Chapter IV: «the Theory of Ionization; Ionization and Electrical Conductivity» (2)

«Faraday's Law.»—If a definite quantity of electricity, a faraday,[93] or 96,600 coulombs, is passed through a solution of hydrochloric acid, a definite quantity (36.5 grams, one mole) of the hydrogen chloride is decomposed, and one gram of hydrogen and 35.5 grams of chlorine are liberated by the discharge of one gram (‹i.e.› one gram-ion) of the hydrogen-ion and 35.5 grams or one gram-ion of the chloride-ion. In a solution of cupric chloride, the chloride-ion is identical in every respect with the chloride-ion found in a solution of hydrochloric acid. In the solution of cupric chloride, however, a molecule of the salt, when it is completely ionized, produces two chloride ions for every cupric ion (CuCl_{2} ⇄ Cu^{2+} + 2 Cl^{−}). Since the solution never shows the presence of an excess of either form of electricity, and the negative charge on each chloride ion is the same as on a chloride ion formed by the dissociation of hydrogen chloride, a cupric ion must hold ‹exactly› double the positive charge that a hydrogen ion does. In modern terms, each hydrogen atom, present as an ion, has lost one electron, and each copper atom present in the form of a cupric ion has lost two electrons. Our unit quantity of electricity, 96,600 coulombs, can discharge therefore ‹only half as many of the cupric› as of the hydrogen ions, and since each cupric ion is 63.6 times as heavy as the hydrogen-ion (Cu = 63.6, H = 1), 63.6 / 2 grams of copper, the ‹equivalent weight›, will be deposited in place of one gram of hydrogen. Similarly, from a solution of ferrous chloride FeCl_{2}, 55.9 / 2 grams of iron (Fe = 55.9) will be deposited, the ferrous ion being Fe^{2+}; while from a solution of ferric chloride FeCl_{3}, only 55.9 / 3 grams of iron will be deposited by 96,600 coulombs, the ferric ion, Fe^{3+}, holding three times the charge that a hydrogen ion does. In other words, a given quantity of current will decompose ‹equivalent› quantities of electrolytes and deposit ‹equivalent quantities› of metals. This is the well-known law of Faraday. The theory of Arrhenius agrees with it, as did the theory of Clausius. It cannot be considered as evidence bearing on the question of the preference to be given to either of the theories of ionization, since the degree of ionization of electrolytes is not involved in the relations covered by the law. But any other relation would have been incompatible with the theory of Arrhenius. The law is of particular importance in giving us [p059] the best clew that we have in regard to the ultimate nature of "valence" (as shown for instance in the difference between the ferrous, Fe^{2+}, and the ferric ions, Fe^{3+}). On the basis of this law, valence may be said to consist simply in the capacity of atoms to hold different multiples of the unit electrical charge (positive or negative). This conception will be of especial value to us when we come to consider the relation of the theory of ionization to oxidation and reduction (Chapters XIV and XV).

«Diffusion of Ions and Concentration Cells.»—When the, apparently, abnormally low molecular weight of ammonium chloride was explained as being due to the dissociation of each molecule of ammonium chloride into a molecule of ammonia and one of hydrogen chloride, the evidence of the correctness of this interpretation was at once forthcoming—the vapor of ammonium chloride, by the unequal rates of diffusion of its components, was proved to be a mixture of the two gases (p. 35). Now, if an electrolyte like hydrochloric acid in aqueous solution is dissociated more or less into separate ions, H^{+} and Cl^{−}, then one may well ask, whether the dissociation cannot be demonstrated by the same kind of experiment, as, for instance, by showing that hydrogen and chloride ions ‹are molecules with unequal powers of diffusion› and ‹by separating them by virtue of such inequality›. Ions being, according to the theory under consideration, independent molecules, except for the attractive and repulsive forces of the electrical charges, they should have, like cane sugar, copper nitrate and other solutes, the capacity for diffusion from regions of higher to those of lower concentration. Further, if ions show different degrees of mobility (p. 53), one would expect the more mobile or faster moving one to diffuse more rapidly than a less mobile ion. Such a relation should hold for the ions in a solution of hydrochloric acid, the hydrogen-ion, according to the calculations of Kohlrausch[94] and the observation of Lodge,[95] moving at a rate about five times as great as that of the chloride-ion, at 18°. Thus, if a rather concentrated solution of hydrochloric acid were covered with a layer of water, or with a very dilute solution of the acid, one might expect the hydrogen ions to migrate faster than the chloride ions from the [p060] point of higher to that of lower concentration, ‹i.e.› from the more concentrated to the dilute acid. When the experiment is tried in this way, no separation of the hydrogen from the chloride ions seems to occur. The reason for the failure of the experiment is as follows: If any such separation did occur, even to the extent of say one milligram-equivalent of hydrogen and chloride ions, we would have a separation of electrostatic charges of 96 coulombs. These charges, on the small areas involved, would inevitably produce enormous potentials, that would operate against the separation. The hydrogen ions, which would tend to move from the concentrated to the dilute acid, would therefore be held back by the powerful attraction between their positive charges and the negative charges left in the concentrated acid (on the Cl^{−} ions). The separation of the electrical charges, incidental to a faster diffusion of hydrogen ions, if it occurred, would result, therefore, in the development of electrical forces of attraction, which would prevent a separation of the oppositely charged particles beyond any but distances too small to be measured. It would follow, however, that no difficulty whatever should be experienced in ‹observing such a separation›, as a result of unequal rates of migration of the ions in question, ‹if provision were made to preserve electrical neutrality in all zones› of the two solutions, ‹i.e.› if provision is made for the immediate discharge of the ions, as they separate by the unequal rates of diffusion. For instance, the part of the liquid into which the positive hydrogen ions move more rapidly, charging it with positive electricity, may be connected, by means of a wire, with the part of the liquid to which the chloride ions, left behind by their slower movements, are imparting a negative charge. In such a circuit, a current of electricity should be produced, the positive current flowing through the wire from the dilute to the concentrated acid. As a matter of fact, we find that a current is produced, when these conditions are observed.

EXP. The lower plate in an Arrhenius cell is covered with concentrated hydrochloric acid. Very dilute acid is allowed to flow slowly on to the surface of the concentrated acid, from a pipette with a curved, narrow point, until the upper plate is submerged. The two plates are connected with a sensitive galvanometer. The current flows in the direction demanded by the observed mobilities of the ions, the positive current entering the galvanometer from the plate covered by the dilute solution, which is charged positively by the faster moving hydrogen ions coming from the concentrated solution. If the cell is [p061] connected with the electrodes of a very small cell containing copper sulphate, in the course of twenty-four hours quite a deposit of metallic copper is formed on the electrode connected with the concentrated solution of hydrochloric acid.

The existence of the products of the electrolytic dissociation, of hydrochloric acid may therefore be demonstrated,[96] by the aid of the individual diffusion of the products of the dissociation, in the same way as was the coëxistence of the products of the gaseous dissociation of ammonium chloride, when the conditions for the experiment are adapted to the nature of the dissociation products. Cells of this type, depending for their current on unequal concentrations of given ions, are called "concentration cells."

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. Lewis[97] 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. Noyes[98] 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."

«The Rôle of the Solvent in Ionization.»—A question that has profoundly interested chemists, particularly during the last few years, has been that of the rôle which the solvent plays in the [p062] dissociation of electrolytes into ions. The most important ionizing solvent is water and, of the common solvents which cause ionization, it is the most powerful in this particular. Alcohols have also ionizing power; methyl or wood alcohol, which stands nearest to water, has a higher ionizing power than ordinary ethyl alcohol. The exact work[99] of Franklin and Kraus, on the conductivity of solutions of salts in liquid ammonia, showed that the same general relations obtain for such solutions as for solutions in water, the differences being differences of degree rather than of kind. Salts are found to be less ionized in liquid ammonia than in equivalent aqueous solutions, but their conductivities are higher, the result of smaller friction in ammonia. Liquid hydrogen cyanide is also a very good ionizing medium.

Solvents which cause ionization only to a minimal extent are benzene (C_{6}H_{6}), 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. Thomson[101] and Nernst[102] 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, H_{2}O_{2} 93
Water, H_{2}O 81
Methyl (wood) alcohol, CH_{4}O 32
Ethyl (ordinary) alcohol, C_{2}H_{6}O 22
Ammonia, H_{3}N 22
Chloroform, CHCl_{3} 5
Ether, (C_{2}H_{5})_{2}O 4
Benzene, C_{6}H_{6} 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 Walden[103] 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(C_{2}H_{5})_{4}I), 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—Walden[104] found the following exceedingly interesting relation between the ionizations in, and the dielectric constants of, various solvents:

‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} : ∛‹c›_{2} = a constant,

where ‹e›_{1} and ‹e›_{2} represent the dielectric constants of different solvents, and ‹c›_{1} and ‹c›_{2} represent the concentrations of the salt in the solvents when the salt is ‹ionized to the same degree[105] 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

«The Ionizing Power of Solvents Related to the Unsaturated Condition of their Simple Molecules and to their Power of Association.»—A careful scrutiny of the group of highly-ionizing solvents (p. 62) brings out another interesting relation, to which attention is called because it is a chemical one, and which should always be considered in connection with reactions in such solvents. It is well known that ammonia is an ‹unsaturated› body, combining readily with all acids, and with many salts, such as copper sulphate. The fact may be recalled, that this unsaturated condition is ascribed to the unsaturated nitrogen atom in the molecule of ammonia, the nitrogen showing a valence of only 3 in ammonia, whereas in the derivatives it forms when it saturates itself with the compounds mentioned, ‹e.g.› in H_{4}NCl, it has five saturated valences. Assuming that a valence consists in a unit charge, positive or negative, on the atom (pp. 42, 59), a view which has almost become a certainty, we should decide that the two free valences in ammonia must consist of a negative and a positive charge, as expressed in H_{3}N^{±}. (We may imagine such a double [p065] charge to be produced by the movement of one electron of the nitrogen atom to a position in that atom which would make one point of the atom negative and the other positive.) As a matter of fact, we find ammonia uniting with hydrogen chloride, by absorbing a positive and a negative fragment of it—producing H_{4}NCl from H_{3}N^{±} + H^{+} + Cl^{−}. It is also evident that, through these charges, ammonia could combine with itself to form larger complexes, ^{+}NH_{3}-NH_{3}^{−}, in which we would still have two opposite charges, presumably removed further from each other than in the simple molecule. The new molecule could, in turn, by virtue of its charges, combine with a further molecule to form a still larger or more ‹associated› molecule, ^{+}NH_{3}-NH_{3}-NH_{3}^{−}, and such ‹association› could evidently go still further. One can readily see that such molecules would be ‹electrically polarized›, and their charges might easily have the ‹power to cause[107] electrolytic dissociation or ionization›. The larger the associated molecule, the further apart might be the positive and negative charges upon it: the further apart the charges, the smaller would be their mutual attraction: and the smaller the mutual attraction, the stronger, presumably, would the dissociating power of such a molecule be. The dissociation may be effected, possibly, by the ‹action of these intensified charges› upon ‹charges already existing›[108] within the molecule of the dissolved ionogen.

In liquid ammonia we might well have, for instance, the action ^{+}NH_{3}-NH_{3}^{−} + HCl ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}, or ^{+}NH_{3}-NH_{3}^{−} + H^{+}Cl^{−} ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}. Now, in liquid ammonia, the salts NH_{4}Cl, NH_{4}NO_{3} [or, more probably, (NH_{3})_{‹x›}HCl, (NH_{3})_{‹x›},HNO_{3}] have the functions of the aqueous acids[109]; that is, the ‹hydrogen-ion› of the acids is found ‹combined with the solvent› ammonia. The ion ^{+}(NH_{3}-NH_{3})H, and similar ions in liquid ammonia, would correspond then to what is considered the hydrogen-ion in aqueous solutions[110] (formed according to HCl ⇄ H^{+} + Cl^{−}, as ordinarily written), and the ‹polarized charges on molecules› like ^{+}NH_{3}-NH_{3}^{−} 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 H_{2}O, 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 H_{2}O but consists of more complex molecules (H_{2}O)_{n}. According to the most recent investigations,[111] while steam is H_{2}O, or monohydrol, ice is trihydrol (H_{2}O)_{3}, and liquid water, at ordinary temperatures, a mixture consisting chiefly of dihydrol (H_{2}O)_{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.

FOOTNOTES:

[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 + H_{2}O → 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, HNO_{3}, H_{2}SO_{4}, 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(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + H^{+} + PO_{4}^{3−}
and Na(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + HPO_{4}^{2−}. 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, PO_{4}^{3−}, being three times as great as that on a sodium,
ammonium, or hydrogen ion; that on the acid phosphate ion,
HPO_{4}^{2−}, 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.

[94] See table, p. 56.

[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 = Λ_{‹v›} / 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).

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