Dissociation Theory

DISSOCIATION THEORY The verification of Kohlrausch's theory of ionic velocity verifies also the view of electrolysis which regards the electric current as due to streams of ions moving in opposite directions through the liquid and carrying their opposite electric charges with them. There remains the question how the necessary migratory freedom of the ions is secured. As we have seen, Grotthus imagined that it was the electric forces which sheared the ions past each other and loosened the chemical bonds holding the opposite parts of each dissolved molecule together. Clausius extended to electrolysis the chemical ideas which regarded the opposite parts of the mole cule as always changing partners independently of any electric force, and regarded the function of the current as merely directive. Still, the necessary freedom was supposed to be secured by inter changes of ions between molecules at the instants of molecular collision only; during the rest of the life of the ions they were regarded as linked to each other to form electrically neutral molecules.

Arrhenius.

In 1887 Svante Arrhenius put forward a new theory which supposed that the freedom of the opposite ions from each other was not a mere momentary freedom at the in stants of molecular collision, but a more or less permanent free dom, the ions moving independently of each other through the liquid. The evidence which led Arrhenius to this conclusion was based on van't Hoff's work on the osmotic pressure of solutions (see SOLUTION). If a solution, let us say of sugar, be confined in a closed vessel through the walls of which the solvent can pass but the solution cannot, the solvent will enter till a certain equi librium pressure is reached. This equilibrium pressure is called the osmotic pressure (q.v.) of the solution, and thermodynamic theory shows that, in an ideal case of perfect separation between solvent and solute, it should have the same value as the pressure which a number of molecules equal to the number of solute mole cules in the solution would exert if they could exist as a gas in a space equal to the volume of the solution, provided that the space was large enough (i.e., the solution dilute enough) for the inter molecular forces betwen the dissolved particles to be inappreci able. Van't Hoff pointed out that measurements of osmotic pres sure confirmed this value in the case of dilute solutions of cane sugar.

Thermodynamic theory also indicates a connection between the osmotic pressure of a solution and the depression of its freezing point and its vapour pressure compared with those of the pure solvent. The freezing points and vapour pressures of solutions of sugar are also in conformity with the theoretical numbers. But when we pass to solutions of electrolytes we find that the observed values of the osmotic pressures and of the allied phenomena are greater than the normal values. Arrhenius pointed out that these exceptions would be brought into line if the ions of electrolytes were imagined to be separate entities each capable of producing its own pressure effects just as would an ordinary dissolved mole cule. Two relations are suggested by Arrhenius's theory. (1) In very dilute solutions of simple substances, where only one kind of dissociation is possible and the dissociation of the ions is com plete, the number of pressure-producing particles necessary to pro duce the observed osmotic effects should be equal to the number of ions given by a molecule of the salt as shown by its electrical properties. Thus the osmotic pressure, or the depression of the freezing point of a solution of potassium chloride should, at ex treme dilution, be twice the normal value, but of a solution of sulphuric acid three times that value, since the potassium salt contains two ions and the acid three. (2) As the concentration of the solutions increases, the ionization as measured electrically and the dissociation as measured osmotically might decrease more or less together.

Depression of Freezing

of freezing point are at present more convenient and accurate than those of osmotic pressure, and we may test the validity of Arrhenius's relations by their means. The theoretical value for the depression of the freezing point of a dilute solution per gram-equivalent of solute per litre is 1.857° C. Completely ionized solutions of salts with two ions should give double this number or 3.714° C, while electrolytes with three ions should have a value of C. The following results are given by H. B. Loomis for the concentration of o•01 gram-molecule cf salt to 1,000 gm. of water. The salts tabulated are those of which the equivalent conductivity reaches a limiting value indicating that complete ionization is reached as dilution is increased. With such salts alone is a valid comparison possible.

At the concentration used by Loomis the electrical conductivity was considered to indicate that the ionization is not complete, particularly in the case of the salts with divalent ions in the second list. The measurements of freezing points of solutions at the ex treme dilution necessary, on the basis of the theory to secure com plete ionization is a matter of great difficulty, but in researches where this difficulty has been overcome results have been ob tained for solutions of sugar, where the experimental number is 1.858, and for potassium chloride, which gives a depression of These numbers agree very closely with those indicated by theory, viz., 1.857 and 3.714, and establishes very definitely the case for complete dissociation of dilute salt solutions.

The Action of Ions.

It is necessary to point out that the dissociated ions of such a body as potassium chloride are not in the same condition as potassium and chlorine in the free state. The ions are associated with very large electric charges, and, what ever their exact relations with those charges may be, it is certain that the energy of a system in such a state must be different from its energy when unelectrified. Again, water, the best electrolytic solvent known, is also the body of the highest specific inductive capacity (dielectric constant), and this property, to whatever cause it may be due, will reduce the forces between electric charges in the neighbourhood, and may therefore enable two ions to sepa rate. This view of the nature of electrolytic solutions at once ex plains many well-known phenomena. Other physical properties of these solutions, such as density, colour, optical rotatory power, etc., like the conductivities, are additive, i.e., can be calculated by adding together the corresponding properties of the parts. This again suggests that these parts are independent of each other.

Electrolytes possess the power of coagulating solutions of col loids such as albumen and arsenious sulphide. The mean values of the relative coagulative powers of sulphates of mono-, di- and trivalent metals have been shown experimentally to be approxi mately in the ratios i :35 :1,023. The dissociation theory refers this to the action of electric charges carried by the free ions. If a certain minimum charge must be collected in order to start coagulation, it will need the conjunction of 6n monovalent, or 3n divalent, to equal the effect of 2n trivalent ions. The ratios of the coagulative powers can thus be calculated to be 1 and put ting x=32 we get 1:32:1,024, a satisfactory agreement with the numbers observed.

An interesting relation appears when the electrolytic conduc tivity of solutions is compared with their chemical activity. The readiness and speed with which electrolytes react are in sharp contrast with the difficulty experienced in the case of non-electro lytes. Moreover, a study of the chemical relations of electro lytes indicates that it is always the electrolytic ions that are concerned in their reactions. The tests for a salt, potassium nitrate, for example, are the tests not for but for its ions K' and and in cases of double decomposition it is always these ions that are exchanged for those of other sub stances. If an element be present in a compound otherwise than as an ion, it is not interchangeable, and cannot be recognized by the usual tests. Thus neither a chlorate, which contains the ion nor monochloracetic acid, shows the reactions of chlorine, though it is of course present in both substances; again, the sulphates do not answer to the usual tests which indicate the presence of sulphur as sulphide. The chemical activity of a sub stance is a quantity which may be measured by different methods. For some substances it has been shown to be independent of the particular reaction used. It is then possible to assign to each body a specific coefficient of affinity. Arrhenius has pointed out that the coefficient of affinity of an acid is proportional to its electrolytic ionization.

Affinities of Acids.

These have been compared in several ways. W. Ostwald (Lehrbuch der allg. Chemie, vol. ii., investigated the relative affinities of acids for potash, soda and ammonia, and proved them to be independent of the base used. The method employed was to measure the changes in volume caused by the action. His results are given in column I. of the following table, the affinity of hydrochloric acid being taken as one hundred. Another method is to allow an acid to act on a salt soluble only with difficulty, and to measure the quantity which goes into solution. Determinations have been made with calcium oxalate, which is easily decomposed by acids, oxalic acid and a soluble calcium salt being formed. The affini ties of acids relative to that of oxalic acid are thus found, so that the acids can be compared among themselves (column II.). If an aqueous solution of methyl acetate be allowed to stand, a slow decomposition goes on. This is much quickened by the presence of a little dilute acid, though the acid itself remains unchanged. It is found that the influence of different acids on this action is proportional to their specific coefficients of affinity. The results of this method are given in column III. Finally, in column IV. the electrical conductivities of normal solutions of the acids have been tabulated. A better basis of comparison would be the ratio of the actual to the limiting conductivity, but since the conductivity of acids is chiefly due to the mobility of the hydrogen ions, its limiting value is nearly the same for all and the general result of the comparison would be unchanged.

It must be remembered that the solutions not being of quite the same strength these numbers are not strictly comparable, and that the experimental difficulties involved in the chemical measure ments are considerable. Nevertheless, the remarkable general agreement of the numbers in the four columns is quite enough to show the intimate connection between chemical activity and elec trical conductivity.

Ostwald's Dilution Law.

On the basis of the theory of par tial dissociation of electrolytes at intermediate concentrations the ordinary laws of chemical equilibrium have been applied to the case of the dissociation of a substance into its ions. Let x be the number of molecules which dissociate per second when the num ber of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, xp is the number when the concentration is p. Recombina tion can only occur when two ions meet, and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second where q is the number of dissociated molecules in I cu. centimetre. When there is equilib rium, xp = If µ, be the molecular conductivity, and its value at infinite dilution, the fractional number of molecules dissociated will be which we may write as a. The number of undissociated molecules is then 1— a , so that if V be the volume of the solution containing 1 gram-molecule of the dissolved substance, we get This constant K gives a numerical value for the chemical affinity, and the equation should represent the effect of dilution on the molecular conductivity of binary electrolytes.

In the case of substances like ammonia and acetic acid, where the dissociation is very small, 1 — a is nearly equal to unity, and only varies slowly with dilution. The equation then becomes a = K, or a = V VK, so that the molecular conductivity is proportional to the square root of the dilution V. Ostwald has confirmed the equation by observation on a large number of weak acids (Zeits. physikal. Chemie, 1888, 1889). Thus in the case of cyanacetic acid, while the volume V was changed in stages by dou bling from 16 to 1,024 litres, the values of K were 373, 374, 361, 362, 361, 368. The mean values of for other com mon acids were : formic, 2.14 ; acetic, 1.80; monochloracetic, dichloracetic, 5,100; trichloracetic, 12I,000; propionic, 1-34. From these numbers we can by help of the equation calculate the con ductivity of the acids for any dilution. The value of K, how ever, does not keep constant so satisfactorily in the case of highly dissociated substances. The anomalies in the dilution law when applied to strong electrolytes, have now been elucidated by means of the theory of complete dissociation.

Degree of Dissociation.

According to the law put forward by Kohlrausch of the independent migration of ions, it follows that the equivalent conductivity of an electrolyte is given by the expression : (u+v)F, where is the equivalent conductivity at the limiting dilution when the electrolyte is completely dissociated, u and v are the velocities of anion and cation respectively in cm. per sec. for a potential gradient of i volt per cm. and F is the faraday or number of units of current associated with i gm. equivalent of matter. In accordance with the theory of partial dissociation for a degree of dissociation a, the quantity of electricity trans ported by the ions will be given by (u+v)aF, where A, is the equivalent conductivity for the concentration c. This law has been found to be closely followed in that the conductivity of any given ion is independent of the nature of an ion of opposite polarity with which it is associated. On dividing this equation by the preceding one, we obtain or the degree of dissociation is expressed in terms of the equivalent conductivity ratio. In this derivation, however, it is assumed that the velocities of the ions are independent of the ,concentration.

The viscosity of the electrolyte may, however, change with the concentration and accordingly the velocities will require the foregoing expression to be modified to Aclrl0, where and no represent the viscosity of the solution and the solvent respectively. To correct for the effect of varying vis cosity Washburn (J. Amer. Chem. Soc., 1911) suggests for cal culating ionization the equation A/Ao 0010) m, and shows that the value of na never differs from unity by more than 0.2. The calculation of ionization from the equivalent con ductivity ratio or the equivalent conductivity-viscosity ratio may be affected by the influence on mobility exerted by the electric charge on the ions as is discussed below, or by changes in the chemical composition of the ions. A decrease in the hydration of the ions takes place in many cases at high concentration and this will presumably cause an increase of the mobility.

Hydrolysis.—A further important chemical change is hydrol ysis, which takes place especially with salts of weak acids or bases. The following table shows the percentage hydrolysis ( ioo h) calculated by the approximate mass-action equation, cKAorB where KA and KB are the ionization (or dissociation) constants of water, acid and base respectively. The value of K. is taken as Io i4 Another uncertainty of a different nature involved in the calculation of variation from the equivalent conductivity ratio arises from the fact that the maximum value of A is not fully attained even at the smallest concentrations at which accurate measurements have so far been made and that therefore, must be obtained by extrapolation from the A values at higher con centrations. In this derivation it is necessary to assume that the fractional relation between equivalent conductivity and concentration, which is found empirically to hold at higher con centrations, continues to hold down to zero concentration.

Change of Equivalent Conductivity.

To express the change of equivalent conductivity with concentration use has generally been made of the function =K(cA)n which corresponds to the ionization relation (ca)n/c(1—a) =K. It is found, however, that the values of n for the concentration in tervals 0.1-20 and 10-200 milli-equivalents per litre as a rule differ considerably, showing that the function or its equivalent (ca)n=Kc(1—a) with a single value of the exponent, does not express the change of equivalent conductivity satisfactorily through the range of concentration from 0•000i to 0.2 normal. At lower concentrations, however, the values of a become nearly identical and equal to about 1.5 for both mono- and divalent salts. A relation found by Kohlrausch to apply closely for many univalent salts between the concentra tions 0.001 and o•IN is of the form It is found that by correcting for viscosity the term An/no is closely proportional to the concentration for uni-univalent salts between the con centrations of i and 200 millinormal but that considerable de viations occur with uni-bivalent salts.