to be valid for many 1:1 strong electrolytes [46], [48] and also monovalent sulphates [54]; (some up to saturation). The linearity of the graph of surface vs bulk hydration numbers for the electrolytes in Table 3, is shown in Fig. 8.

 

IV.3: Guldberg and Waage’s law found valid for 1:1 strong electrolytes

 

    The finding that the dissociation constant, Km = a2m/(1 - a) is not a constant, had led L & R [7] to suggest g±, the activity coefficient, as a correction factor for m. The author [43], [46], [48] found that the nonconstancy of Km was due to the use of m as the unit of concentration. The actual dissociation constant Kd involves “concentrations“ am/(Vi)soln and (1 - a)m/(Vip)soln, where (Vi)soln and (Vip)soln are the volumes of solution occupied by the ions and ions pairs respectively. The dissociation “constant“, Kd is given by,

 

Kd = {(am/Vi)2/[(1 - a)m/Vip]}soln

          = Kcr = [Vcr/(V+ + V-)2]cr = const

 

where Vcr and (V++V-) are the volumes per mole of the crystal and ions respectively. For NaCl (aq) at 25 oC, from „zero to saturation“, Kd = 0.080 mol.cm-3.

    Thus, the dissociation takes place in solution such that Kd = Kcr = constant, which demonstrates the beautiful and simple workings of “Nature“ - (Occam’s rule!).

 

IV.4: Bjerrum’s theory found valid for 1:1 strong electrolytes

 

    Bjerrum [9] thought that the critical distance (q = 3.57 Å at 25oC) of approach of the oppositely charged ions in 1:1 electrolytes was too large for ion pair formation. Since now the degrees of dissociation are known, the author used Bjerrum‘s equation [9], [12],

 

(1- a) = [2.755 f(a)]c

 

where f(a) is a function of the mean distance of closest approach, a, of the oppositely charged ions, to calculate (for the first time) the distance, a, for NaCl(aq) from “zero to saturation“. The value of a was found to increase from 1.85 Å at 0.1m to 3.53 Å (< q) at saturation. See [47], [51] and Fig. 9.

 

 

 

 

V: Conclusion

 

    The author would like to conclude by quoting the words (valid today!) of Dr. H. R. Törnebladh, President of the Royal Swedish Academy of Sciences, in his Nobel Prize Presentation Speech (on December 10, 1903):

“Doctor. The world of science already recognizes the importance and value of your theory, but its lustre will continue to increase in the days to come, as you yourself and others use it to advance the science of chemistry.“

 

 

 

 

 

 

 

 

 

 

References

 

I – III:

1. Arrhenius, S.: Z. Physik. Chem. I (1887) 631; Nobel Lecture, December 11, 1903; J. Amer. Chem. Soc., 34 (1912) 353.                

 

2. van’t Hoff, J. H.: Z. Physik. Chem. I (1887) 481.

 

3. Ostwald, W.: Z. Physik. Chem. 2 (1888) 270.

 

4a. Waage, P. and Guldberg, C. M.: Forhandlinger: Videnskabs-Selskabet i Christiana 1864, 35; from: http://chimie.scola.ac-Paris.fr/sitedechimie/hist_chi/text_origin/guldberg_waage/Concerning-Affinity.htm; see also [4b].

4b. Moelwyn-Hughes, E. A.: “Physical Chemistry“, Pergamon, London, 1957.

 

5. Bousfield, W. R.: Trans. Faraday Soc., 13 (1917) 141.

 

6. Raoult, F. M.: Z. Physik. Chem. 2 (1888) 353.

 

7. Lewis, G. N. and Randall, M.: J. Amer. Chem. Soc., 43 (1921) 1112.

 

8a. Debye, P. and Hückel, E.: Phys. Zeit., 24 (1923) 185.

8b. Onsager, L.: Phys. Zeit., 27 (1926) 388.

8c. Kohlrausch, F. and Maltby: Wiss. Abh. D. Physik. Technischen Reichsanstalt, 3 (1900) 155; from [4b].

 

9. Bjerrum, N.: K. Danske Vidensk. Selsk., 1926, 7; Proc. 7th Internl. Congr. Of Appl. Chem., London, 1909, p. 55.; from [4b] and [10].

 

10. Robinson, R. A. and Stokes, R. H.: “Electrolyte  Solutions“, Butterworths, London, 1955 & 1970.

 

11. Archer, D. G.: J. Phys. Chem. Ref. Data, 20 (1991) 509; 21 (1992) 793; 28 (1999) 1.

 

12. Pitzer, K. S., Peiper, J. C. and Bussey, R. H.: J. Phys. Chem. Ref. Data, 13 (1984) 1; Krumgalz, R., Pogorelsky, R. and Pitzer, K. S.: J. Phys. Chem. Ref. Data, 25 (1996) 663.

 

13. Darvell, B. W. and Leung, V. W-H.: Chemistry in Britain, 27 (1991) 29; Franks, F.: Chem. Britain, 27 (1991) 315.

 

14. Ohtaki, H. and Fukushima, N.: J. Solution Chem., 21 (1992) 23; Ohtaki, H.: Pure Appl. Chem., 65 (1993) 203

 

IV: [15] – [62], author:  R. Heyrovská:

(Full list in: http://www.jh-inst.cas.cz/~rheyrovs)

 

15. Dependence of van't Hoff‘s factor, partition function, Yesin-Markov and transfer coefficients on the partial molar volume.

157th Meeting of Electrochemical Society, USA, St. Louis, Vol. 80-1 (1980) Extd. Abstr. no. 526. 

 

16. van't Hoff's factor for non-ideality of gases and aqueous solutions; hydration numbers from osmotic coefficients; Langmuir's formula extended for space coverage.

159th Meeting of Electrochemical Society, USA, Minneapolis, Vol. 81-1 (1981) Extd. Abstr. no. 487.

 

17. Simple inter-relations describing the concentration dependences of osmotic pressure, degree of dissociation and equivalent conductivity of electrolyte solutions.

165th Meeting of Electrochemical Society, USA, Cincinnati, Vol. 84-1 (1984) Extd. Abstr. no. 425.

(100th Anniversary: Arrhenius‘ Ph.D. thesis in 1884.)

 

18. A simple equation connecting diffusion coefficient, coefficient of viscosity, concentration and osmotic pressure of electrolyte solutions; dynamics of Brownian motion.

165th Meeting of Electrochemical Society, USA, Cincinnati, Vol. 84-1 (1984) Extd. Abstr. no. 426.

(100th Anniversary: Arrhenius‘ Ph.D. thesis in 1884.)

 

19. A unified representation of properties of dilute and concentrated solutions without activity coefficient, further support: the linear dependence of E.M.F. on lnpos

166th Meeting of Electrochemical Society, USA, New Orleans, Vol. 84-2 (1984) Extd. Abstr. no. 653.

(100th Anniversary: Arrhenius‘ Ph.D. thesis in 1884.)

 

20. Concise equations of state for gases and solutions: PVf = i*RoT and posVAfB = i*RoT

166th Meeting of Electrochemical Society, USA, New Orleans, Vol. 84-2 (1984) Extd. Abstr. no. 652.

(100th Anniversary: Arrhenius‘ Ph.D. thesis in 1884.)

 

21. Thermodynamic interpretation of the E, lnp+/- linear dependence of E.M.F. of concentration cells, without activity coefficient.

168th Meeting of Electrochemical Society, USA, Las Vegas, Vol. 85-2 (1985) Extd. Abstr. no. 442.

 

22. Dependence of the specific and equivalent conductivities and transport numbers on the degree of dissociation of electrolytes.

168th Meeting of Electrochemical Society, USA, Las Vegas, Vol. 85-2 (1985) Extd. Abstr. no. 443.

 

23. Thermodynamic interpretation of the ionic association / dissociation equilibrium in solutions of electrolytes, without activity or osmotic coefficients.

168th Meeting of Electrochemical Society, USA, Las Vegas, Vol. 85-2 (1985) Extd. Abstr. no. 444.

 

24. Dissociation and solvation of 1:1 strong elecrolytes in aqueous solutions.

1st Gordon Research Conference on Physical Electrochemistry, New London, (1986). (Poster)

 

25. A simple proof for the incomplete dissociation of 1:1 strong electrolytes in aqueous solutions: interpretation of density.

171st Meeting of Electrochemical Society, USA, Philadelphia, Vol. 87-1 (1987) Extd. Abstr. no. 463.

(100th Anniversary: Arrhenius‘ important paper in Zeitschrift für physikalische Chemie, I, 631, 1887.)

 

26. Hydration numbers and degrees of dissociation of some strong acids, bases and salts in aqueous solutions at 25oC.

171st Meeting of Electrochemical Society, USA, Philadelphia, Vol. 87-1 (1987) Extd. Abstr. no. 472.

(100th Anniversary: Arrhenius‘ important paper in Zeitschrift für physikalische Chemie, I, 631, 1887.)

 

27. Physical Chemistry of solutions without activity coefficients: solvation and incomplete dissociation of strong electrolytes.

8th International Symposium on Solute-Solute-Solvent Interactions, Regensburg, Germany (1987), Extd. Abstr. no. L.1.19.

(100th Anniversary: Arrhenius‘ important paper in Zeitschrift für physikalische Chemie, I, 631, 1887.)

 

28. Dependence of e.m.f. of concentration cells on actual concentrations of ions, and `true pH'.

8th International Symposium on Solute-Solute-Solvent Interactions, Regensburg, Germany (1987),
(poster) Extd. Abstr. no. P.2.23.

(100th Anniversary: Arrhenius‘ important paper in Zeitschrift für physikalische Chemie, I, 631, 1887.)

 

29. Quantitative interpretation of properties of aqueous solutions on the basis of hydration and incomplete dissociation of electrolytes.

172nd Meeting of Electrochemical Society, USA, Hawaii, Vol. 87-2 (1987) Extd. Abstr. no. 1454.

(100th Anniversary: Arrhenius‘ important paper in Zeitschrift für physikalische Chemie, I, 631, 1887.)

 

30. Quantitative interpretation of properties of aqueous solutions in terms of hydration and `true ionic concentrations'.

International Symposium on Molecular and Dynamic Approaches to Electrolyte Solutions, Tokyo (1988), Extd. Abstr. p. 44.

 

31. Interpretation of properties of aqueous electrolyte solutions in terms of hydration and incomplete dissociation.

Collection of Czechoslovak Chemical Communications, 53 (1988) 686. 

 

32. A re-appraisal of Arrhenius' theory of partial dissociation of electrolytes.*

3rd Chemical Congress of North America and 195th Meeting of the American Chemical Society, Toronto, (1988):
In Book: Chapter 6, Same title*,"Electrochemistry, Past and Present", American Chemical Society Symposium Series 390, Editors: J.T. Stock and M.V. Orna, American Chemical Society Publications, Washington DC, (1989).

 

33. A re-appraisal of Arrhenius' theory of partial dissociation of electrolytes.

2nd Gordon Research Conference on Physical Electrochemistry, New London, (1988) (Invited Poster)

 

34. Degrees of dissociation and hydration numbers of six tetra alkyl ammonium halides and nineteen 2:1 strong electrolytes in aqueous solutions at 25oC.

Collection of Czechoslovak Chemical Communications, 54 (1989) 1227.

 

35. Effective radii of alkali halide ions in aqueous solutions, crystals and in the gas phase, and the interpretation of Stokes ionic radii.

Chemical Physics Letters, 163 (1989) 207.

 

36. Interpretation of A) solution properties in terms of solvation and incomplete dissociation and B) Stokes ionic radii in terms of ion-solvent interactions.

Proceedings II, J.H. Centennial Congress on Polarography and 41st Meeting of the International Society of Electrochemistry, Prague, 1990. (Poster) Extd. Abstr. Fr-112.

 

37. Ionic concentration outlives ionic strength.

Chemistry in Britain, 27 (1991) 1114.

 

38. Degrees of dissociation and hydration numbers of twenty six strong electrolytes in aqueous solutions at 25oC.

Collection of Czechoslovak Chemical Communications, 57 (1992) 2209. 

 

39. A: Incomplete dissociation of NaCl and 99 other strong electrolytes in a `sea' of water; B: "Ionic radii" and the mystery of "Stokes ionic radii".

"Futures in Marine Chemistry, XIIth International Symposium", May 1993, Brijuni, Croatia. (2 posters in English)

 

40. Physical electrochemistry of strong electrolyte solutions based on partial dissociation and hydration.

187th Mtg of the Electrochemical Society, USA, Reno, USA, Vol. 95-1 (1995) Extd. Abstr. no.662

(100th Anniversary: ARRHENIUS was appointed as Professor of Physics in Stockholms Högskola in 1895.)

 

41. YES ARRHENIUS, alkali halides are incompletely dissociated at all concentrations in water.

The Autumn Meeting of The Royal Society of Chemistry, Sheffield, UK, Sept. (1995). (Poster)

(100th Anniversary: ARRHENIUS was appointed as Professor of Physics in Stockholms Högskola in 1895.)

 

42. Physical chemistry of the kitchen salt in aqueous solutions.

The Autumn Meeting of The Royal Society of Chemistry, Faraday Symposium on "Ions in Solution", Sheffield, UK, Sept. (1995). (Lecture)

(100th Anniversary: ARRHENIUS was appointed as Professor of Physics in Stockholms Högskola in 1895.)

 

43. Physical electrochemistry of strong electrolytes based on partial dissociation and hydration: quantitative interpretation of the thermodynamic properties of NaCl(aq) from "zero to saturation".

Journal of Electrochemical Society, 143 (1996) 1789; (with Tables of data). Text in: http://www.jh-inst.cas.cz/~rheyrovs

(100th Anniversary: ARRHENIUS at the top of the world  in Spitzbergen with the Polar explorer Andree, 1896!)

 

44. Partial dissociation and hydration of strong acids and the significance of "pH".

Abstract, p. 13, Moderni Elektroanalyticke Metody XVI, Harrachov, Czech Rep., May 14-16, 1996. (in English)

(100th Anniversary: ARRHENIUS at the top of the world  in Spitzbergen with the Polar explorer Andree, 1896!)

 

45. Degrees of dissociation and hydration numbers of alkali halides in aqueous solutions at 25oC (some up to saturation)

Croatica Chemica Acta, 70 (1997) 39. (with Tables of data)

 

46. Equations for densities and dissociation constant of NaCl(aq) at 25oC from "zero to saturation" based on partial dissociation

Journal of Electrochemical Society, 144 (1997) 2380.

 

47. Bjerrum's theory for ionic association in NaCl(aq) at 25oC from "zero to saturation".

Abstract p.12. International Conference on Inorganic Environmental Analysis & Quality Assurance, Pardubice, Czech Rep., Sept. 2-5, 1997. (Poster in English)

 

48. Physical electrochemistry of solutions of strong electrolytes (partial dissociation and hydration from "zero to saturation")

Chemicke Listy, 92 (1998) 157. (A review in English), with Tables of data, also in: http://www.jh-inst.cas.cz/~rheyrovs

 

49. Notes on hydration theory

In Book (in Chapter 11): "Ionic Equilibrium", Ed.: J. N. Butler (John Wiley and Sons, New York, (1998).

 

50. No kidding! Strong electrolytes are only partially dissociated in aqueous solutions at all concentrations as Arrhenius supposed!

216th National Meeting of the American Chemical Society, Boston, Aug. 1998, short abstract no. 82. (Poster)

 

51. A remark on Bjerrum's theory of ionic association: partial dissociation of NaCl(aq) from "zero to saturation" at 25oC.

Journal of Molecular Liquids 81 (1999) 83; (with a Table of data).

 

52. Festina Lente (Hurry Slowly): The development of the theory of electrolytes.

Chemical Heritage Magazine, March 1999. (Abstract of talk by R. Heyrovská) 

 

53. Volumes of ions, ionpairs and electrostriction of alkali halides in aqueous solutions at 25oC

217th National Meeting of the American Chemical Society, Anaheim, March 1999, Abstract no. 61.

Marine Chemistry, 70 (2000) 49. (Proceedings, Dedicated to Frank J. Millero on the occasion of his 60th birthday); (with Tables of data)

 

54. Degrees of dissociation and hydration numbers of M2SO4 (M = H, Li, Na, K, Rb, Cs and NH4) in aqueous solutions at 25oC.

1999 Joint International Meeting (196th Meeting of The Electrochemical Society, USA, 1999 Fall Meeting of The Electrochemical Society of Japan with technical cosponsorship of The Japan Society of Applied Physics), Honolulu, Hawaii, October 1999, Extd. Abstr. of the ECS, Vol. 99 –2, no. 2041, 1999; (with a Table of data).

 

55. Thermodynamic significance of transfer coefficients. (Involves partial dissociation)

2nd Workshop of Physical Chemists and Electrochemists: "Physical chemistry and Electrochemistry at the end of the second Millenium", Masaryk University, Brno, February 2000. Book of Abstracts, page 11. (in English)

 

56. The Theory of Electrolytes.

Chemical Heritage 18 (2000) 29; (by M. V. Orna, abstract of talk by R. Heyrovska')

 

57. Sorry Lewis, Bancroft was right: the concentration/activity controversy and the survival of the Journal of Physical Chemistry.

219th Meeting of The American Chemical Society, San Francisco, March 2000, Abstr. no. 37.

 

58. J. Heyrovsky's data in 1923 on the deposition potentials of alkali metal cations interpreted here in terms of partial dissociation and hydration.

J. Heyrovsky Memorial Symposium on Advances in Polarography and Related Methods, Prague, Czech Republic, August/September 2000. Extended abstract, p. 36 (in English).

 

59. Recent success of the theory of partial dissociation and hydration of electrolytes (A tribute to van't Hoff and Arrhenius on the occasion of the Nobel Centennial, 2001)

Prague - Dresden Electrochemical Seminar, Jetrichovice, Czech Republic, December 2001. Book of Abstracts, p. 15 (in English)

 

60. E.m.f. of cells: simple dependence on hydration, partial dissociation and transfer coefficient (not on activity coefficients and extended Debye-Huckel equations!)

3rd Workshop of Physical Chemists and Electrochemists, Masaryk University, Brno, February 2002, Book of abstracts, page 24. (In English)

 

61. Comments on the Pitzer equations formulated on the assumption of complete dissociation of strong electrolytes.

Journal of Physical and Chemical Reference Data, Volume 29, No. 4, 2000 (assigned volume and number after accepting and proof-reading, but the article was not published!)

 

62. A Concise Equation of State for Aqueous Solutions of Electrolytes Incorporating Thermodynamic Laws and Entropy.

(Invited paper) Special Issue of ENTROPY, December 1, 2003.

(100th Anniversary: ARRHENIUS was awarded the Nobel Prize in 1903!)

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 1a: Dilute Solutions

 

 

Fig. 1b: 0.05 to 3.75M

 

 

From: R. Heyrovská, Chapter 6 "Electrochemistry, Past and Present", ACS Symp. Series 390, Eds: J.T. Stock and M.V. Orna, ACS Publications, Washington DC, (1989).

 

                                                                                                                                             

 

 

 

 

 

 

 

 

 

Fig. 2.  KBr, “0 to 3.75M”

 

 

 

From: R. Heyrovská, Chapter 6 "Electrochemistry, Past and Present", ACS Symp. Series 390, Eds: J.T. Stock and M.V. Orna, ACS Publications, Washington DC, (1989).

 


 

 

 

 

 

 

 

 

 

    Fig. 3. NaCl(aq) at 250C: “0 to saturation (6.14m)”

 

 

 

 

    Slope = - nb = -2.457 (S.E., 0.001); intercept = 55.51 (S.E., 0.01)

 

         From: R. Heyrovská, Journal of Electrochemical Society, 143 (1996) 1789.

 

 

 

 

 

 

 

 

             Fig. 4. NaCl(aq), “0 to saturation”

 

 

 

From: R. Heyrovská, Journal of Electrochemical Society, 143 (1996) 1789.


Table 1. NaCl(aq), a at various m

 

Degrees of dissociation (a) at various molalities (m)
(6.144m: satd. soln.) for NaCl (aq) at 25oC, RAf (Eq. 7)

 and the comparison of f (Eq. 4) with f.14 

--------------------------------------------------------------------------

  m       f14      f(Eq.4)   RAf    a(Eq.6)  a(Eq.4)

---------------------------------------------------------------------------
0,000   1,000    1,000   1,00000   1,000    1,000
0,001   0,988    0,988   0,99998   0,976    0,976
0,002   0,984    0,984   0,99996   0,968    0,968
0,005   0,976    0,976   0,99991   0,952    0,952
0,010   0,968    0,968   0,99983   0,935    0,935
0,020   0,959    0,959   0,99965   0,916    0,916
0,050   0,944    0,944   0,99915   0,884    0,884
0,100   0,933    0,933   0,99832   0,858    0,858
0,200   0,924    0,924   0,99667   0,832    0,832
0,300   0,921    0,921   0,99503   0,818    0,818
0,400   0,920    0,920   0,99339   0,808    0,807
0,500   0,921    0,921   0,99173   0,801    0,801
0,600   0,923    0,923   0,99006   0,797    0,797
0,700   0,926    0,926   0,98837   0,795    0,795
0,800   0,929    0,929   0,98667   0,792    0,792
0,900   0,932    0,932   0,98497   0,790    0,790
1,000   0,936    0,936   0,98323   0,789    0,789
1,200   0,944    0,944   0,97973   0,788    0,788
1,400   0,953    0,953   0,97616   0,788    0,788
1,600   0,962    0,962   0,97253   0,787    0,788
1,800   0,973    0,973   0,96878   0,791    0,791
2,000   0,984    0,984   0,96497   0,793    0,794
2,500   1,013    1,013   0,95507   0,801    0,802
3,000   1,045    1,045   0,94459   0,812    0,812
3,500   1,080    1,080   0,93345   0,826    0,825
4,000   1,116    1,116   0,92174   0,837    0,837
4,500   1,153    1,153   0,90944   0,847    0,847
5,000   1,191    1,192   0,89656   0,856    0,855
5,500   1,231    1,231   0,88298   0,863    0,863
6,000   1,270    1,270   0,86900   0,865    0,865
6,144   1,281    1,280   0,86491   0,864    0,865

 

From: R. Heyrovská, Journal of Electrochemical Society, 143 (1996) 1789.

 

 

 

Table 2. NaCl(aq), d and V vs dcal and Vcal at various m

 

 

The densities (d) (g/cm3),18 molal volumes (V) (cm3), degrees
of dissociation (a), and ionic molalities (am) of NaCl(aq) at 25oC. Vcal
and dcal are the calculated values. Km values are as per Eq. 8. d for the
saturated solution is from Ref. 25.

----------------------------------------------------------------------------------

m         d             V               a         am        Vcal      d - dcal       Km

-----------------------------------------------------------------------------------

0.000   0.99709   1002.92   1.000   0.000   1002.86   -0.00006   ------
0.100   1.00117   1004.67   0.858   0.086   1004.63   -0.00003    0.52
0.250   1.00722   1007.34   0.825   0.206   1007.38    0.00005    0.97
0.500   1.01710   1011.92   0.801   0.401   1012.03    0.00012    1.61
0.750   1.02676   1016.63   0.793   0.595   1016.69    0.00006    2.28
1.000   1.03623   1021.44   0.789   0.789   1021.34   -0.00010    2.95
2.000   1.07228   1041.60   0.794   1.587   1041.64    0.00004    6.10
3.000   1.10577   1062.91   0.812   2.436   1062.65   -0.00027  10.52
4.000   1.13705   1085.06   0.837   3.348   1085.21    0.00015  17.19
5.000   1.16644   1107.83   0.855   4.275   1108.14    0.00033  25.21
6.000   1.19423   1130.99   0.865   5.190   1130.78   -0.00022  33.25
6.144   1.1978     1134.64   0.865   5.315   1133.86   -0.00082  34.05

 

 

From: R. Heyrovská, Journal of Electrochemical Society, 143 (1996) 1789.


 

 

 

  Fig. 5. f, g± (complete dissocn.) & a (partial dissocn.)

 

 

 

From: R. Heyrovská, Chemicke Listy, 92 (1998) 157.

 

 


 

 

Fig. 6. DE vs. ln (am/nAf)

 

 

 

 

From: R. Heyrovská, first graph obtained in April 1994.

 


 

 

 

Fig. 7. Vm (c.d.) vs Vm (p.d.) “0 to saturation”

 

 

X-axis: Vm (c.d.) calculated from the parameters of Krumgalz, Pogorelsky and Pitzer equation, JPCRD, 1996.

Y-axis: Vm (p.d.) calculated from volumes of ions, ion pairs, water and electrostriction.

 

R. Heyrovská, Journal of Electrochemical Society, 143 (1996) 1789; 144 (1997) 2380.

   

 

 

 

 

 

Fig. 8. Surface vs bulk hydration numbers: (ns vs nb)

 

 

 

 

 

From: R. Heyrovská, Chemicke Listy, 92 (1998) 157.

 

 


 

Table 3

 

From: R. Heyrovská, Chemicke Listy, 92 (1998) 157.

 

 

 

 

 

 

          Fig. 9. NaCl(aq) at 250C, “0 to saturation”

 

        (Distance of closest approach, a vs m)

 

 

 

From: R. Heyrovská, Journal of Molecular Liquids 81 (1999) 83.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Photos, I & II

I: From: E. Crawford, “Arrhenius: Ionic theory to the greenhouse effect”, 1996

 

 

 

 

 

 

 

II. Photo of the same place in 1967 (by R. Heyrovská)