f REESE LIBRARY UNIVERSITY OF CALIFORNIA ^ecerceJ /6^ ,'il ''h'l V.V S 10 1 1 N . V( ) . ^ Q / f *f. > ;; ' '-ft m M 1 i .: " - ffl : .- AN OUTLINE OF THE THEORY OF SOLUTION AND ITS RESULTS. FOR CHEMISTS AND ELECTRICIANS. BY J. LIVINGSTON R. MORGAN, PH.D. 'LEIPZIG,) Instructor in Quantitative A nalysis, Polytechnic Institute, Brooklyn. FIRST EDITION. FIRST THOUSAND. f OFTHE ^ >. (UNIVERSITY) \^ op ^/ NEW YORK: JOHN WILEY & SONS. LONDON : CHAPMAN & HALL, LIMITED. 1897. Copyright, 1897, BY J. L. R. MORGAN ROBERT DRUMMOND, ELECTROTYPER AND PRINTER, J:: V\ V 1 ', where V and V represent respectively the volumes before and after the pressure is changed from P to P' . Volumes of gases are measured in cubic centimeters at a certain temperature and pressure, while pressures 2 THE THEORY OF SOLUTION. are measured in millimeters of mercury (in a barom- eter). The Law of Charles is: The pressure remaining the same, tJie volume of a given quantity of a gas is directly proportional to its absolute temperature. It has been found that a gas expands (contracts) 1/273 of its volume, at o centigrade (C.), for every increase (decrease) in temperature of i C. ; hence, if a volume of gas, at o C., should have its temperature lowered through 273, the contraction would equal the volume. This point (273 below o C.) is called the absolute zero, and temperatures reckoned from this point absolute temperatures. The proportion then for this law T : T' :: V : V where T is equal to the centigrade temperature -|- 273, and V is as before. The Law of Dalton is best expressed, perhaps, in the following form: The pres- sure exerted upon the walls of a vessel, containing a mix- ture of gases, is equal to the sum of the pressures which the single gases would exert, were they alone in the vessel. The law of Avogadro is of paramount impor- tance. According to it: All gases, under the same con- ditions of pressure and temperature, contain in unit volume the same number of molecules. The law of Mariotte is generally written, when the temperature does not vary, pv = constant, for we know that / and v are inversely proportional, and hence when one increases the other decreases by THE THEORY OF SOLUTION. 3 the same amount, and consequently the product remains constant. The law of Mariotte and that of Charles are usually united in a form which gives the state of the gas under all conditions. If, for example, we have a gas at a certain volume at o and 760 mm. pressure and keep the pressure constant, allowing the temperature to vary, the volume becomes v = v.(i + at). If now, instead of keeping the pressure constant, we vary it and keep the volume constant, then the pres- sure must increase just as the volume did before. That is, /=A(i + "0- The v and / refer to the standard state (o and 760 mm. pressure). By uniting these two we obtain t); ^ j>v = j> 9 v.(i + at but /= r-273 and (a == ^fa) hence 273 4 THE THEORY OF SOLUTION. 1) i) As will be seen, this term is a constan The 273 letter R is usually substituted for it, so that we have, as the equation of state of a perfect gas, fv = RT\ or, since R is found, by calculation, to be equal to 84700 centimeter-grams,* pv = 84700 T. This R, which refers to only one mol (molecular weight in grams) of gas, is called the gas constant. According to Avogadro's law, equal volumes of all gases contain the same number of molecules. This gives us a method of determining the molecular weight of substances in gas form, which has been used very largely. By Avogadro's law, m. m~ m H -~ - * = -T- constant, a t a* a H where ;,, ;, , m n , are molecular weights, and d^ , d^ , d n are the densities of the corresponding gases. If * As calculated for one mol of oxygen, but it is the same for one mol of any other gas. z/ (i gr. O at 76 cms. pressure and o C.) = 699.25 c.c., / = 76 cms. of a column of mercury i cm. in diameter. Sp. gr. of Hg = 13.5. Hence the weight of the column = 76 X 13.5 = 1033.2 grms., T 273 Therefore ~ for 32 grams (mol) = 32 X = 8468S cm . grmji> (84700 in round numbers), i.e. , equal to an energy whit h would lift 84700 grms. i cm. in I second. THE THEORY OF SOLUTION. 5 we now take hydrogen as unity, with respect to atomic weight and density,' then m t (H) will equal 2 (two atoms to one molecule), d l = I, and any other molec- ular weight, m^ , can be found by solving the equation m hence That is, the molecular weight of any substay.ce is equal to twice its density in gas form, hydrogen being unity. So much for the laws of gases. I have given them in this short and concise form, for we will have to refer to them very often, and they are all necessary, for, as we will find, they are also, with a few modifications, the laws for solution The dissolved substance acts in its solution just as a gas would when shut into a cer- tain volume, the volume of the solvent being the vol- ume, and the substance itself as the gas. The term which is equivalent to pressure will be developed later. ABNORMAL RESULTS WITH GASES. The laws for gases, given in the last section, do not hold strictly for all gases, but do (fairly) for all per- fect ones. The vapors of many substances, however, were found to give very strange results; and upon these we will dwell in this section. Thus, long ago, it was found that the vapor of ammonium chloride gave a density which was but one half what it should be, according to its accepted molecular weight. There are but two ways of explaining this abnormal action, THE THEORY OF SOLUTION. viz. : either Avogadro's law does not hold good, or the substance is decomposed by the heat into its constit- uents, according to the equation NH 4 Clti;NH,+ HC1. The sign ^ meaning that the reaction goes forward or backward, according as the temperature is high or low. Avogadro's law, however, holds for all other sub- stances, so that it was concluded at the time that the latter reason was the true one, and somewhat later it was proven conclusively to be so. This process is called dissociation. Of course if the vapor density is just one half what it should be, then the substance must be completely dissociated, according to the above reaction; i.e., for every molecule present before the process, we have two after. Then since the number of molecules is twice as large, if we start with one volume of NH 4 C1 gas, we will have two volumes of the mixed gases under the same conditions. These two volumes, however, weigh the same as the original one volume; and conse- quently one volume would weigh but one half what it should; i.e., the vapor density is one half the normal. These results were found to depend on the temperature, i e., the higher the temperature the smaller (down to a certain limit) the vapor density. The method by which this dissociation was proven depended upon the unequal velocity of diffusion of NH 3 and HC1 gas through a porous plate. In this way the two free gases were separated, the undecomposed NH 4 C1 gas not interfering with them. THE THEORY OF SOLUTION. J The simplest way of studying the laws governing this dissociation is to inclose a solid, which decom- poses by heat into two gases, in a vessel provided with a source of heat, a pressure-gauge, and a ther- mometer. If we now raise the temperature the solid volatilizes, and the NH 4 C1 gas dissociates until the NH 4 C1, the NH 8 , and the HC1 gases reach a certain pressure (corresponding to the certain temperature) when it ceases. If now, after equilibrium is estab- lished, we open the stop-cock, some of the gas es- capes and the pressure falls, it rises again, however, as soon as the cock is closed, and continues to rise until that same pressure is reached which existed before at' that temperature. Let us now consider, for the sake of simplicity, a case where the solid NH 4 C1 is dissociated completely into NH 3 and HC1 gas. This will act just as the other if we open the cock. We will- now, however, imagine NH S gas forced into the vessel, and will see what will happen. We observe no change in the pressure, but only that solid NH 4 C1 is formed; that is, the pressure of the ammonia becomes so great that it condenses its form, and in so doing unites again with the HC1 forming NH 4 C1. This process continues until all the HC1 is used up, and then the condition is altered, for one of the constit- uents in the equilibrium disappears, and then, and then only, does the pressure rise. In this latter case, after all the HC1 is used up, we are simply compress- ing the NH 3 gas. All this can be proven experimentally, and we always find that if we add an amount of one of the products of dissociation, the dissociation goes backivard 8 THE THEORY OF SOLUTION. in a corresponding degree, and the pressure remains con- stant. Addition of an indifferent gas, except that it increases the total pressure according to Dalton's laws, has no effect, The equilibrium which is reached after a certain time is not necessarily a state of absolute rest, but rather a case of where the amount of NH 4 C1 formed, in unit of time, is the same as that decomposed. It is then a simple exchange of matter, the total amount of the gas remaining the same.* With this we will close our consideration of gases; but it will be well to understand their behavior thor- oughly before proceeding farther, for the behavior of substances in solution is exactly analogous. To explain our abnormal results it has been assumed (and proved) necessary to consider them as dissociated into smaller particles, and even this we will find to be true also for solutions. SOLUTION. If in a tall jar we place a layer of pure water over a solution of sugar, being careful not to mix them, the sugar molecules immediately begin to diffuse through the water, and only cease when the solution through- out is homogeneous, i.e., of the same concentration. Let us now suppose, in this experiment, a semi- permeable partition (which allows passage to the water molecules, but not to those of sugar) to be * It may be well to mention here that all cases of equilibrium are considered in this way. THE THEORY OF SOLUTION'. 9 placed between the water and the solution. Imme- diately a pressure is exerted upon the partition which has for its cause, just as with gases, the tendency of the molecules to get out of the space in which they are inclosed. Here the sugar molecules are striving to wander to the water, but are prevented by the partition; and consequently they exert a pressure upon it which is equal to the sum of those of the single sugar molecules. By a contrivance for utilizing this pressure (if one could be found), we could run an engine, just as we do now with gas by its pressure upon a piston. The first pressure, as will be seen later, can be calculated in the same manner as the second. This pressure in solutions has been measured by Prof. Pfeffer (and others), and called by him Osmotic Pressure. The great objection to his method is the difficulty experienced in preparing the semi-permeable partition ; still Pfeffer has succeeded in making very good ones from copper ferrocyanide and other sub- stances.* His apparatus consists of a porous cell which he coats with the semi-permeable film and fills with the solution to be used; this is then connected tightly with a long tube containing mercury, by which the pressure is measured. To make a determination he places the cell in a jar of water and, after allowing it to stand, notes the height of the mercury in the tube; this gives the desired pressure. These osmotic pressures are enormous, as may be * See Pfeffer, Osmotische Untersuchungen (Leipzig, 1887), for apparatus and results. OF THE UNIVERSITY; 10 THE THEORY OF SOLUTION. seen by a glance at the following table from Pfeffer.* Under c is the percentage of sugar in the solution, and under p the pressure resulting in centimeters of mercury. Sugar Solution. '(ft /(cm.) t c I 53.8 53.8 I 53.2 53.2 2 101.6 50.8 2.74 151.8 55.4 ' 4 208.2 52.1 6 307-5 5i-3 i 53-5 53-5 The last column, -, contains the ratio of osmotic c pressure to concentration of sugar. Considering the size of the possible experimental error, it remains quite constant; thus proving that osmotic pressure is propor- tional to the concentration of substance in tJie solution. The higher pressures seem to be slightly too small, P thus making - too small; this is explained by the fact that, for such high pressures, the film is not entirely impassable for sugar molecules, and so a few go through, thus causing a loss of pressure. It has been found that osmotic pressure is also pro- portional to the absolute temperature (i.e., C. -|- 273). These laws have been found to be true not only for 1. c. THE THEORY OF SOLUTION. II sugar, but for all substances which do not conduct (or conduct very slightly) the electric current. We must remember here that the partition is not the cause of the pressure, but simply the condition necessary to make it visible and determinable. The cell acts as if there is a partial vacuum in it for water, and this flows inside, and continues to flow, if not prevented, until the concentration in the cell and out of it is the same. This pressure becomes smaller as the difference of concentration does. There is a tendency always to reduce the difference of concentration, i.e., the pressure, of the two liquids, just as there is with gases. The pressure, in our ex- ample, of the sugar molecules to get to the water is the same as that of the water to get to the sugar. It is thus a mutual affinity, and so we would expect to get different pressures for different solvents (which we do). If then the sugar molecules cannot get out of the cell, the water goes in, and thus exerts the same pressure inward as the sugar does outwards. The water not being able to go in, in our experiment, the mercury is raised to a height corresponding to the pressure. These enormous pressures appear, at first glance, to be impossible, for it does not seem possible that any substance could resist them. But when we remember that our vessels have not semi-permeable walls, and so the pressure is not exerted upon them, the diffi- culty of belief is removed. If they had such walls, they could not resist, but would burst immediately, as do plant-cells (containing concentrated solution) when placed in water. 12 THE THEORY OF SOLUTION. Let us now recall, for a moment, the equation of state, for gases; it is pv = RT. (R = 84700 cm.gms.). We have found that is a constant for solutions. c This is the same as pv (where/ is osmotic pressure) for - = v\ and we know that osmotic pressure is pro- portional to the absolute temperature. Hence we have, for solutions, the equation of state pv R'T, (R' = constant) which is of the same form as the one for gases. We will now calculate R' and see if it has any relation to R, the gas constant. We must remember, however, that R, in the gas equation, was calculated for one mol of gas; so in this case we will also consider R f for one mol of substance in solution. This was first done by van't HofT, the originator of the Theory of Solu- tion. For a one per cent solution of sugar (o C.) Pfeffer found an osmotic pressure of 49.3 cms. of mer- cury, which is equal to 49.3 X 13.59 671 grams per square centimeter. The molecular weight of sugar (C 12 H aa O n ) is 342; the volume therefore, in which one mol is dissolved (i$ solution), is 34200 c.c., and T = 273 ; hence /?'. 671 X ioo -.-- 342 -- = 84200 cm. grms.,* ioo cc. contain i gram. THE THEORY OF SOLUTION. 1 3 and we have practically the same constant as for gases. In the same way van't Hoff* found all the gas laws to hold for solutions, when by v we understand the dilution ( ), and by/ the osmotic pressure. This astonishing fact is the basis of the Theory of Solution, and van't Hoff announced it as follows: The osmotic pressure of a substance in solution is the same pressure as it would exert were it in gas form, at the same temperature and occupying the same volume. In other words, a mol of any substance dissolved in a given amount of water exerts the same osmotic pres- sure, at the same temperature, as does a mol of any other substance in the same volume. The value of the above will be appreciated by the following adaptation of the law for gases. One mol of oxygen (32 grams) occupies at standard pressure and temperature 22.4 liters, f as does, by Avogadro's law, the mol of any other gas. If now, instead of allowing the mol to occupy 22.4 liters, we compress it into one liter, the pressure, by Mariotte's law, becomes 22.4 atmospheres, instead of i, and the volume I, instead of 22.4 liters. From this, since the gas laws hold for solutions, one mol of any sub- stance dissolved in one liter of water must exert an osmotic pressure of 22.4 atmospheres. Accordingly then, we can determine molecular weights of substances *Zeit. f. phys. Chem. I. p. 481 (1887). f i gr. O 699.25 cc. 32 gr. O = (i mol) = 32 X 699.25 = 22.376 liters, or in round numbers 22.4 liters. 14 THE THEORY OF SOLUTION. in solution. Thus a 2% solution of sugar gives an osmotic pressure of IOI.6 cm.; then (2% per liter = 20 grms.) 20 : M :: IOI.6 : (22.4 X 76). 20 M = while theoretically we have 342 ; a very good agree- ment, considering the difficulties with the semi-per- meable film. In the case of saltpeter, and all other inorganic salts of the type, these laws do not hold; and the pressure is always greater than it should be. Thus de Vries,* by a method based upon the behavior of plant-cells, found that solutions of sugar and saltpeter, containing the same number of mols in equal volumes, gave osmotic pressures related as I ; 1.6 (instead of as I : i); and the more dilute the solutions were, the greater was the difference, Granting now that sugar and other organic sub- stances act normally (which has since been proven), then there must be more molecules of saltpeter present than there should be; i.e., each molecule must split up into two or more. This is the same assumption that we had to make for gases. In that case the number of molecules increased and so, under the same pressure, enlarged the volume. In the case of solution, how- ever, the volume (of liquid) remains the same, and consequently the pressure must increase in the same proportion, as the volume did before. * Pringsheims Jahrbiich, 14. 427. THE THEORY 0^ 1 5 Results, by the method of osmotic pressure, are so difficult to obtain that other methods have been devised which depend, in principle, upon the same factor (concentration) as does the osmotic pressure. These are used now in its place, for from the con- centration and absolute temperature we can calcu- late, for all normal substances, the osmotic pressure. Further work upon the inorganic salts, by all methods, showed conclusively that these gave pres- sures greater than they should give by the law. Here, however, a fact was discovered by Arrhenius that led to the theory of electrolytic dissociation in solution, which was the second step towards our theory of solution, osmotic pressure being the first. Arrhenius found that those substances, and only those, which give abnormal osmotic pressures are capable of conducting the electric current; and if these substances are dissolved in any other solvent, in 'which they act normally, they lose that power. Before going farther, we will consider for a moment how electricity is conducted in a liquid, in order to see just what this strange action means. Grotthus was the first to discover that solutions conduct electricity in a manner different from metals, and he showed that the electricity was carried bodily, by particles of the dissolved substance, from one pole to the other. When these arrived at either pole they dischaiged their electricity; when the current was broken they disappeared again from the solution. The assumption was then that the current first decomposed the sub- stance into smaller particles, and that these then, by electrostatic attraction and repulsion, moved through l6 THE THEORY OF SOLUTION. the liquid, carrying their charges with them. Fara- day also did a great deal of work upon this subject, and gave the name ions to the particles, and gave out and proved the following law, which is the basis of all electrochemical work: . All movement of electricity in electrolytes occurs only by the concurrent movement of the ions; and in the following manner, equal amounts of electricity move chemically equivalent amounts of the different ions. We can now understand what Arrhenius' discovery means. He found that all substances which conduct electricity (and only such) give abnormal osmotic pres- sures, i.e., have too great a number of molecules present. We know that all substances in solution which conduct electricity do so by virtue of particles, which are formed from the molecules of the substance. Hence, since all electrolytes give pressures which are too high, they must have these particles (ions) present in them, under all circumstances, which act as mole- cules, and so increase the osmotic pressure. This is the assumption made by Arrhenius* in 1887, the process which produced them was called by him electrolytic dissociation. In the next section we will study it more in detail, and find the laws which govern it. ELECTROLYTIC DISSOCIATION. Arrhenius found that the electrical conductivity of all substances increased with increasing dilution (i.e., decreasing concentration). That is, the more dilute * Zeit. f. phys. Chem., I. 631. ..- - THE THEORY OF SOLUTION. IJ the solution is, the greater the proportion of ions present. He then divided the molecules in solution into two groups, the inactive ones, or molecules which can split into ions, and the active ones, which are the ions. The first do not take any part in conducting the current, that being done by the ions (active). In the case of osmotic pressure, however, the inactive as well as the active ones have their influence, and so dilute solutions should give results more abnormal than others, which is a fact. In contrast to this, all sub- stances which do not conduct electricity (sugar) give normal pressures, for there is no dissociation and conse- quently no ions, and the pressure is caused by the in- active molecules alone. The osmotic pressure, then, in a solution is, as it is for a gas by Dalton's law, the sum of the individual osmotic pressures. Unlike ions, then, added to a solution only increase the total pressure, while like ions have an influence upon the equilibrium, just as with gases (NH 4 C1), as will be explained later. Arrhenius called the ratio of the ions present in a certain volume to those at infinite volume the degree of dissociation (a)\ i.e., a = where JJ V and nj* are the so-called molecular conduc- tivities at the two volumes v and v^. The molecular conductivity is found by multiplying the specific con- ductivity. expressed in terms of the conductivity of a column of mercury, by the molecular weight. The *To find ^ see Chap. II. 1 8 THE THEORY OF SOLUTION. value of a is found to increase with the dilution. This does not mean that there are more ions present in a dilute than in a strong solution, but that the propor- tion is greater. In a dilute solution we would thus have a larger proportion of a smaller total number, and vice versa for a strong one; the latter, in each case, would thus have the greater absolute number of ions, but would have, in proportion, a larger num- ber of inactive molecules. At this time it was found that these ions were also the active members in chemical reactions, and that, in a solution of a substance, only those elements present as ions gave their characteristic reactions. Thus in the case of CH 8 C1, which dissociates into CH 2 C1 and H, no reaction for chlorine with AgNO, can be obtained until the complex ion CH,C1 is decomposed, Cl ions set free. The power to conduct electricity and chemical affinity are thus closely related, and the value of the one gives that of the other; for both depend upon the same condition, i.e., the pres- ence of ions. We have thus far followed logically and historically the development of the theory of solution, as based upon the electrolytic dissociation, from the laws governing the behavior of gases, and have seen how each fact has led to a new assumption, and this by being proven has in turn led to another. We will now drop this method of treatment, and give simply the results of the modern investigations, and thus gain a view of the perfected theory as it exists to-day. In the first place we will state that important law, as discovered by Kohlrausch, which he calls the Law THE THEORY OF SOLUTION-. 19 of the Independent Wandering of tJie Ions. According to it the movements of an ion are independent of those with which it is in equilibrium. That is, a chlorine ion moves with the same velocity (and each ion has a certain velocity in water, which has been determined) when in combination with hydrogen ions as it does when with ions of sodium or any other substance. By Faraday's law each ion can carry with it a cer- tain amount of electricity; so that this, in combination with the above, shows that each ion always carries the same amount of electricity no matter in what com- bination it exists. It has been found necessary to assume that as soon as a substance dissolves and dis- sociates the ions receive enormous charges of elec- tricity* (calculated below by Faraday's law), and that one is negatively and the other positively charged, in a binary electrolyte, and with equal amounts of electricity (-)- and ). With one gram of hydrogen ions (Faraday's law) there are 96537 coulombs of electricity carried; conse- quently one coulomb causes o.ooooi gram of hydro- gen ions to move. Thus to prove that the ions are charged with electricity is an extremely difficult thing, for the charges are so large for infinitely small amounts of substance; but Ostwald and Nernst f have proved * This is not so hard to believe as many have tried 10 make it for we know that dissociation can only take place when equal amounts of positive and negative electricity are given to the ions. As to the enormous charges, they can be explained in the same manner as is the fact that from a piece of amber, by rubbing we can obtain an almost infinite amount of static electricity. The actions are probably somewhat similar. fZeit. f phvs. Chen,, III. UNIVERSITY X. /S AI .L.KIlk. ^S 20 THE THEORY OF SOLUTION. it notwithstanding by very delicate apparatus. Later we will see how the considerations of a voltaic cell also go to prove it. The simplest way of grasping the theory will be to study the state of a dilute solution, and see how it acts chemically and electrically. We will consider a dilute solution of sodium chloride (i mol to 10,000 liters); here, practically, we have complete dissocia- tion, according to the scheme / ; /DO oo *OQ , NaCl = Na + Cl. The signs * and ' stand respectively for the number of equivalents of positive and negative electricity. Thus for Ca we have two positive ones, Ca; and for SO 4 two negative ones, SO 4 . It is hard to imagine free sodium and free chlorine j to exist in water; but we must remember that these are ions, and charged with enormous amounts of electricity, and consequently different from the ele- -v,? ments as we know them. This will remove the diffi- culty, particularly when we find that, on losing their K* charges (by electrolysis), they again assume their well- 1) ^ known properties, and the Na decomposes the water ^o and gives off H gas at one pole, while Cl gas is given ? V off at the other. If now we place two platinum plates, connected with a source of electricity, in this solution, and pass the current through it, the following action takes place. First the plates become charged, and these charges rwork electrostatically upon the charged ions of the solution. The positive ions (Na) will be attracted by THE THEORY OF SOLUTION. 21 the negatively charged plate and repelled by the other; the negative ions (Cl) on the other hand will be attracted by the positive plate and repelled by the negative. In this way the positive and negative ions will be separated (to an amount equal to the difference between the electrostatic power of the plates and that of the unlike ions, for these attract one another), and a storing up of ions will take place on either plate. When the potential becomes high enough, the attrac- tion of the plates will become so great as to rob the ions (in equivalent amounts) of their electricity (-f- and ) and the current flows and the elements (Na (or H) and Cl) appear. Before a current passes through, the charged (-(- and ) ions will have been arranged in a state of equi- librium. Afterwards, however, if the current is broken, like ions will be together, and, as they repel one another, a new equilibrium will be established. As no one ion has ever been found to act as both positive and negative, elements in solution are never dis- sociated. A solvent always seems to be necessary, for molten salts do not conduct electricity to a very great extent. When water is placed on sodium chloride, the action which takes place is exactly analogous to that of the dissociation of solid NH 4 C1. The volume of the sol- vent here being the volume, in which the substance is confined. Molecules of sodium chloride go into solu- tion, and there dissociate into Na and Cl ions. This process continues until a certain osmotic pressure (for that temperature) is reached for each of the three members, NaCl, Na, and Cl, when it ceases. If we 22 THE THEORY OF SOLUTION. enlarge the volume (i.e., add water), more salt dis- solves and more NaCl molecules dissociate, until the osmotic pressures are the same as before (at that tem- perature). Ostwald proved, by means of the electrical conductivity, that the relation between the dissociated portions arid the undissociated one is expressed, for binary electrolytes, by the equation I KC = c,c a , c t - no c v - where C is the concentration of the undissociated part, expressed by the number of mols per liter; C, and C, those of the two ions(+ and ); and K is a constant, called the dissociation constant, which depends in value upon the temperature. If we add now to our solution of sodium chloride, another chloride, as that of potassium, what will be the action ? The ions of potassium will exert no in-. fluence upon the reaction (as has been proven by experiment), but the Cl ions^will be increased in con- centration, and the equilibrium disturbed. Before adding KC1, our equilibrium is % expressed by the formula KC = QC,. C, Cl ions. If now we add Cl ions in a' concen- tration C , our formula will be transformed into In the first equation C + C, = A, the total concen- tration of the NaCl; .in the second C' + C' a must THE THEORY OF SOLUTION. . 23 c>c_ again = A, consequently C' must be larger than C (and C, > C',), for K is a constant. That means that the dissociation goes back and the undissociated por- tion increases, just as it did with gaseous dissociation. (NH 4 C1). This was proven experimentally by Ar- rhenius* for acetic acid and sodium acetate, and a number of other salts. By aid of this formula it is possible to find C , i.e., the concentration of added Cl ions, by solving the equation for C . In general, then, tJie addition of an indifferent ion has no effect upon the equilibrium; while that of a like ion drives back the dissociation to the amount expressed in our formula. We must keep in mind here that when an ion is driven back into the undissociated portion, it takes with it the other ion, with which it was in equilibrium. Thus in our formulae C' 2 is smaller than C a , and in the same degree is C', smaller than Q. We will now consider the case of water and what effect its slight dissociation has upon chemical reac- tions. At first water was thought to be undissociated, but Kohlrausch found it to be dissociated to a very small extent. This fact" makes clear one chemical phenomenon that could never be explained before. When strong acids neutralize bases, it was observed that the same amount of heat was developed. This is now quite easy to understand; the reaction, for example, HC1 + KOH = H a O + KC1, *Zeit. f. phys. Chem., V. i (1890). 24 THE THEORY OF SOLUTION. written with respect to the ions, becomes: H + C'l + K + OH = H a O + K + Cl. That is, H and OH ions cannot exist beside one another (except to a very slight extent) and thus unite and form undissociated water; the K and Cl re- maining in the ionic state. Most of the strong acids contain the same number of H ions in equal volumes, and so, with equivalent amounts of each, the same amount of water is formed, and hence the heat is the same. This is found to be true for all acids and bases when their degrees of dissociation are taken into consideration. Thus if an acid is dissociated in such a way as to have present, for equal volumes, but one half the number of H ions that HC1 has, then the heat is but one half as great, for but one half the amount of water is formed. Just so with the bases. i H The ions of water are H and OH, and not HH and O as one might suppose. The effect produced by the fact that water is but slightly dissociated can be more clearly understood from the following example. Since the dissociation constant, for water, is very small, only a very small number of ions of OH and H can exist together; in other words, if they are placed together they unite and form, as above, undissociated water. Thus if we have a hydroxide of an element in solid form, in water, ions of the element and of OH are present, to a certain degree (even though it be small), and the addition of an acid, i.e., free hydrogen ions, must form undissociated water, and a dissociated salt of the element with the negative element of the acid. UJNIVERSITT) ^^SAJJORNJ^^ THE THEORY OF SOLUTJUTTT 2$ By this, however, OH ions disappear and more are formed and used, and again more are formed, etc. In this way each new dissociation gives off ions of the metal, these form an equilibrium with the negative ion of the acid, and finally, if enough acid is added, the hydroxide goes into solution, forming a salt (dis- sociated) and water. , When a substance dissociates into *a simple and a complex ion, the general rule is that by increasing the dilution (decreasing the concentration) some of the substance dissociates further, to a very small extent, into its ultimate ions. Thus H 2 SO 4 = H + HSO 4 , and, to a very small extent, H 2 SO 4 = HH + SO, which amount increases with decreasing concentration. Also H 3 P0 4 = H + H 2 P0 4 and H 3 PO 4 = H + H + HPO 4 to a small extent. This is also true with regard to KAgCN 3 and salts of that description. Thus then to a lesser degree, Rotassium -f- AgCN 2 = Potassium + AgCN + CN, 26 THE THEORY OF SOLUTION. where AgCN is neutral, and this then dissociates, to a very slight extent indeed, into AgCN = Ag+CN. In a i/io normal solution, the first step is nearly complete; the second to a degree that the CN ions have a concentration of 2.76 X io~ 3 normal, i.e., about 5$ dissociated; and the third to a concentration of Ag ions of 3.65 X io~" normal.* So much for the present for electrolytic dissociation itself, but, as later in each of the other chapters it is the basis of our work, a number of new aspects of it will be developed which can find no place here. * The author. Zeit. f. Phys. Chem., XVII. 513-535(1895). CHAPTER II. METHODS FOR THE DETERMINATION OF ELEC- TROLYTIC DISSOCIATION.* THESE methods can be divided into three groups. I will describe those in each group, as far as concerns the principles upon which they are based, and will refer the reader elsewhere for details. FIRST 'GROUP. Osmotic Pressure, Lowering of the Freezing-point, Increase of the Boiling-point, etc. These methods are not as valuable as those of the other two gr-oups; as not only the number of ions, but also the number of inactive molecules, are found by them. We have considered osmotic pressure already, so we will first turn to the freezing-point method. In the last century it was found that the addition of a soluble substance to a liquid lowered the freezing-point of the same, and this lowering was proportional to the amount of substance added. In 1884 Raoult improved the method, and found that one mol of any substance like sugar (undis- sociated as we now know them to be) in one hun- dred mols of solvent lowered the freezing-point of the same 0.63 C. For an electrolyte (dissociated * For details see Ostwald, Hand- und Hilfsbuch zur ausfiih- rung Physiko-chemischer Messungen (Leipzig, 1893). 27 28 THE THEORY OF SOLUTION. substance), if the molecular weight is known, this method can be used to determine the degree of dis- sociation; while for a non-electrolyte whose molecular weight is unknown, the method can be used to find it. Thus if an electrolyte in solution, I mol to 100 mols of water = iSoogrms., gives a lowering of 1.2 C., then there must be nearly two mols present and hence the substance is nearly completely dissociated. The re- sults, for small degrees of dissociation, are complicated by the action of the inactive molecules, and the latter in strong solutions may form more complex molecules, which would further affect the results. The apparatus of Beckmann consists, in principle, of a tube, a deli- cate thermometer, and a freezing bath. The freezing- point of the pure solvent is first determined, and then a weighed amount of the substance added and the freezing-point of the solution found. The difference in the two is proportional of course to the amount of substance added; and from it, the weight of substance added, and the molecular weight, we can find the de- gree of dissociation. The boiling-point method is based upon the same principle as that of the freezing-point. When we add substance to a solvent, the boiling-point of the same is increased by an amount proportional to the amount of substance added. Beckmann has also devised an apparatus for this purpose. A solvent which has a low boiling-point, as ether, is usually used, and as almost no dissociation takes place in it, the method gives normal results and so is employed principally for determining molecular weights and not dissociation. SECOND GROUP. The method of this group is that ELECTROL YT1C D IS SO CIA TION. 2g of electrical conductivity, as originated by Kohlrausch and Ostwald. We know that only the ions conduct electricity, and that at infinite dilution only ions are present, and consequently the ratio of conductivity at a certain volume, to that at infinite volume gives the ratio of free ions present to those that could be present, i.e. the degree of dissociation (#). We have then ft* Of course, as it is a ratio, the specific conductivity might be used, but it is always well to use, as above, the molecular conductivity, for salts of the same series (and acids also) have almost the same molecular conductivity; and in addition we usually find the term /^ in those units. The apparatus consists of a glass vessel, in which the solution is placed, which is provided with platinum electrodes. The arrangement is the ordinary one for determining the electrical resistance (reciprocal of conductivity), except that an induction-coil and tele- phone receiver are used to find the neutral point in place of the flowing current and galvanometer. If a flowing current were used, electrolysis would take place and the elements would appear at the electrodes, thus decreasing the concentration and causing the conductivit} 7 to vary. With the alternating current, however, all the substance separated out by the stream in one direction will redissolve when the direction of the current is reversed, and consequently the poles are changed, and the conductivity is constant, 30 THE THEORY OF SOLUTION. For this purpose, then, the current from a battery is passed through the current-breaker, and then sent through the cell, which is connected to a rheostat and regular Wheatstone bridge arrangement. When the buzzing in the telephone is at a minimum, then the resistance of the cell is equal to a certain part, as shown on the bridge, of the rheostat resistance, and so we can easily calculate the resistances of the cell. The conductivity is the reciprocal of the resistance; the specific conductivity multiplied by the molecular weight is the molecular conductivity, and is the sum of the molecular conductivities of the ions (present in that volume) of which it is composed. The conduc- tivity varies greatly with the temperature, and so this must be kept constant to i/io of i C. during the measurement. The value /^ can be found by adding together the molecular conductivities (for infinite dilu- tion) of the ions of which the substance is composed.* Kohlrausch, by aid of his law of independent wander- ing of the ions, has determined this value for all ions, and so we can take the necessary values from the table and add them together, and we have the desired value. In many cases it is possible to attain this state practically, and the results so obtained agree very well with those calculated. According to Kohlrausch's law, u x = u-\- v, * In calculating theoretically the ^values ju v and //, we take for //j, the sum of the molecular conductivities of the ions and multiply it by a. n^ is where a = i. Py = (mol. cond. of -f- ion + mol. cond. of ion)cr, ELECTROLYTIC DISSOCIATION. 31 where u and v are the molecular conductivities of the two ions, and JJL is the molecular conductivity, at infinite volume, of the substance. We can find, by altering this equation slightly, the value for /* at any dilution (see page 30, note) if we know v/hat value a has for it. Thus In the first case a = i, and we have JH M = u -\- v, as above. In the last chapter it was said that Ostwald proved the equation where C = mols (or fraction of a mol) of undissociated substance per liter; C, and C 2 being those of the two ions, and K is the dissociation constant. He did this by aid of the conductivity, but with the equation in a different form than the above. It is more convenient to use dilution, instead of concentration, particularly for dilute solutions. Thus instead of speaking of a sub- stance as i/io normal, it is simpler to say a dilution of 10 liters (i.e., the number of liters in which one mol is dissolved). Then, again, since molecular con- ductivity varies directly with dilution (inversely with concentration), it is clearer to have it as a term in our equation. We will now transform this equation and get it in the form that Ostwald did, and show how he proved K to be a constant. Our formula to start with is KC = C.C,. 32 THE THEORY OF SOLUTION. Let us suppose the total amount of substance dissolved is equal to I ; then, a = degree of dissociation, a -c v " or v(i - or)' K = But a= ; .-. K = This is the formula used by Ostwald, and by it he tound K to be constant for all the weaker acids, but not so for the stronger ones, as HC1. The reason for this is still unexplained. The value of K for the organic acids is larger or smaller as the acids are stronger or weaker. It is thus a measure of the chemical affinity of substances. To give some idea of the size of this constant, a few examples are given. Formic Acid. ju = 376; IOOK = k 0.0214. Acetic Acid //<* 364; IOOK = k = 0.00180. Butyric Acid. yuoo = 359; IOOK = k = 0.00134. ELECTRQL YTIC DISSOCIA TION. 33 These values are the means of a long series of determinations. As will be seen, the three examples given above are placed in order of their activity, formic acid being the most active, and so its constant is the largest; but this is merely another way of say- ing that it has more H ions present in it than the others. THIRD GROUP. To this group belong all methods which allow us to determine the presence of one ion, and its amount. If there is but one other ion, in equilibrium with it, to form the undissociated portion, then ions of other kinds added to the solution will have no effect upon the equilibrium. The effect of adding an amount of the ion, with which it is in equi- librium, has already been pointed out. This princi- ple we will use later. These methods are of great value to us, for they allow us to follow the course of the dissociation, and to ascertain just what ions are present and to what concentration. The methods are restricted, however, at present to the determina- tion of but a few ions; but soon we may hope to have all those necessary to follow any reaction. For a long time it has been known that addition of acid to a sugar solution accelerates the rapidity of its inversion, as the breaking down into dextrose and laevulose is called. The rapidity depends upon the strength of the acid used; and as this depends upon the number of hydrogen ions present, the rapidity must also. The reaction is a strange one, for the acid does not change its composition, and the same amount is present after the action has ceased, as before. Such an action is called a catalytic one. Trevor made OF THE UNIVERSITY 1 34 THE THEORY OF SOLUTION. of this catalytic action of hydrogen ions upon the inversion of cane-sugar to determine the concentra- tion of the H ions, and with very good success. He worked at 100 C., starting with a solution of sugar whose strength he determined by aid of a polariscope; he then determined it after intervals of time, and thus found the velocity of change without acid. Then by adding acid solutions containing a known strength of H ions, and determining again the amount of sugar present, he was able to find just what effect a certain amount of hydrogen in ionic form had, and to form an equation expressing it. Of course, then, it was possi- ble to determine unknown amounts, and this he did in a large number of cases. Thus we have one good method for determining H ions; and there is another still, devised by Ostwald, which depends upon the E.M.F. of a Grove gas-cell, but farther into that we will not go. In the next chapter is described a method, by Ostwald, for determining dissociation by aid of the electromotive force of a specially prepared cell. This allows us to determine the concentration of ions of all metals, as long as they give good constant electrodes, as, for example, silver. This method can also be ex- panded for negative ions. By it the author* was able to determine Cu ions and also the dissociation constant of hydrocyanic acid, a number too small to be accurately determined by any other method. We will take it for granted, then, that the concentration of Ag ions in KAgCN, can be determined by aid of the * Zeit. f. Phys. Chem., XVII. 513-535 (1895). ELECTROLYTIC DISSOCIATION. 35 E.M.F., and explain the principle of the method. Silver ions are in equilibrium here (Chap. I) with CN ions. If we add to the solution a substance contain- ing CN ions, those of Ag will be driven back propor- tionally. By determining this new concentration of Ag ions, that of the CN ions added can be found. A formula, however, cannot be used here, on account of the large amount of CN ions which are present, and yet are not in equilibrium with the Ag, to form un- dissociated AgCN. A solution of sodium cyanide of known dissociation was then used, and its effect on the Ag ions of the KAgCN 2 noted, and the relation expressed by means of a curve, of which E.M.F. and concentration of CN ions were the coordinates. In this way, after adding CN ions, the E.M.F. was deter- mined and the amount of CN ions found by interpola- tion. Of course the KAgCN 2 solution was always kept at the same concentration. By aid of some compound (of the nature of KAgCNJ containing Cl or other ions, these also could be determined. CHAPTER III. THE THEORY OF THE VOLTAIC CELL. IN our first chapter an outline of the new theory of solution, as based upon electrolytic dissociation, was given in brief. In the present chapter we will see what a great influence it has had upon the theory of electric batteries, and what new insight it has given us concerning the ways of electrical energy and its relations to chemical energy. According to the law of the conservation of energy, the electricity generated in a reversible battery is equal to the energy generated by the chemical reac- tion which takes place in it. In other words, the energy of the chemical reaction, turned into electrical units, is the energy of the cell. Thus, for example, in the Daniell battery of zinc in zinc sulphate, and copper in copper sulphate, the chemical process con- sists in dissolving the Zn and separating Cu. The formula is Zn + Cu + SO 4 = Zn + SO 4 + Cu. The chemical energy (expressed as heat) is here 501 calories (K*), while the electrical energy, volts (ex- * K as used by Ostwald = 100 cals. 36 THE THEORY OF THE VOLTAIC CELL. 37 pressed as heat), is 505 K. This shows that the theory as above sketched is correct; but with most other combinations widely differing results are ob- tained. But this has been shown to be due to the temperature coefficient of the cell. At 273 C. (ab- solute zero) the chemical energy is always equal to the electrical, but at higher temperatures the electrical is usually higher. In the case of the Daniell cell this coefficient is very small, and so makes little difference. The relation is E e = c + e where E e = electrical energy ; E c = chemical ' ' e = amount of electricity; ~TJ-'=- r i se m potential n for i absolute tem- perature. We will now consider what takes place between two solutions of the same substance but of different strength. According to Faraday's law, differences of poten- tial in electrolytes are only possible by irregular arrangement of the ions, in such a way that one place has an excess of positive ions, and another an excess of negative ones. Wherever such an irregularity is found we must find there a difference of electrical potential, i.e., an electro- motive force. Such a state as this was first recognized * Ostwald, Lehrbuch der allg. Chem., II. 819. 38 THE THEORY OF SOLUTION. by Nernst* as due to the unequal velocity of the ions in a solution (Chap. I). If, for instance, over a solu- tion of hydrochloric acid we have a very dilute solu- tion of the same, then in the strong solution both ions H and Cl will be present in the same number and under the same osmotic pressure, and consequently driven with the same force into the dilute solution. Their velocities are, however, as we know, different; and so this produces a separation of the ions and con- sequently a difference of potential between the solu- tions. In this, however, electrostatic attraction and repulsion enters into account (for like ions all go in the same direction), which retards the faster ions and accel- erates the slower ones until the velocities have been equalized, when it ceases. The more dilute solution must then acquire the polarity of the fastest ion. Since H and OH are the fastest ions, every acid must be negative against a more dilute solution of the same, and every base positive. This explains those momentary differences of poten- tial which are so often observed, and which then sud- denly disappear. This E.M.F. can be calculated by means of a formula, and Nernst has done it and found the explanation to be the correct one. We will now consider a constant which belongs to each metal, and which will help us to understand the process which takes place at each electrode. Let us imagine a metal in a solution of one of its salts; it must either dissolve, precipitate the ions out of the solution upon itself, or remain unaltered. Therefore *Zeit. f. Phys. Chem., II. 617 (1887). THE THEORY OF THE VOLTAIC CELL. 39 Nernst ascribes to each metal a certain pressure, P, with which it strives to send its ions into the solution. If/, the osmotic pressure of the metal ions in the solu- tion, is less than this, the metal dissolves to a certain extent; if equal, nothing happens; and if greater, metal ions go from the solution and give up their elec- tricity to the electrode and become metallic. This pressure, P, is called by Nernst the electrolytic tension of solution. It is a constant which depends upon the absolute temperature, and usually increases with it, and also upon the nature of the solvent. We will now see what happens when a metal, with a high solution tension, Zn, is placed in a solution of one of -its salts, ZnSO 4 . The pressure Pis here much larger than /, the osmotic pressure of the Zn ions in the solution, and so the Zn plate dissolves, and Zn ions (+) go into the solution from it, and leave negative electricity on the plate. According to the present physical theory, all neutral substances are charged with electricity, both positive and negative, but in equal amounts; and so if we remove the posi- tive, the negative remains behind, as above. This works electrostatically upon the positive ions in the liquid, and in that way diminishes the solution tension. The process continues until equilibrium is reached between the solution tension and the electrostatic attraction, when it ceases. To bring about this state, however, we need but a very small quantity of metal, for the electrical charges of the ions are enormous. We have now the following state. The zinc has an amount of negative electricity upon its surface which electrostatically attracts the positive ions in the solu- 4O THE THEORY OF SOLUTION. tion. The solution has an excess of positive ions in it and is consequently positive. Therefore metals with large solution tensions in solutions of their salts form always the negative pole of the cell, t/*e positive pole being tJie solution. The negative electricity of the metal, attracting the positive of the solution, forms an equilibrium in the form of what Helmholst calls an electrical double layer. These, according to Helmholst, always form whenever two conductors of different potential come together. As soon as the solution and metal are connected outwardly, this double layer is broken up and the true potential difference of the two bodies is shown; on breaking again the outward connection, the double layer is formed just as before. Equilibrium will be reached with metals of this kind the sooner, the smaller the concentration of the metal ions in the solution is, and the potential difference will be the greater. We will now consider a metal (Cu) with a very small solution tension. In this case the osmotic pressure of the metal ions in the salt solution will be greater than the solution pressure of the metal, and so metal ions will go to the electrode and there give up their positive charges and become metallic. The metal in this case b.ecomes charged with positive electricity, and equilibrium will be reached when the electrostatic repulsion of the metal ions by the positive plate becomes equal to the osmotic pressure of the ions in solution. With metals of this type the equilibrium will become established the sooner, the more dilute the solution is, and the potential difference will be smaller. (Contrast with the first case.) THE THEORY OF THE VOLTAIC CELL. 4! According to the conception of solution tension, evejy metal should show a certain potential in a solu- tion of one of its salts (of a ceitain concentration), and this we find to be a fact. It also holds for the metals in acids, for by aid of the oxygen of the air (which can- not be excluded) traces (at any rate) of metal are dis- solved, and so a dilute solution formed, which acts just as any other solution. Of course these results are not so constant, for the element of chance enters into it, as far as the amount dissolved is concerned. What small amounts of metal dissolved will give these results we will calculate later. Nernst, by considering these two pressures (i.e., osmotic and solution) just as we would gaseous pres- sures, has succeeded in working out a formula for each electrode, giving just the E.M.F. that is pro- duced.* The formula for each single electrode is 7f l = cog ~ t 7t^ = og~, P\ Pi and the total E.M.F. of a cell made up of two such electrodes is 0.0002W, . where c is a constant = - (n t = valence of * He assumes that an electric cell is a machine run by dif- ferences of pressure, and all his assumptions have been proven correct, as have the formulae. For details see Zeit. f. Phys. Chem., IV. 149 (1889). 42 THE THEORY OF SOLUTION. metal, and n l the number of the ions of that kind pro- duced by the dissociation of one molecule), T is the absolute temperature, P 1 and /* are the two solution pressures, and p l and p^ the corresponding osmotic pressures. 7/j and n t are the differences of potential caused by contact of the two liquids and the two metals; these, however, we can neglect. Although it is not possible for us here to follow the mathematical development of the formula, still we will probably be able from the sketch of the process to understand it. The constant c (whose value is given above) is simply a constant which causes the results to be given in volts. By the aid of the formula given for each separate electrode, P Tr^cTlog- 1 , it has been possible to calculate the different values of P in atmospheres. The values vary greatly ; some are enormous, others very small, n in the formula is the potential of the metal against a normal (i liter) solution of one of its salts, /, being the osmotic pres- sure of the metal ions of the solution, i.e., a X 22.32 atmospheres,* for if entirely dissociated, the ion con- sidered would have a pressure of 22.32 atmospheres. Metals. Symbol. P (atmospheres). Zinc Zn 2.7x10" Cadmium Cd 7-4 X io 6 Thallium Tl 2.1 X io 3 Iron Fe 3.2X10* * Neumann, Zeit. f. Phys. Chem., XIV. 223. THE THEORY OF THE VOLTAIC CELL. 43 Cobalt Co 5.2 X 10 Nickel Ni 3.5X10 Lead Pb 3.1 X io~ Hydrogen H 2.7 X 10 Copper Cu 1.3 X 10 Mercury , Hg 3.iXiO~ 18 Silver Ag 6.4 X IO~ 17 Palladium Pd 4.0 X 10 _3 -19 -36 These metals are arranged in the order of the old contact series (Volta) for air, and with one or two exceptions it seems to be also the proper one for solutions. We must remember the greater the solu - tion pressure is the more negative a metal will be as against its solution. In a Daniell cell the E.M.F. is 1.06 volts; here the osmotic pressures are insignificant as compared with the solution pressures; thus in our formula (P l = Zn, P. = Cu) we can cause /, and p^ to be the same, and so they disappear and our formula becomes or log /in = 36. $/>Cu, Or P Zn = 10*5/> C 44 THE THEORY OF SOLUTION. According to our results, as found experimentally for the single electrodes (see table), we have which can be looked upon as a very good agreement, considering all the circumstances, and goes to prove that our theory of a cell is the correct one. We are now in position to calculate the amounts of metal ions in a solution which are necessary to give a potential in connection with the metal. This is for the case of metals in acids in which they are not solu- ble, spoken of before. We will assume that P Cu = io~ l8 atmospheres (which is certainly too large). A solution of a copper salt at 20 liters dilution has an osmotic pressure of Cu ions of one atmosphere. To have a solution with a pressure of io~ l8 atmospheres it is only necessary to take the 2O X IO" l8 part of a mol; and this would still be greater than the solution pressure of the metal, and so give a potential differ- ence. The amount of Cu (20 X io~ l8 mol), however, is so small that we cannot detect it analytically by any known method, and it approaches in size a mole- cule. According to the latest measurements in one mol there are, in round numbers, 5 X io 23 atoms, i.e., in one liter of the above solution there are about 25,000; so that in one cubic centimeter 25 atoms suffice to cause such a pressure that the copoer in its solution has a potential of zero. There is a certain type of cell which was impossible to understand by the old theory, for no chemical action takes place in it; but by the new theory, as we have sketched it, it becomes very simple. I refer to THE THEORY OF THE VOLT^TC~CE'LL. 45 concentration cells, i.e., where the same metal is used on both sides as electrodes, and the solutions are the same substance but of different concentration. An example of this is which gives an electromotive force of o. 116 volts, or Ag | AgNO, T VN-KN0 3 -KAgCN, T VN | Ag. E.M.F. (TT) =1.14 volts. The KNO 3 is used as a connecting link in the first, to remove any E.M.F. that would arise by contact of the two liquids; and in the second for the same reason, and also because the two salts form a precipitate when they come in contact. In cases like the first, how- ever, the KNO 3 is not necessary if we make allowance for the E.M.F. generated by the contact of the two solutions in the formula, as Nernst has done. The experimental .and the theoretical results obtained by him were found then to agree very well. For our purpose, however, simplicity is important, so we will use the KNO 3 . According to our earlier considera- tions the E.M.F. of such a combination will be expressed by the formula 7t nr C T \ log log ~" P l and P^ ~ solution pressure for silver, which is con- stant for same solvent and temperature, and hence P l and P n cancel. Our formula is then 46 THE THEORY OF SOLUTION. where / a is the osmotic pressure on the more concen- trated side, and /, that on the other. Silver has a negative solution pressure, and so ions of silver will leave the solution and discharge on the electrodes. This will happen on both sides, but with a different pressure of silver ions on the two sides. Thus both silver electrodes are positive, but the one on the concentrated side is more positive than the other, and so it will be our positive pole; i.e., elec- tricity (-f) will go from the concentrated side through a wire to the other. A contrary-directed current of negative electricity will go through the liquid to the concentrated side. As soon as Ag ions have been precipitated upon the concentrated side their elec- tricity will drive silver ions out on the other, and this action will continue until the two solutions are of the same concentration, when it will cease. There is another type of cell differing in action apparently from any we have as yet considered ; it is the so-called oxidation and reduction * element. In principle it is very simple, and may be thoroughly understood from the following typical example: If we have a Pt electrode (coated with platinum black) in a solution of stannous chloride on the one side, and another in a solution of ferric chloride on the other, and connect the two with a wirr, a current of elec- tricity passes from the one on the iron side, through the wire to the one in the Jn solution, f and vice versa through the solution. The iron ions () on * Bancroft, Zeit. f. Phys. Chem. f Of course to get a current it is also necessary to connect the two solutions with a siphon. VOLT A. THE THEORY OF THE VOLTAIC CELL. 4/ the one side strive to get into the divalent form, and so give up one equivalent of electricity to the elec- trode, and this goes to the other electrode (through the wire) and allows the tin ions () to get into the tetravalent state (by absorbing electricity). The action is thus one of oxidation on the one side and reduction on the other. The above action of course only takes place when the electricity given up by the iron ions (Fe*** to Fe"), can be used by the Sn ion (Sir- to Sir---). We have a true oxidation when negative electricity is formed on an ion, or when positive is given up by an ion. A reduction is naturally the opposite to this; that is, when positive electricity is formed on an ion, or when negative is given up. If only negative ions are given up, then the process is one of oxidation. All solutions, however, can cause either oxidation or reduction (according as the -f- or ions disappear or are formed), for in them there are present equal amounts of positive and negative ions. From the above it is apparent that the process in cells of this type does not differ so widely from that of the Danieli. In the latter case the reduction takes place at the zinc electrode, the oxidation at the copper. But this is simply a case of two reductions where the one (Zn) is greater than the other, for all metals give out only positive ions, but to different pressures, and this difference causes the current. DISSOCIATION BY AID OF THE E.M.F. Before closing this chapter with a brief account of the processes taking place in practical and storage 48 THE THEOR Y OF SOL U TION. batteries, it will be well to consider the method of Ostwald's, mentioned before, of determining concen- tration of metal ions by aid of the E.M.F. As osmotic pressure is proportional to concentration, we can substitute for ' their values -^ in the equation and we get n=cT\og$*. C 9 (mols per liter) of solution on the positive side, C l that on the other. If we know * TT,, T, and C, we can find C t . This formula was used first by Ostwald for the cell with AgNO,f\ and KAgCu a f v ff , n = 1.14 volts, log C, = -- i, T 273 + 17 = 290; hence * * ~ .0002 X 290' log C, = -- i 19.6 = 20.6, C v = io- 20 - 6 . That is, there are 108 grams (one mol) of silver ions in io 20 - 6 liters of T ^KAgCu a . This amount is so small as not to be shown by any analytical method, for a reason to be given later. But just here is the value of the method, for the smaller the number of Ag ions present the larger the E.M.F. is, and so the greater the THE THEORY OF THE VOLTAIC CELL. 49 accuracy. This method can be used for all metals forming good constant electrodes, but unfortunately that number is not large. This is the method as used by the author to determine CN ions (Chap. I). PRACTICAL PRIMARY AND SECONDARY BATTERIES.* By the aid of the knowledge we have gained by our consideration of the voltaic call (that is, the relations of the osmotic pressure of the ions to the solution pressure of the metals) we are now in position to dis- cuss and understand the practical batteries with which we come in contact every day. Of course in practice the concentration cells are of but little use to us, for their age is too short, i.e., the concentrations become equalized very rapidly, and so the current soon ceases to flow. Still a knowledge of them in connection with one of solution pressure is of great value to us, for in them, as in all other batteries, the process depends upon the same factors. The process taking place in the Daniell cell, as has already been mentioned, consists of formation of ions of Zn and the disappearance of an equal number of those of Cu, caused by the great difference of the solu- tion pressures of Zn and Cu. We will now consider another constant cell, i.e., one giving a constant E.M.F. The Clark standard cell consists of Zn in a solution of ZnSO 4 and Hg covered with a paste of Hg 2 SO 4 . * In this chapter Le Blanc's Lehrbuch der Elektrochemie has been freely used. SO THE THEORY OF SOLUTION. This Hg 3 SO 4 is insoluble, but, as will be seen in the next chapter, all salts are soluble to a certain extent (even though it be very small), and so we can assume that there are HgHg and SO 4 ions present. The process then is the following: Positive Zn ions are forced (by solution pressure) into the solution, and these go through the solution and drive (by electro- static repulsion) the Hg ions out to the electrode, where they give up their charges and assume the metallic form. Thus the Zn losing positive electricity (with the ions) is the negative pole; while the Hg receiving positive charges from the ions is the positive one. That is, the current goes through the wire from Hg to Zn, while in the liquid it goes from Zn to Hg. The Daniell cell is more valuable for giving a cur- rent than the Clark, but for simply a known constant E.M.F. the latter has the advantage. The tempera- ture coefficient (increase of E.M.F. for i C.) is, however, large in both; but that is true of all elements using saturated solutions. Of course, as there are but few ions of Hg present in the Clark, they are soon used up, if the current is allowed to flow (unless through a large resistance), and then the E.M.F. falls;. but the cell recovers on standing, as then more ions of Hg are given off by the Hg 2 SO 4 . This is not such a great disadvantage, for the Clark cell is used as a standard for the E.M.F., and always has a compen- sating E.M.F. against it, and so does not become used up. To this type of cell belong also those of the Helmholst and Weston pattern ; and their action is very similar. To the type of inconstant cells belong all those from THE THEORY OF THE VOLTAIC CELL. 5 1 which we obtain large amounts of electricity at a large E.M.F., and where the latter is not required to be constant. The Leclanche cell consists of a solution of ammo- nium chloride in which are placed the two electrodes Zn and carbon -|- MnO 2 (manganese dioxide). Here we have to distinguish between the action of the car- bon alone and the carbon -\- MnO 2 . First we will assume Zn and carbon alone as electrodes, and see what disadvantages the cell has; then we will bring the MnO 2 into play, and see how it changes the reac- tion and removes the disadvantages. If the elec- trodes of the cell Zn - NH 4 C1 - C, are connected, the Zn ions will go into solution (great solution pressure of Zn), and hydrogen gas be given off at the C pole. The zinc ions go through the solu- tion and, being positive, act electrostatically upon those of NH 4 , driving them toward the carbon. Here a storing up of an excess of positive ions takes place, and as H ions give up their electricity more easily than NH 4 ions, H gas collects on the carbon, and it receives the electricity. The NH 4 ions then form an i equilibrium with those of OH. The Zn electrode is the negative pole, having lost positive electricity, and the C the positive one, having received the -f- charges from the H ions. The hydrogen gas is absorbed by the carbon plate and then given off in the air; but this giving off of hydrogen gas is not rapid enough, and the plate becomes saturated with it and so pre- vents, partly, other ions from discharging to it, and in consequence the E.M.F, falls rapidly. In order to 52 THE THEORY OF SOLUTION get rid of this objection the MnO 3 is used. With it, however, the action is entirely changed, and now goes as follows: We know that every substance is soluble to a certain extent (Chap. IV), even though it be very small, so we know that there are ions of Mn present. The reaction is MnO, + 2H a O = Mn + 4OH. These tetravalent ions of Mn have the tendency, as before remarked, to give up two equivalents of elec- tricity and to assume the form of divalent ions, Mri. In consequence of this the zinc ions go through the solution as before, but this time drive the Mn ions to the electrode, where they give up the two equivalents of electricity (more easily even than do those of H) and become MnCl,(Mn + 2Cl). This action takes place evenly, until the concentration of Zn ions in the solution becomes so great that no more can be formed by the Zn; then the E.M.F. falls. New NH 4 C1 solution, however, renews the action. The other primary element of this type that we will discuss is the combination Zn - H,SO 4 + K 2 Cr 2 O 7 - C. At the negative electrode here Zn ions are also driven into the solution; at the positive pole (C), however, the action is more complicated. The action of H,SO 4 THE THEORY OF THE VOLTAIC CELL. 53 upon K 2 Cr 2 O 7 is practically to form chromic acid (H 2 CrO 4 ) ; this, however, dissociates to a large degree into HH a +CrO 4 . As we know, substances which dissociate in this way usually dissociate further, to a slight degree, into metal ions (Chap. I); this is the case with chromic acid. H 3 CrO 4 + 2H a O = Cr + 6OH. These hexavalent Cr ions have the tendency to give up three equivalents of electricity and assume the trivalentjorm Cr*". Accordingly the zinc ions (just as before with the Mn"**) drive the Cr ions to the electrode, where they give up three equivalents and become Cr*", in equilibrium SO 4 as Cr 2 (SO 4 ) 3 . This is what happens in all cases when, in a cell, the valence of an element changes, for they give up their extra equivalents much more readily than any element could give up its entire charge. Accumulators, Storage or Secondary Batteries. A cell of this description is any one in which electrical energy can be stored up in the form of chemical energy, and used as required. All reversible * cells can be used as storage batteries by passing a current through them, so that the reaction goes in the opposite direction from which it goes in the cell. Thus a Daniell element which has been used up * A reversible cell is one in which all the products of the reac- tion still stay in accessible form in the cell. If a gas is formed, the cell is not reversible. 54 THE THEORY OF SOLUTION. (i.e., when so much zinc has been dissolved as to prevent further formation of Zn ions) can be regen- erated by passing a (-(-) current through the Cu, and so on through the liquid to the Zn ; this sends Cu ions into solution, and precipitates the Zn ions upon the Zn as metal. The element is thus brought into its original state again and can be used once more. Thus we have Zn + Cu + SO 4 X Zn + SO 4 + Cu. The left side represents the cell when ready for use, the right when used up. The lead accumulator is, however, the one generally used. It consists before being charged of two lead plates, one being coated with litharge (PbO) in a 20$ solution of sulphuric acid. If now we pass a current of electricity through this (PbO on -j- pole), superoxide of lead (or supersulphate) is formed on the PbO side and spongy lead on the negative one. The cell when fully charged is then an element with PbO a and Pb as electrodes in sulphuric-acid solution. By discharging the reaction is PbO a + 2H 2 SO 4 Aq + Pb = 2PbSO 4 + Aq + 8;oK. that is, the PbO a and the Pb are transformed into PbSO 4 . According to this reaction the E.M.F. should be 1.9 volts at o ; the higher potentials are caused by the positive temperature coefficient, i.e., where the potential one increases with increased tem- perature. Now for the process that takes place on THE THEORY OF THE VOLTAIC CELL. 55 discharging. The PbO 2 is soluble to a slight extent, and with water dissociates as follows: PbO, + 2H 2 O = Pb- + 4OH. These tetravalent Pb ions have, however, the ten- dency to give up two of their equivalents of electricity and to go into the state Pb". From the lead plate, when the two are connected, ions of lead are given up and drive the Pb ions electrostatically to the PbO, plate, where they lose their two charges and become PbSO 4 . From the lead plate the pressure of Pb ions is greater than from the other, and so the former drive those of the latter through the solution. The PbO plate is thus positive, against the one of Pb. According to Le Blanc the principal source of the E.M.F. of this cell is the change of valence from Pb to Pb-. The tetravalent ions of Pb as they are used up are supplied by the PbO 2 plate. The Pb" ions from the negative plate go into solution and form PbSO 4 , but the formation of this has but little influence upon the E.M.F. So much for the theory of this cell; the explanation of its irregularities and certain others of its character- istic actions can be found in Dr. Le Blanc's book.* We will only add here that all the processes have been made clear, and are described in full, with reference to our theory, in the above work. * See Preface. CHAPTER IV. ANALYTICAL CHEMISTRY FROM THE STANDPOINT OF ELECTROLYTIC DISSOCIATION. THIS subject has been so thoroughly treated by Ostwald that here only enough will be given to show what great value our theory possesses in this branch, as well as in the treatment of electrical elements. Those wishing to follow the subject into its details are referred to Ostwald's book.* Analytical chemistry has always been an empirical science, i.e., we know that certain things occur under certain conditions, but do not know why they do so. Ostwald has, however, succeeded in removing the greater part of this difficulty by the aid of the theory of electrolytic dissociation. We found in Chapter I that the ions are the active parts in a chemical reaction, and that when they are present they give well-known reactions, but not when the element is a part of a complex ion. According to this, then, we must always consider in reactions the ions and their quantity, rather than the substances themselves. When a substance dissociates there is a certain rela- tion between the dissociated and undissociated parts * Scientific Aspects of Analytical Chemistry. Trans, by McGowan. (Macmillan, 1895.) 56 ANALYTICAL CHEMISTRY. 57 which is expressed for a substance which falls into two ions by the formula c,d, = KC, I where C t is the kathion () and C a () is the anion, C the concentration of undissociated portion, and K the dissociation product. This is also expressed (Chap. II) by where a = degree of dissociation, and v = dilution (number of liters in which i mol is dissolved). Thus for large v, a is also large. For the neutral salts K is very large, and differs for the different ones but slightly, while for acids it is small, and is greater or smaller according as the acid is strong or weak. This difference becomes smaller, the weaker the solution; for an infinite dilution, all would be equally strong, for all would be completely dissociated. All substances are soluble to a certain extent even though it be very small, and this part in solution we can assume without error to be very largely dissoci- ated. Nernst * has proved the following two laws: I. In a saturated solution of a partly dissociated substance, the active mass of the undissociated portion remains constant under all conditions, even when a second substance is added. II. The product of the active masses of the ions *Zeit. f. Phys. Chem., IV. 372 (1889). $8 THE THEORY OF SOLUTION. formed by the dissociation also remains constant, when the solution is saturated. The task for the analytical chemist is then to make this dissociated part as small as possible. This is accomplished by adding another substance with an ion in common, thus driving the dissociated portion back into the undissociated portion. The solution, how- ever, is already saturated with this, and when more is formed it is precipitated out as insoluble. For elements or indifferent substances there is no way to do this but by lowered temperature, or by adding some other solvent in which the solubility is less; these cases, however, we will leave out of con- sideration, for they are neither numerous nor of much importance. In a saturated solution we have a complex equi- librium between, first, the solid body and the undis- sociated part (small) in solution; second, this undisso- ciated part in solution and the ions of the same. The first, however, by the first law of Nernst, remains constant. For the second case we have, for binary electrolytes, C,C 2 = KC. Since C, as we have just found, is constant (for a cer- tain temperature) in saturated solutions, therefore KC is also, and also C,C a . Thus for equilibrium between a precipitate and its solution the product of the con- centrations of its ions (C, and C,) must reach a certain value; this value is called the solubility product. From another standpoint it means this: tJiat a precipitate can form only when the product of the concentrations of ANALYTICAL CHEMISTRY. 59 the ions (7, and C y ) has reached a certain value. This follows simply from the above, for it is the condition of equilibrium between a solid and a solution; and no precipitate can form without equilibrium, for in that case it would immediately redissolve. In analytical chemistry the object is to separate one element in insoluble form, and then to weigh it. Let us take for example the case of the determination of SO 4 with BaCl 3 . If we add just enough Ba salt, then some SO 4 ions will remain free, but not enough with the Ba ions present to reach in value the solubility product of BaSO 4 . This amount can, however, be made insignificant by adding more Ba salt, for the greater the concentration of that is, the smaller will be the' amount of SO 4 ions necessary to reach in value the solubility product. Still the amount of SO 4 ions can never be made zero, for that of the Ba ions can never be made infinite; but the amount is so small that even if we did precipitate it we could not find any difference in our two weights. This was long ago discovered practically, when it was found best always to add an excess of the precipi- tate; but for its scientific explanation Ostwald must receive the credit. Of course the more soluble the precipitate the greater must be the excess of the pre- cipitant. For to decrease the solubility to \/n of what it is in pure water, it is necessary to add n times the amount of the other ion. A small excess, how- ever, is all that is necessary in practice, for all the pre- cipitates used are very insoluble, and so have of them- selves a very small solubility constant. All this holds also in washing our precipitates; thus 60 THE THEORY OF SOLUTION. we often use water containing one of the ions of the solid, in order to keep it insoluble. For example, we wash lead sulphate with a dilute solution of sulphuric acid, and mercurous chromate with mercurous nitrate; but of course we must use those substances which can be removed most easily, so as not to interfere with the other operations. It is perhaps confusing to think f hat the ions are the active members of a chemical equation ; for then it would seem that we would get only such an amount of precipitate as corresponds to the number of ions present. A minute's thought, however, will clear away all doubt, and show that all the substance pres- ent enters into the reaction. If we have a solution which is 10$ dissociated into two ions, and we add a substance in such an amount as just to combine with all these ions and form an insoluble compound, then it is natural to think that a further addition will pro- duce no more of the precipitate, for we have used up all the ions. But we forget that as soon as those ions disappear, more of the salt must dissociate until the pressure of the ions is the same as before; then an addition of the precipitate will combine with these, and the process will go on until all the salt has been dissociated by steps. The solubility product explains why, in cases where we know ions to be present to a very small amount, we cannot prove their presence by analytical means, for their concentration is so small that almost an in- finite amount of the ions of the precipitant would have to be added before the solubility product could be reached. ANALYTICAL CHEMISTRY. 6 1 As we have seen, the neutral salts are always more completely dissociated than the corresponding acids. This is well shown by the fact that calcium salts are precipitated by all carbonates, but free carbonic acid has no action upon them. Carbonic acid in water is but slightly dissociated into ions, and so the product of the concentration of CO 3 ions, and that of the Ca ions (even though present in large amounts) does not attain the value of the solubility product of CaCO 3 . With regard to lead salts this is somewhat different. Lead carbonate is more insoluble than calcium car- bonate and so the product is smaller, and so is reached with a solution of carbonic acid and a precipitate forms. This precipitate is, however, but a portion of the total amount of lead present. Carbonic acid in wate.r dissociates to a small extent into HH and CO 3 . If we use lead nitrate, the Pb ions disappear from the solution, and more are formed and finally an equilib- rium is established between the H ions of the car- bonic acid and the NO 3 of the Pb(NO 3 ) 2 ; these H ions, however, act upon those of the carbonic acid, sending them back into the undissociated portion, and of course the CO 3 ions go with them, and so no more PbCO 3 is formed. This takes place with Pb(NO 3 ) after a very small amount of PbCO 3 has been formed; because HNO 8 is a strong acid and very largely dis- sociated. With lead acetate, however, it takes place after it is two thirds decomposed, for acetic acid is but little dissociated, and so much more of it must be formed before the osmotic pressure of H ions is as great as in the case of IINO 3 (at the end of the reac- tion). 62 THE THEORY OF SOLUTION. In exactly the same way most of the reactions of analytical chemistry can be explained. Those that have been given, however, show the influence of the theory upon analytical chemistry* as well as a large number would ; and so we will close with a few con- siderations concerning indicators for volumetric analy- sis, which will explain their behavior and help to retain their applicability in our minds. INDICATOR FOR VOLUMETRIC ANALYSIS. Under this head we will consider only those used in acidimetry and alkalimetry. An indicator is a sub- stance which possesses a different color when in acid and alkaline solutions. They are either acids or bases and are but very slightly dissociated, the less so the more accurate they are. Phcnolplithalcin is a weak acid indicator, whose molecule is colorless and whose ion is an intense red It dissociates into H and the ion of the complex radicle, which is red. If added to an acid, the large number of H ions of the acid drive those of the indicator back, forming the colorless undissociated molecule. If added to a base, then water and a salt are formed; but, as we know, all salts are dissociated more than their corresponding acid, and so the red color due to the complex ion is at once seen. Ammonia is too weak a base to form a neutral salt in very dilute solu- tions, and so the results obtained in its presence are not sharp. For acids this indicator is very good * These cases have been taken from Ostwald's book, and a large mass of others will be found there, to which I would refer the reader. ANALYTICAL CHEMISTRY. 63 when the amount of free acid is titrated back with a solution of barium hydroxide; but for alkalies it is not so good, as it is restricted to the very strong ones (i.e., those that are largely dissociated). Methylorange is a medium strong acid the ion of which is yellow, the undissociated portion being red Addition of a strong acid causes the hydrogen ions to go back into the undissociated portion, and its color (red) appears. If it is mixed with a base, water and a salt are formed, and the salt being dissociated shows the yellow color. If, however, to methylorange a weak acid is added, as carbonic, its small number of H ions will not be enough to drive those of the indicator back, and so no sharp reaction will be produced. Thus methylorange cannot be used for all acids, but only for the stronger, largely dissociated, ones. For weak bases methylorange is the better, for weak acids phenolphthalein. Between these two extremes the other indicators lie, and their actions can be explained in the same way. We have now finished our sketch of the theory of solution, and its importance can be appreciated. We have taken up only the more important parts; but if they are thoroughly understood, little difficulty will be found in following the investigations of the present day. 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