If it can be shown that the flow of electricity, resulting from such unequal diffusibility of ions, is a function not only of the difference in the total concentration of the electrolyte in the two solutions brought into contact with each other, but is also a function of the relative degrees of ionization of the electrolyte in the two solutions, as defined by the theory of Arrhenius, then this method of experimentation may be used as a further test of the validity of this theory as against that of Clausius. It is obvious that if such currents are the results of the diffusion of ions from higher to lower concentrations, then the essential concentrations do not embrace all of the electrolyte, but only the ionized part. W. K. Lewis97 has rather recently shown that the degrees of dissociation of electrolytes may be measured by the use of concentration cells, and that the results agree well with the determinations of the degree of dissociation from conductivity measurements (p. 50). From calculations, based on Jahn's accurate measurements of the electromotive forces of concentration cells, A. A. Noyes98 finds that "when the conductivity ratio is assumed to represent the degree of ionization of the salt, the calculated values of the electromotive force of concentration cells exceed the measured ones by only about one per cent, in the case of potassium and sodium chloride between the concentrations of 1 / 600 and 1 / 20 molar."
Solvents which cause ionization only to a minimal extent are benzene (C6H6), carbon bisulphide, ether, chloroform, petroleum ether (gasoline) and similar solvents. Hydrogen chloride dissolved in benzene has an extremely small conductivity, indicating only a trace of ionization.100
The question may be raised, why the first solvents mentioned should have the power to cause ionization, while the second series of solvents named do not have this power, or have it only to a very slight extent. Without attempting to enter into an elaborate discussion of this important question, it may be said that J. J. Thomson101 and Nernst102 suggested that the ionizing powers of solvents must be intimately connected with their dielectric behavior, and this view has now been well established. It may be said, in simple terms, that the so-called dielectric constant of a solvent determines the force with which electrical charges will attract and repel each other; the higher the dielectric coefficient of a medium, the smaller will be the attraction between opposite electrical charges, other conditions being the same. In solvents, then, of high dielectric powers, the coëxistence of oppositely charged particles must be more favored than in solvents of low dielectric powers. The dielectric constants of a number of solvents are given in the following table: [p063]
| Hydrogen cyanide, HNC | 95 |
| Hydrogen peroxide, H2O2 | 93 |
| Water, H2O | 81 |
| Methyl (wood) alcohol, CH4O | 32 |
| Ethyl (ordinary) alcohol, C2H6O | 22 |
| Ammonia, H3N | 22 |
| Chloroform, CHCl3 | 5 |
| Ether, (C2H5)2O | 4 |
| Benzene, C6H6 | 2 |
It is quite apparent that the good ionizing media have, as a matter of fact, the highest constants; those which cause ionization, at most minimally (e.g. benzene), the lowest.
Recent extended and exact investigations by Walden103 have succeeded in bringing the ionizing power of solvents into definite quantitative relations to their dielectric constants, with the result that order has been brought out of a condition of chaos that, for a number of years, existed in this field, as the result of conclusions based on incomplete data. Conductivity being a function both of the proportion of dissociated electrolyte and of the mobility of the ions in a given solution, Walden determined, for a certain salt (an organic derivative of ammonium iodide, namely, tetraethyl ammonium iodide N(C2H5)4I), for all solvents used, not only the conductivities for finite dilutions but also, by extrapolation, the limiting values for infinite dilution. He was thus able to determine the degree of ionization of the salt. Some of his results are particularly interesting; for instance, a poorly conducting solution, such as that of the salt in glycol, a solvent resembling glycerine in general character, may contain the dissolved electrolyte in a highly ionized state, while in a much better conducting solution the degree of ionization may be much smaller—the low conductivity of the first solution being the result of a very high friction and of the slow motion of the ions, while the well-conducting solution might show a very high degree of mobility of the ions. The mobility changes with the nature of the solvent, and the limit, Λ∞, of the equivalent conductivity of the salt, as found by Walden, ranges from 8 in glycol, which is a thick, viscous oil like glycerine, to 200 in acetonitrile, a thin mobile solvent. In the one solution, an observed conductivity of 4 represents 50% ionization of the salt, in the other only 2%.
Now, for solutions of a given electrolyte—tetraethyl ammonium iodide was used—Walden104 found the following exceedingly interesting relation between the ionizations in, and the dielectric constants of, various solvents:
where e1 and e2 represent the dielectric constants of different solvents, and c1 and c2 represent the concentrations of the salt in the solvents when the salt is ionized to the same degree105 in the two solutions.
The bearing of the relation is apparent from the data in the following [p064] table.106 The upper half of the table gives the dielectric constants (column two) of the solvents named in column one; the concentrations which show identical degrees of ionization—47%—are given in the third column, and the last column gives the value of the relation e : ∛c. The lower half of the table presents the same kind of data, for the same salt, when its degree of ionization is 91%, in the different solutions examined. It is clear that the numbers in the third column of each part represent approximately constants.
All solutions, including aqueous solutions, are thus brought into one general relation.
| Solvent. | e | c | e : ∛c |
|---|---|---|---|
| Methyl alcohol | 32.5 | 0.125 | 65 |
| Ethyl alcohol | 21.7 | 0.020 | 80 |
| Acetyl bromide | 16.2 | 0.010 | 75 |
| Benzaldehyde | 16.9 | 0.016 | 78 |
| Acetonitril | 35.8 | 0.100 | 77 |
| Water | 80 | 0.00910 | 383 |
| Furfurol | 39.4 | 0.00125 | 365 |
| Nitromethane | 40 | 0.00125 | 371 |
| Acetonitril | 36 | 0.00100 | 358 |
| Methyl alcohol | 32.5 | 0.00050 | 365 |
In liquid ammonia we might well have, for instance, the action +NH3-NH3− + HCl ⇄ +(NH3-NH3)H + Cl−, or +NH3-NH3− + H+Cl− ⇄ +(NH3-NH3)H + Cl−. Now, in liquid ammonia, the salts NH4Cl, NH4NO3 [or, more probably, (NH3)xHCl, (NH3)x,HNO3] have the functions of the aqueous acids109; that is, the hydrogen-ion of the acids is found combined with the solvent ammonia. The ion +(NH3-NH3)H, and similar ions in liquid ammonia, would correspond then to what is considered the hydrogen-ion in aqueous solutions110 (formed according to HCl ⇄ H+ + Cl−, as ordinarily written), and the polarized charges on molecules like +NH3-NH3− appear thus as possible active agents in this dissociation of the hydrogen chloride molecules. [p066]
Now, it is a significant fact that all the best ionizing solvents are compounds whose simple molecules are unsaturated exactly like those of ammonia; this is true for water H2O, the unsaturated character of whose oxygen atom is now universally recognized. It is now a familiar fact that liquid water is not represented by the formula H2O but consists of more complex molecules (H2O)n. According to the most recent investigations,111 while steam is H2O, or monohydrol, ice is trihydrol (H2O)3, and liquid water, at ordinary temperatures, a mixture consisting chiefly of dihydrol (H2O)2, some trihydrol, and very little monohydrol. The proportion of the last appears to increase with a rise of temperature; the proportion of trihydrol seems to increase with a fall in temperature. One can easily see how such aggregates would result from the saturation of the free charges on oxygen, by further molecules of water. One can also see that such an association of water molecules could leave a positive and a negative charge on the associated molecules, which would be polarized and more effective than the simple molecule would be.
That the molecule of hydrogen cyanide contains a similarly unsaturated atom was demonstrated by Nef.112 He proved that the behavior of hydrocyanic acid agrees with the structure expressed by the formula HN═C═, which we may well write HN═C±. In sulphur dioxide, another good ionizing solvent, we have, similarly, unsaturated sulphur, the sulphur atom being here quadrivalent, whereas its maximum valence is six.
Now, the ionizing power of solvents like water, ammonia, etc., has been ascribed, by various chemists, not only to their dielectric properties, but also to the unsaturated condition of their molecules, and particularly to their powers of association into large molecules. The relations developed suggest that all three properties are most intimately related, the dielectric properties and the powers of association being consequences, possibly, of the fundamental condition of unsaturation, and of the great tendency toward self-saturation,113 of the simple molecules of the best ionizing solvents. From Walden's work it appears that the dielectric constant finally determines the quantitative ionizing effect of a solvent.
[49] From the molecular weights of elements and compounds, the atomic weights of elements may be determined, with the aid of analysis. (Cf. Smith, Inorganic Chemistry (1909), p. 196, or General Chemistry for Colleges (1908), p. 130 (Stud.), or Remsen, Inorganic Chemistry, Advanced Course (1904), pp. 71–80 (Stud.).)
[50] The weight of a small volume of a gas or vapor, at any definite temperature and pressure, is determined. With the aid of Boyle's and Gay-Lussac's laws, this observed volume is then reduced to standard conditions. Finally, the weight of 22.4 liters, under standard conditions, is obtained by calculation.
[51] For the deduction of formulæ see Smith, Inorganic Chemistry, 196, 203; College Chemistry, 40; or Remsen, ibid., p. 79 (Stud.).
[52] Kopp, Liebig's Ann., 105, 390 (1858); Kékulé, ibid., 106, 143 (1858) (Stud.).
[53] Liebig's Ann., 123, 199 (1862) (Stud.).
[54] Wanklyn and Robison, Compt. rend., 52, 549 (1863) (Stud.).
[55] For instance in a test tube held in a horizontal position.
[56] By applying the corrections demanded by the kinetic theory (van der Waals's equation) to gases even under ordinary pressures, Guye and D. Berthollet have obtained, with the aid of Avogadro's hypothesis, values for the molecular weights of gases and for the atomic weights of their components, which compare in accuracy with the best analytical work on solutions and solids.
[57] The usual experimental methods consist in determining the elevation of the boiling-point, or the lowering of the freezing-point, or the lowering of the vapor tension of a solvent by a solute, methods which were discovered by Raoult and used empirically until van 't Hoff developed their relations to the Avogadro principle. The calculation of a molecular weight is much simplified by the use of the different specific constants expressing the lowering or elevation produced by one gram-molecule or mole, dissolved either in one liter or in 100 grams of each specific solvent.
[58] See Arrhenius, Z. phys. Chem., 1, 631 (1887).
[59] Or, on the basis of the accepted molecular weights, abnormally high osmotic pressures, abnormally great lowerings of the freezing-point, raisings of the boiling-point, etc., were obtained. Van 't Hoff, originally, on account of these discrepancies, considered this extension of the Avogadro Hypothesis to hold only for the "majority" of substances in solution, not for all (Arrhenius, loc. cit.). It was considered to have universal application (for dilute solutions) only after Arrhenius had explained the exceptions with the aid of his theory of electrolytic dissociation.
[60] That is, hydrogen chloride, in aqueous solution, depresses the vapor tension and the freezing-point and elevates the boiling-point considerably more than an equimolecular quantity, for instance, of glucose does, and gives a considerably higher osmotic pressure. The differences are relatively greater, the more dilute the solutions used.
[61] A fourth interpretation advanced at one time in opposition to the theory of ionization is that salts like sodium chloride and zinc chloride are hydrolyzed and thereby produce more solute molecules, e.g. NaCl + H2O → NaOH + HCl. Aside from the fact that such hydrolysis of salts, when it does occur (Chapter X.), is easily detected, and that it can be proved not to occur appreciably in the case of sodium chloride (loc. cit.), this interpretation fails utterly to account for the results obtained with acids, e.g. HCl, HNO3, H2SO4, and with bases, e.g. NaOH, Ba(OH)2, which in aqueous solutions show an increase in the number of molecules as great as shown by salts. This explanation is therefore untenable.
[62] Z. phys. Chem., 1, 631, (1887). Previous papers were published in the transactions of the Royal Academy of Sweden (Stockholm). For a history of the theory see Ostwald, Z. phys. Chem., 69, p. 1 (1909), and Arrhenius, The Willard Gibbs Address, J. Am. Chem. Soc., 1911 (Stud.).
[63] In the case of double salts, such as sodium-ammonium phosphate, and similar compounds, the dissociation leads to the formation of more than two products. The molecules of two or more different products may then be charged positively and, conversely, there may be two or more different products of dissociation carrying negative charges. We have, for instance, Na(NH4)HPO4 ⇄ Na+ + NH4+ + H+ + PO43− and Na(NH4)HPO4 ⇄ Na+ + NH4+ + HPO42−. In all cases the rule concerning the sum of all the charges, as expressed in (2), must be fulfilled, the charge on the phosphate ion, PO43−, being three times as great as that on a sodium, ammonium, or hydrogen ion; that on the acid phosphate ion, HPO42−, being twice as great.
[64] Ion = the going or the migrating particle.
[65] See Washburn, J. Am. Chem. Soc., 31, 322 (1909), in regard to the values of x and y, the quantities of water carried by certain ions.
[66] Vide J. J. Thomson, Electricity and Matter (1905) and Corpuscular Theory of Matter (1907) (Stud.). Vide R. A. Millikan, Science, 32, 436 (1910), on the discrete or "granular" nature of electricity (Stud.).
[67] See Millikan, loc. cit., as to the exact value of this "unit charge."
[68] Cf. McCoy, J. Am. Chem. Soc., 33, March, 1911, in regard to electropositive, composite (i.e. nonelementary) "metals."
[69] The symbol ε is used to designate an electron. The loss of one electron by an atom leaves a unit positive charge on the particle.
[70] In Chapter XV (q. v.) the affinity of the elements for electrons and the reactions, of the nature of oxidation and reduction, depending on this affinity, are discussed in detail.
[71] J. J. Thomson, Corpuscular Theory of Matter, p. 120.
[72] A. A. Noyes (Carnegie Institution Publications, No. 63, p. 351 (1907)), believes that we may have two kinds of molecules, HCl and H+Cl−, as well as the ions H+ and Cl−.
[73] Modern theory thus is reverting to the Berzelius theory of chemical affinity [Vide Meyer's History of Chemistry (translated by M'Gowan) 1891, 220–265, or Ladenburg's History of Chemistry (translated by Dobbin) 1900, 86, 88, etc.]
[74] To a saturated solution of cupric nitrate may be added a small amount of a saturated solution of potassium permanganate, sufficient to give a decided purple color to the mixture. Potassium chromate, as recommended by A. A. Noyes, may be used in place of the permanganate. (Cf. Noyes and Blanchard, J. Am. Chem. Soc., 22, 726 (1900).)
[75] Exp.; cf. Eckstein, J. Am. Chem. Soc., 27, 759 (1905) (Stud.).
[76] W. A. Noyes, J. Am. Chem. Soc., 23, 460 (1901); Stieglitz, ibid., 23, 796 (1901); Walden, Z. phys. Chem., 43, 385 (1903).
[77] Corpuscular Theory of Matter, p. 130 (1907).
[78] The experiment is an adaptation of a similar one described by A. A. Noyes and Blanchard, J. Am. Chem. Soc., 22, 726 (1900).
[79] The copper electrodes are polarized by the formation of hydrogen on the cathode, but, in the course of a few seconds, the current becomes rather constant and is then read. The polarization may be considered as simply reducing the potential of the cell, and since, within the range of concentrations of acid used,—4-molar to 1/8-molar—the polarization current does not vary markedly, as compared with the potential of the storage cell, the total potential used through the series of dilutions may be considered sufficiently constant for the purposes of the experiment. Readings are made three or four seconds after each dilution, when the polarization has been fully established. Polarization may be entirely avoided by the use of a silver nitrate solution and silver electrodes or of a cupric salt solution and copper electrodes (Noyes and Blanchard). Hydrochloric acid is used here in order to carry the discussion in the text as far as possible with this typical ionogen. If one takes care to make readings as described, the result is quite satisfactory, as is shown by the comparison of the ratios of the readings with the ratios calculated from the known conductivities of the various dilutions (see table below).
[80] Current = (Potential Difference) / Resistance, or Current = (Potential Difference) × Conductivity. For a constant potential difference, then, Current ~ Conductivity.
[81] The specific conductivity of a solution (commonly designated by κ) is the conductivity of a cube of 1 cm. edge; the molecular conductivity is the conductivity of a mole of the electrolyte; the equivalent conductivity (designated by Λ) is the conductivity of a gram-equivalent of the electrolyte. Λ = κ × v, where v is the volume, expressed in cubic centimeters, containing the gram-equivalent. For instance, the resistance of 0.1 molar hydrochloric acid in a cube of 1 cm. edge is 28.5 ohms and its conductivity (κ) therefore 1 / 28.5 or 0.0351 reciprocal ohms. Since 10 liters or 10,000 c.c. of 0.1-molar hydrochloric acid is the volume (v) containing one mole of the acid (the molar and the equivalent conductivities, for a monobasic acid being the same) Λ = 0.0351 × 10,000, or 351.
[82] Kohlrausch and Holborn, p. 200.
[83] Cf. Kahlenberg, Transactions of the Faraday Society, 1, 42 (1905).
[84] Clausius, Poggendorf's Ann., 101, 347 (1857) (Stud.). His theory replaced the older one of Grotthuss.
[85] Phil. Mag., 5, 729 (1903), and Transactions of the Faraday Society, 1, 55, (1905).
[86] Vide, Hudson, J. Am. Chem. Soc., 31, 1136 (1909), for a recent summary of results.
[87] Lectures on Physical Chemistry, 1, p. 131.
[88] Vide A. A. Noyes and Blanchard, J. Am. Chem. Soc., 22, 726 (1900).
[89] The concentrations are figurative, but may be taken to represent actual concentrations, such as 0.015 molar, etc.
[90] Kohlrausch and Holborn, loc. cit., p. 200.
[91] Raoult, Ann. de Chim. et de Phys. (6), 2, 84 (1884).
[92] The degree of ionization of mercuric chloride is based on Raoult's freezing-point measurements and is subject to revision, and the limit of the mobility of the mercuric-ion (½ Hg) is assumed to be 48, close to the values found for the ions of zinc and cadmium, elements in the same family as mercury.
[93] Lehfeldt's Electrochemistry, 1904, p. 3.
[95] Report of the British Association for the Advancement of Science, 1886, p. 389.
[96] With the aid of more elaborate apparatus rigorous demonstrations and measurements of such diffusion currents of so-called "concentration cells" are made.
[97] Z. phys. Chem., 63, 174 (1908). The work was carried out in Abegg's laboratory.
[98] Report of the St. Louis Congress of Arts and Sciences, IV, 314 (1904).
[99] Am. Chem. J., 20, 21, 23 (1898–1900).
[100] Kablukoff, Z. phys. Chem., 4, 429 (1889).
[101] Phil. Mag. (5), 36, 320 (1893).
[102] Z. phys. Chem., 13, 531 (1893).
[103] Walden, Z. phys. Chem., 54, 129 (1906); McCoy, J. Am. Chem. Soc., 30, 1074 (1908).
[104] Z. phys. Chem., 54, 229 (1906).
[105] The degrees of ionization were always determined from the relation α = Λv / Λ∞ according to the method discussed on page 50.
[106] Walden, loc. cit.
[107] Cf. Arrhenius, Theories of Chemistry, p. 83 (1907).
[108] In hydrogen chloride, the hydrogen and the chlorine atoms may be held in the molecules H+Cl− by the electric attraction of a positive charge on the hydrogen, and a negative charge on the chlorine atom (see p. 43).
[109] Franklin and Kraus, Am. Chem. J., 23, 305 (1900) (Stud.)
[110] It is very likely that in aqueous acids, a large proportion, at least, of the hydrogen-ion is similarly combined with water. (Lapworth, J. Chem. Soc., (London) 93, 2187 (1908). See Chapter XII.)
[111] Vide the discussion on the "Constitution of Water," and the summary by J. Walker, Transactions of the Faraday Society, VI, 71–123 (1910).
[112] Proc. Am. Acad., 1892; Liebig's Ann. 287, 263 (1895).
[113] Cf. Walden, Z. phys. Chem., 55, 683 (1906).
We will turn now to the consideration of evidence bearing on the theory of ionization, found in the data on osmotic pressure. The apparent molecular weight of hydrogen chloride is found to be smaller than 36.5, when determined in aqueous solution (p. 37), and it is found to approach the limit 18.25 as a more and more dilute acid is used.114 The value found represents the average molecular weight of all the molecules in any solution, the osmotic pressure, freezing-point or boiling-point of which has been taken. It is evident that, if there is dissociation of hydrogen chloride into hydrogen and chloride ions, the average values found for the molecular weight must be lower than 36.5, must be variable, and must approach the limit 18.25, as the dissociation into the smaller molecules becomes more and more complete. Such a result is, therefore, what we would anticipate on the basis of the theory of ionization. For a salt like potassium chloride KCl, a similar tendency toward a minimum, average molecular weight of (K+ + Cl−) / 2 or (39.1 + 35.5) / 2 = 37.3 would be anticipated, and, as a matter of fact, molecular weight determinations with potassium chloride in aqueous solution give results agreeing with such a tendency.115 For a salt like calcium chloride, on the other hand, we would expect that its ionization into three ions, according to the equation CaCl2 ⇄ Ca2+ + 2 Cl−, would give a minimum, not of one-half the formula weight, but of one-third, viz., (Ca2+ + 2 Cl−) / 3 or (40 + 71) / 3 = 37, when the molecular weight determination is carried out in aqueous solution. As a matter of fact, with salts of this type, the determinations, by osmotic pressure methods, indicate a dissociation into three smaller components, as required by the theory. It may be added that, for [p068] a salt, sodium mellitate, Na6(C12O12), the salt of a hexabasic acid, Taylor found average molecular weights tending to a minimum of one-seventh of the formula weight, as we should expect from the ionization of the salt into seven smaller molecules, (C12O12)Na6 ⇄ 6 Na+ + (C12O12)6−.