ELECTROLIER

electrolier, a fixture, usually pendent from the ceiling, for holding electric lamps. the word is analogous to chandelier, from which indeed it was formed. electrolysis (formed from gr. [greek: lyein], to loosen). when the passage of an electric current through a substance is accompanied by definite chemical changes which are independent of the heating effects of the current, the process is known as _electrolysis_, and the substance is called an _electrolyte_. as an example we may take the case of a solution of a salt such as copper sulphate in water, through which an electric current is passed between copper plates. we shall then observe the following phenomena. (1) the bulk of the solution is unaltered, except that its temperature may be raised owing to the usual heating effect which is proportional to the square of the strength of the current. (2) the copper plate by which the current is said to enter the solution, i.e. the plate attached to the so-called positive terminal of the battery or other source of current, dissolves away, the copper going into solution as copper sulphate. (3) copper is deposited on the surface of the other plate, being obtained from the solution. (4) changes in concentration are produced in the neighbourhood of the two plates or electrodes. in the case we have chosen, the solution becomes stronger near the anode, or electrode at which the current enters, and weaker near the cathode, or electrode at which it leaves the solution. if, instead of using copper electrodes, we take plates of platinum, copper is still deposited on the cathode; but, instead of the anode dissolving, free sulphuric acid appears in the neighbouring solution, and oxygen gas is evolved at the surface of the platinum plate. with other electrolytes similar phenomena appear, though the primary chemical changes may be masked by secondary actions. thus, with a dilute solution of sulphuric acid and platinum electrodes, hydrogen gas is evolved at the cathode, while, as the result of a secondary action on the anode, sulphuric acid is there re-formed, and oxygen gas evolved. again, with the solution of a salt such as sodium chloride, the sodium, which is primarily liberated at the cathode, decomposes the water and evolves hydrogen, while the chlorine may be evolved as such, may dissolve the anode, or may liberate oxygen from the water, according to the nature of the plate and the concentration of the solution. _early history of electrolysis._--alessandro volta of pavia discovered the electric battery in the year 1800, and thus placed the means of maintaining a steady electric current in the hands of investigators, who, before that date, had been restricted to the study of the isolated electric charges given by frictional electric machines. volta's cell consists essentially of two plates of different metals, such as zinc and copper, connected by an electrolyte such as a solution of salt or acid. immediately on its discovery intense interest was aroused in the new invention, and the chemical effects of electric currents were speedily detected. w. nicholson and sir a. carlisle found that hydrogen and oxygen were evolved at the surfaces of gold and platinum wires connected with the terminals of a battery and dipped in water. the volume of the hydrogen was about double that of the oxygen, and, since this is the ratio in which these elements are combined in water, it was concluded that the process consisted essentially in the decomposition of water. they also noticed that a similar kind of chemical action went on in the battery itself. soon afterwards, william cruickshank decomposed the magnesium, sodium and ammonium chlorides, and precipitated silver and copper from their solutions--an observation which led to the process of electroplating. he also found that the liquid round the anode became acid, and that round the cathode alkaline. in 1804 w. hisinger and j.j. berzelius stated that neutral salt solutions could be decomposed by electricity, the acid appearing at one pole and the metal at the other. this observation showed that nascent hydrogen was not, as had been supposed, the primary cause of the separation of metals from their solutions, but that the action consisted in a direct decomposition into metal and acid. during the earliest investigation of the subject it was thought that, since hydrogen and oxygen were usually evolved, the electrolysis of solutions of acids and alkalis was to be regarded as a direct decomposition of water. in 1806 sir humphry davy proved that the formation of acid and alkali when water was electrolysed was due to saline impurities in the water. he had shown previously that decomposition of water could be effected although the two poles were placed in separate vessels connected by moistened threads. in 1807 he decomposed potash and soda, previously considered to be elements, by passing the current from a powerful battery through the moistened solids, and thus isolated the metals potassium and sodium. the electromotive force of volta's simple cell falls off rapidly when the cell is used, and this phenomenon was shown to be due to the accumulation at the metal plates of the products of chemical changes in the cell itself. this reverse electromotive force of polarization is produced in all electrolytes when the passage of the current changes the nature of the electrodes. in batteries which use acids as the electrolyte, a film of hydrogen tends to be deposited on the copper or platinum electrode; but, to obtain a constant electromotive force, several means were soon devised of preventing the formation of the film. constant cells may be divided into two groups, according as their action is chemical (as in the bichromate cell, where the hydrogen is converted into water by an oxidizing agent placed in a porous pot round the carbon plate) or electrochemical (as in daniell's cell, where a copper plate is surrounded by a solution of copper sulphate, and the hydrogen, instead of being liberated, replaces copper, which is deposited on the plate from the solution). [illustration: fig. 1.] _faraday's laws._--the first exact quantitative study of electrolytic phenomena was made about 1830 by michael faraday (_experimental researches_, 1833). when an electric current flows round a circuit, there is no accumulation of electricity anywhere in the circuit, hence the current strength is everywhere the same, and we may picture the current as analogous to the flow of an incompressible fluid. acting on this view, faraday set himself to examine the relation between the flow of electricity round the circuit and the amount of chemical decomposition. he passed the current driven by a voltaic battery znpt (fig. 1) through two branches containing the two electrolytic cells a and b. the reunited current was then led through another cell c, in which the strength of the current must be the sum of those in the arms a and b. faraday found that the mass of substance liberated at the electrodes in the cell c was equal to the sum of the masses liberated in the cells a and b. he also found that, for the same current, the amount of chemical action was independent of the size of the electrodes and proportional to the time that the current flowed. regarding the current as the passage of a certain amount of electricity per second, it will be seen that the results of all these experiments may be summed up in the statement that the amount of chemical action is proportional to the quantity of electricity which passes through the cell. faraday's next step was to pass the same current through different electrolytes in series. he found that the amounts of the substances liberated in each cell were proportional to the chemical equivalent weights of those substances. thus, if the current be passed through dilute sulphuric acid between hydrogen electrodes, and through a solution of copper sulphate, it will be found that the mass of hydrogen evolved in the first cell is to the mass of copper deposited in the second as 1 is to 31.8. now this ratio is the same as that which gives the relative chemical equivalents of hydrogen and copper, for 1 gramme of hydrogen and 31.8 grammes of copper unite chemically with the same weight of any acid radicle such as chlorine or the sulphuric group, so4. faraday examined also the electrolysis of certain fused salts such as lead chloride and silver chloride. similar relations were found to hold and the amounts of chemical change to be the same for the same electric transfer as in the case of solutions. we may sum up the chief results of faraday's work in the statements known as faraday's laws: the mass of substance liberated from an electrolyte by the passage of a current is proportional (1) to the total quantity of electricity which passes through the electrolyte, and (2) to the chemical equivalent weight of the substance liberated. since faraday's time his laws have been confirmed by modern research, and in favourable cases have been shown to hold good with an accuracy of at least one part in a thousand. the principal object of this more recent research has been the determination of the quantitative amount of chemical change associated with the passage for a given time of a current of strength known in electromagnetic units. it is found that the most accurate and convenient apparatus to use is a platinum bowl filled with a solution of silver nitrate containing about fifteen parts of the salt to one hundred of water. into the solution dips a silver plate wrapped in filter paper, and the current is passed from the silver plate as anode to the bowl as cathode. the bowl is weighed before and after the passage of the current, and the increase gives the mass of silver deposited. the mean result of the best determinations shows that when a current of one ampere is passed for one second, a mass of silver is deposited equal to 0.001118 gramme. so accurate and convenient is this determination that it is now used conversely as a practical definition of the ampere, which (defined theoretically in terms of magnetic force) is defined practically as the current which in one second deposits 1.118 milligramme of silver. taking the chemical equivalent weight of silver, as determined by chemical experiments, to be 107.92, the result described gives as the electrochemical equivalent of an ion of unit chemical equivalent the value 1.036 x 10^(-5). if, as is now usual, we take the equivalent weight of oxygen as our standard and call it 16, the equivalent weight of hydrogen is 1.008, and its electrochemical equivalent is 1.044 x 10^(-5). the electrochemical equivalent of any other substance, whether element or compound, may be found by multiplying its chemical equivalent by 1.036 x 10^(-5). if, instead of the ampere, we take the c.g.s. electromagnetic unit of current, this number becomes 1.036 x 10^(-4). _chemical nature of the ions._--a study of the products of decomposition does not necessarily lead directly to a knowledge of the ions actually employed in carrying the current through the electrolyte. since the electric forces are active throughout the whole solution, all the ions must come under its influence and therefore move, but their separation from the electrodes is determined by the electromotive force needed to liberate them. thus, as long as every ion of the solution is present in the layer of liquid next the electrode, the one which responds to the least electromotive force will alone be set free. when the amount of this ion in the surface layer becomes too small to carry all the current across the junction, other ions must also be used, and either they or their secondary products will appear also at the electrode. in aqueous solutions, for instance, a few hydrogen (h) and hydroxyl (oh) ions derived from the water are always present, and will be liberated if the other ions require a higher decomposition voltage and the current be kept so small that hydrogen and hydroxyl ions can be formed fast enough to carry all the current across the junction between solution and electrode. the issue is also obscured in another way. when the ions are set free at the electrodes, they may unite with the substance of the electrode or with some constituent of the solution to form secondary products. thus the hydroxyl mentioned above decomposes into water and oxygen, and the chlorine produced by the electrolysis of a chloride may attack the metal of the anode. this leads us to examine more closely the part played by water in the electrolysis of aqueous solutions. distilled water is a very bad conductor, though, even when great care is taken to remove all dissolved bodies, there is evidence to show that some part of the trace of conductivity remaining is due to the water itself. by careful redistillation f. kohlrausch has prepared water of which the conductivity compared with that of mercury was only 0.40 x 10^(-11) at 18 deg. c. even here some little impurity was present, and the conductivity of chemically pure water was estimated by thermodynamic reasoning as 0.36 x 10^(-11) at 18 deg. c. as we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that, in most cases, practically all the current is carried by the salt. at the electrodes, however, the small quantity of hydrogen and hydroxyl ions from the water are liberated first in cases where the ions of the salt have a higher decomposition voltage. the water being present in excess, the hydrogen and hydroxyl are re-formed at once and therefore are set free continuously. if the current be so strong that new hydrogen and hydroxyl ions cannot be formed in time, other substances are liberated; in a solution of sulphuric acid a strong current will evolve sulphur dioxide, the more readily as the concentration of the solution is increased. similar phenomena are seen in the case of a solution of hydrochloric acid. when the solution is weak, hydrogen and oxygen are evolved; but, as the concentration is increased, and the current raised, more and more chlorine is liberated. an interesting example of secondary action is shown by the common technical process of electroplating with silver from a bath of potassium silver cyanide. here the ions are potassium and the group ag(cn)2.[1] each potassium ion as it reaches the cathode precipitates silver by reacting with the solution in accordance with the chemical equation k + kag(cn)2 = 2kcn + ag, while the anion ag(cn)2 dissolves an atom of silver from the anode, and re-forms the complex cyanide kag(cn)2 by combining with the 2kcn produced in the reaction described in the equation. if the anode consist of platinum, cyanogen gas is evolved thereat from the anion ag(cn)2, and the platinum becomes covered with the insoluble silver cyanide, agcn, which soon stops the current. the coating of silver obtained by this process is coherent and homogeneous, while that deposited from a solution of silver nitrate, as the result of the primary action of the current, is crystalline and easily detached. in the electrolysis of a concentrated solution of sodium acetate, hydrogen is evolved at the cathode and a mixture of ethane and carbon dioxide at the anode. according to h. jahn,[2] the processes at the anode can be represented by the equations 2ch3.coo + h2o = 2ch3.cooh + o 2ch3.cooh + o = c2h6 + 2co2 + h2o. the hydrogen at the cathode is developed by the secondary action 2na + 2h2o = 2naoh + h2. many organic compounds can be prepared by taking advantage of secondary actions at the electrodes, such as reduction by the cathodic hydrogen, or oxidation at the anode (see electrochemistry). it is possible to distinguish between double salts and salts of compound acids. thus j.w. hittorf showed that when a current was passed through a solution of sodium platino-chloride, the platinum appeared at the anode. the salt must therefore be derived from an acid, chloroplatinic acid, h2ptcl6, and have the formula na2ptcl6, the ions being na and ptcl6", for if it were a double salt it would decompose as a mixture of sodium chloride and platinum chloride and both metals would go to the cathode. _early theories of electrolysis._--the obvious phenomena to be explained by any theory of electrolysis are the liberation of the products of chemical decomposition at the two electrodes while the intervening liquid is unaltered. to explain these facts, theodor grotthus (1785-1822) in 1806 put forward an hypothesis which supposed that the opposite chemical constituents of an electrolyte interchanged partners all along the line between the electrodes when a current passed. thus, if the molecule of a substance in solution is represented by ab, grotthus considered a chain of ab molecules to exist from one electrode to the other. under the influence of an applied electric force, he imagined that the b part of the first molecule was liberated at the anode, and that the a part thus isolated united with the b part of the second molecule, which, in its turn, passed on its a to the b of the third molecule. in this manner, the b part of the last molecule of the chain was seized by the a of the last molecule but one, and the a part of the last molecule liberated at the surface of the cathode. chemical phenomena throw further light on this question. if two solutions containing the salts ab and cd be mixed, double decomposition is found to occur, the salts ad and cb being formed till a certain part of the first pair of substances is transformed into an equivalent amount of the second pair. the proportions between the four salts ab, cd, ad and cb, which exist finally in solution, are found to be the same whether we begin with the pair ab and cd or with the pair ad and cb. to explain this result, chemists suppose that both changes can occur simultaneously, and that equilibrium results when the rate at which ab and cd are transformed into ad and cb is the same as the rate at which the reverse change goes on. a freedom of interchange is thus indicated between the opposite parts of the molecules of salts in solution, and it follows reasonably that with the solution of a single salt, say sodium chloride, continual interchanges go on between the sodium and chlorine parts of the different molecules. these views were applied to the theory of electrolysis by r.j.e. clausius. he pointed out that it followed that the electric forces did not cause the interchanges between the opposite parts of the dissolved molecules but only controlled their direction. interchanges must be supposed to go on whether a current passes or not, the function of the electric forces in electrolysis being merely to determine in what direction the parts of the molecules shall work their way through the liquid and to effect actual separation of these parts (or their secondary products) at the electrodes. this conclusion is supported also by the evidence supplied by the phenomena of electrolytic conduction (see conduction, electric, s ii.). if we eliminate the reverse electromotive forces of polarization at the two electrodes, the conduction of electricity through electrolytes is found to conform to ohm's law; that is, once the polarization is overcome, the current is proportional to the electromotive force applied to the bulk of the liquid. hence there can be no reverse forces of polarization inside the liquid itself, such forces being confined to the surface of the electrodes. no work is done in separating the parts of the molecules from each other. this result again indicates that the parts of the molecules are effectively separate from each other, the function of the electric forces being merely directive. _migration of the ions._--the opposite parts of an electrolyte, which work their way through the liquid under the action of the electric forces, were named by faraday the ions--the travellers. the changes of concentration which occur in the solution near the two electrodes were referred by w. hittorf (1853) to the unequal speeds with which he supposed the two opposite ions to travel. it is clear that, when two opposite streams of ions move past each other, equivalent quantities are liberated at the two ends of the system. if the ions move at equal rates, the salt which is decomposed to supply the ions liberated must be taken equally from the neighbourhood of the two electrodes. but if one ion, say the anion, travels faster through the liquid than the other, the end of the solution from which it comes will be more exhausted of salt than the end towards which it goes. if we assume that no other cause is at work, it is easy to prove that, with non-dissolvable electrodes, the ratio of salt lost at the anode to the salt lost at the cathode must be equal to the ratio of the velocity of the cation to the velocity of the anion. this result may be illustrated by fig. 2. the black circles represent one ion and the white circles the other. if the black ions move twice as fast as the white ones, the state of things after the passage of a current will be represented by the lower part of the figure. here the middle part of the solution is unaltered and the number of ions liberated is the same at either end, but the amount of salt left at one end is less than that at the other. on the right, towards which the faster ion travels, five molecules of salt are left, being a loss of two from the original seven. on the left, towards which the slower ion moves, only three molecules remain--a loss of four. thus, the ratio of the losses at the two ends is two to one--the same as the ratio of the assumed ionic velocities. it should be noted, however, that another cause would be competent to explain the unequal dilution of the two solutions. if either ion carried with it some of the unaltered salt or some of the solvent, concentration or dilution of the liquid would be produced where the ion was liberated. there is reason to believe that in certain cases such complex ions do exist, and interfere with the results of the differing ionic velocities. [illustration: fig. 2.] hittorf and many other observers have made experiments to determine the unequal dilution of a solution round the two electrodes when a current passes. various forms of apparatus have been used, the principle of them all being to secure efficient separation of the two volumes of solution in which the changes occur. in some cases porous diaphragms have been employed; but such diaphragms introduce a new complication, for the liquid as a whole is pushed through them by the action of the current, the phenomenon being known as electric endosmose. hence experiments without separating diaphragms are to be preferred, and the apparatus may be considered effective when a considerable bulk of intervening solution is left unaltered in composition. it is usual to express the results in terms of what is called the migration constant of the anion, that is, the ratio of the amount of salt lost by the anode vessel to the whole amount lost by both vessels. thus the statement that the migration constant or transport number for a decinormal solution of copper sulphate is 0.632 implies that of every gramme of copper sulphate lost by a solution containing originally one-tenth of a gramme equivalent per litre when a current is passed through it between platinum electrodes, 0.632 gramme is taken from the cathode vessel and 0.368 gramme from the anode vessel. for certain concentrated solutions the transport number is found to be greater than unity; thus for a normal solution of cadmium iodide its value is 1.12. on the theory that the phenomena are wholly due to unequal ionic velocities this result would mean that the cation like the anion moved against the conventional direction of the current. that a body carrying a positive electric charge should move against the direction of the electric intensity is contrary to all our notions of electric forces, and we are compelled to seek some other explanation. an alternative hypothesis is given by the idea of complex ions. if some of the anions, instead of being simple iodine ions represented chemically by the symbol i, are complex structures formed by the union of iodine with unaltered cadmium iodide--structures represented by some such chemical formula as i(cdi2), the concentration of the solution round the anode would be increased by the passage of an electric current, and the phenomena observed would be explained. it is found that, in such cases as this, where it seems necessary to imagine the existence of complex ions, the transport number changes rapidly as the concentration of the original solution is changed. thus, diminishing the concentration of the cadmium iodine solution from normal to one-twentieth normal changes the transport number from 1.12 to 0.64. hence it is probable that in cases where the transport number keeps constant with changing concentration the hypothesis of complex ions is unnecessary, and we may suppose that the transport number is a true migration constant from which the relative velocities of the two ions may be calculated in the matter suggested by hittorf and illustrated in fig. 2. this conclusion is confirmed by the results of the direct visual determination of ionic velocities (see conduction, electric, s ii.), which, in cases where the transport number remains constant, agree with the values calculated from those numbers. many solutions in which the transport numbers vary at high concentration often become simple at greater dilution. for instance, to take the two solutions to which we have already referred, we have-- +----------------------------------+------+------+------+------+------+------+------+-----+-----------+ |concentration | 2.0 | 1.5 | 1.0 | 0.5 | 0.2 | 0.1 | 0.05 | 0.02|0.01 normal| |copper sulphate transport numbers | 0.72 | 0.714| 0.696| 0.668| 0.643| 0.632| 0.626| 0.62| .. | |cadmium iodide " " | 1.22 | 1.18 | 1.12 | 1.00 | 0.83 | 0.71 | 0.64 | 0.59|0.56 | +----------------------------------+------+------+------+------+------+------+------+-----+-----------+ it is probable that in both these solutions complex ions exist at fairly high concentrations, but gradually gets less in number and finally disappear as the dilution is increased. in such salts as potassium chloride the ions seem to be simple throughout a wide range of concentration since the transport numbers for the same series of concentrations as those used above run-- potassium chloride-- 0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506. the next important step in the theory of the subject was made by f. kohlrausch in 1879. kohlrausch formulated a theory of electrolytic conduction based on the idea that, under the action of the electric forces, the oppositely charged ions moved in opposite directions through the liquid, carrying their charges with them. if we eliminate the polarization at the electrodes, it can be shown that an electrolyte possesses a definite electric resistance and therefore a definite conductivity. the conductivity gives us the amount of electricity conveyed per second under a definite electromotive force. on the view of the process of conduction described above, the amount of electricity conveyed per second is measured by the product of the number of ions, known from the concentration of the solution, the charge carried by each of them, and the velocity with which, on the average, they move through the liquid. the concentration is known, and the conductivity can be measured experimentally; thus the average velocity with which the ions move past each other under the existent electromotive force can be estimated. the velocity with which the ions move past each other is equal to the sum of their individual velocities, which can therefore be calculated. now hittorf's transport number, in the case of simple salts in moderately dilute solution, gives us the ratio between the two ionic velocities. hence the absolute velocities of the two ions can be determined, and we can calculate the actual speed with which a certain ion moves through a given liquid under the action of a given potential gradient or electromotive force. the details of the calculation are given in the article conduction, electric, s ii., where also will be found an account of the methods which have been used to measure the velocities of many ions by direct visual observation. the results go to show that, where the existence of complex ions is not indicated by varying transport numbers, the observed velocities agree with those calculated on kohlrausch's 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 looked on the opposite parts of the molecule 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 interchanges 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. in 1887 svante arrhenius, professor of physics at stockholm, 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 instants of molecular collision, but a more or less permanent freedom, 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 equilibrium pressure is reached. this equilibrium pressure is called the osmotic pressure 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 molecules 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 intermolecular forces between the dissolved particles to be inappreciable. van 't hoff pointed out that measurements of osmotic pressure confirmed this value in the case of dilute solutions of cane sugar. thermodynamic theory also indicates a connexion 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 mineral salts and acids--to solutions of electrolytes in fact--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 molecule. two relations are suggested by arrhenius' theory. (1) in very dilute solutions of simple substances, where only one kind of dissociation is possible and the dissociation of the ions is complete, the number of pressure-producing particles necessary to produce 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 extreme 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, though, since the thermodynamic theory only holds when the solution is so dilute that the dissolved particles are beyond each other's sphere of action, there is much doubt whether this second relation is valid through any appreciable range of concentration. at present, measurements of freezing point are more convenient and accurate than those of osmotic pressure, and we may test the validity of arrhenius' relations by their means. the theoretical value for the depression of the freezing point of a dilute solution per gramme-equivalent of solute per litre is 1.857 deg. c. completely ionized solutions of salts with two ions should give double this number or 3.714 deg., while electrolytes with three ions should have a value of 5.57 deg. the following results are given by h.b. loomis for the concentration of 0.01 gramme-molecule of salt to one thousand grammes 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. _molecular depressions of the freezing point._ _electrolytes with two ions._ potassium chloride 3.60 sodium chloride 3.67 potassium hydrate 3.71 hydrochloric acid 3.61 nitric acid 3.73 potassium nitrate 3.46 sodium nitrate 3.55 ammonium nitrate 3.58 _electrolytes with three ions._ sulphuric acid 4.49 sodium sulphate 5.09 calcium chloride 5.04 magnesium chloride 5.08 at the concentration used by loomis the electrical conductivity indicates that the ionization is not complete, particularly in the case of the salts with divalent ions in the second list. allowing for incomplete ionization the general concordance of these numbers with the theoretical ones is very striking. the measurements of freezing points of solutions at the extreme dilution necessary to secure complete ionization is a matter of great difficulty, and has been overcome only in a research initiated by e.h. griffiths.[3] results have been obtained for solutions of sugar, where the experimental number is 1.858, and for potassium chloride, which gives a depression of 3.720. these numbers agree with those indicated by theory, viz. 1.857 and 3.714, with astonishing exactitude. we may take arrhenius' first relation as established for the case of potassium chloride. the second relation, as we have seen, is not a strict consequence of theory, and experiments to examine it must be treated as an investigation of the limits within which solutions are dilute within the thermodynamic sense of the word, rather than as a test of the soundness of the theory. it is found that divergence has begun before the concentration has become great enough to enable freezing points to be measured with any ordinary apparatus. the freezing point curve usually lies below the electrical one, but approaches it as dilution is increased.[4] returning once more to the consideration of the first relation, which deals with the comparison between the number of ions and the number of pressure-producing particles in dilute solution, one caution is necessary. in simple substances like potassium chloride it seems evident that one kind of dissociation only is possible. the electrical phenomena show that there are two ions to the molecule, and that these ions are electrically charged. corresponding with this result we find that the freezing point of dilute solutions indicates that two pressure-producing particles per molecule are present. but the converse relation does not necessarily follow. it would be possible for a body in solution to be dissociated into non-electrical parts, which would give osmotic pressure effects twice or three times the normal value, but, being uncharged, would not act as ions and impart electrical conductivity to the solution. l. kahlenberg (_jour. phys. chem._, 1901, v. 344, 1902, vi. 43) has found that solutions of diphenylamine in methyl cyanide possess an excess of pressure-producing particles and yet are non-conductors of electricity. it is possible that in complicated organic substances we might have two kinds of dissociation, electrical and non-electrical, occurring simultaneously, while the possibility of the association of molecules accompanied by the electrical dissociation of some of them into new parts should not be overlooked. it should be pointed out that no measurements on osmotic pressures or freezing points can do more than tell us that an excess of particles is present; such experiments can throw no light on the question whether or not those particles are electrically charged. that question can only be answered by examining whether or not the particles move in an electric field. the dissociation theory was originally suggested by the osmotic pressure relations. but not only has it explained satisfactorily the electrical properties of solutions, but it seems to be the only known hypothesis which is consistent with the experimental relation between the concentration of a solution and its electrical conductivity (see