TABLEA OF EQUILIBRIUM (SOLUTION-TENSION) CONSTANTS (IN MOLAR TERMS) AND OF POTENTIAL DIFFERENCES BETWEEN ELEMENTS AND THEIR IONS IN UNIMOLAR AQUEOUS SOLUTIONS.
| Element, Ion. | E.P.El.,Ion. | KIon. |
|---|---|---|
| K, K+ B | (−2.92) | 6E50 |
| Na, Na+ C | −2.44 | 2.5E42 |
| Ba, Ba2+ | (−2.54) | 2.1E88 |
| Sr, Sr2+ | (−2.49) | 4.0E86 |
| Ca, Ca2+ | (−2.28) | 2.0E79 |
| Mg, Mg2+ | (−2.26) | 4.1E78 |
| Al, Al3+ D | −0.999 ? | 1.3E52 |
| Mn, Mn2+ | −0.798 | 5.7E27 |
| Zn, Zn2+ | −0.493 | 1.4E17 |
| Cd, Cd2+ | −0.143 | 9.5E4 |
| Fe, Fe2+ E | −0.122 ? | 1.8E4 |
| Co, Co2+ F | +0.0138 ? | 0.3314 |
| Ni, Ni2+ G | +0.108 ? | 1.8E−4 |
| Sn, Sn2+ | <+0.085 | <1.1E−3 |
| Pb, Pb2+ | +0.129 | 3.3E−5 |
| H2, H+ H | +0.277 | 1.52E−5 |
| Cu, Cu2+ | +0.606 | 8.3E−22 |
| As, As+++ | <+0.570 | <2.7E−30 |
| Bi, Bi3+ | <+0.668 | <1.4E−35 |
| Sb, Sb3+ | <+0.743 | <1.7E−39 |
| Hg, Hg+ | +1.027 | 1.38E−18 |
| Ag, Ag+ | +1.048 | 6E−19 |
| Pt, Pt4+ | <+1.140 | 5E−80 |
| Au, Au3+ | <+1.356 | <1.8E−71 |
| F3, F− H | (+2.24) | 9.0E88 |
| Cl2, Cl− H | +1.694 | 3.16E29 |
| Br2, Br− | +1.270 | 1.23E22 |
| I2, I− | +0.797 ? | 7.26E13 |
| O2, HO− I | +0.698 | 1.36E12 |
[A] The table is based on Wilsmore's compilation of solution-tension potentials, Z. phys. Chem., 36, 91 (1901).
[B] Values in parentheses have been estimated by indirect measurements.
[C] G. N. Lewis, J. Am. Chem. Soc., 32, 1467 (1910).
[D] Values marked with? are uncertain.
[E] Calculated from the data of Richards and Behr (Z. phys. Chem., 58, 301 (1907)), who found the potential of iron against 0.5 molar FeSO4 to be −0.15 volt. The degree of ionization of 0.5 molar FeSO4 is taken as 22%. [Λ = 25.8 (Kohlrausch and Holborn, loc. cit., p. 152) and Λ∞ is taken as 117, as for ZnSO4 (ibid., p. 200).] On account of the doubtful value for the degree of ionization, the values in the table are marked?, but the value found by Richards and Behr appears to be quite accurate.
[F] Calculated from the data of Schildbach (Z. für Elektroch., 16, 967 (1910)). The same uncertainty as to the degree of ionization exists as that discussed in the previous footnote.
[G] Calculated from the data of E. P. Schoch (Am. Chem. J., 41, 208 (1909)). The same uncertainty as to the degree of ionization exists as that discussed in footnote 5, p. 294.
[H] The values for gaseous elements refer to the gases under one atmosphere pressure.
[I] The potential of oxygen at 18°, 760 mm., against an alkaline solution in which [HO−] = 1. KIon refers to the concentration of HO−, with which oxygen under atmospheric pressure would be directly in equilibrium, at 18°.
The potential differences, given in the table, are based on the assumption that the absolute zero of potential is at such a point, that the so-called standard normal calomel electrode has a value of +0.56 volt relative to this zero (cf. Ostwald, Z. phys. Chem., 36, 97 (1901)). The exact determination of this value is a very difficult matter. Recently Palmaer (ibid., 59, 129 (1907)), located the absolute zero at a point 0.04 volt more positive than the above, making the absolute potential of the normal calomel electrode, approximately, +0.52 volt. To refer potentials, given in this book, to this new zero, one would subtract 0.04 volt from all positive potentials and add 0.04 to the numbers representing negative potentials (e.g. E. P.Zn,Zn2+ would become −0.569 in place of −0.529 volt). Since the equilibrium (solution-tension) constants are calculated from the potential differences referred to the absolute zero (p. 259), any change in the zero involves corresponding changes in the values of the equilibrium constants, as calculated for this book. However, it should be noted that all potential differences would be corrected by the same constant quantity (0.04 volt for Palmaer's zero): all the equilibrium constants for univalent metallic ions would be increased proportionally to a constant factor c (c is very nearly equal to 5, for Palmaer's zero), the equilibrium constants for bivalent metallic ions would be increased proportionally to c2, etc. The equilibrium ratio for two metals and their ions would in no wise be changed by these alterations: e.g. for the equilibrium between zinc and copper and [p296] their ions (p. 267), Kequil. = KZn2+ / KCu2+; the factor c2 would be introduced into both terms of the ratio and would not affect the value of the latter. For the condition of equilibrium between silver and copper and their ions (p. 267) Kequil. = KAg+2 / KCu2+, and since (c)2 = c2, this equilibrium ratio would also not be affected. For elements, which produce negative ions, the corresponding correction factors would be 1 / c, 1 / c2, etc., and the equilibrium relations between two such elements and their ions likewise would remain unchanged. Since these equilibrium relations are the significant ones in this work, and since our conclusions have been based on them, it is clear that a change in the absolute zero would not affect the conclusions reached.
On account of the uncertainty attaching to the determination of the absolute zero of potential, it is preferred, in practice, to report the experimentally determined potentials as measured against a constant, well-defined electrode (such as the calomel electrode or a hydrogen electrode) and thus to eliminate the variation, which a change in the determination of the zero potential would make necessary. However, for an elementary discussion of oxidation-reduction reactions, from the same viewpoint as is used in considering all other reversible chemical actions, the idea of the absolute potential has certain advantages, making a uniform treatment possible.
1. Meaning of KIon. Under KIon is given, for each element, the concentration of its ion, with which the element would be directly in equilibrium at the ordinary temperature (see p. 258). The constants for gaseous elements represent the constants of the gases under atmospheric pressure.
2. The Condition for Equilibrium between Two Elements and Their Ions. The condition of equilibrium in a system of two elements and their ions may be found with the aid of the constants KIon, as follows: For Zn ↓ + Cu2+ ⥂ Zn2+ + Cu ↓ we have for the condition of equilibrium (see p. 267)
Zinc-ion must be present in enormous excess in the condition of equilibrium and zinc will precipitate copper from solutions of cupric salts until this relation is established. The suppression of the cupric-ion—by precipitation in the form of insoluble salts or by conversion into very stable complex ions—makes [Cu2+] exceedingly small and makes it increasingly difficult for zinc to precipitate copper, and, under certain conditions, the ordinary course of the action may be reversed (p. 268).
For Cu ↓ + 2 Ag+ ⥂ Cu2+ + 2 Ag ↓, we have (p. 267)
3. Potential Differences Calculated with the Aid of KIon. For metallic elements, which send out positive ions, in contact with an aqueous solution containing the ion in concentration [C], the potential difference is (see p. 261)
In these equations v represents the valence of the ion. It is clear that for the condition of equilibrium, in which [C] = KIon, the potential is 0. Further, for the potential difference between copper and a cupric salt solution in which [Cu2+] = 1, we would have
4. Meaning of E.P.Element, Ion. Under E.P.Element, Ion the table gives the potential difference in volts, calculated for the element named and an aqueous solution of its ion in unit concentration (one gram-ion per liter). For instance, for zinc and [Zn2+] = 1 (65.4 grams zinc-ion per liter), we have a potential E.P.Zn, Zn2+ = −0.493. The signs used, in accordance with the convention adopted (p. 261), indicate the character of the charge on the element electrode (which is named first in the subscript to E.P.). For instance, zinc in a solution in which [Zn2+] = 1 would acquire a negative charge (p. 266), the potential difference E.P.Zn, Zn2+ being −0.493 according to the table; silver, immersed in a solution in which [Ag+] = 1, would acquire a positive charge, the potential difference E.P.Ag, Ag+ = +1.048.
The potentials given for the gaseous elements represent the potentials of the gases under 760 mm. pressure.
5. Potential Differences Calculated with the Aid of E.P.Element, Ion. The potential corresponding to any concentration [C] of a metal ion may be found from the equation588
and the potential for any concentration [C] of the ions of elements forming negative ions is found588 according to
6. The Condition for Equilibrium between Two Metals and Their Ions, Calculated with the Aid of E.P.Element, Ion. The condition for equilibrium in a system of two metals and their ions is determined by the fact that the potential of the system must be 0 when equilibrium is established. We have, for instance for the two metals zinc and copper and their ions, Zn2+ and Cu2+, for Zn ↓ + Cu2+ ⇄ Cu ↓ + Zn2+ the condition for equilibrium that εCu, Cu2+ − εZn, Zn2+ = 0. According to the equation given in § 5, we have, then, for the condition of equilibrium,
Then
From the last relation we find log([Zn2+] / [Cu2+]) = 38.2261, and therefore, for the condition of equilibrium, [Zn2+] / [Cu2+] = 1.7E38.
7. Equilibrium Constants for Elements with Variable Concentration. The concentration of a pure metal at a given temperature may be considered a constant, except in the case of extremely thin films of the metal (p. 258). The concentration of hydrogen, and of the non-metallic elements given in the table, is variable, and KIon has a definite value only when the concentration of the element is defined (see the preceding table, footnotes 3, 4, p. 295). For certain estimations the equilibrium constants, which show the relation between the two variables, namely the concentration of the element and that of its ion, are very helpful (see pp. 274 and 275). In the following table some of the more important equilibrium constants of this nature are given.
TABLE OF EQUILIBRIUM CONSTANTS.
| Element. | Kequil.. |
|---|---|
| Hydrogen: [H+]2 : [H2] | 5.6E−9 |
| Oxygen: [HO−]4 : [O2] | 8.2E49 |
| Chlorine: [Cl−]2 : [Cl2] | 2E60 |
| IodineA: [I−]2 : [I2] | 5.6E29 |
The significance of the constants is indicated by the ratios given in the table. The relation of these constants to those given in the first table may be seen from the following illustration. For hydrogen we have H2 ⇄ 2 H+. The first table tells us that hydrogen, at 18° under atmospheric pressure, is in equilibrium with its ion when the concentration of hydrogen-ion is 1.52E−5 (under KIon). Now, a mole of hydrogen at 18° occupies 22.4 × 291 / 273 = 23.9 liters under atmospheric pressure, and its concentration (per liter) is therefore 1 / 23.9 mole. Then equilibrium exists, when [H2] = 1 / 23.9 and [H+] = 1.52E−5 and Kequil. = [H+]2 : [H2] = (1.52E−5)2 × 23.9 = 5.6E−9.
[553] These constants are calculated from data given in Wilsmore's tables (loc. cit.) on the solution tension of hydrogen. Hydrogen, at 18° under one atmosphere pressure, produces a potential of εH2, H+ = +0.277 (see p. 261, in regard to the sign) against a solution containing hydrogen-ion in a concentration [H+] = 1 (see the table at the end of this chapter). Now, there must be some concentration of hydrogen-ion, which we will call [C], with which hydrogen at 18° and 760 mm. pressure is directly in equilibrium, with the potential 0. For any concentration of hydrogen-ion [H+], other than [C], a potential is produced according to εH2, H+ = 0.0575 log([H+] / [C]). If we insert into this equation the values [H+] = 1 and the potential ε = +0.277, and if we solve the equation for [C], we find [C] = 1.52E−5. That is the concentration of H+, with which hydrogen of one atmosphere pressure at 18° is directly in equilibrium. Since under these conditions of temperature and pressure [H2] = 1 / 23.9 mole, we have for the condition of equilibrium [H+]2 / [H2] = K : (1.52E−5)2 : (1 / 23.9) = 5.55E−9 = K.
[554] Experimentally the relations for an "oxygen electrode" are much more complicated than for a hydrogen electrode, as a result, apparently, of the oxidation of the metal (e.g. platinum), with the aid of which the electrode is prepared. For a critical review and summary of the more recent results on this point, vide Schoch, J. phys. Chem., 14, 665 (1910). For the purposes of this book it will be sufficient to limit our discussion to the behavior of an ideal oxygen electrode.
[555] The bivalent oxygen ions, O2−, combine with hydrogen ions (formed, for instance, by the ionization of water) and form the more stable hydroxide ions (p. 246): O2− + H+ + HO− ⇄ 2 HO−, or simply, O2− + H+ ⇄ HO−. Then, [O2−] × [H+] / [HO−] = k and [O2−] = k × [HO−] / [H+]. But since we have [H+] × [HO−] = KHOH for the ionization of water (p. 176), we also have:
By substituting this value for the concentration [O2−] of the oxide-ion in equation (1), equation (2) is obtained. The constant K2 includes then the constants k and KHOH.
[556] The constants are calculated from the estimated potential of the oxygen-hydrogen cell, +1.231 volt, at 18°. (Vide G. N. Lewis, Z. phys. Chem., 55, 465 (1906); Nernst and Wartenberg, ibid., 56, 534 (1906); Brönsted, ibid., 65, 91 (1908); and a summary and discussion by Schoch, loc. cit.) At 18° oxygen, under one atmosphere pressure, gives an estimated potential εO2, HO− = +1.508 against an acid solution, in which the concentration of the hydrogen-ion [H+] = 1 (see the table at the end of this chapter). Since at 18° [H+] × [HO−] = 0.81E−14, the value for [HO−] in this acid solution is 0.81E−14. Now, for oxygen, at 18° and 760 mm., there must be some concentration of hydroxide-ion, which we will call [C], at which the tendency of the oxygen to ionize is exactly balanced by the tendency of the hydroxide-ion to form oxygen—at this point the potential is 0. For any concentration [HO−] of the hydroxide-ion, other than [C], a potential will exist εO2, HO− = 0.0575 log([C] / [HO−]). Since for [HO−] = 0.81E−14, we have a potential εO2, HO− = +1.508, these values can be introduced into the equation and the latter solved for [C]. We find thus [C] = 1.36E12, and oxygen, at 18° and 760 mm. pressure, would be directly in equilibrium with a solution in which [HO−] = 1.36E12. At 18° and 760 mm. pressure a liter of oxygen contains 1 / 23.9 mole, and thus we have for the condition of equilibrium [HO−]4 : [O2] = K : (1.36E12)4 : (1 / 23.9) = 8.2E49 = K.
[557] The most convenient form of electrode for this purpose consists (see Fig. 14) of a cylinder (about one inch long) of platinum gauze, which is fused to a glass tube and connected with a wire leading through the tube to some mercury, held in a small branch tube, fused into the main tube near its upper end. The gas is easily conducted to the platinum gauze electrode through such a tube. The cylinder of platinum gauze may be made by joining the ends of rolled gauze with pieces of molten glass. It is coated with platinum black.
[560] See Ostwald, Z. phys. Chem., 11, 521 (1893), Arrhenius, ibid., 11, 805 (1893), and Nernst, ibid., 14, 155 (1893), for a detailed discussion of oxygen-hydrogen gas cells. For more recent work, vide G. N. Lewis, J. Am. Chem. Soc., 28, 158 (1905), where references to other recent investigations are given.
[563] Fredenhagen, Z. anorg. Chem., 29, 424 (1902), has brought interesting experimental evidence of the charging of an electrode with gaseous oxygen, when ferric-ion is the oxidizing agent in aqueous solutions. Whether the oxygen, which is liberated by the action of the ferric-ion on water, 4 Fe3+ + 4 HO− ⇄ 4 Fe2+ + O2 + 2 H2O, is always the intermediate product and the direct oxidizing agent in aqueous solution, can hardly be considered decided by the experiment—it may well be the product of a parallel action, which must take place to a certain extent, according to the laws of equilibrium, in a system containing both Fe3+ and HO− ions. The result hardly proves that oxygen must be the intermediate product in the main action, when ferric ions act as the oxidizing agent. We may consider, for instance, a solution containing an iodide and a ferric salt: iodide ions have a far smaller affinity for their negative charges (electrons) than hydroxide ions have, and, consequently, will transfer their negative charges (electrons) more readily to the ferric ions than the hydroxide ions would. The action, if oxygen were first liberated, would lead to the same ultimate result, but the observation made by Fredenhagen would not prove that the main action would not nevertheless go by the shorter direct path rather than through an intermediate formation of oxygen.
[564] According to the theory, that arsenic acid is an oxidizing agent because it gives up oxygen of a definite pressure, this pressure would be the more effective, the more completely the opposing hydroxide-ion is suppressed by added acid (p. 280; see also p. 272, on the action of ferro-ion on silver-ion in the presence and in the absence of fluorides).
[565] Only the simplest form of basic ionization of arsenic acid is considered. Intermediate ionization into As(OH)4−, As(OH)32−, etc. (see p. 249), is, of course, to be assumed in any complete investigation of the subject.
[566] Arsenious acid As(OH)3, or HAsO2, as well as its anions AsO33− and AsO2−, may have their own characteristic tendencies to assume positive charges and be oxidized to arsenic acid and its derivatives (see footnote 1, p. 270). In alkaline solutions these tendencies, and the potentials corresponding to them, might well be more important factors in determining the course of an action, than the tendency of As3+ to form As5+. The discussion in the text, which deals primarily with acid solutions, does not exclude such relations.
[567] A millivoltmeter is used for this experiment.
[568] See footnote 1, p. 284, in regard to the interpretation of this experiment on the basis of the theory of liberation of oxygen by arsenic acid.
[569] Cf. Smith's General Inorganic Chemistry, p. 712.
[570] The essential feature of this point of view was first published by Abegg, Z. anorg. Chem., 39, 330 (1904), and Z. phys. Chem., 43, 385 (1903); vide also Stieglitz, Am. Chem. J., 39, 51 (footnote) (1908), and Qualitative Analysis Notes, University of Chicago (1905). Abegg's view has recently received support from J. J. Thomson in his Corpuscular Theory of Matter, p. 118.
[571] H+ does not change its valence (charge) in the action, and yet it appears as an essential component in both styles of the current equations for the oxidation-reduction reaction.
[572] A somewhat similar development of these relations, for arsenic acid, has been found in Abegg's Anorg. Chem., III, 3, p. 552 (1907).
[573] Luther and Michie, Z. für Elektroch., 14, 826 (1908).
[574] The calculation is based on the results obtained by Luther and Michie.
[575] The proportion of UO22+ converted into U6+ would be so minute, that in an experimental determination of the concentration [UO22+], the concentration [U6+] would no doubt be a negligible quantity.
[576] Peters, Z. phys. Chem., 26, 193 (1898).
[577] In other instances, the action of the hydrogen-ion in facilitating and accelerating chemical actions (often called its "catalytic effect") has been explained, in a similar fashion, as being based on salt formation, followed by the ionization of the salts formed, the active components being the ions (vide, for instance, Bredig, Z. für Elektroch., 9, 118 and 10, 586 (1904) and Stieglitz, Report of the Congress of Arts and Sciences, St. Louis, 4, 276 (1904) and Am. Chem. J., 39, 29, 415 (1908) and later articles). In many of these cases, the ion concentrations of the reacting components have not yet been accessible to direct measurements, but the viewpoint has been sustained by quantitative studies of analogous reactions, which were selected for study, because the factors involved could be measured (cf. Stieglitz, loc. cit.).
[578] Usher and Priestley, Proc. Roy. Soc., B, 77, 369 (1905); 78, 318 (1908).
[579] Tollens, Ber. d. chem. Ges., 15, 1635 (1882).
[580] [Ag+] × [NH3]2 / [Ag(NH3)2+] = 1 / 107.
[581] Methylene CH2, itself, has never been isolated, but derivatives of it are known, such as the cyanides, C(NH), C(NK) (see pp. 66, 237).
[584] If a negative charge is an electron, a positive charge the absence of an electron in an atom, the bivalent carbon atom loses two electrons, when it is oxidized.
[585] See Stieglitz, Science, 27, 774 (1908).
[586] The oxidation occurs essentially in the same manner as described (p, 292) for the action of formaldehyde on ammoniacal silver solution, when they are brought together in a single vessel. In the present case, where the action is used to produce an electric current, there is a migration of negative ions into the formalin solution through the salt-bridge (p. 254). For every two silver ions discharged on the electrode in the silver nitrate solution, two hydroxide ions are liberated in the formaldehyde solution, as a result of this migration, and they combine with the oxidized carbon atom. The oxidation may be expressed, then, simply as follows:
By comparison with the equations given on p. 292, it is evident, that the only difference lies in the fact that the positive charges, in the present case, are carried to the formaldehyde salt through metal wires and a metal electrode, while previously they were discharged directly by silver ions on the formaldehyde salt.
[587] Cf. Nernst, Theoretical Chemistry (1904), p. 739, and the applications mentioned there.
[588] Le Blanc, Elektrochemie, p. 215; v is the valence of the ion.
The systematic analysis for acid ions is made on a plan differing in an important particular from the systematic analysis for metal ions. The latter, as has been seen, are divided into groups, which, by precipitation or solution of characteristic salts, are successively separated from subsequent groups, before the isolated groups are analyzed. That is, in general, a group of metal ions is examined in the absence of the ions of all other groups. Acid ions are also divided into groups, but, as a rule, the groups are not separated from each other for analysis. The reason for this difference in procedure is found, chiefly, in the fact that foreign acid ions interfere589 to a smaller degree with the specific tests for the ions of a group, than is the case in the analysis for metal ions.
If acids were present only in the form of the free acids or of their alkali salts, the division into groups could naturally and profitably be made to include groups, which are identified by reactions carried out in neutral or alkaline solution, as well as by such as are made in acid solutions. Now, cations other than the alkali ions are liable to interfere with tests designed for alkaline or neutral solutions. For instance, a group of acid ions, in which the phosphate-ion is included, is characterized by the fact that the acids form barium salts, which are soluble in acid but not in neutral or alkaline solutions. The absence or presence of such a group may be recognized, if no cations other than the alkali metal ions are present, by the addition of barium chloride to the solution and by careful neutralization of any free acid, by ammonium [p300] hydroxide. Barium phosphate and the barium salts of the other acids of the group will be precipitated, if their ions are present. It is clear, however, that a number of metal ions must interfere with the test. For instance, a solution of aluminium nitrate or of ferric chloride, treated with barium chloride, and with ammonium hydroxide to neutralize the acid present in the solution as a result of the hydrolysis of the salt, would give a precipitate of aluminium hydroxide or of ferric hydroxide, and not of barium salts. The formation of a precipitate under these conditions evidently will not constitute any basis whatever for reaching a conclusion as to the presence or absence of acid ions, such as can form precipitates of barium salts under the same circumstances.