Chapter X), the trivalent bases, such as [p107] ferric hydroxide

and aluminium hydroxide, are found to be much weaker than bivalent bases like cadmium, zinc and lead hydroxides,[195] but the data are not sufficient for the calculation of any constants, or for distinguishing between the ionization of the first, second and third hydroxide groups.

The difference in ionization and in chemical activity between a strong base, like sodium or potassium hydroxide, and a weak base, like ammonium hydroxide, has already been discussed and illustrated (see p. 77). In analysis, advantage is frequently taken of these relations.[196]

«The Ionization of Salts.»—While we read and hear a good deal about strong and weak acids, and strong and weak bases, the expression "strong" or "weak" salt is never heard; as a matter of fact, all salts, with very few exceptions, ionize exceedingly readily—about as readily as the strongest acids and bases. There are minor differences, but none of great moment—none of the kind indicated by the wide range of constants for the acids and bases. There are only a few important exceptions to this general rule—the most important ones, among the common salts, being mercuric chloride and mercuric cyanide: their exceptional behavior in regard to ionization, as indicated by their conductivities (see below), is found side by side with an exceptional chemical behavior, exactly as the theory of ionization would lead us to anticipate, and it renders necessary certain precautions, particularly in analytical work, which will be discussed later (Chap. VI). Ordinary salts are all ionized readily: for instance, whereas acetic acid in molar solution is ionized only to the extent of 0.37 per cent, its salts are highly ionized, the degree of ionization of sodium acetate, for example, being 52.8% in molar solution. As in the case of the strong acids and bases, salts of the type MeX, which ionize according to the equation MeX ⇄ Me^{+} + X^{−} and which, according to the law of chemical equilibrium, might be ‹expected› to give a constant ratio [Me^{+}][X^{−}] / [MeX], do ‹not› give a ‹constant ratio›. That is, when the values obtained for the concentrations of the ions and of the nondissociated molecules, in solutions of various [p108] strengths, are substituted in this formula, different values are obtained.[197] For potassium chloride, we have the following relations:

Molar Per cent Ratio. Concentration. Conductivity. Ionized. 0. 131.2 100 — 0.001 127.6 97.3 0.035 0.01 122.5 93.4 0.130 0.05 115.9 88.4 0.335 0.10 111.9 85.1 0.485 0.20 107.7 82.1 0.754 0.50 102.3 77.9 1.38 1.00 98.2 74.9 2.23

«The Ionization of Strong Electrolytes and the Law of Chemical Equilibrium.»—The fact that the ionization of good electrolytes does not seem to conform to the law of chemical equilibrium is an exceedingly important one—it is, perhaps, the most important problem demanding rigorous investigation, which is before chemists at the present time. It has been used as an argument against the whole theory of ionization, and is the most important objection that has been urged against it. But, to the impartial observer, this single discrepancy, between observation and what we might have anticipated, will only prove a stronger stimulus to keener investigation and to more rigorous analysis of relations, since the latter are more complex than was at first expected. Without considering the mass of evidence in favor of the theory, found in other fields of chemistry and in physics, a part of which has been given above, we must remember that this fundamental law of chemical equilibrium has already decided unequivocally in favor of the theory in hundreds of cases of the ionization of weak acids and weak bases[198] and that these are the cases where the conditions are most simple.[199] [p109]

It would lead too far from our subject to enter into a full discussion of this important question. It will be sufficient here to indicate two directions of inquiry, which promise to lead to an explanation of the apparent contradiction between the demands of the law of chemical equilibrium and the ionization of strong electrolytes.

In the first place, the law of chemical equilibrium is based thermodynamically, ‹i.e.› from the point of view of the ultimate energy relations involved, on the assumption that none but negligible forces of attraction or repulsion exist between the molecules, whose concentrations are factors in the equilibrium equations (‹cf.› p. 95).[200] Now, in solutions of electrolytes this condition is not strictly fulfilled under any circumstances; the attractions between ions of opposite charge and the repulsions of ions of like charge, as well as the effect of charged particles on neutral molecules, come into play. For strong electrolytes, where the proportion of charged particles is always a large one, the deviations from the simpler conditions to which alone the law is really applicable must be very much greater than for weak electrolytes. It is, therefore, probable that these electrical forces[201] are the source of the deviation of the ionization of strong electrolytes from the law of chemical equilibrium: although ionization is a reversible reaction, forces come into play which make the ‹simple law inapplicable›, and it is altogether likely, therefore, that we shall find, when all the factors have been investigated, that strong electrolytes should not and cannot obey ‹this law alone›.[202] In confirmation of this conclusion, recent careful calculations[203] have shown that entirely analogous deviations from the equilibrium law become perceptible in rather ‹concentrated› solutions of weak electrolytes, such as acetic acid, in which there is an accumulation of charged particles, more nearly akin to that present in ‹dilute› solutions of strong electrolytes. So it appears more and more certain that the deviations are a result of the presence of electrically charged components in the solutions, the amount of deviation depending on their concentration.

«The "Salt Effect".»—In the second place,[204] it seems possible that the presence of strong electrolytes in a solution may modify the ‹ionizing power of the solvent› in such a way as to increase it, and to increase it the more, the more concentrated the ions are in the solution.[205] The ionizing power of solvents, as has been explained, is intimately connected with their dielectric properties. [p110]

Now, solid ‹salts› have higher dielectric constants than has[206] solid water, and the dielectric constant of a compound is usually much higher in the liquid than in the solid form.[207] It is possible, therefore, that the presence of salts in the solution increases the dielectric or, at any rate, the ionizing power of the solvent and there are many facts which would be explained by such a behavior. Unfortunately for any decision of the question, determinations of the dielectric constants of salt solutions have given contradictory results; the more recent, and possibly more reliable results of Drude[208] indicate that salt solutions show approximately the same dielectric behavior as water itself. Smale, in Nernst's laboratory, on the other hand, obtained results indicating that salt solutions have decidedly higher dielectric constants than pure water.[209] A final decision in the matter would be of great importance.[210] But, as explained before (p. 64), there are other properties of a solvent which seem to be intimately related to its ionizing power and which may be modified by the presence of salts, ‹i.e.› of strong electrolytes. The value obtained for the proportion [Me^{+}] × [X^{−}] / [MeX] grows rapidly with increasing concentration, ‹indicating a disproportionately large ionization in the more concentrated solutions›—which is what one would expect, if ‹electrolytes or their ions in some way increased› the ionizing power of the medium. In agreement with such a conclusion, Arrhenius found[211] that ‹the ionization of weak acids›, like acetic acid, is increased by the presence of ‹foreign neutral› salts, such as sodium chloride. This means, of course, that the strength of acetic acid, as an acid, is increased likewise.

EXP. 0.5 c.c. of 0.1 molar acetic acid is added to 100 c.c. of a dilute solution of methyl orange in each of three test glasses. When some solid sodium chloride (3 grams, and then 3 grams more—altogether 0.1 mole) is added to the one solution, a plain increase in the intensity of the acid tint is observed.[212] The addition of cane sugar to a second solution has no such effect. The addition of sodium chloride to a fourth portion of the methyl orange, to which no acetic acid has been added, shows that its color remains unchanged: the effect on the indicator in the first case, then, is the result of the action of the salt on the acetic acid.[213] [p111]

The so-called "salt-effect" on the ionization of ammonium hydroxide may be illustrated in a similar way.

EXP. 0.5 cc of 0.1 molar ammonium hydroxide is added to each of two portions (100 c.c.) of a dilute solution of phenolphthaleïn. When some sodium chloride solution is then added to one of the two portions, the basicity of the solution is distinctly increased. The addition of sodium chloride to a third portion of the phenolphthaleïn solution shows that its own reaction to the indicator is neutral.

If the ionizing power of a solvent is changed by the presence of an electrolyte, then the law of chemical equilibrium, in its simple form, would not apply to the ionization of such electrolytes in varying concentrations—as little as we should expect to obtain the same constant for acetic acid in aqueous solution and in alcoholic solution, the ionizing power of alcohol being much smaller than that of water. The deviation from the law, naturally, would be most marked in the case of those electrolytes which ionize so easily as readily to produce high concentrations of ions.

It may be said that ‹laws based on the electrical properties of salt solutions› seem to be the predominating laws governing the ionization of electrolytes and modifying, in certain cases, the chemical laws based on the study of non-electrolytes.[214]

For the purposes of qualitative analysis, it will suffice to bear in mind the fact that the ionization[215] of salts, strong acids and strong bases does not conform to the laws of mass action, and the fact that practically all salts (with the notable exceptions, among common salts, given on p. 107) ‹are very readily ionized› in aqueous solution, namely to the extent of 40 to 85% in solutions of such moderate concentration as 0.1 molar.[216]

«Some Applications of the Law of Chemical Equilibrium.»—According to the discussions given above, for the ionization of acetic acid, CH_{3}CO_{2}H ⇄ CH_{3}CO_{2}^{−} + H^{+} we have the relation

[CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] = K_{ionization}.

[p112]

If the concentrations of the components are modified in any way, the condition of equilibrium is disturbed and change will result, always toward the restoration of equilibrium. The changes, in the case of purely ionic actions, are found to take place with an enormous velocity, equilibrium being restored almost instantly.

(1) If the solution of acetic acid, represented in the above equation, is diluted by an equal volume of water, the condition of equilibrium is disturbed:

½ [CH_{3}CO_{2}^{−}] × ½ [H^{+}] / (½ [CH_{3}CO_{2}H]) < K_{ionization.}

The ratio is smaller than that required for equilibrium, and there will be a change towards increasing the ratio. The acid will ionize more rapidly than it will be formed from the acetate and hydrogen ions (which collide less frequently in the diluted solution) and a new condition of equilibrium will be reached, when more of the acid is ionized. We found, as a matter of fact, that the more a solution of acetic acid is diluted, the larger is the proportion of ionized acid (see p. 99).

(2) If the concentration of the acetate-ion is increased in the solution by the addition of a salt of acetic acid, say sodium acetate, we have

‹x› [CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] > K_{ionization.}

The ratio is larger than allowed by the equilibrium law, and the acetate ions will combine with the hydrogen ions to form acetic acid more rapidly than the ions are formed from it, until equilibrium is reëstablished. In a molar solution of acetic acid, 0.42% of the acid is ionized, and we have

[CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] = 0.0042 × 0.0042 / 0.9958 = 1.8E−5.

If an equivalent quantity of sodium acetate should be added, ‹i.e.› one mole or 82 grams of the salt per liter, the salt being ionized to the extent of 53%, we would have

0.534 × 0.0042 / 0.9958 > 1.8E−5.

The equilibrium constant will be satisfied (and the velocity of ionization of the acetic acid will become equal to the velocity of its [p113] formation from its ions) when[217] [CH_{3}CO_{2}^{−}] = 0.53, [H^{+}] = 0.000,034 and [CH_{3}CO_{2}H] = 0.999,966. If we use two characteristic places in the decimals, we have

(0.53 × 0.000034) / 1 = 1.8E−5.

The most significant fact in the new condition of equilibrium is the ‹extremely small concentration of hydrogen-ion› in the solution. Since the acid properties of acetic acid are due to its forming hydrogen-ion, we would conclude that such properties of acetic acid are ‹very much weakened› by the presence of its own salts. This conclusion has been fully verified by careful quantitative measurements and can be demonstrated as follows[218]:

EXP. To two of three portions of a dilute solution of methyl orange equal quantities of acetic acid are added (‹e.g.› 0.5 c.c. molar acid), the third portion being reserved to show the color of the neutral solution of the indicator. Now, if into one of the solutions, to which acetic acid has been added, a few crystals of sodium acetate are gradually dropped, the color reverts gradually to the color of the original neutral solution; the concentration of hydrogen-ion becomes so small, that it does not visibly affect this indicator, which is not very sensitive to acids, (H^{+}).[219]

The solution, according to the views expressed, ‹should still be very slightly acid›, and by the use of an indicator (litmus paper) which is much more sensitive to the hydrogen-ion than is methyl orange, no difficulty is found in recognizing this fact also. As a matter of experiment, then, an acid like acetic acid ‹is very much weaker in the presence of its own salts than in their absence›, and the equilibrium constant and the concentrations of the components used determine the extent to which the hydrogen-ion is suppressed. The same must be true for all weak acids and similar relations must [p114] hold for all weak bases[220]—in general, ‹weak acids and weak bases are very much weakened by the addition of their own salts›.

The importance of recognizing such changes, in considering analytical reactions, may be illustrated as follows:

EXP. A solution of ferrous acetate (ferrous chloride with an equivalent quantity of sodium acetate) is treated with hydrogen sulphide; a precipitate of black ferrous sulphide is formed. A second portion of the solution is first decidedly acidified with acetic acid: hydrogen sulphide does not precipitate any ferrous sulphide. Some crystals of sodium or ammonium acetate are added to the mixture and a black precipitate of iron sulphide immediately appears around the salt as it dissolves, and on mixing the contents a heavy precipitate of the sulphide throughout the vessel is formed.

It is evident that the addition of a neutral salt, containing the same negative ion as the added acid, may completely reverse the net result of a test with hydrogen sulphide.

(3) If the concentration of the hydrogen ions in the solution of acetic acid is increased by the addition of hydrochloric, or some other strong acid, equilibrium between the acetic acid and its ions will likewise be disturbed and the new condition of equilibrium will show a suppression of the acetate-ion. Instances of such ‹action of a strong acid in suppressing the characteristic ions of weaker acids› will be discussed in detail in connection with the analytical applications of hydrogen sulphide (Chap. XI), where the action is of peculiar importance. Strong bases have a similar effect on weak bases.

(4) If one of the ions of acetic acid is ‹suppressed› by the addition of some agent, equilibrium is again destroyed and the resulting change is always in the direction of reëstablishing a condition of equilibrium on the basis of the law of equilibrium. Instances of this common case, such as the ‹neutralization› of acetic or any other acid by a base, or the ‹driving out› of a ‹weak› acid, from its salts, by a strong acid, or of a ‹weak› base by a ‹strong› base, considered from the point of view of the equilibrium law, should be worked out by the student.[221] [p115]

(5) The displacement of an acid (or base) in salts by another acid (or base) is subject always to the law that equilibrium is reached, when all the equilibrium constants are satisfied in the system. Very frequently, the application of the law will lead, apparently, to the incorrect conclusion that the stronger acid (or base) will ‹always› displace, more or less completely, the weaker[222]—an inference, out of which grew, indeed, the characterization of acids and bases as strong and weak. Yet, when the laws of equilibrium, as the result of the peculiar values of constants, demand that, on the contrary, a strong acid or base should be displaced by a weak, or even a feeble one, we find that the change in this direction occurs with equal ease. Numerous instances will be given where a weak acid (or a weak base) does this to a certain extent (Chap. X), and others where precipitation of salts facilitates the action of weaker acids greatly by the introduction of new, physical constants. The following case of the liberation of hydrochloric acid by the exceedingly weak acid, hydrocyanic acid, is important because it shows a reversal of the common action without the formation of any precipitate, and especially because it brings out most strikingly the relations between ionization and chemical activity in a case of special importance to analytical chemists.

«The Exceptional Ionization of Mercuric Cyanide and Its Consequences.»—We have found that practically all salts are very readily ionized. But it was mentioned that there are a few exceptions to this rule, and mercuric chloride and especially mercuric cyanide were named as the most important exceptions from the point of view of analytical chemistry. The difference in ionization between these two salts and ordinary salts may be shown readily by the apparatus previously used to demonstrate the difference in the ionization of various bases and acids.

EXP. Into the parallel tubes of the conductivity apparatus (p. 77) equivalent quantities[223] of solutions of mercuric cyanide[224] Hg(CN)_{2}, mercuric chloride [p116] HgCl_{2}, and barium chloride BaCl_{2}, are introduced. The barium chloride represents an ordinary salt of the same type as the mercury salts, and the current passing through its solution makes the little lamp glow. The electrodes in the mercuric chloride solution must be brought ‹quite close› together before sufficient current will pass through the solution to bring its little lamp to redness. In the case of the cyanide we can, at most, get a faint, dull glow by bringing the electrodes together as closely as we can, without allowing them to touch each other and short-circuit the current.

It is evident that these mercury salts are not as readily ionizable as are ordinary salts. This difference, as may be anticipated, shows itself also in the ‹chemical behavior› of their solutions and makes ‹necessary special precautions on the part of the analyst in examining mercury compounds›. For instance, whereas mercuric oxide is readily precipitated by the addition of sodium hydroxide to solutions of the nitrate and even of the moderately ionized chloride, one fails to get a precipitate of oxide from the cyanide solution (‹exp.›), and if we relied on this test, we should overlook the mercury entirely. That traces of the mercuric-ion are present, as indicated by the minimal conductivity of the cyanide, is confirmed by the fact that from the cyanide solution the sulphide, which is much less soluble than is the oxide, may be precipitated by the addition of ammonium sulphide (‹exp.›). That the sulphide is in fact less soluble[225] than the oxide is shown by the conversion of the latter into the former by the action of ammonium sulphide (‹exp.›).

As a further result of the abnormally slight ionization of these mercury salts, the analyst, unless he is on his guard, may also have difficulty in discovering the presence of their negative ions. Thus, while sodium chloride readily gives hydrogen chloride when treated with concentrated sulphuric acid, mercuric chloride, although it is a soluble salt, does not (‹exp.›), and reliance on this test alone might lead to a gross error.[226] In the case of the cyanide, it is correspondingly difficult to recognize the [p117] cyanide-ion (see the laboratory experiment, Part III). The ordinary tests fail to show its presence until the mercury has been removed from the solution by precipitation as a sulphide. Mercuric cyanide being a deadly poison which analysts are liable to meet and have met with in criminal cases, it is clear that a knowledge of these facts is vital to analytical accuracy.

Now, the very slight ionization of mercuric cyanide enables us to realize, in the following experiment, the case where an exceedingly weak acid without the formation of any precipitate involving physical constants, may displace a much stronger acid from its salts. Hydrocyanic acid is one of the weakest acids (table, p. 104), the constant for the ratio [H^{+}] × [CN^{−}] / [HNC] being 0.7E−9. It is so weak an acid that the addition of a dilute solution to methyl orange will not redden the indicator, but will have only a barely perceptible effect on it (‹exp.›). Mercuric chloride solutions also are almost neutral to methyl orange (‹exp.›) (very slight decomposition of the salt by water makes the solution very slightly acid, not enough to produce more than an orange color with methyl orange). Now, mercuric chloride, while it is not very easily ionized, is, we found, very much more readily ionized than is mercuric cyanide. The consequence is that when we add hydrocyanic acid to a mercuric chloride solution, the equilibrium between mercuric chloride and its ions and between hydrocyanic acid and its ions will be decidedly displaced, ‹the mercuric-ion combining with the cyanide-ion to form the scarcely ionizable mercuric cyanide›. As a result, more and more of the molecular mercuric chloride and hydrocyanic acid will be ionized; and since the other ions, the chloride and the hydrogen ions, form a readily ionizable electrolyte, hydrochloric acid, ‹these ions› (H^{+} and Cl^{−}) ‹will accumulate in the solution› and we shall have sufficient ‹ionized hydrochloric acid› liberated to make the solution decidedly acid.

EXP. When the two solutions described above are mixed, a strongly acid solution, colored a bright pink, results.

In the following equations the dark arrows indicate the direction in which the action goes when the solutions are mixed:

HgCl_{2} ⥂ Hg^{2+} + 2 Cl^{−}

2 HCN ⥂ 2 CN^{−} + 2 H^{+}

2 CN^{−} + Hg^{2+} ⥂ Hg(CN)_{2}

2 Cl^{−} + 2 H^{+} ⇄ 2 HCl

FOOTNOTES:

[166] ‹Concentrations are usually measured in moles or gram-molecular weights per liter, and a gram-molecular or molar weight of a compound is its molecular weight expressed in grams.› Hence the number of grams of a given substance in a liter divided by its molecular weight represents its concentration.

[167] Nernst, ‹Theoretical Chemistry›, 423, 433; Ostwald, ‹Lehrbuch›, II_{2}, 104, etc., 296; Walker, ‹Introduction to Physical Chemistry› (1909), 259, etc.

[168] Not every collision of a molecule of ‹A› with one of ‹B› is supposed to result in a chemical interaction, but the number of collisions with such a result is considered to be directly proportional to the total number of collisions. Van 't Hoff, ‹Lectures on Physical Chemistry›, I, 104.

[169] Since in any chemical action, which has not reached a condition of equilibrium, the concentrations of the reacting substances change continuously, the relation between the velocity of the action and the concentrations, for any moment, is found by the application of the calculus to the experimental data. (‹Cf. Elements of Calculus›, by Young and Linebarger (1900), 168, 181, 240; Mellor, ‹Higher Mathematics for Students of Chemistry and Physics› (1902), 197.)

[170] Nernst, ‹loc. cit.›, 541, etc.; Ostwald, ‹loc. cit.›, 107, etc.; Walker, ‹loc. cit.›, 257; Smith, ‹loc. cit.›, 250, and 180 (‹Stud.›).

[171] If a component takes part more than once in the action, its concentration is raised to the power corresponding to the coefficient expressing the number of its molecules taking part in the action. For instance, for ‹A› + 2 ‹B› → ‹C› + ‹D›, ‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›]^2; (see below).

[172] ‹Cf.› Van 't Hoff, ‹loc. cit.›, I, 206.

[173] The concentrations are calculated from the data given by Bodenstein, ‹Z. phys. Chem.›, «22», 16 (1897). (‹Cf.› Van 't Hoff ‹loc. cit.›, «I», 110.)

[174] The fundamental meaning of the law is most accurately defined in thermodynamic terms, that is, in terms of the work or energy relations connected with changes of gaseous or osmotic pressures.

[175] Van 't Hoff, ‹loc. cit.›, «I», 104, 159, etc.

[176] In regard to the variations of the equilibrium constant with changes of temperature and the relations which govern these changes see Smith's ‹Inorganic Chemistry› (1909), p. 260.

[177] The limitations are indicated in the preceding section.

[178] Stieglitz, ‹Am. Chem. J.›, «23», 406 (1900).

[179] ‹Vide› Stieglitz, ‹loc. cit.›

[180] The table is based on the results of Noyes and Cooper, given in "The Electrical Conductivity of Aqueous Solutions," ‹Carnegie Institution Publications›, No. «63», pp. 138, 141 (1907).

[181] Ostwald [‹Z. phys. Chem.›, «2», 278 (1888)], was the first to develop this relation from the conductivity data for so-called "weak acids," and the law of chemical equilibrium, holding in such and similar cases, is often called ‹Ostwald's Law of Dilution›.

[182] The equilibrium ratio, used as an illustration in the text, is the equilibrium ratio for monobasic acids. For polybasic acids, the ratio would have the form demanded by the rule given p. 94. For instance, for H_{2}X ⇄ 2 H^{+} + X^{2−}, the expression [H^{+}]^2 × [X^{2−}] / [H_{2}X] should be constant, provided the ionization occurs according to the law of chemical equilibrium in its simplest terms. In point of fact, for ‹strong› acids, this ratio holds as little as does the equilibrium ratio for the monobasic acids.

[183] Owing to the instability of carbonic acid, which breaks down into carbon dioxide and water (H_{2}CO_{3} ⇄ H_{2}O + CO_{2}), the carbonic acid is, in turn, in equilibrium with the carbon dioxide. For the sake of simplicity, this relation is not included in the detailed discussion, and wherever the symbols H_{2}CO_{3} and [H_{2}CO_{3}] are used, they are intended to represent ‹the total carbonic acid, present› as such and as carbon dioxide. The detailed discussion of the complication mentioned will be given in connection with the analogous case of ammonium hydroxide and ammonia, and, as will be shown there, ‹with the significance just attached to the symbols›, the relations developed in the text are a rigorous expression of the facts.

[184] [H^{+}], in all the equations used, represents as usual, the total concentration of hydrogen-ion.

[185] Walker and Cornack, ‹J. Chem. Soc.› (London), «77», 20 (1900).

[186] McCoy, ‹Am. Chem. J.›, «29», 437 (1903); Stieglitz, ‹Carnegie Institution Publications›, No. «107», p. 245 (1909).

[187] In a solution of phosphoric acid, all the possible forms of ionization, described in the text, occur simultaneously, but the secondary and tertiary forms of ionization, as far as the concentration of the hydrogen-ion is concerned, are entirely subordinate to the primary ionization.

[188] ‹Vide› footnote, p. 79.

[189] Luther, ‹Z. Elektrochem.›, «3», 296 (1907). Noyes and Eastman, ‹Carnegie Institution Publications›, «63», 274 (1907). Noyes and Stewart, ‹J. Am. Chem. Soc.›, «32», 1133 (1910).

[190] The apparatus described on p. 77 is used. ‹Vide› Noyes and Blanchard, ‹loc. cit.›

[191] Hydrogen ions move five to ten times as fast as the anions and carry 80–90 per cent of the current; see p. 56.

[192] The solution of these salts is due to the action of hydrogen ions on their anions; see Chap. VIII.

[193] Goodwin, ‹Z. phys. Chem.›, «21», 1 (1896).

[194] See Kohlrausch and Holborn, ‹loc. cit.›, p. 194. Their values for K (last column) must be divided by 100 to express the constants in terms of the same units as those used in the above table.

[195] J. H. Long, ‹J. Am. Chem. Soc.›, «18», 693 (1896). Ley, ‹Z. phys. Chem.›, «30», 322 (1899); Bruner, ‹ibid.›, «32», 133 (1900); Walker, ‹J. Chem. Soc.›, (London), «67», 585 (1895).

[196] Instances are found in the laboratory experiments, Parts III and IV.

[197] The ionization of salts of other types, ‹e.g.› MeX_{2}, Me_{2}Y, etc., likewise fails to conform to the law of chemical equilibrium.

[198] See below (pp. 112–4), also, further, confirmatory evidence, derived from the application of the same law to the influence upon the degree of ionization of weak acids and weak bases, exerted by the presence of their own salts.

[199] See below, in regard to evidence that the disturbing factors, predominant with strong electrolytes, are exhibited in much slighter, but perceptible measure in the case of the weak electrolytes.

[200] See also the interpretation of the law of chemical equilibrium from the viewpoint of the kinetic theory, Nernst, ‹Theoretical Chemistry›, p. 428.

[201] For a more detailed discussion of these views, see Lehfeldt's ‹Electrochemistry› (1904), pp. 78, 79.

[202] Various empirical laws, expressing the behavior of strong electrolytes, have been suggested: see Nernst, ‹Theoretical Chemistry›, p. 498, as to Rudolphi's and van 't Hoff's rules; see also A. A. Noyes, ‹Report of the Congress of Arts and Science›, «IV», p. 316 (1904).

[203] Wegscheider, ‹Z. phys. Chem.›, «70» (I), 603 (1909).

[204] It is possible that this effect is only another form of expressing the very relation discussed in the preceding paragraph.

[205] Arrhenius, ‹Z. Elektrochem.›, «6», 10 (1899); ‹Z. phys. Chem.›, «31», 197 (1899).

[206] Salts have constants averaging about 7, and running from 5 to 28; the constant for ice is about 3. Landolt, Börstein, Meyerhoffer, ‹Tabellen›, p. 766 (1905).

[207] We have: Ice, 3, water (at 0°), 80; glacial acetic acid, 2.8, acetic acid (liquid), 10; cane sugar, 4, cane sugar in aqueous solution (40%), 67.5, (6.5%), 45.3. ‹Ibid.›

[208] ‹Z. phys. Chem.›, «23», 280 (1897).

[209] ‹Wiedemann's Ann.›, «60», 625 (1897).

[210] See Walden, ‹Z. phys. Chem.›, «61», 636 (1908), in regard to the difficulties of the problem.

[211] ‹Loc. cit.›

[212] ‹Cf.› Szyszkowski, ‹Z. phys. Chem.›, «58», 420 (1907).

[213] Arrhenius made a calculation of the effect, taking into account all the rather involved changes produced by the salt. ‹Loc. cit.›

[214] For instance, the principle of "isohydric solutions," discovered by Arrhenius, has been established empirically and it involves relations which are in marked disagreement with the demands of the law of chemical equilibrium. ‹Vide› A. A. Noyes, ‹Report of the Congress of Arts and Sciences›, «IV», p. 318 (1904).

[215] The most reliable estimates of the concentrations of ions in these solutions are based on determinations of the degrees of ionization by means of conductivity measurements (see Chap. IV, and the previous footnote).

[216] Salts MeX ionize more readily (80–85% in 0.1 molar solution) than do salts Me″X_{2} or Me_{2}X″ (50 to 70% in 0.1 molar solution), and these, again, more readily than salts Me″X″ (about 40% in 0.1 molar solution).

[217] The calculation of the condition of equilibrium can be made, with sufficient accuracy for our purpose, as follows: The denominator 0.9958 in the original proportion, being near its limit (its highest possible value is 1 in a molar solution), cannot change appreciably. Consequently, when the one factor in the numerator, [CH_{3}CO_{2}^{−}], is made 0.53 / 0.0042, or 126 times as large as it was, the other factor, [H^{+}], to maintain a constant proportion, must be made 1 / 126th of its original value and 0.0042 / 126 = 0.000,034. For more exact work, the new concentrations of the three components may be found by solving a simple quadratic equation.

[218] Küster, ‹Z. für Elektrochem.›, «4», 110 (1897).

[219] See note, p. 79.

[220] See Part III for the application of this principle to ammonium hydroxide and its experimental confirmation. (‹Cf.› Arrhenius, ‹Z. phys. Chem.›, «2», 28 (1888); Stieglitz, ‹Am. Chem. J.›, «23», 406 (1900).)

[221] For instance, in the first place, the action of 0.1 mole of HCl on 0.1 mole of C_{2}H_{3}O_{2}Na, dissolved in a liter of water, and, in the second place, the action of 0.1 mole of NaOH on 0.1 mole of NH_{4}Cl, in a liter of water, may be considered. The strong electrolytes (HCl, C_{2}H_{3}O_{2}Na, NaCl, NH_{4}Cl, NaOH) may be taken to be (roughly) 80% ionized. From the concentrations given and the constants involved, the direction and the presumable intensity of the main change in each of the two cases should be determined.

[222] Instances of such displacement are given in the footnote of the previous paragraph.

[223] ‹E.g.› 50 c.c. of 0.2 molar solutions.

[224] Mercuric cyanide and mercuric chloride are largely present in aqueous solution as [Hg(CN)_{2}]_{2} and [HgCl_{2}]_{2}; see Chap. XII.

[225] See Chapter VIII in regard to this proof that mercuric sulphide is less soluble than mercuric oxide and in regard to the question how, by a continuous disturbance of the equilibrium conditions, all the mercury may be precipitated from the cyanide solution as the sulphide, in spite of the very slight degree of ionization of the cyanide.

[226] The chloride is, however, sufficiently ionized to make possible the precipitation of the very insoluble silver chloride, when silver nitrate is added to its solution.

[p118]