Perhaps the most instructive case of this kind, that we can study, is that of iron in ferrous and ferric salts. Exceedingly sensitive tests are known for the ferrous and the ferric ions. Thiocyanates produce an intensely red salt, Fe(SCN)3, when added, for instance, to ferric chloride; potassium ferrocyanide, K4Fe(CN)6, precipitates ferric ferrocyanide, Fe4[Fe(CN)6]3, Prussian blue, from ferric chloride solutions; ammonium hydroxide precipitates quantitatively the insoluble red ferric hydroxide (exps.). With ferrous salts, potassium ferricyanide K3Fe(CN)6 precipitates ferro-ferricyanide Fe3[Fe(CN)6]2, Turnbull's blue; ammonium sulphide precipitates black ferrous sulphide (exps.). Now, in two of the reagents used, potassium ferro- and ferricyanide, iron is present according to the formulæ given. If one should attempt to demonstrate its presence by means of these tests—among the most sensitive and most reliable tests known in analysis—one would fail utterly. Thiocyanates do not produce even the faintest tinge of pink in potassium ferricyanide solution163; ammonium hydroxide does not precipitate any ferric hydroxide (exps.). Ammonium sulphide does not precipitate the least trace of a black sulphide from a ferrocyanide solution, and when the latter is mixed with the ferricyanide solution, no trace, either of Prussian or Turnbull's blue, is shown (exps.). The contrast between the behavior of these salts and ferrous and ferric salts is now sharply and definitely interpreted, as being the result of the contrast in their ionization,—the color tests we use are extremely sensitive tests only for the ferric and ferrous ions, Fe3+ and Fe2+, respectively,—but potassium ferrocyanide ionizes into potassium ions and the negative ferrocyanide ions Fe(CN)64−, and shows the actions of ferrous ions as little as chlorate ions ClO3− exhibit the reactions of chloride ions Cl−. Potassium ferricyanide, in turn, gives rise to trivalent, negative ferricyanide ions Fe(CN)63− and not to ferric [p089] ions.164 If any doubts arise on this point, one can decide the question readily by experiment. When a concentrated solution of potassium ferricyanide is placed in a U-tube under a solution of some colorless electrolyte, such as sodium sulphate, and plates connected with a battery are inserted, there is no difficulty (exp.) in seeing that the yellow ion,165 containing the iron, moves to the positive pole and not to the negative. The iron is, therefore, as a matter of experiment, part of a negatively charged substance.
That iron is really present in these compounds can be shown most effectively if we destroy the salts:
Exp. Dry, pulverized potassium ferrocyanide is intimately mixed with dry potassium carbonate and the mixture heated in a hard glass test tube. When the whole mass has become red-hot, insuring complete decomposition, the hot (not red-hot) tube is plunged into water; the salts are extracted and particles of metallic iron are left undissolved. The action is
If the iron is dissolved in a little dilute hydrochloric acid and oxidized to the ferric condition, by the addition of a few drops of bromine water, the intensely red solution characteristic of ferric salts may be readily obtained, when a thiocyanate is added to the solution.
[114] Loomis. (Cf. Whetham, Theory of Solution, p. 320 (1902).)
[115] Loomis; and E. H. Griffith. (Cf. Whetham, loc. cit.)
[116] Expressed in moles per liter.
[117] Δ1 : Δ2... = C1 : C2...or Δ1 / C1 = Δ2 / C2 = a constant.
[118] Cf. Whetham, loc. cit., pp. 147, 158.
[119] Ibid., p. 320.
[120] In regard to the degrees of ionization, as shown by freezing-point depressions and conductivities of salts, see also A. A. Noyes, Report of the Congress of Arts and Sciences, St. Louis, 1904, Vol. IV, p. 313.
[121] See Chapter XII, in regard to so-called "complex ions" and their salts.
[122] The term "acid ion" is used to designate the "acid radical," when it exists, in solution, as an independent charged particle or ion. "Acid ion" is thus a convenient synonym for anion, just as "metal ion," designating the metal or metal-like radical of a salt, is used as a synonym for cation. The term, acid ion, has been found to convey more quickly and definitely to the student's mind, than does the term anion, which component of an acid or salt is referred to. While it is not, in some respects, an ideal term, yet its use seems justified by its very close relation to the term "acid radical" and by its practical advantages.
[123] The principle was first applied by Hittorf.
[124] This does not preclude the possibility that the ion is combined with more or less water and is Na(H2O)x+; see pp. 42, 65.
[125] Baker, J. Chem. Soc. (London), 65, 611 (1894), 73, 422 (1898). On page 623 of the first article is given a list of chemical actions for which the effect of the presence of moisture has been investigated (Stud.).
[126] Hughes, Phil. Mag., 34, 117 (1892) (Stud.).
[127] Gore, Proc. Royal Soc., 14, 204 (1841). Gore found that aluminium was dissolved and that sodium and potassium were attacked by the gas, even before its liquefaction. It is uncertain whether these positive reactions are reactions of absolutely anhydrous hydrogen chloride or the result of the presence of moisture in the experiments in question, since Cohen [Chem. News, 54, 305 (1896)], drying the gas more carefully than did Gore, found, in contrast to the latter, that metallic sodium may be exposed for several weeks to dry hydrogen chloride gas and retain its lustre. In all experiments demanding the rigorous exclusion of moisture, more weight must be attached to negative results (showing lack of activity) than to positive results. [Cf. the controversy between Baker, loc. cit., and Gutmann, Liebig's Ann., 299, 3 (1898)].
[128] Nernst's Theoretical Chemistry, p. 375. Kablukoff, Z. phys. Chem., 4, 430 (1889).
[129] In regard to the behavior of zinc, see below, p. 84. (Cf. Kahlenberg, J. Phys. Chem., 6, 13 (1902) (Stud.).)
[131] The acid character, in particular, is due to the hydrogen-ion, H+; see below.
[132] The fusion is conveniently made in a platinum dish; the dish and a platinum cathode are connected with the lighting circuit and an electric lamp.
[133] See Smith, Inorganic Chemistry, pp. 550, 569, 578, 588, 608, 610, 683: College Chemistry, 361, 373, 380, 389, 404, 405, 443 (Stud.).
[134] J. Chem. Soc. (Abstracts) (London), 40, 504 (1881).
[135] For positive evidence of the ionizing power of light, see Haber, Z. Elektrochem., 11, 847 (1905). For evidence as to the negligible rôle of ionization in the combination of chlorine and hydrogen, see Mellor, Chemical Statics and Dynamics (1904), p. 290.
[136] The apparatus described by A. A. Noyes and Blanchard for comparing acids is used [J. Am. Chem. Soc., 22, 737 (1900)].
[137] The conductivity depends in this case chiefly on the migration of the fast moving hydroxide ions (p. 56), common to the three bases. There is little difference in the rates at which the cations move.
[138] The water should be free from carbonic acid.
[139] The various indicators show different, specific degrees of sensitiveness to acids (to hydrogen ions) and to bases (to hydroxide ions). That is, different concentrations of hydrogen-ion or of hydroxide-ion are required to change their colors. As they are particularly useful in demonstrating varying concentrations of these ions, they will frequently be used in illustrating conclusions reached in the course of our work, just as they are used extensively in practical analysis. The following tables are intended to give some definite information on this valuable quality. The fourth column of the first table shows the concentration of hydrogen-ion, required to change the color of the indicator from the tint given in the second column to the tint given in the third column. The second table gives, similarly, the concentrations of hydroxide-ion required to produce the changes of tint indicated. The tables refer to results obtained when 0.1 c.c. (about two drops) of a 0.1 to 0.15% solution of the indicator is added to 10 c.c. of the solution examined.
Table of Sensitiveness to Acids (to Hydrogen-ion)
| Indicator. | From | to | Concentration H+. |
|---|---|---|---|
| Phenolphthaleïn | Pink | Colorless | 10E−9 |
| AzolitminA (litmus) | Violet | Violet pink | 1E−6 |
| Methyl orange | Yellow | Reddish orange | 1E−3 – 0.1E−3 |
[A] Azolitmin is an important component of litmus.
Table of Sensitiveness to Bases (to Hydroxide-ion)
| Indicator. | From | to | Concentration HO−. |
|---|---|---|---|
| Phenolphthaleïn | Colorless | Pink | 10E−6 |
| Azolitmin | Violet | Violet blue | 1E−6 – 0.1E−6 |
| Methyl orange | Orange | Yellow | 1E−9 |
It is clear that of the three indicators given in the table, phenolphthaleïn is the most sensitive to acids, methyl orange the most sensitive to bases. An extended table of the sensitiveness of many indicators, on which the above tables are based, is given by Salm, Z. phys. Chem., 57, 471 (1907). The theories (of Ostwald, Bernthsen, and others) regarding the color changes, and the theory (of Ostwald) concerning the sensitiveness of indicators, are discussed (with references to the literature) by Stieglitz, J. Am. Chem. Soc., 25, 1117 (1903). Later modifications of the views on color changes are discussed in papers by Stieglitz, Am. Chem. J. 39, (1908), and by Acree, ibid., 37, 39, 42, and in these papers references to the literature will be found. For investigations on the sensitiveness of indicators, see McCoy, ibid., 31, 508 (1904), Salm, loc. cit., and A. A. Noyes, J. Am. Chem. Soc., 32, 815 (1910).
[140] Z. phys. Chem., 2, 289 (1888). Note the remarks in the footnote following.
[141] The formation of an ammonium salt in the latter action still further reduces the concentration of the hydroxide-ion (Chapter VI) and retards the action; but the solution, in equal measure, becomes less active toward the indicator, phenolphthaleïn (p. 114). The experiment shows, therefore, rather fairly, the relative activities of the bases. The exact work of Arrhenius included consideration of the effect of the ammonium salt, and the clearing up of the mystery of this effect (p. 114) formed one of the greatest triumphs of his theory.
[142] Arrhenius, Electro-chemistry, p. 184 (1902). A second accelerative factor, the so-called "salt effect" (Chap. VI, q. v.), is more pronounced in the case of 0.1 molar hydrochloric acid than in that of 0.1 molar acetic acid, as the result of which the activity of the hydrochloric acid should be increased about ten per cent; the ratio, therefore, of the speeds of reaction, both the degrees of ionization of the acids and the "salt effect" being considered, should be approximately 83 : 1, whereas the ratio found by experiment is 79 : 1.
[143] Vide also A. A. Noyes, Report of the Congress of Arts and Science, Vol. IV, p. 311 (1904).
[144] Haber, Z. für Elektrochem., 10, 775 (1904); see Chapter XII.
[145] This is, essentially, the old Berzelius view of chemical action.
[146] Vide, for instance, Stieglitz, Report of the Congress of Arts and Sciences, St. Louis, IV, 276 (1904); W. A. Noyes, Ibid., 285; Nef, J. Am. Chem. Soc., 30, 645 (1908). For the application of the electron theory to organic compounds, see Falk and Nelson, School of Mines Quarterly, 30, 179, and J. Am. Chem. Soc., 32, 1637 (1910). (Cf. also Chapter XV.)
[147] J. Phys. Chem., 6, 1 (1902), and other papers in the same Journal.
[148] Cf. Patten, ibid., 7, 168 (1903), and Falk and Waters, Am. Chem. J., 31, 398 (1903). According to the latter investigators, the evolution of hydrogen is slow and weak.
[149] Patten, loc. cit.
[150] Students will not be capable of following the argument given in the succeeding passages and would better omit this part until Chapter XV has been studied.
[151] Kablukoff, Z. phys. Chem., 4, 430 (1889). See also Nernst, Theoretical Chemistry, p. 373.
[152] In view of the low order of accuracy of the data, and of the approximate method of calculation, this result is only qualitative, but even with an error of 102 to 104 the argument in the text would hold.
[153] For hydrogen under atmospheric pressure, the equilibrium ratio, [Zn2+] / [H+]2, is, approximately, 1027.
[154] Vide Sackur, Z. Elektrochem., 11, 387 (1905). Kahlenberg holds a different view; ibid.
[155] The negative results obtained with aluminium and magnesium are possibly more interesting than the positive action observed with zinc, but their inactivity may be due to thin films of protective chloride or oxide or to a passive condition (vide Smith's Inorganic Chemistry, pp. 723, 753; College Chemistry, p. 475).
[156] The work of Ostwald, Arrhenius, Nernst and many others shows conclusively that the liberation of hydrogen by metals and the precipitation of metals by one another is a function of ion concentrations (Chapter XIV). Vide Nernst, Theoretische Chemie (1905), p. 245.
[157] See above.
[158] In a 0.1 molar solution of potassium cyanide, the potassium hydroxide formed by the decomposition of the cyanide by water is approximately 0.0013 molar and the concentration of hydrogen-ion is reduced to 10−11 (Chapter X), a value roughly of the same order as that calculated above as a possible concentration of hydrogen-ion in a benzene solution of hydrogen chloride. In spite of this small concentration of hydrogen-ion in the cyanide solution, the reactions in which it is involved are, as far as known, completed in a few moments. Only for much smaller concentrations of ions have any doubts as to their direct action been aroused; in Chapter XII this question, as raised by Haber, is discussed for concentrations of ions of the order of 10−23. Haber considers that ionic concentrations of 10−14 can still account for very fast actions.
[159] Cf. Abegg., Theorie der Elektrolytischen Dissociation (1903), 255; Lehfeldt, Electro-chemistry (1904), 87.
[160] There is probably minimal ionization in all these cases, especially in the case of ammonia (NH3 ⇄ NH2− + H+), but not enough to yield a sufficient supply of hydrogen-ion to show its common properties.
[161] Vide Jorgensen, J. prakt. Chem., 16, 349 (1877).
[162] See Chapter XII in regard to the stability of (PtCl62−) as a complex ion.
[163] Freshly prepared solutions must be used.
[164] See Chapter XII as to the decomposition of the "complex ions."
[165] K+ and CN− are colorless ions. The yellow color of the ion moving to the positive electrode shows the presence of the iron in it—a fact that can be confirmed by testing the solution round the anode for ferricyanide by the method discussed further on in the text.
The theory of ionization, as studied so far, gives us simple, rational explanations of many of our qualitative reactions—explanations which agree with phenomena taken from separate fields of investigation. But, if our study of the theory ceased at the present stage without further elaboration, we should fail to find in it a satisfactory explanation of a number of other important facts of analysis—notably, why certain reactions, the occurrence of which we might anticipate, do not take place. For instance, the addition of a soluble carbonate to a barium chloride solution precipitates almost all the barium as barium carbonate (exp.); we have 2 Na+ + CO32− + Ba2+ + 2 Cl− → BaCO3 ↓ + 2 Na+ + 2 Cl−. But the addition of carbonic acid to barium chloride solutions fails to produce the slightest precipitate (exp.), although carbonic acid also gives rise to the carbonate-ion, CO32−. In the same way silver nitrate readily precipitates silver phosphate from sodium phosphate solutions (exp.), but not from a solution of phosphoric acid (exp.). Hydrogen sulphide precipitates zinc sulphide from a zinc sulphate solution (exp.), Zn2+ + SO42− + 2 H+ + S2− → ZnS ↓ + 2 H+ + SO42−; but the addition of hydrochloric acid effectually prevents the precipitation (exp.), although the hydrogen sulphide is still ionized, as is apparent from the precipitation of copper sulphide when copper sulphate is added to the mixture (exp.). In the negative results, we have instances of a very large number of cases which require closer study, and a further development of the theory, if we wish to interpret them satisfactorily. The line of development to be followed is indicated perhaps most sharply by the following experiment.
Exp. Some sodium tetraborate (borax) is dissolved in a little water and silver nitrate is added to a small part of the solution. A pure white precipitate (silver borate) results. Another portion of the borate solution is diluted with a large quantity of water, and then silver nitrate is added; quite a different result is obtained—a brown precipitate (silver oxide) is formed. [p091]
The change in the quantity of water brought about the difference in result—the quantitative relations were altered thereby. In order to follow intelligently this and the other actions referred to, the study of reactions in solutions must be taken up from the quantitative side—the development heretofore has been essentially qualitative in character. On several occasions we have found that all electrolytes do not ionize equally well, and that the intensity of their action, demonstrated, for instance, for potassium and ammonium hydroxides, varies accordingly. We shall now have to study these relations in greater detail.
For our purpose, the study of two of the fundamental quantitative laws governing action in solution and of their application to analytical phenomena, will be sufficient: these are, the law of chemical or homogeneous equilibrium, in which the law of mass action is included, and the law of physical or heterogeneous equilibrium.
in which A, B, C and D represent four different substances reacting in the molecular proportions indicated by their symbols, which as usual represent molecular weights. And the condition for equilibrium may be expressed in the mathematical equation
[A], [B], [C] and [D] are used to represent the concentrations166 of [p092] the four reacting substances and k is some definite number, called the equilibrium constant.
The law was discovered by Guldberg and Waage in 1867, and, with certain limiting conditions (see below) it has been fully established by extensive experimental work.167 The significance of the law may be interpreted on the basis of the following considerations. If we start with the two substances A and B alone and have one mole of each in one liter (as gas or in solution) at a given temperature, then, all the conditions being given,—the temperature, the concentrations, and the nature of the substances,—the reaction A + B → C + D, leading to the formation of C and D, will proceed with a perfectly definite velocity. The molecules of A and of B move in all directions (kinetic theory of gases and solutions), and molecules of A will collide with molecules of B a definite number of times in unit time and will form a definite number168 of molecules of C and D per minute. The velocity of chemical change of a given substance (chemical velocity) is also measured in terms of moles, and is represented by the number of moles or the fraction of a mole changed per minute. If v′1 stands for the velocity of the action between A and B, under the given conditions, then
where k1 is some number. Now, if the concentration of one of the components, e.g. A, should be doubled, then the chances for collision and for action between molecules of A and B will be twice as great as before and the velocity of the action will be doubled. If only one-tenth of the concentration of A (one-tenth mole) is used, the velocity will only be one-tenth as great as originally, and, in general terms, if [A] moles of A are used per liter, the velocity of the change will be proportional to [A], and equal to k1 × [A]. If the concentration of the other reacting component, B, is now doubled, the chances for action are again doubled, and, in general, the velocity of the action will be proportional also to the concentration [p093] [B] of the second reacting substance. For the velocity, v1 of the action for any concentrations, [A] and [B], of A and B at any moment at a given temperature, we have
Hence, if by the symbols [A] and [B] the concentrations at any given moment are represented, we may say that the velocity of the formation of C and D at that moment169 is proportional to the product of the concentrations of A and B, and to some constant, which is characteristic of the interaction of A and B.
The validity of this conclusion has been fully verified by experiment.170 The case is an instance of the law of mass action, which states that in chemical changes the velocity of the action is proportional at any moment to the molecular concentrations171 of the reacting components, and to a constant, which is characteristic of the chemical nature of the reacting components (and of the temperature).
If we start with the reversed action
the relation may be developed in the same way. Thus the two substances C and D will react upon each other, at the given temperature, with a velocity proportional to a constant, k2, and, at any given moment, proportional also to their respective concentrations at that moment:
Equilibrium will be reached when the substances A and B are formed at any moment from C and D just as rapidly as they are used up to produce C and D, and vice versa. Such is the case, [p094] when the velocities of the two opposite reactions are equal to each other. For the condition of equilibrium, then, v1 must be equal to v2 and therefore
or
In this way the meaning of the fundamental law of chemical equilibrium may be developed from the consideration of the velocities of the reversible actions, such as are involved in all conditions of equilibrium, and the equilibrium constant represents the ratio of the velocity constants of the two opposite reactions. This conclusion has been fully verified by experiment, the equilibrium constant being, as a matter of fact, found equal to the ratio of the velocity constants.172
The relations, so far considered, have been those of the simplest type of reversible reaction. We may now discuss the modifications required for other types of reaction by the law of equilibrium.
When two molecules of any reacting component take part in a reaction—for instance, in A + 2 B ⇄ C + D—the concentration of this component is raised to the second power in the mathematical expression of the law of equilibrium; when three molecules of a component take part, its concentration is raised to the third power, etc.
For instance, hydrogen iodide is decomposed, reversibly, into hydrogen and iodine, according to 2 HI ⇄ H2 + I2. A condition of equilibrium is reached, at a given temperature when