10 1 24 EXCHANGE With the Compliments of YALE UNIVERSITY LIBRARY NEW HAVEN, CONN.. U. S. A. YALE UNIVERSITY MRS. HEPSA ELY SILLIMAN MEMORIAL LECTURES THEORIES OF SOLUTIONS * 4 - SILLIMAN MEMORIAL LECTURES PUBLISHED BY YALS UNIVERSITY PRESS ELECTRICITY AND MATTER. By JOSEPH* JOHN THOMSON, D.Sc., LL.D., Ph.D., F.R.S., Fellow of Trinity College, Cambridge^ Cavendish Professor of Ex>eri- mental Physics, Cambridge. 400 NaCl 9.25 MgSO 4 0.217 KI 16.2 KCL 9.03 K 2 SO 4 0.204 KBr 12.5 MBa(OH) 2 0.42 K 2 Cr 2 O7 0.194 KNO 3 11.9* H 2 SO 4 about0.5 KBaCl 2 9.64 T1 2 SO 4 0.219 The bases (Ba0 2 H 2 ) rank here with the salts of divalent anions (S0 4 and Cr 2 7 ) ; a far smaller influence is exerted by the salts of monovalent ions and the mono- valent acids give an exceptionally low effects Also organic anions are much more effective than inorganic ones, according to Linder and Picton. The hydrogen ion has a suspending power for positively charged suspensions. The rule of the greater effectiveness of polyvalent ions was first found by Schulze in 1882; his experiments dealt only with sols of A^Ss and Sb 2 S 3 ; but this rule has been verified in all the cases thoroughly examined by the following investigators. 46 THEOKIES OF SOLUTIONS. The chemical behavior of suspended particles of noble metals was very thoroughly examined by Sved- berg and his pupils. Just as spongy platinum destroys hydrogen peroxide, so platinum sol has the same effect, but in a still higher degree corresponding to its fine division. Bredig and Mueller von Berneck shook together fulminating gas and 2.5 c.c. water containing about 0.17 milligrams of suspended platinum and found that the reaction went on with constant velocity, as was quite natural, since the concentration of fulminating gas always remained the same throughout the shaking. The combined quantities are seen hi the following figures (valid at 25 C.) : Time Minute*. Combined Gas c.o. Velocity c.c. per Min. 10 17.8 1.78 20 35.8 1.80 30 54.8 1.90 40 72.4 1.76 50 90.2 1.78 After two weeks, during which this liquid had been shaken in the day-tune with a total resulting combina- tion of about 10,000 c.c. of fulminating gas, it was tried again and found to cause 98.2 c.c. of fulminating gas to combine in 50 minutes. The effectiveness of the platinum-sol had therefore not diminished. They then investigated the decomposition of hydro- gen peroxide hi neutral or weakly acid (through an addition of srVff c - c - NaH 2 P0 4 ) solution. They found that the reaction was of the monomolecular type, i. e., that the quantity of H 2 O 2 decomposed per minute was proportional to the concentration of H 2 2 , as was to be expected. SUSPENSIONS. 47 A totally different set of relations is obtained if sodium hydrate is added. With increasing quantity of the hydrate the velocity of reaction at first increases, then reaches a maximum when the solution is about 0.02 normal in regard to the alkali, and afterwards it decreases again if the concentration of the latter is further increased. This is evident from the following figures, which indicate the time which is necessary for decomposition of -fa normal H 2 2 to its half strength. The quantity of platinum was always the same, ^WirTfTF normal. Cone, of NaOH. 1/512 1/256 1/128 1/64 1/32 1/16 1/8 1/4 1/2 1 Time in minutes 255 34 28 24 25 22 34 34 70162520 Here the rate of decomposition is for low concentra- tions of NaOH almost independent of the concentration of H 2 O 2 , whereas at higher concentrations of NaOH the reaction follows the monomolecular formula, i. e. t the rate is proportional to the concentration of H 2 2 as is seen from the following figures (valid at 25 C.). 1/512 NaOH. Time. a z * t k 23.9 6 22.4 0.0047 0.25 15 19.65 0.0057 0.28 25 16.5 0.0064 0.30 40 11.17 0.0083 0.32 55 6.35 0.0105 0.32 1/128 n NaOH. Time. a * * x * 23.83 6 21.15 0.0086 0.45 15 16.67 0.0104 0.48 25 11.6 0.0125 0.49 40 5.33 0.0153 0.46 48 THEORIES OF SOLUTIONS. 1/32 n NaOH. Time. ax k^ k 23.9 6 20.02 0.0128 0.65 15 15.4 0.0127 0.57 25 10.9 0.0136 0.52 40 6.13 0.0148 0.44 a-x is the quantity of H 2 2 present, determined by titration. fc is the constant giving the velocity of reaction according to the monomolecular formula, k Q on the other hand the velocity of reaction, calculated on the supposition of a constant rate from the beginning. In the first instance (1/512 n NaOH) &i increases in the proportion 1 to 2.25 during the time of reaction. Even the quantity k Q is not absolutely constant, but shows an obvious tendency to increase with time. The second case (1/128 n NaOH) gives almost the same behaviour, but k Q is very nearly constant. In the third instance ki increases slightly (about 15 per cent.) with time, so that the reaction proceeds almost as a mono- molecular one; on the other hand k Q decreases by about a third of its original value. Similar irregularities are often found in the investiga- tion of the catalytic action of ferments; and therefore Bredig calls platinum-sol and similar substances inor- ganic ferments. A maximum effect in the presence of a certain quantity of sodium hydrate has been observed by Jacobson for the decomposition of H 2 2 by means of emulsin, pancreatic juice and malt-ferment. In the inversion of cane-sugar by means of invertin the maxi- mum effect is attained if a certain quantity of acid is present. In this case also the quantity of cane sugar decomposed in unit time is nearly independent of the concentration of the sugar, if this exceeds 2 per cent., SUSPENSIONS. 49 but at very low concentration (below 0.5 per cent.) the rate of inversion follows the monomolecular formula. The similarity between ferments and platinum-sol is still more strikingly manifested in the fact that in each case their action is paralysed by the presence of very small quantities of " poisons." Hydrocyanic acid, car- bon monoxide, iodine, mercuric chloride, hydrogen sul- phide, etc., exert such an action on platinum-sol. The first-mentioned has a very peculiar action; at first it paralyses the sol, but later on this recovers and has an even greater effect than without the poison. A similar recovery of emulsin and of pancreatic ferment after their paralysis by HCN has been observed by Jacobson. In these changes, the reacting substances probably condense upon the finely divided metallic particles, as we shall see in the next chapter, and in such condensed systems the chief reaction takes place. This is prob- ably the case with many gas-reactions in the presence of finely divided platinum, for instance, the oxidation of S0 2 by means of oxygen to S0 3 , which has been examined by Fink. Wallach found that the terpenes and their derivatives may easily give addition-products with hydrogen in the presence of finely divided pal- ladium, prepared according to Bredig's method (cf. next chapter), which is known to condense hydrogen on its surface very strongly. Evidently the organic sub- stances are also concentrated around the palladium particles and in these surface-layers the reaction takes place. These reactions proceed just as if the reagents were subjected to a high pressure, which is also favor- able to them 5 50 THEORIES OF SOLUTIONS. The magnitude of the suspended particles is highly dependent upon the concentration of the solutions from which they are precipitated, as Biltz in particular has proved. On this magnitude the optical properties of the suspension, color and translucence, which are caused by diffraction of the light, depend. Thus Schulze as early as 1882 observed that if he prepared two suspensions of A^Ss the one from a concentrated, the other from a dilute solution of As20 3 by leading in H 2 S (cf. p. 36), and then diluted the former until the concentration of As20a was the same as in the latter, the suspension containing the coarser particles were less translucent and possessed a clearer yellow colour, than the yellowish red suspension of finer particles. Svedberg subjected this peculiarity to a closer investi- gation. He used, for instance, the method of reducing gold from its chloride by means of chlorhydrate of hydrazin and obtained the figures given hi the following table, where c is the concentration (normality) of the solution of gold chloride (AuCl 3 ) used and k the depth of its colour determined by dilution until the colour was not longer perceptible. m Colour 343 bluish grey, blue, blue, 37 fuchsin red. 20 c 1 50,000 X 10- 7 2,000 21,000 5,000 10,000 75,000 7,500 200,000 6,000 250,000 3,300 200,000 1,700 125,000 1,000 100,000 500 200 50,000 15 17,000 7 25,000 13 M SUSPENSIONS. 51 The intensity k of the colour of solutions containing the same quantity of gold at first increases when the gold particles diminish and thereafter decreases. The diameter of the particles, in millionths of a miUimeter is tabulated under m\ it diminishes rapidly with c, and at the same tune the colour changes. Emulsions con- taining still smaller particles of gold reduced by means of an ethereal solution of phosphorus (Zsigmondy's method) are ruby red to reddish yellow according to the fineness of the particles. This last column reminds one of that of gold chloride, which has a value of A: = 5,000. Similar maxima of k although not so strongly marked have been obtained by Svedberg for suspensions of Fe(OH) 3 and of As2S 3 . If a solution of phenol in water is cooled, droplets of phenol separate out and two coexisting phases are formed. Similarly when a solution of gelatine is cooled it gives a solid jelly which after all consists of two different phases, one of gelatine with a small per- centage of water and one of water with a small content of gelatine, as Buetschli at first demonstrated as prob- able. Similar properties are found with some emulsions, and especially with those of sulphur prepared according to Rappo by allowing a saturated solution of sodium thiosulphate to drop into cold concentrated sulphuric acid. Rappo found that this emulsion is precipitated by the addition of certain salts such as NaCl, KN0 3 , KC1, Na2 S0 4 or K 2 S0 4 , although NH 4 -salts do not seem to possess this power. The precipitates made by means of sodium salts, dissolve in increased quantities of water or at higher temperatures. 52 THEORIES OF SOLUTIONS. Svedberg and his pupil Oden investigated this phe- nomenon. They found that the solubility of this sulphur increased with temperature approximately according to an exponential law, which holds good also for the change of solubility of other substances with temperature. From this it is possible to calculate the heat of solution of the sulphur (cfr. Lecture V) and in this manner I have found the following values per grammolecule: Normal Cal. Solubility at 20 in 0.2 NaCl 42,400 (between 14.8 and 25.0) 14.1% in 0.3 NaCl 22,000 (between 16.5 and 38.5) 1.2 in 0.4 NaCl 33,100 (between 23.1 and 47.5) 0.3 in 0.5 NaCl 33,400 (between 31.9 and 41.8) 0.08 in 0.2 NaBr 36,600 (between 14.9 and 19.7) 11.0 in 0.2 (mol.) NaS04 42,500 (between 13.9 and 22.6) 4.1 The experimental errors are very great, so that the calculated values of the heat of solution may be regarded as agreeing rather well with the mean value 36,200 cal., an unusually high value for a heat of solution. The figures giving the solubility at 20 indicate that NaCl and NaBr have nearly the same influence on the colloidal sulphur, while Na^SOd has a greater influence than NaCl if in equimolecular, but less in- fluence if in equivalent solution. Oden has investigated this last property more fully. He finds that different preparations of suspended sulphur behave rather differently, and this explains the irregularity in Svedberg's figures. He finds that if the solubility of the sulphur (in per cent.) at 16 C. is represented by S and the normality of the NaCl by n then the following experimental formula holds good: S = 32,810 SUSPENSIONS. 53 as is seen from the following figures: 0.21 0.34 0.46 0.58 0.74 6'obg. 5.43 1.68 0.74 0.36 0.07 Scale. 6.51 1.69 0.73 0.38 0.19 Diff. -1.08 0.01 +0.01 -0.02 -0.12 Different salts have very different powers of causing precipitates. The following figures give the inverse values of the quantities in gram equivalents per liter, which must be added in order to produce precipitation. The solutions lose their transparency at a certain concentration, which may be determined rather ac- curately. The inverse value of their concentration in gram equivalents per litre is given below : LiCl 1.1 KC1 47.5 MgS0 4 54 ZnS04 6.6 NILCl 2.3 K 2 S0 4 39.7 MgN 2 6 63 CdN 2 10.2 (NEU) 2 S04 1.7 KNO, 45.5 CaCl 2 123 A1C1. 76 NH4NOs 2.0 RbCl 63 CaN 2 124 CuSO 4 51 NaCl 6.1 CsCl 108 SrN 2 193 MnN 2 O 53 Na 2 S0 4 5.7 BaCl 2 238 NiN 2 6 11.2 NaNO, 6.1 BaN 2 6 231 UO 2 N 2 O 6 36.5 An addition of acids increases the stability of the suspension, so that much greater concentrations of the salts are needed in order to produce precipitation, than if the acid is not present. HN0 3 and H 2 S0 4 have the greatest influence, HC1 and HBr much less, about 60 per cent, of that of HNO 3 or H 2 SO 4 in equimolecular solution. This so-called dispersing action increases till it reaches a maximum at a certain concentration and thereafter it diminishes again. Formic acid has about 14 times less action than HN0 3 or H 2 S0 4 in concentra- tions below normal. It does not possess a maximum 54 THEORIES OF SOLUTIONS. of action at any concentration. Acetic acid possesses a very small activity in this respect. It seems very difficult to draw general conclusions from all these figures. In groups of similar salts, as for instance the salts of the alkali-metals, the precipitat- ing influence of the salt increases very rapidly with the atomic weight of the metal, and metals of a high valency generally have a greater influence, but the regularity is not very pronounced. LECTURE IV. THE PHENOMENA OF ADSORPTION. IN the year 1777 two chemists, the German, R. Scheele and the Italian, F. Fontana independently discovered that charcoal has a great tendency to take up and retain gases from its surroundings. This phe- nomenon was then studied by a great number of scientists, amongst whom the renowned French savant Saussure (1814) deserves special mention. In 1791 Lowitz found that charcoal is also able to take up coloring matter from solutions, so that a complete decoloration of fluids could be brought about by simply filtering them through carbon, a method which is of the greatest value for many industrial processes. Payen afterwards showed that a great number of salts and other substances were condensed upon charcoal. In further investigations it was discovered that not only carbon but even other substances, which are finely divided or consist of agglomerations of fine fibres, such as finely divided platinum, iridium, powdered glass or glass-wool, powdered silicic acid, clay, kaoline, metastan- nic acid, meerschaum, asbestos, paper, cotton, leather, silk or wool possess the same attracting or condensing power as charcoal. On this property of fibres of mineral, vegetable, or animal origin many dyeing and tanning processes de- pend; further the retention of carbonic acid, moisture and salts necessary for the vegetation in different soils 65 56 THEORIES OF SOLUTIONS. as well as the hygroscopic nature of various materials are consequences of adsorption processes. Clearly they are of the greatest practical importance and they have therefore attracted the keen interest of many investi- gators. The chief problem, which these investigators have had in view, was to determine how great the quantity taken up by the porous substance was, and how it changed with the concentration of the surrounding gas or solution and with the temperature. The phenome- non itself is according to a suggestion by E. du Bois Reymond called " adsorption," which is meant to indicate that the " adsorbed" substance does not enter into the interior of the " adsorbent," but is only at- tracted to its surface, in contradistinction to solution (especially solid solution) or chemical interaction. These two latter processes sometimes accompany ad- sorption and so exert a disturbing influence. It was found, as one would expect, that the adsorbed quantity increases with the concentration of the sur- rounding gas or solution. In some cases there exists a proportionality, reminding one of the law of Henry, for instance, with gases in general at high temperatures and with hydrogen and helium even at rather low tem- peratures ( 80 C.). But in the majority of cases the adsorbed quantity increases much more slowly than the concentration considered, and this was expressed by means of a formula, which has often proved very useful in interpolations, namely, a = kc n , where a is the adsorbed quantity per g. of adsorbent, k THE PHENOMENA OF ADSORPTION. 57 a constant (the adsorption constant), c the pressure of the surrounding gas or the concentration of the sur- rounding liquid studied and finally n is an exponent less than unity. The formula was controlled by giving it the form log a = log k + n log c and plotting log a against log c as abscissa. The points thus determined were joined together by a curve, which ought to be a straight line if n is constant, as it was generally found to be (cf. diagram p. 66). As examples the following figures may be given: ADSORPTION OP CARBONIC ACID ON CHARCOAL AT 0. n = 0.333; k = 2.96 (Travers). c a (observed). a (calculated). 0.41 1.94 2.21 2.51 3.94 3.99 13.74 7.65 7.00 41.64 10.49 10.1 85.86 12.97 12.9 Here, as is usually the case with gases, the concentra- tion is expressed as gas-pressure in cm. of mercury; a in cubic centimeters (at 0, and 76 cm.) of the adsorbed gas on one gram of the adsorbing substance. In this case the value of a at low pressures falls a little short of the calculation, i. e. y the straight line is bent down somewhat towards the abscissa axis. This phenomenon is general with gases at low pressures. ADSORPTION OF ACETIC ACID ON CHARCOAL AT 14 n - 0.25; k = 2.112 (G. C. Schmidt). o a (observed). a (calculated). 0.0365 0.93 0.923 0.084 1.15 1.137 0.135 1.248 1.282 0.206 1.43 1.423 0.350 1.62 1.625 58 THEORIES OF SOLUTIONS. The agreement between the observed and the calcu- lated values is in this case very good. Many similar cases were investigated and on the whole it may be said that the calculated values were in good accord with the observed ones. It was therefore generally assumed that the equation above represents the adsorp- tion phenomenon at constant temperature, i. e., gives the so-called adsorption-isotherm. As will be seen later on, this hypothesis is rather far from the truth, and when we look critically at the tabulated observa- tions we find in most cases, that the intervals in which the values of a have changed are very limited, as for example, hi the last case between 0.93 and 1.62, i. e., not fully hi the proportion 1 to 2. With regard to the influence of temperature, it was found to be rather insignificant for the adsorption of substances from their solutions especially at higher temperatures, as Freundlich showed. With gases the constant k decreased exponentially with increasing tem- perature and n increased with temperature in the man- ner indicated by the following figures for the adsorption of carbonic acid on charcoal according to Travers's measurements. t A- (observed). k (calculated). n - 78 14.29 16.62 0.133 2.96 2.96 0.333 35 1.236 1.364 0.461 61 0.721 0.768 0.479 100 0.324 0.324 0.518 The calculated values of k are found by means of the following formula: log k t = log k - 0.009608 t where i is the temperature in centrigade degrees and the logarithms are to the base 10. THE PHENOMENA OF ADSORPTION. 59 If the temperature were increased sufficiently n would approach very near to 1; on the other hand at very low temperatures approaching to absolute zero n takes values decreasing very nearly to 0. The exponential formula given above indicates that the adsorbed quantity should increase to infinity if the pressure or osmotic pressure of the examined substances were to increase without limit. This was also believed to be the case until quite recently G. C. Schmidt found some cases (adsorption of acetic acid or of iodine on carbon) in which the adsorption reached a very well marked maximum, S, which was arrived at asymptot- ically on increasing the concentration, and which could therefore not be exceeded. He therefore proposed a new formula of the type where &, A and S are constants. This formula has the weakness that it contains three constants to be deter- mined experimentally, and this gives it only the value of an interpolation formula which may lack a higher physical meaning. If a approaches very near to S we find that the logarithmic term increases very rapidly towards infinity, i. e., c must also approach infinity, i. e., S is a, maximal value of a. It would increase the value of the formula to a high degree if A were zero or if it were a function of S, for then there would be only two constants and the formula might be more a rational one. Schmidt soon found that A was not zero and therefore determined it experi- mentally. On inspecting the values of A determined 60 THEORIES OF SOLUTIONS. by Schmidt I was surprised to see that the product AS was very nearly a constant namely, 0.4343, the ratio between common and natural logarithms. In gen- eral it was a trifle lower, as is indicated by the following values of S and A given by Schmidt. 8A System 0.484 Acetic acid, charcoal from cane sugar. 0.414 Acetic acid, charcoal of animal origin. 0.4453 Iodine in benzene, char- coal of animal origin. 0.4218 Acetic acid, charcoal from cane sugar. 0.3570 Acetic acid, charcoal of animal origin. 0.4057 Acetic acid, charcoal from cane sugar. I therefore recalculated Schmidt's figures under the supposition that the product SA was really 0.4343 and found for instance the following results for Schmidt's Tab. 12, which may also give an insight into the real meaning of an upper limit to the adsorbed quantity. SCHMIDT'S TAB. 12 100 c.c. ACETIC ACID WITH 10 g. CHARCOAL FROM CANE SUGAR. S = 0.905. Schmidt's Tab. 8 s gives 0.88 A 0.55 Tab. 9 " 2.48 0.1670 " 10 " 1.36 0.3275 " 12 " 0.9052 0.4660 " 14 " 1.4570 0.245 " 16 " 1.7829 0.2276 0.00884 0.03217 0.0372 0.2116 1.161 3.759 3.752 5.602 9.175 16.60 29.38 30.6 0.05223 0.1006 0.1259 0.3224 0.5879 0.7952 0.8105 0.8284 0.901 0.905 0.902 0.904 k 12.60 11.90 8.65 5.81 6.87 7.05 6.34 8.33 4.77 THE PHENOMENA OF ADSORPTION. 61 As is seen from the figures at the bottom of the table a increases very slowly with increase of c, after the latter has reached a value higher than 0.9 (grams per 100 c.c.). The three last figures for a are to be regarded as con- stant within the errors of observation. Schmidt there- fore took a mean value of those and some other figures 0.905 (g in 10 g carbon.) as giving the limiting value which the adsorption of acetic acid might reach in solutions as highly concentrated as possible. The value under k should be a constant, whereas it in reality changes in about the proportion 1 to 2. But as a matter of fact these discrepancies are rather insignificant. As regards the end value 4.77, the cor- responding value of a (0.901) lies so very near to the limit value S (0.905) that an error in either of these values of 0.004, which might well occur would render k infinite. The second and the third observations lie very near to each other (in regard to the value of c) and ought to approximately give the same value of k. But for these weak concentrations again, a small experimental error gives a very great error in k. The third experiment gives very nearly the right value of /c, i. e., about the average one. We therefore conclude that A: is a constant within the limits of the experi- mental errors. As will be seen later on it is very probable that the fc-values increase somewhat with dilution just as in the case cited here. The equation of Schmidt with AS = 0.4343 corre- sponds to a very simple differential equation, namely, da = 1 S - a dc ~~ k a This means that if we have a solution of the concentra- 62 THEORIES OF SOLUTIONS. tion c in equilibrium with charcoal every 10 grams of which carry a grams of solute and if we then increase the concentration by dc y it is sufficient to add a quantity da to the adsorbed layer in order that the equilibrium should be maintained. The equation denotes that da is zero, when S = a, i. e., the limiting adsorption has been attained. It also denotes that do/dc is infinite for a = 0, i. e., that on the addition of a small quantity of dissolved substance to pure water and pure charcoal, the latter takes away all the acetic acid from the solu- tion. We also see from the figures above how c in- creases hi a ratio nearly proportional to the square of the ratio in which a simultaneously increases. From this it follows that c: a at infinite dilution is zero, as is shown by the differential equation. This corresponds also to the well-known fact, that on filtering dissolved dyes through charcoal, all the color is taken away at once, a fact which is used in practice for purifying solutions, e. g., of cane sugar, etc. The analogous fact that at low temperatures charcoal adsorbs all of a surrounding gas is well known; it is to the great credit of Sir James Dewar that he has introduced this very convenient method of preparing high vacua. As I had convinced myself that the new, highly accurate measurements of G. C. Schmidt agree very well within the errors of observation with the equation given above, I enquired next as to how gases would behave. From older investigations it was perfectly clear that they would not follow the equation in ques- tion at high temperatures. Now there have appeared during the past year two very accurate series of measurements on the adsorption THE PHENOMENA OF ADSORPTION. 63 of gases, carried out by the Russian Titoff and by Miss Ida Homfray, who worked in the laboratory of Sir William Ramsay. It seemed very probable from what they had said regarding their observations, that they had also observed a maximum charge S for gases, al- though they had not given such an explanation to their results. Titoff says, that at high charges of the carbon there comes a point where c increases with extreme rapid- ity as compared with a. For carbonic acid and am- monia at 76.5 and 23.5 he observed values of a amounting to 114.1 and 154.4 c.c. per g. carbon, respec- tively, whereas according to the formula given above, I calculated the limiting values S = 114.6 and 158, re- spectively. Titoff had then practically reached this limit, especially in the case of carbonic acid. As is seen from my calculations, the limiting value of S is independent of temperature and may therefore be called the constant of saturation. For carbonic acid Titoff has given two series of observations at 0, which I quote here calculated according to the same formula as was used for the solutions, c is expressed as pressure in cm. Hg. CARBONIC ACID AT ADSORBED BY COCOANUT-CHARCOAL, ACCORD- ING TO TlTOFP. c a k 0.05 0.8491 24.9 0.32 3.4601 159 1.09 8.5059 89 2.54 15.148 60.5 8.30 27.782 52.0 17.35 39.898 48.9 31.59 50.241 52.7 45.42 56.818 56.0 58.91 61.372 58.9 70.32 64.529 61.6 75.51 65.854 62.2 64 THEORIES OF SOLUTIONS. Regarding the first two observations Titoff says himself that measurements in which c is less than one, are very unreliable. We therefore find here the two extreme values of k. By a chance their geometrical mean, about 63, is very near to the mean value of k. There- after k is nearly constant, sinking a little to begin with, and then increasing again. This last increase may be due to a small inaccuracy in the value of S and is therefore not of much importance, but the decrease of k at the beginning of the series is characteristic and agrees with the experiments of Schmidt. I also succeeded in calculating the figures of Miss Homfray in the same manner and give below the experimental results of a series of investigations regard- ing methane. METHANE AT -33 ADSORBED BY COCOANUT-COAL, ACCORDING TO Miss HOMFRAY, S = 274. c a k 0.45 35.21 140.6 0.66 44.64 101.5 0.94 55.36 89.5 1.28 64.65 88.0 1.65 73.80 85.1 2.13 83.20 83.9 2.68 92.12 84.0 3.37 100.9 84.9 4.10 109.5 85.3 This series shows a high degree of regularity, which is partially explained by the relatively small variation of c. It gives occasion for similar remarks concerning the variation of the constant k as did the carbonic acid series of Titoff. At higher temperatures the gases do not obey the law expressed by the formula so far made use of. This THE PHENOMENA OF ADSORPTION. 65 depends upon the variation in the heat of adsorption. Titoff has made some very interesting experiments regarding this quantity. He found in agreement with some old experiments of Chappuis that the first traces of gas to be adsorbed always evolved more heat than the subsequent additions, as will be clear from the following figures, observed by means of an ice-calorim- eter, i. e. y at 0. 9o Qo q\ Q Nitrogen 0.330 7392 0.21C 4700 Carbonic acid 0.347 7772 0.293 6564 Ammonia 0.502 11245 0.384 9408 (jo is the number of calories developed by one cubic centimeter of gas during its adsorption in a large quantity of carbon; #1 is the corresponding heat de- veloped, when the adsorption has already proceeded to a certain degree. Qo and Qi are the same figures for one grammolecule, corresponding to 22,400 cubic centi- meters. Now the second law of thermodynamics demands that dlogp _ Q dt " 1.985 T 2 ' Here p is the pressure of gas which is in equilibrium with a certain adsorbed quantity a. Therefore if Q were constant and if we plotted log p as a function of log a at different temperatures the curves so obtained for two different temperatures should be equidistant from one another for all values of p or a. But if Q is not constant but greater for low values of a, as is actually the case, then the distance between the two curves ought to be greater at lower values of a than at higher, as is really found, for instance with carbonic acid ac- cording to the measurements of Titoff, one of whose 66 THEORIES OF SOLUTIONS. diagrams I have reproduced here. If the curves were absolutely equidistant the whole way and our equation were valid for one of them, for instance that at 0, then it would hold for higher temperatures, with only a change hi the constant k. Now we know that at low values of a the distance will be greater than at higher values, i. e., p must be too great and as k is proportional -W o FIG. 1. 0.5 1.0 2.0 to p (or c, cf. the formula of Schmidt) k also must be too great. This is the real reason why we observe an increase of k with diminishing a and p in the tables given above. At higher temperatures this disagreement with our formula will increase more and more, the curves will become steeper and steeper. The slope of the upper curves towards the left is 26. 57, corresponding to a tan- gent = 0.5 and for them a is nearly proportional to the square root of p (at low values of a). The slope THE PHENOMENA OF ADSORPTION. 67 of the lowest curve on its left side is nearly 45, corre- sponding to a tangent = 1, indicating that p and a are proportional to each other. This proportionality is characteristic for gases at small pressures and high temperatures; for hydrogen according to Titoff the rule holds even at the lowest temperature examined ( 79) and the highest pressure (72 cm. Hg). Therefore in the diagram for carbonic acid with the exception of helium and hydrogen, all gases examined behave in the same manner the curves will on the left hand have a fan-like distribution with an angle of 18 6 .43. At suf- ficiently low temperatures even helium and hydrogen would without doubt obey this general rule. It may be remarked here that in some cases a tangent exceeding 1 has been observed; thus for helium in one case (at 78) 1.68, and for methane in another case (at 182) 1.91 and other values above 1 are to be found in nearly all series of observations, but probably they are due to accidental errors of observation. Titoff remarked that the five gases observed by him showed a great regularity, indicating that the quanti- ties of different gases adsorbed under a pressure of 10 cm. Hg run parallel to the values of a in van der Waals' equation, which indicate the attraction of the mole- cules upon one another. This is true also for the gases observed by Miss Homfray as may be seen from the table on page 68. a gives the constant of van der Waals, A the quantity of gas adsorbed on one g. of cocoanut-charcoal at a pressure of 10 cm. Hg and at C. T is the absolute critical temperature and S the maximum quantity of gas (in cm. of and 76 cm. pressure) which can be 68 THEORIES OF SOLUTIONS. adsorbed by this amount of charcoal. It should be pointed out how well the figures of Titoff (marked T.) agree with those of Miss Homfray (marked H.); as a rule the charcoal of Miss Homfray seems to have ad- sorbed about 10 per cent, less than that of Titoff. a A T S Ethylene 0.00883 41H. 284 58 Ammonia 0.00808 71T. 403 158 Carbonic acid 0.00701 30T. 28H. 304 116 Methane 0.00367 9.4H. 178 91 Carbonic oxide 0.00280 3.2H. 133 60 Oxygen 0.00269 2.5H. 155 87 Nitrogen 0.00268 , 2.35T. 2.0H. 127 90 Argon 0.00259 1.67H. 154 87 Hydrogen 0.00042 0.227T. 32 There seems to be an exception to the rule given above, in that A is less for ethylene than for ammonia. This depends upon the fact that the ethylene was very near to its saturation point at C. and 10 cm. pressure. If we take 100 C. and 3.4 cm. pressure we find by interpolation from Titoff s figures for ammonia A = 2.86 c.c. whereas Miss Homfray gives for ethylene under similar conditions A = 3.07. The exception is there- fore probably not genuine, and one should take values of A for adsorbed quantities far below the limiting values S. The parallelism between adsorption and the constant a suggested the idea that this phenomenon depends upon the attraction of the molecules of the adsorbed substance and the carbon. It then is very similar to the compression of a liquid under high pressure. In the one case through increased pressure new molecules are carried into the sphere of the molecular attraction of the carbon, in the same way in the other case, new molecules are forced into the sphere of molecular THE PHENOMENA OF ADSORPTION. 69 action. Just as in discussions on capillarity, we may regard this sphere as having a definite radius; if it has not, but if the attraction decreases continuously out- wards, as is probably the case, it does not make any great difference, for we have then only to consider the space around a molecule in which the molecular action reaches a certain value. The quantity contained in this corresponds to the adsorbed quantity a; it is propor- tional to the density of the fluid. The acting pressure is equal to the sum of the external pressure and the term a/0 2 in van der Waals' formula. From this point of view I have calculated the figures of Amagat on the compressibility of liquids and I quote the exceedingly regular figures for ethyl alcohol at 0. COMPRESSIBILITY OF ALCOHOL AT ACCORDING TO AMAGAT, S = 1.2729. 5,081 +3,000 atm. 1.1521 12,836 4,937+2,500 " 1.1355 12,838 4,775+2,000 " 1.1169 12,767 4,592+1,500 " 1.0952 12,633 4,385 + 1,000 " 1.0703 12,437 4,140+ 500 " 1.0399 12,126 3,838+ 1 " 1.0000 11,690 The agreement is excellent. Here k decreases with decreasing pressure in contradistinction to the case with adsorption. This depends upon the fact that the heat of evaporation is greater for the compressed fluid than for the non-compressed, and the difference is the heat of compression. The latter, Q, may be calculated accord- ing to the following formula, deduced from the second law of thermodynamics: Q = 0.024 Tpa, where T is the absolute temperature, p is the external pressure in atmospheres I have taken 2000 in my 70 THEORIES OF SOLUTIONS. calculations and a is the coefficient of cubical ex- pansion from to 1. In this way I obtained the following table, where Q indicates the latent heat of evaporation at atmospheric pressure, feooo and ki the values of the constant of our equation at 2000 and at 1 atm. pressure respectively. B Q Qo & *,ooo *, ** Ethyl ether 1.2642 21.2 93.5 1.227 6530 5078 1.284 Ethyl alcohol 1.2729 14.5 236.5 1.0613 12767 11690 1.092 Sulphide of carbon 1.224 15.7 90.0 1.175 9755 8700 1.121 With increasing temperature Q generally decreases, Q on the contrary increases, since a as well as T does so. Therefore we might expect that the constant k would increase the more rapidly with pressure the higher the temperature, and as a matter of fact, this rule also holds good, the ratio K 2 ooo : Ki being 1.363 for ether at 50, 1.106 for ethyl alcohol at 40.4 and 1.144 for sulphide of carbon at 49. 15. Evidently adsorption is a manifestation of molecular attraction. It has been often maintained that it is due to surface tension, and the aggregation of the adsorbed molecules to the adsorbing substance was said to diminish the surface tension. On the other hand Walden has shown that according to an idea suggested by Stefan, the surface tension of a liquid is proportional to the surface pressure, which again is proportional to van der Waals' constant a divided by ft, where n is the molecular volume. Hence as a rule gases ought to be the more easily adsorbed, the greater the surface tension of the adsorbed layer against the gas would be, which is precisely opposite to the current ideas. Lewis also has shown that the surface tension theory of adsorption, developed by Gibbs, does not THE PHENOMENA OF ADSORPTION. 71 agree quantitatively with the facts of experience. It seems therefore as if surface tension did not play the chief r61e in adsorption phenomena. I wish only in conclusion to call attention to a pe- culiarity which has been observed by physiological chemists, who have investigated the adsorption of colloidal substances. They have found that in most cases the adsorbed quantity is nearly independent of the concentration of the colloid in the surrounding solution provided that the same quantity of adsorbing powder was used. (Landsteiner and Uhlirz for the adsorption of euglobulin on kaolin: Michaelis and Rona for the adsorption of albuminoses or peptones.) This regu- larity seems at first to indicate that a kind of compound, in constant proportions, is formed between the adsorb- ing powder and the adsorbed colloid. But it is very difficult for a chemist to accept such a solution. Evi- dently the right explanation is that as a rule substances with the highest critical points, i. e., the lowest vapor pressures possess the greatest values of a, as an inspec- tion of the tables of Landolt-Boernstein will show. The colloids investigated possess a very low vapor tension and therefore they are strongly adsorbed, so that the limiting adsorption is nearly reached even at compara- tively low concentrations, and therefore adsorption ap- parently occurs in nearly constant proportion to the amount of adsorbent used. Of course, the limiting value is never absolutely reached, but within the errors of ob- servation it may already be reached at low concentra- tions in cases such as those mentioned. This instance is certainly not devoid of interest, for it shows that con- stant proportions may rule in aggregates of a rather loose nature. LECTURE V. THE ANALOGY BETWEEN THE GASEOUS AND THE DIS- SOLVED STATES OF MATTER. IT is well known to all of us that the present great advance in physical chemistry is due chiefly to the introduction of two theories, the one expressing the far-reaching analogy existing between the gaseous and the dissolved states of matter, with which follows the thermodynamic treatment of chemical equilibria in solutions, and the other indicating that salts (acids and bases are regarded as hydrogen salts and as hydrates respectively) are in solution partially dis- sociated into their ions. As a rule it is said that this new development came abruptly and many people believe that for this reason the merit of these theories is greatly increased. I am of quite an opposite opinion. The ideas mentioned may be found in a less fully developed state in older speculations regarding the chemical behavior of solutions and we ought to lay great stress upon this fact, for it is the most convincing proof of their soundness that they should have de- veloped quite continuously and organically from all the results of chemical experience. Of course when they at first took form, the ideas were deduced from a rather small number of observations, so that their use- fulness was not very evident and on the other hand, the conservative majority of scientists were opposed to the introduction of new notions which seemingly compli- 72 ANALOGY BETWEEN STATES OF MATTEK. 73 cated their conception of Nature. The new points of view therefore lived a latent life, being again and again indicated, until there had been collected together a quantity of experimental material sufficient to demand the explanation which they were capable of giving. At such a stage in the evolution of new ideas, a rapid propagation of them takes place under sharp opposition from the teachers of the old conceptions and in the end they receive an overwhelming support simply because of the great importance of the phenomena which they alone are able to explain. This normal course of evolution may easily be traced for the modern theory of physical chemistry. The chief progress in it is due to the discovery that the molecules of dissolved substances behave in a manner very similar to that of gases. The laws governing the properties of gases are well known and simple; by their application to the much greater and more important group of solutions we have won an extremely valuable knowledge of the nature of solutions which play by far the fore- most role in chemistry. At the same time the far- reaching use of the laws of thermodynamics in this new chapter gave it its strength and high value. In reality the first application of thermodynamics to the phenomena peculiar to solutions is independent of the introduction of the laws of gases in this chapter. Therefore, in the first instance, we have to treat the growth of the idea of the analogy between gases and dissolved substances as the chief progress and there- after to regard the increasing application of the laws of thermodynamics to the doctrine of solutions as the means of making the greatest possible use of 74 THEORIES OF SOLUTIONS. the simultaneous concepts regarding the nature of solutions. It is here in place to recall the interesting statement of Newton that the dissolved molecules in a solution tend to get away from each other so that they finally become distributed uniformly in the solvent. In reality this idea gives a neat explanation of the phenomena of diffusion, which are so closely related to the force of osmotic pressure. Newton regarded this tendency of dissolved molecules as due to reciprocal repulsion of the dissolved molecules, just as the diffusion of gas-molecules may be regarded as effected by the mutual repulsion of those molecules. One might well say that the modern views regarding the analogy be- tween gaseous and dissolved substances might well have been developed from this conception of Newton. But the time was then not ripe. The experimental knowl- edge of chemical phenomena was too scarce for the formulating of laws regarding them. In the year 1839 Gay-Lussac expressed opinions which possess a startling suggestion of modernity. "As the effects of affinity do not change with temperature (he would better have said change but slowly with temperature), whereas dissolution (solubility) is in a high degree dependent upon it, it is very difficult to avoid the assumption that in dissolution as well as in evaporation the product is essentially limited, at a given temperature, by the number of molecules which are able to exist in a certain volume of the solvent They are separated from this, just as gaseous molecules are precipitated by a lowering of temperature Dissolution is therefore hi a high degree connected with evaporation, namely in this ANALOGY BETWEEN STATES OF MATTER. 75 respect that both of them depend on the temperature and are subject to its variations. Hence they ought to show if not a complete identity in their effects at least a great analogy." The objection that in some cases, e. g., with sulphate or selenate of sodium, the solubility- curve shows a break and sometimes a fall with increas- ing temperature, whereas this is not the case with the vapor-tension, is refuted by means of the assertion that at the temperature where the break occurs, the substance undergoing solution is subject to a transfor- mation. There is, however, a difference between a gas and a dissolved substance. "The molecules of the gas do not need a solvent to hold them in suspension in a certain volume; their mutual repulsion is enough for that purpose. On the other hand, when a solid or liquid substance is dissolved, its molecules would not remain in the limited volume if they were not united by their affinity to the molecules of the solvent." In the same memoir Gay-Lussac criticises the theory of Berthollet according to which the precipitation of, e. g., sulphate of calcium from a mixture of potassium sulphate and acetate of calcium is due to a force of cohesion (measured by the insolubility) between the molecules of the sulphate of calcium, which acts even before the substance is formed. Gay-Lussac expressed the opinion that when the solu- tions of two salts of different acids and bases were mixed all the four possible salts were formed, e. g., in the example above there existed in the mixed solution not only K 2 S0 4 and Ca(CH 3 C0 2 ) 2 but also KCH 3 C0 2 and CaS0 4 . If then one of these four is very slightly 76 THEORIES OF SOLUTIONS. soluble, so that the solution is supersaturated with regard to it, it is precipitated, and thereupon new molecules of CaS0 4 may be formed in the liquid and a further precipitate occur. In the same way, the vola- tility of one of the products may exert its effect, as Berthollet contended. Gay-Lussac termed "this prin- ciple of the indifference of permutation" between the acids and bases present in the salts, according to the chemical doctrines of that time, equipollency, and the principle has found its simple explanation through the electrolytic dissociation theory. Shortly afterwards a Venetian professor Bartholomeo Bizio expressed similar ideas (1845). He came back to them more clearly in a paper of 1860, printed in the memoirs of the "Istituto veneto." Bellati gives (1895) an analysis of Bizio's work. He says that " Bizio re- garded the dissolved substance as an elastic vapor distributed in the solvent. The difference between a dissolved substance and a gas is that the gas does not need the presence of the molecules of the solvent and their affinity to sustain it in the occupied space." This is almost word for word the statement of Gay-Lussac. The different colors of concentrated and diluted solutions of copper chloride were explained by Bizio as being due to a condensation or attenuation of the molecules, i. e., a kind of dissociation. Of course this idea does not at all imply a dissociation of CuCl 2 into its ions Cu and 2C1, as Bellati seems inclined to suppose. "The lack of precision in the mechanical conceptions of Bizio hindered their acceptance" says Bellati. Another man who adhered to the idea of a close analogy between the gaseous and the dissolved states ANALOGY BETWEEN STATES OF MATTER. 77 was Rosenstiehl, who expressed his views in a note published in Paris in 1870. Rosenstiehl says that he has heard that Arago has been the first to compare the phenomenon of solution with that of evaporation but that he has not been able to find the quotation in which this view is expressed. Probably Arago has been confused with Gay-Lussac. Rosenstiehl drew the re- markable conclusion that "the osmotic force is analo- gous to the elastic force of vapors. Between the fluid column, which rises in an osmometer and the piston lifted by the elastic force of a vapor there is no other difference than that of the medium in which the work is effected." In 1869 and 1873 Horstmann deduced from thermo- dynamics the laws of chemical equilibrium between gaseous substances. As he had already tested his theoretical results on known equilibria between gases, he next subjected an equilibrium between dissolved substances, namely the sulphates and carbonates of potassium and of barium in the presence of precipitates of the two barium salts, to the same formula as that which had proved valid for gases. This equilibrium had been studied by Guldberg and Waage. In 1864 they had elaborated a theory of chemical mass-action according to which the " chemical force " with which two substances A and B in concentra- tions C A and CB, act upon each other is proportional to the product of these concentrations raised to certain powers, i. e., to C A . C^. If then two new substances E and F were formed, as for instance in the interaction of two salts, and equilibrium was reached when the con- centrations of those substances were C E and Cp then 78 THEOEIES OF SOLUTIONS. the chemical forces on both sides must be of the same magnitude, i. e., K.C a A .C b = Ktf'z . C f F . In 1867 they simplified this formula by assuming a = & = e=/=l, so that the exponents were omitted. But on the other hand they introduced a complication by supposing that the chemical forces between A and B were not only dependent on their own concentrations but also on the concentrations of all other substances present in the solution. This complication was intro- duced in order to explain the influence observed in many cases of foreign substances on the equilibrium. In order to test then- ideas Guldberg and Waage carried out a great number of experiments both on the velocity of reaction on the solution of metals in acids (in which case the velocity was taken as a measure of the acting chemical force) and also on equilibria in which class that existing between K 2 C0 3 and BaS0 4 on the one hand, and K 2 S0 4 and BaC0 3 on the other was the principal example. It was these experiments which Horstmann calcu- lated by means of the formula which had proved valid for gases and he found them to be in good agreement with it. He concluded that the "disgregation" of a (dissolved) salt depends on the distance between its molecules, in the same manner as the corresponding property of a permanent gas, an assumption which also from other considerations seems to be probable. In 1879 Guldberg and Waage again modified their theory and, citing Horstmann, they discarded from their equation the terms referring to the secondary action of foreign substances. In this way the analogy between ANALOGY BETWEEN STATES OF MATTER. 79 the gases and the dissolved substances in their chemical action was made perfect. They say that " these secondary actions may be neglected if the solutions are so highly diluted, that a further addition of solvent (water) gives rise to no sensible development of heat." Julius Thomsen, the renowned Danish thermochemist, was very well acquainted with the work of Guldberg and Waage and probably he was influenced by it when he concluded the first volume of his "Thermochemische Untersuchungen" (1882) with the following words: "The aqueous solutions of substances contain them in a condition which, just as the gaseous state, reveals their physical qualities in the simplest manner, so that a direct comparison of the two states is permissible." At that tune the kinetic theory of heat was widely accepted by physicists and chemists. It was supported and had been worked out by such authorities as Clausius, Maxwell and Boltzmann. It was, in fact, regarded as absolute truth, almost like the two laws of thermodynamics. This whole subject was therefore often called " the mechanical theory of heat." Later on came a more sceptical time, when it was strongly main- tained that thermodynamics may exist independently of the kinetic theory of heat and when it was regarded as a sign of progress to be able to discard all mechanical views regarding the nature of heat. Nowadays we have come back to the old view, and regard it as proved that the molecules possess a motion, the energy of which is proportional to the absolute temperature (cf. Lecture II). Regarded from this point of view the sublimation of a solid substance such as camphor or iodine depends 80 THEORIES OF SOLUTIONS. upon the fact that some of its molecules possess such a violent motion that they can remove themselves from the sphere of attraction of the neighboring molecules. In the same manner the solution of a solid in a liquid must be explained as a consequence of molecular motion according to the mechanical theory of heat. This idea was expressed by Tilden and Shenstone (1883) "The solution of a solid in a liquid would accordingly be analogous to the sublimation of such a solid into a gas and proceeds from the intermixture of molecules detached from the solid, with those of the surrounding liquid. Such a process is promoted by rise of tempera- ture, partly because the molecules of the still solid substance make longer excursions from their normal centre, partly because they are subjected to more violent encounter with the moving molecules of liquid." . . . "Such a theory however, serves to account only for the initial stage in the process of solution, and does not explain the selective power of solvents nor the limitation of solvent power of a given liquid." Walden cites Mendelejeff as a precursor of the sup- porters of an analogy between gases and dissolved substances. Mendelejeff had stated (1884) that the densities of aqueous solutions containing 1 molecule of salts to every 100 molecules of water generally increase with the molecular weight of the salt. (There are some exceptions to this rule, e. g., solutions of Li-salts are denser than equivalent solutions of Nils-salts ; compare ' ' Valson's moduli, ' ' Lecture VI) . "In extremely dilute solutions the dissolved substance exists in a dispersed or attenuated state similar to that in the gaseous state. Therefore we may hope, through the investigation of ANALOGY BETWEEN STATES OF MATTER. 81 the densities of solutions to find a method of determining molecular weights." On closer inspection we find that the observed regularity does not tell us much more than that salt- solutions generally possess higher densities, the more concentrated they are. This depends upon the high specific weight of salts and especially of those with high molecular weights compared with water. If we extend the comparison to solutions of substances of a lower density than water, such as alcohol, the cause of the regularity is evident. We must therefore reject the claims raised in favor of Mendelejeff in this depart- ment. As is seen from the quotations above, the great analogy between gases and dissolved substances was admitted by a great number of leading chemists. In order to give the required force to these opinions it was necessary to apply the laws of thermodynamics to them and this was done by van't Hoff. To understand the development of this side of chemical science we shall give a short review of the earliest work in this line. As early as 1858 Kirchhoff had published some theoretical thermo-dynamical considerations on the va- por pressures of solutions, especially of sulphuric acid. In 1867, 1868 and especially in 1870, Guldberg worked out this important section of science in a most remark- able manner. He demonstrated that the lowering of the freezing point of a solution under that of the solvent as well as the corresponding increase of its boiling point is proportional to the corresponding lowering of its vapor tension and gave the constants which represent the factors of proportionality. He verified his theo- 82 THEORIES OF SOLUTIONS. retical deductions by means of the figures of Wullner and of Riidorff concerning the behavior of salt solutions in water. We now know quite well how important the similar deductions were later on in the hands of van't Hoff. Raoult (1878 and 1882) deduced these laws experimentally a little while afterwards and found the true law of depression of the vapor-pressure: - 1 n where p and pi are the vapor-pressures of pure solvent and of the solution in which n molecules of dissolved substance are mixed with N molecules of solvent. Guldberg also in 1870 deduced the law of change of solubility with temperature and pressure later deduced by van't Hoff. He even showed how the relative de- pression of the vapor-pressure changes with temperature. Another great advance was made in 1869 in Horst- mann's application of Carnot's theorem (or its special form, the formula of Clapeyron) to the evaporation and simultaneous dissociation of sal-ammonia, and he cal- culated its heat of evaporation from the observed vapor- pressure and found it to correspond very well with that experimentally determined by Marignac. The calcula- tion was exactly similar to that by which the heat of evaporation of water is found from its vapor-pressure at different temperatures. A similar calculation was made by him in 1870 for the evolution of carbonic acid from carbonate of calcium according to Debray's experiments and for the dissociation of Na^HPC^ + 12H 2 into NasHP0 4 + 7H 2 O and water vapor. In 1872 Guldberg made similar calculations for the dissociation pressure ANALOGY BETWEEN STATES OF MATTER. 83 of calcium carbonate and deduced the famous formula: where p is the dissociation pressure, T the absolute temperature, R the gas constant, A the inverse value (1/426) of the mechanical equivalent of heat, and q the heat of dissociation of 1 gram. This formula is sim- plified to the second form if Q is the heat of dissociation of 1 grammolecule, since then AR = 2 (better 1.985), as Guldberg had shown in 1870.' In 1873 Horstmann wrote his famous "Theorie der Dissociation" where he treats the general problem of dissociation of gaseous substances, and applies the results to the investigations of Wiirtz on amylene hydrobromide C 6 HnBr and to those of Wiirtz and Cahours on pentachloride of phosphorus (PC1 5 ). Here he finds the great analogy between dilute solu- tions and gases. He quotes the figures of Thomsen regarding the " avidity" of sulphuric and nitric acid towards sodium hydrate and those of Guldberg and Waage on the reaction between barium sulphate and potassium carbonate at 100 which had served the latter when testing then* law of mass action, a law which is also valid for the reactions of gases. In this way Horstmann was led to the conclusion regarding the analogy between dilute solutions and gases, cited above. In 1878 appeared the far-reaching investigations of Willard Gibbs on the application of thermo-dynamics to chemical equilibria. In this work all conceivable problems in this field of science are treated theoretically. 84 THEORIES OF SOLUTIONS. But his important deductions were concealed in academ- ical transactions, which were only very little known and therefore did not exert any sensible influence on scientific development. In 1882 Helmholtz independ- ently wrote his well-known memoir on "free energy ," containing general deductions very similar to those of Gibbs. In 1885 Le Chatelier published his interesting memoir, in which he, basing his theory on Wiillner's experiments, shows that the equation of Clapeyron may be used for calculating the change of the solubility of a substance with temperature. The ground was therefore very well prepared from the theoretical side. But the last simple grasp of the problem failed, until van't Hoff in 1885 demonstrated the widely extended analogy between substances at high dilution and gases in their physical and chemical behavior. A year before this, he had published his important "Etudes de dynamique chimique," where he gave the formula found before byGuldbergfor the change of the pressure of dissociation with temperature and showed that it also holds good for the change of the constant of a chemical equilibrium with temperature, if this constant replaces p and if Q represents the heat evolved in the reaction considered. A similar expression was used by Boltzmann in the same year for calculating the heats of dissociation of iodine and of N 2 4 . And also in the same year Le Chatelier had a little earlier than van't Hoff found the same general qualitative ex- pression for the change of chemical equilibrium with temperature as is contained in van't HofFs quantitative formula. Van't HcfTs fundamental discovery in 1885 was ANALOGY BETWEEN STATES OF MATTER. 85 directly due to the investigations of De Vries and Pfeffer on the osmotic pressure of certain plant cells. They investigated a property well-known to cell-phys- iologists, namely that if cells are placed in aqueous solutions they take water from the solution, if this is weak, and give up water to it, if it is strong. With a certain concentration of the solution equilibrium is obtained. De Vries found that solutions of glycerol or of cane sugar, which contain the same number of molecules per liter, are in equilibrium with the same cells. Also equimolecular solutions of KC1, NaCl, KN0 3 and NaN0 3 are found to be in equilibrium with the same cells. But these salt solutions are only 0.6 times as concentrated as the corresponding solutions of glycerol or cane sugar which are in equilibrium with the same cells. Now Moritz Traube in 1867 had given a method of preparing artificial cells, which possess the properties of attracting water from or of giving it up to surrround- ing aqueous solutions according to their concentrations, just like natural cells. In 1877 Pfeffer used Traube's cells for measuring the force with which distilled water was attracted into such a cell filled with a solution of, e. g. y 1 per cent, cane sugar. If the solution in the cell is subjected to a certain pressure the water is driven out from the sugar solution : the sugar itself does not pass through the cell walls, which latter consisted of a thin membrane of ferro-cyanide of copper, precipitated in the porous walls of an earthenware vessel. At a certain pressure, which was found to be 505 millimeters of mercury at 6.8 C., equilibrium was reached so that no water went into the cell from the surrounding dis- 86 THEORIES OF SOLUTIONS. tilled water and no water was pressed out from the solu- tion of cane sugar through the cell walls. This pressure, the so-called osmotic pressure of a solution of 1 per cent, cane-sugar, increases with temperature. It is nearly proportional to the concentration of the sugar-solu- tion when this is changed. These results of Pfeffer's measurements were com- municated to van't Hoff by his friend De Vries, who asked for a theoretical explanation. Van't Hoff made the following simple calculation. A gas containing one gram molecule in 22,400 c.c. at C. possesses a pressure of just 1 atmosphere or 760 millimeters of mer- cury. At 6.8 C. the pressure is a little higher, namely 779 millimeters, according to the law of Gay-Lussac. If this gas was expanded until it contained one molecule in 34,200 c.c., which is the concentration of a 1 per cent, so- lution of cane sugar the molecular weight of cane sugar being 342 its pressure at 6.8 C. would according to Boyle's law be 508 millimeters. This figure agrees within 1 per cent, and within the errors of observation in Pfeffer's experiments with that, 505 mm., found for the osmotic pressure of an equi-molecular solution of cane sugar. In other words the osmotic pressure of this solution is equal to the pressure of a gas containing the same number of molecules in the same volume. Since further the osmotic pressure increases proportionally to the concentration (just as the gas pressure does according to Boyle's law) and within the errors of experiment as van't Hoff deduced from Pfeffer's fig- ures, also to the absolute temperature (as in Gay- Lussac's law for gases), there exists a perfect analogy between the osmotic pressure of a solution (of cane sugar) ANALOGY BETWEEN STATES OF MATTER. 87 and the pressure of a gas containing the same number of molecules in the same volume. As soon as this fundamental fact was stated, van't Hoff applied all the laws which had been deduced from thermodynamics for the pressures of gases and for saturated vapors, which correspond to saturated solutions, to the osmotic pressures of dissolved sub- stances. Thus he found that he was able to deduce the general law of chemical equilibria (Guldberg and Waage's law); the law of the influence of pressure on chemical equilibria (Le Chatelier's law); the law of the temperature-variation of chemical equilibria; the law of partition of a substance between two different phases (law of Henry and law of Berthelot and Jung- fleisch); the laws of vapor pressure and freezing point of solutions (laws of Raoult; the third law of Raoult regarding the boiling points was a little later deduced by Arrhenius, the connection between these laws having already been pointed out by Guldberg); the law of isotonic solutions (law of De Vries) ; the law governing the partition of a base between two acids according to the experiments of Jellet, Julius Thomsen and Ostwald; the law of the change of solubility with temperature, partially deduced before by Guldberg; the regularities found in the action of water on salts, according to ex- periments of Ditte; and the law with regard to the electromotive force of galvanic cells, concerning which Gibbs and Helmholtz had some years before (1878 and 1882) written fundamental works, in which they intro- duced the conception of "free energy." The whole investigation of van't Hoff (1885) was 88 THEORIES OF SOLUTIONS. a triumphal march through the different domains of physical chemistry; only one difficulty, but a rather severe one, was found. The great majority of sub- stances examined did not follow the law of Avogadro, as cane sugar did. This was already manifest from De Vries' investigations, according to which one molecule of sodium chloride exerts the same osmotic pressure as about 1.7 molecules of cane-sugar dissolved in the same quantity of water. To account for this difference, van't Hoff introduced a coefficient i (the isotonic co- efficient) which was determined experimentally. This coefficient entered as an exponent into the formula for the chemical equilibrium, so that Guldberg and Waage's law was reduced to its first form (of 1864). This was a great inconvenience, for it really spoilt the analogy between the dilute and the gaseous states of matter, but it was very soon eliminated by the theory of electrolytic dissociation. Therefore in the second edition (1887) of his fundamental memoir van't Hoff added the following remarkable words regarding the necessity of introducing the coefficient!: " Thus it seems rather adventurous to put Avogadro's law so strongly in the foreground, as I have done in this memoir " (in the memoir of 1885 very much less stress was laid on the validity of Avogadro's law for solutions) "and I would not have decided to do so, if Arrhenius had not, in a letter, pointed out the probability, that with salts and similar substances the question is really one of their division into ions." A theoretical deduction of the law of van't Hoff regarding the analogy of the dilute and the gaseous ANALOGY BETWEEN STATES OF MATTER. 89 state of matter was given by Planck (1887) in order to explain the anomalies which led van't Hoff to intro- duce the coefficient i. He started from the hypothesis that for the energy U of a dilute solution containing n molecules of solvent and HI, n 2 , n 3 , etc., molecules of dissolved substances the following expression is valid (at constant temperature): where u, Ui, u%, u z , etc., may be regarded as the partial energies of one molecule of solvent or of dissolved substances, respectively, in very dilute solutions so dilute that on further addition of solvent no heat is evolved. The same expression is valid for a mixture of gases in the same proportions. Therefore the gas- laws hold good for dissolved substances. The abnormal behavior of salts is due to a dissociation of their molecules. The weakness of this deduction is evident; it might be that the expression quoted was true only for solu- tions so extremely dilute that they were not capable of being measured. Planck also conceded (1892) that by means of thermodynamics "nothing could be demonstrated regarding the qualities of the dissolved molecules, either in respect to their chemical or electrical properties, and that to this method could be ascribed no convincing conclusion, but only a heuristic significa- tion." Certainly the adherence of Planck and at the same time of Boltzmann, the two most prominent representa- tives of mathematical physics in Germany, helped in a 90 THEORIES OF SOLUTIONS. high degree to protect the new theory from the attacks of physicists. By their great authority they also gave a strong support to the new ideas in the eyes of chemists and of scientists hi general, and this was of a value which should not be underestimated, especially during the first years of the growth and propagation of these ideas, which otherwise seemed revolutionary and there- fore evoked a rather determined resistance. LECTURE VI. DEVELOPMENT OF THE THEORY OF ELECTROLYTIC DISSOCIATION. THERE have been two different roads, which have led to views related to the modern theory of electrolytic dissociation, one empirical and one theoretical. The empirical one, inaugurated by Valson, is founded on the so-called additive properties of salt-solutions, the theoretical one, first entered upon by Gay-Lussac, Williamson and Clausius, is based upon considerations of the progress of chemical processes or the passage of electricity through salt solutions. Under salts are here included even acids and bases. Valson measured the height to which salt-solutions rise in capillary tubes of glass. These heights are pro- portional to the capillary constant and inversely pro- portional to the density of the solution (provided of course that the internal diameter of the capillary tube remains the same). When he compared normal solu- tions, which contain equivalent weights of different salts in one liter of the solution, he stated that the capillary height might be conveniently calculated as the sum of three components, the one the capillary height of pure water and the other two corrections, which should be added, the one for the positive radical (now we say ion) of the salt and the other for its nega- tive radical. These two corrections, which are gen- erally negative, always remain the same for the same 91 92 THEORIES OF SOLUTIONS. radical independent of the other radical to which it is bound in the investigated salt. This is most clearly demonstrated in the so-called additive scheme, which shows that the difference of the investigated property (here capillary height) between a chloride and a nitrate is the same for the potassium salts as for the sodium or lithium or calcium salts, if the solutions possess the same number of equivalents per liter. The same is true of the difference between chlorides and sulphates, chlorides and carbonates and so forth. As an example we give the following differences in millimeters of the capillary heights for normal solutions. (The diameter of the glass tube was 0.5 mm., the temperature + 15 C.): NH4C1 60.9, KC1 59.3, Y 2 CdCl 2 56.5, LiCl 60.8, Y 2 SrClj 58.0, Yz BaCl 2 56.9, Yz ZnCl 2 58.1, NaCl 59.6, H 2 O 60.6. Cl-Br: NH 4 2.2, K 2.2, Y 2 Cd 2.0, Mean 2.1. Cl-I: Li 3.8, K 3.9, Yz Ba 3.8, Yz Zn 4.1, Yz Cd 4.0, Mean 3.9 Cl-SO 4 /2: NH 4 1.2, K 1.1, Na 1.2, Yz Zn 1.1, Yz Cd 1.2, Mean 1.2. C1-NO 3 : NH 4 1.1, K 0.9, Yz Sr 1.1, Yz Ba 1.0, Mean 1.0. The capillary height of water was 60.6 mm., and was only exceeded by the capillary heights of normal solu- tions of NH 4 C1 and LiCl, amongst the solutions exam- ined. At the head are written the capillary heights of the chlorides from which the corresponding values of the other solutions may be calculated. The third line regarding Cl-Br indicates that the capillary height of a normal solution of NH 4 Br is 60.9-2.2 = 58.7, of KBr 59.3 - 2.2 = 57.1 and of ^CdBr 2 56.5 - 2.0 = 54.5. The additive scheme demands that all the figures for Cl-Br should be equal and so forth. In reality this was found by Valson to correspond very nearly to his measurements. THEORY OF ELECTROLYTIC DISSOCIATION. 93 Valson has drawn some conclusions from his measure- ments which I cite verbally because they have some- times been misunderstood, which can well happen, as many technical terms were used in a different sense than now. He says: " Experience shows that the effects of capillarity are nearly proportional to the quantity (concentration) of the examined substance, but this is not true for concentrated solutions, in which the actions of the molecules are not independent of each other. It therefore seems that it is necessary that the saline molecules occur in a medium of sufficient volume, in order that they may be regarded as having reached the state of liberty. It is something analogous to the circumstances of the dissociation phenomena as stated by Mr. Henri Sainte-Claire-Deville, according to which the molecules of different substances do not manifest their specific properties and do not give their characteristic effects, if they are not brought to a suitable degree of attenuation (desagrgation)." Here there is no question of a dissociation of the salt molecules, into their ions, or even of the additive properties, but only of the regularity that the difference of the capillary height of water and that of a dilute salt solution is proportional to its concentration, from which Valson concludes that the molecules are in an ideal state showing many regularities when they are diluted with a great quantity of water. This ideal state vanishes with higher concentrations, for which the said regularity is not observed. This opinion of Valson is still more emphasized in the following words: "If one combines the metals with different metalloidic radicles as for instance oxygen, chlorine, bromine, iodine, etc., 94 THEORIES OF SOLUTIONS. one finds that the caloric equivalents of the binary compounds, referred to the dissolved state, exhibit con- stant differences amongst each other. One may explain this analogy in remarking that the capillary phenomena as well as the calorific ones, depend finally on the same property of the molecular movement, which generally is called vis viva." This conclusion is rather confusing, the capillary phenomena really depend upon surface tension and are diminished when the molecular move- ment (vis viva) increases with temperature. In reality the circumstance, that the additive scheme holds to a certain but rather low degree even for the heats of combination, reduced to the dissolved state, has been taken as an argument against the dissociation theory, and therefore we shall come back to this special case later on. The capillary height is proportional to the capillary constant, which shows very small inequality for different normal solutions, and inversely proportional to the specific weight of the solution, which latter is subject to a rather great variation. Therefore the values of the capillary height show nearly the same regularities as the specific weights of normal solutions, or better, as the inverse value of this property, which is generally called the specific volume. It was therefore an advance when Valson a little later examined the specific weights of normal solutions and there found regularities similar to those for the capillary height. Later on Favre and Valson examined the changes of volume which occur on the solution of salts in water. On absolutely inad- missible grounds they calculated the heat which occurs on compressing one liter of water to 999 c.c. at 15 C., THEORY OF ELECTROLYTIC DISSOCIATION. 95 to be 7,576 cal., whereas in reality it is only 22.3 cal. (cf . p. 69 above) . On the solution of one gram equivalent of a salt in water sometimes a contraction of 20 c.c. is observed, which on their supposition corresponded to about 150,000 cal., and arguing from this, they stated that an enormous change of the salt had taken place, which manifested itself as a "reciprocal independency" of the radicals of the salt "which it would be difficult to define now but which is very different from then* original state." "The solution has the effect that it gives the elements of the dissolved substances an independency of each other." It may be remarked here that the solution of non-electrolytes, e. g., of alcohol, in water, gives rise to similar great changes of volume. Evidently this whole calculation and its consequences are absolutely erroneous. This becomes quite clear when we say that Favre and Valson would have found an infinite value for the calculated evolution of heat, if they had chosen the temperature at which water has its maximal density, and this value would have been + oo above and oo below this temperature. The authors demonstrated by experiments that the different kinds of alums are to a great extent decom- posed upon dilution into the two component sulphates, but that is something wholly different from the now pretended decomposition of, e. 0., NaCl intoNa and Cl. We must therefore say that the ideas which have been developed by Favre and Valson are rather far remote from the theory of electrolytic dissociation. On a closer investigation of the properties of salt solutions their additive character was shown in many 96 THEORIES OF SOLUTIONS. cases. Thus Kohlrausch found that the conductivity of a salt solution might be expressed as the sum of two conductivities, the one valid for the anion, the other for the cation of the salt. This rule of the " independent movement of the ions" held only within the same group of salts, e.g.j the salts composed of two monovalent ions such as KC1. Other values of the conductivity of the different ions were obtained for salts consisting of one bivalent and two monovalent ions such as K 2 S0 4 orBaC! 2 and still others for salts composed of two bivalent ions such as MgS0 4 . Gladstone and Bender observed simi- lar regularities for the refractive index of solutions, Jahn for the magnetic rotation of the plane of polariza- tion, G. Wiedemann for the molecular magnetism, Oudemans and Landolt for the natural rotatory power of the plane of polarization. The most evident example was the thermoneutrality of salts stated by Hess as early as 1840. The most accurate measurements concerning the additive properties of salt solutions and just those properties which were at first considered by Valson, are due to Rontgen and Schneider. For the relative compressibilities of 0.7 normal salt solutions (that of water = 1,000) they found the following values I H Diff. NH 4 954 Diff. 14 Li 940 Diff. 8 K 932 Diff. 8 Na 924 N0 3 981 27 954 20 934 4 930 8 922 Br 981 28 953 19 934 4 930 7 923 Cl 974 29 945 17 928 9 919 2 917 OH 1,000 (8) 992 (97) 895 11 884 3 881 2^04 970 (117) 853 (40) 813 9 804 1 803 jCOs - 798 1 797 Mean 28 17 THEORY OF ELECTROLYTIC DISSOCIATION. 97 The relative molecular volumes of 1.5 normal solu- tions were: NH 4 Diff. K Diff. H Diff. Li Diff. Na I 1,048 7 1,041 - 1,025 2 1,023 N0 3 1,043 11 1,032 14 1,018 2 1,016 -1 1,017 Br 1,038 13 1,025 14 1,011 1,011 1 1,010 Cl 1,028 12 1,016 14 1,002 1 1,001 1,001 OH 1,036 (52) 984 (-16) 1,000 (30) 970 970 2bO 4 1,066 1,027 (20) 1,007 2C0 3 1,012 984 Mean 10 14 1 1 By molecular volume of the solution is here under- stood its volume compared with that of water con- taining the same total number of molecules at the same temperature; in the experiments it was 18 C. By normal solution is understood a solution containing one gram equivalent in 1000 grams of water. The corresponding values for the constants of capil- larity of 1.5 normal solutions were found to be: H Diff. NH Diff. Li Diff. K Diff. Na I 113.14 - .09 113.23 -.36 113.58 -.26 113.84 NO 3 109.75 -4.11 113.86 - .36 114.22 +.30 113.92 -.33 114.25 Br 110.40 -3.93 114.33 - .10 114.43 -.25 114.68 -.05 114.73 Cl 110.88 -3.60 114.48 - .53 115.01 +.22 114.79 -.26 115.05 OH 111.45 (+5.36) 106.81 (-8.40) 115.21 -.33 115.54 -.33 115.87 112.49 (-3.42) 116.91 (- .70) 117.61 118.23 117.54 -3.88 - .27 -.09 -.25 These figures are very instructive. The additive scheme does not hold for all the solutions examined, as is seen from the figures put in brackets. It is necessary to take away some solutions, especially those indicated, namely, HOH, NH 4 OH and ^H 2 S0 4 , in order to find the regularities prevailing. These exceptions, which caused great difficulty for the pure empirical rule, will 8 y THEORIES OF SOLUTIONS. be seen later on to give the best proof of the applicability of the dissociation theory. It should be mentioned that Rontgen and Schneider emphasized the applicability of the rule of additivity with some marked exceptions just those cited above but did not feel justified to conclude that a dissociation of the salts into then* ions takes place, notwithstanding that the corresponding theory was worked out par- tially before the authors published their work (1886). In a memoir of 1885, hi which Raoult gives the final results of all his measurements regarding the freezing points of salt solutions, he comes to the conclusion that this property is strongly additive in regard to the radi- cals of which the salt is composed. The molecular lowering of the freezing point might be calculated as a sum of the lowerings produced by the constituent radicals. For each negative monovalent radical, such as chlorine, bromine, hydroxyl, CH 3 C0 2 , N0 3 , the lower- ing is 20; for bivalent negative radicals, such as S0 4 , Cr0 4 , 11; for monovalent positive radicals such as H, K, Na, NH 4 , 15; and for bi- or poly-valent electropositive radicals, such as Ba, Mg, A1 2 , 8. Thus for instance the molecular lowering for nitric acid, HN0 3 = 15 + 20, i. e., 35, it was observed to be 35.8; for aluminium chloride, A1 2 C1 6 , it is calculated to be 8 + 6-20 = 128, found 129, etc. Raoult cites some other investigations, indicating the additivity of different properties characteristic for salt solutions and then continues: "Then, the diminishing of the capillary heights, the increase of the densities, the contraction of the protoplast (the osmotic pressure investigated by De Vries), the lowering of the freezing THEORY OF ELECTROLYTIC DISSOCIATION. 99 point, briefly most of the physical effects produced by salts on the water dissolving them are the sum of effects pro- duced separately by their constituent electropositive and electronegative radicals, which act as if they were simply mixed in the liquid. This fact, although it is no necessary consequence of the dualistic electrochemical theory of the salts, nevertheless confirms it in its principle. It indicates that the salts dissolved in water should be regarded as systems of particles, of which everyone is composed of solidary atoms and retains, unaffected by its state of combination (e*tat de combinaison) with the others, a great part of its individuality, its action and its proper characters." That there is in reality no question of a real dissocia- tion (it is even said that the particles, i. e. y the ions are in a state of combination) is evident from the fact that, if this were the case, all the radicals ought to possess the same influence on the depression of the freezing point, whereas the action varies between 20 and 8. It is also clear from the utterance (1. c., p. 406) that "the weak acids (such as HCN, CH 3 C0 2 H, H 2 C 2 4 ) always give an abnormal lowering of the freezing point which is about only half the normal value, as if the majority of their molecules were united two and two." There is also a great number of other anomalies summed up in the following table: Salt. Molecular lowering Ratio. Calculated. Obseryed. Cu, (CH 3 CO 2 ) 2 8 + 2-20= 48 31.1 1.54 Pb, (CH 3 C0 2 ) 2 8 + 2-20= 48 22.2 2.16 H, (CH 3 C0 2 ) 15 +20 = 35 19.0 1.84 A1 2 , (CH 3 CO 2 ) 6 8 + 6-20 = 128 84.0 1.52 Fe*, (CH 3 C0 2 ) 6 8 + 6-20 = 128 58.1 2.20 100 THEORIES OF SOLUTIONS. Salt. Molecular lowering Batio. Calculated. Observed. K, SbO, C^Ofl 2-15+11 = 41 18.4 2.23 Hg, Cl a 8 +2-20=48 20.4 2.35 Pt, CU 8 + 4-20= 88 29.0 3.04 Raoult tries to explain all those anomalies by suppos- ing that double or triple molecules of these salts are formed in their solutions. The ratios given in the last columns indicate, according to Raoult's method of determination, the complexity of the supposed salt molecules. It varies between 1.52 and 3.04. In reality there is a great number of minor exceptions, which are not so very easy to determine, because the experimental errors in this older work of Raoult are rather great. With Raoult 's memoir of 1885 the arguments based upon the additive properties have reached their highest point. They did not lead to the hypothesis of a real dis- sociation, but only to the consequence "that the salts (e. g., NH 4 N0 3 , Na^SOO should be regarded as systems of particles (in these cases NH 4 and N0 3 or 2Na and S0 4 respectively) of which each is composed of solidary atoms (i. e., atoms which are wholly bound to each other as, e. g., N and 4H in NH 4 , N and 30 in N0 3 ) and retains unaffected by its state of combination with the other (e. g., S0 4 with the 2Na) a great part of its individual- ity." This is exactly the theory of radicals, according to which a molecule for instance of alcohol (C 2 H 5 OH) is composed of radicals, here C 2 H 5 and OH, which "unaffected by their combination with each other re- tain a great part of their individuality." These argu- ments could never lead further, because of the many exceptions stated, which are, as we know now, due to a very low degree of dissociation. The non-conformity THEORY OF ELECTROLYTIC DISSOCIATION. 101 of these arguments to fact consists in supposing that the same degree of independency (dissociation) always occurs for the radicals, whereas hi reality the degree of dissociation varies from very nearly zero (in weak acids such as HCN) up to nearly unity (strong acids and salts of monovalent ions in high dilution). As we know now, the exceptions, e. g. y water, ammonia, sulphuric acid, from the rule of additivity all possess a degree of dissociation which is notably different from unity, and the additivity holds strictly only for com- pletely dissociated salts but practically for such as are dissociated to about 80 or 90 per cent. the agreement with the rule being the greater the nearer the dissocia- tion is to unity. As I have said above, E. Wiedemann has adduced just one of the examples of additivity cited by Valson to show that the dissociation theory is false. He argued in the following manner: "If we replace chlorine by bromine in very dilute solutions of hydro- chloric acid and of potassium chloride, the quantity of heat developed is the same in both cases." "Chlorine and bromine are certainly not dissociated at common temperature." The same is valid in the case of the displacement of chlorine by NOs or OH in dilute solu- tion, in which case we have to calculate the heat of formation of, e. g., KN0 3 and KOH respectively from their elements K, N and 30 or K, and H and of its following solution in a great quantity of water. This is easily done by aid of the tables given by thermo- chemists. The results of such calculations were given by myself in the following table, giving the heat of replacement in great calories (1000 cal.) per gram equiv- alent. 102 THEORIES OF SOLUTIONS. Max. H K. Na Tl Ca %Sr %Ba Diff. C1-N0 8 : -19.9 -13.9 -13.7 - 9.6 -16.4 -17.6 -15.7 10.3 NO 3 -Br: +33.5 +24.4 +25.5 +16.9 +30.9 +31.0 +28.1 16.6 Br-OH: (-49.6) - 8.1 - 6.1 -15.7 -37.0 -28.4 -22.5 30.9 OH-I: (+64.1) +23.1 +32.8 +26.8 +53.7 30.6 The figures regarding water are put in brackets because they are not valid for a very dilute aqueous solution (but for concentrated water) and therefore do not agree with the conditions demanded by Valson and Wiede- mann. Compare this table with the following one of the corresponding heats of neutralization of strong bases with strong acids hi dilute solution, adduced by myself in favor of the dissociation theory: KOBE NaOH LiOH KOH HC1, HBr or HI 13.75 13.75 13.9 13.8 HNOi 13.8 13.7 13.7 Max. %CaO,H, %SrO,H 2 % BaO.H, Diff. HC1, HBr or HI 14.0 14.1 13.85 0.35 HNO, 13.9 13.9 13.9(14.15) 0.2 (0.45) The figures for HC1, HBr and HI are as Berthelot has tabulated them. For J^Ba(OH) 2 Berthelot gives 13.9, Thomsen 14.15 without doubt the figure of Ber- thelot is the probable one. All the figures are valid for common room temperature (18 C.). The values given in the last column are the differences between the smallest and the greatest figure in every horizontal line. This maximal difference ought to be zero or fall within the magnitude of experimental errors if perfect additivity prevailed, as is really the case for the heat of neutralization, but not at all for the heat of displacement, which therefore has been wrongly THEORY OF ELECTROLYTIC DISSOCIATION. 103 cited by Valson and by E. Wiedemann as a (nearly) additive property. The theory proposed by Gay-Lussac regarding the "equipollency " of salts in solution is the first one (1839) that reminds us of the theory of electrolytic dissocia- tion. In 1850 Williamson gave a theoretical explana- tion of the fact that in the formation of ethyl ether C2H 5 OC 2 H5 in the presence of sulphuric acid, H 2 S0 4 , this latter is not consumed by the chemical process, which therefore is a catalytic one according to the terminology proposed by Berzelius. Williamson expressed the opin- ion that in the first stage C 2 H 5 .OH and H 2 .S0 4 exchange radicals through double decomposition so that HOH and C 2 H 6 .H.S0 4 are formed. After this process a second one takes place in which C 2 H 6 .H.S0 4 and C 2 H 5 O.H change radicals through double decomposition so that ethyl ether C 2 H 5 O.C 2 H 5 and sulphuric acid H.H.S0 4 are formed. The total change due to the two processes is therefore a formation of ethyl ether C 2 H 5 .O.C 2 H 5 and water H.O.H from two molecules of alcohol C 2 H 6 .O.H. The quantity of sulphuric acid is unchanged, it serves only to bind the water formed during the process. It should be observed that C 2 H 5 OH in the first process is decomposed into C 2 H 5 and OH, in the second one into C 2 H 5 and H. This corresponds to fact. Williamson generalized this idea and said that in a solution there is a perpetual change of radicals between the molecules. In this way the fact was explained that, in mixing two salts consisting of different radicals, all the four possible salts were rapidly formed as Gay- Lussac maintained (cf. p. 75 above). The same must also be true regarding molecules of similar composition. 104 THEORIES OF SOLUTIONS. Thus for instance in a solution of hydrochloric acid, H.C1, an atom H does not always remain bound to the same atom of chlorine but exchanges it for new atoms of chlorine, the one after the other. He gives still another example: if we mix a solution of Ag 2 S0 4 with one containing HC1, then some few molecules of H 2 S0 4 and AgCl are immediately formed. The AgCl-mole- cules are very slightly soluble and precipitate so that HC1 and Ag2S0 4 are not formed again. But new mole- cules of H 2 S0 4 and AgCl appear in the solution and the newly formed AgCl precipitates again. The proc- ess goes on in only one direction until there remains only such a small quantity of AgCl that the solution is just saturated in regard to it. This coincides wholly with the theory on "equipollency" of salts in solution proposed by Gay-Lussac in 1839. It is not by chance that Williamson has chosen the electrolytes (salts, acids and bases) as example of his principle. For in the electrolytic solutions these changes of radicals we now say ions go on instan- taneously as hi the example above. All attempts to measure the velocity of reaction in cases, when elec- trolytes exchange their ions, have been in vain on account of their extreme rapidity. On the other hand similar reactions, in which non-electrolytes (or perhaps better stated extremely weak electrolytes) play a part, generally proceed slowly, as we shall also see later in regarding the processes characteristic of the formation of ethyl ether. According to the law of Faraday each monovalent ion carries a charge of about 4.5. 10~ 10 electrostatic units, the positive ions as H, NH 4 , K and generally metals, of THEORY OF ELECTROLYTIC DISSOCIATION. 105 positive, the negative ions such as Cl, CN, N0 3 , C10 3 , etc., or generally negative radicals, of negative elec- tricity. What will now happen if we place a solution containing an electrolyte in a vessel between two elec- trodes of different potential? The surface of the fluid will instantaneously assume a charge, so that positive ions are driven against the negative electrode and nega- tive ions against the positive one. The different mole- cules will therefore be turned around until they stand with the chlorine ion to the left as in the molecules in the figure representing this case (Fig. 2, line 2). Or at least a majority of the HC1 molecules will turn their chlorine to the left, their hydrogen to the right. In the exchange of ions between the HC1 molecules, a majority FIG. 2. Grotthuss' chain. of the chlorine ions will wander to the left, the majority of the hydrogen ions to the right. Then they carry their charges with them and the said movement of the ions corresponds to a transporting of positive electricity in the direction of the arrow from left to right. Negative electricity wanders from the right to the left, which is equivalent to a wandering of positive electricity in the opposite direction. This is about the position taken by Grotthuss as early as 1825 and represented by Fig. 2. 106 THEOKIES OF SOLUTIONS. It is just this latter idea which has been developed by Clausius in a memoir of 1857 without a knowledge of Gay-Lussac's or Williamson's paper. Clausius tried to explain how the law of Ohm may hold for electro- lytic solutions, which had been proved by experiment. Ohm's law demands that even the least electric force causes a motion of the ions. Hence if these were bound to each other in the electrolytic molecule, so that a certain force were necessary to tear them asunder, as was and is generally believed amongst chemists, just this minimum of electric force (slope of potential) would be necessary for establishing an electric current; this is in contradiction to Ohm's law. Clausius drew the conclusion that the ions in electrolytic molecules are not fixed to each other, but might be exchanged for ions from other molecules just as Williamson had supposed. "The frequency of such mutual decomposi- tion depends upon two circumstances, firstly on the greater or less coherence of the ions with each other and secondly on the violency of the molecular move- ment, i. e., on the temperature." Clausius also considers the theory of Williamson to which a chemist had directed his attention and says that "Williamson speaks of a perpetual change of the hydrogen atoms (between the HC1 molecules), whereas for the explanation of the conduction of electricity it suffices that at the collisions of the molecules now and then, and perhaps relatively seldom, an exchange of the partial molecules (i. e., ions) takes place." "The increase of conductivity with temperature is explained in an unconstrained way by this theory," Clausius says, "because the greater violence of the THEORY OF ELECTROLYTIC DISSOCIATION. 107 molecular movement must contribute to an increased reciprocal decomposition of the molecules." Of course it must be regarded as very much strength- ening the hypothesis of mutual exchange that three leading scientists, of whom two were chemists and the third a physicist, from apparently quite different empir- ical premises have been led to the same conclusion, and therefore it seems just to attach the names of all three of them to their hypothesis. The form given to it by Gay-Lussac and Williamson corresponds better to our present knowledge. A " perpetual exchange" comes much nearer to real dissociation than an "exchange now and then." Further, there have been objections against Clausius that according to his theory the con- ductivity should be proportional to the number of collisions of electrolytic molecules, i. e., to the square of their concentration, whereas it really increases more slowly than in proportion to this quantity. Also the explanation of the increase of conductivity with tem- perature, given by Clausius, has not proved successful. In most cases the degree of dissociation decreases a little with increasing temperature, and the increased conductivity depends upon the diminishing of the internal friction with temperature. The renowned Italian physicist Bartoli has expressed a similar theory, where dissociation is spoken of directly, in the year 1882. He investigated the so-called residual current, which is observed to pass through an electro- lyte, even if the electromotive force necessary for its decomposition is not reached. Bartoli gives two different theories for the explanation of the residual current. Either the polarization, which hinders elec- 108 THEORIES OF SOLUTIONS. trolysis, disappears slowly by means of diffusion of the polarizing substances from the electrodes, or there is a dissociation of the electrolytic molecules. The first theory is generally accepted as the right one and was already at that tune after Helmholtz's and Witkowski's important investigations (1880). The second one fur- ther demands that the degree of dissociation is pro- portional to the third power of the acting electromotive force, that is, if no electromotive force acts, it is zero (to the third power), and this case is just the one for which the modern dissociation theory demands a high degree of dissociation, which is further independent of the acting electromotive force, if there is such a one. The claims of priority raised by Bartoli in 1892 regard- ing the theory of electrolytic dissociation can therefore not seriously be discussed. It ought well be said that it would have been much more adequate if he, like his predecessors, from Gay-Lussac to Valson had, refrained from drawing such a wide-reaching conclusion, as that salts are dissociated, from such a small number of facts. In 1883 I investigated the conductivity of electro- lytes as depending on their concentration and tempera- ture and came to the conclusion (published 1884) that their solutions contain two different kinds of molecules, of which the one is a non-conductor, the other conduct- ing electricity in consequence of properties attributed to it by the hypothesis of Gay-Lussac, Williamson and Clausius. These latter were simply called active mole- cules. The number of active molecules increases with dilution at the expense of the inactive ones and tends to a limit, which is probably first reached when all inactive molecules have been transformed into active THEORY OF ELECTROLYTIC DISSOCIATION. 109 ones. At very high dilutions the additive property of the conductivity postulated by Kohlrausch is not only true within certain groups of electrolytes of similar composition but for all electrolytes of whatsoever com- position. An acid is the stronger the greater its con- ductivity is. At infinite dilution all acids have the same strength. These assertions were demonstrated to be in accord with the thermochemical measurements of Berthelot and Thomsen. Similar rules are valid for bases. Chemical activity therefore coincides with elec- trical activity. Water, alcohols, phenols, aldehydes, etc., which exchange ions with electrolytes are also electrolytes. The relative conductivity of water in- creases more rapidly with temperature than that of acids, bases or salts. Therefore the hydrolysis of salts increases with temperature. The results of Thomsen's, Guldberg's and Waage's, and especially of Ostwald's measurements of chemical equilibria were discussed and their discrepancies with Guldberg and Waage's law explained as dependent on the lowering of the activity of the examined weak acids caused by the presence of their salts and of strong acids. The heat evolved in the neutralization of a wholly active acid with a wholly active base is always the same and equal to the heat which is consumed in the activation of an equivalent quantity of water. The deviation of the heat of neu- tralization of weak acids or weak bases from the said value is due to the heat necessary for their activation. In a reaction of ferrocyanide of potassium K 4 .C 6 N 6 Fe, the ions of which are 4K and the rest, with other electrolytes, ferrocyanides and potassium-salts are al- ways formed but not ferrous or ferric salts, because there 110 THEOKIES OF SOLUTIONS. occurs only a rearrangement of the ions. Therefore the ion contained in the ferrocyanides cannot be de- tected by means of ordinary reagents on iron, which are all electrolytes. When this memoir was written (1883) the measure- ments of Raoult on the freezing point of salt solutions had not appeared. Therefore it was regarded as too bold to state verbally that the active molecules were dissociated into their ions and it was only maintained that they should be subject to the conditions demanded by the hypothesis of equipollency. Soon afterwards Raoult's aforementioned measurements were published and their theory given by van't Hoff (1885). Im- mediately after that I calculated the coefficient of activity from the conductivity figures and the degree of dissociation which was necessary to explain the values i of van't Hoff, calculated from Raoult's data. A very good agreement was found and then the basis for an open declaration of the state of dissociation of elec- trolytes was found strong enough (1887). The word activity was replaced by the word electrolytic dissocia- tion. Immediately after my memoir of 1884 had appeared, Ostwald carried out a great number of measurements, showing that the velocity of reaction, when different acids exert a catalytic action, is, as my theory de- manded, nearly proportional to their conductivity, and further that the relative strength of weak acids increases with dilution. In 1889 I showed that the catalytic action of different acids on inverting cane sugar, if it is corrected for the so-called salt-action, is proportional to the concentration of the hydrogen-ions present. THEORY OF ELECTROLYTIC DISSOCIATION. Ill Ostwald, Planck and van't Hoff and Reicher simul- taneously and independently of each other applied the law of mass-action on the equilibrium between ions and undissociated molecules of an electrolyte (1888). Ost- wald found that this law really holds good for weak acids. Van't Hoff and Reicher were not content with the figures already published regarding the conductivity of weak acids and therefore they performed extremely accurate redeterminations, which gave an excellent agreement with the demands of the said law, which was called for this special case Ostwald's law. Planck finally did not succeed with the application of this law to salts, and this disagreement for strongly dis- sociated electrolytes still persists. Later on (1894) Bredig proved that Ostwald's law is valid also for weak bases. From the law of van't Hoff regarding the change of chemical equilibria with temperature (cf . p. 83 and 84) I calculated the heat of electrolytic dissociation of differ- ent weak acids and showed it to be in perfect agreement with the observed heats of neutralization. Kohlrausch and Heydweiller did the same work for the most im- portant and most difficultly determined of all examined electrolytes, namely water. In two new memoirs I de- termined the general laws of equilibrium between elec- trolytes. Ostwald demonstrated the extreme useful- ness of the new theory for general and analytical chemistry. (1900 and 1904.) The chief points of the theory of electrolytic dissocia- tion were then fixed. LECTURE VII. VELOCITY OF REACTION. THE first velocity of reaction studied was that on the inversion of cane-sugar investigated by Wilhelmy, in the year 1850. This process has a great practical use, as the determination of the quantity of cane sugar in a solution depends upon it. Wilhelmy used the saccharimeter of Soleil, the same instrument which was in use in the sugar-factories. It was known that the hydrolysis (decomposition with addition of water) of cane sugar may be carried out at low temperatures if an acid was added to the sugar solution. It was the velocity of this latter reaction, which was a typical example of what Berzelius called catalytic processes, that was the object of Wilhelmy 's investigation. He stated that temperature exerts a great influence, he therefore tried to carry out his experiments at a not too variable temperature by placing his vessels con- taining the solutions of cane-sugar in a large vessel of water, heated by a spirit flame of constant size, or at lower temperature in a very large heat-isolated vessel filled with water. Wilhelmy found that the general law, which holds for the fall of temperature to that of the surrounding temperature (Newton) or for the loss of electricity from a charged conductor (Coulomb), is also true for the trans- formation of cane sugar, namely that the transformed quantity in a given short time is proportional to the 112 VELOCITY OF REACTION. 113 remaining quantity. The strong acids : sulphuric, hydro- chloric, nitric and phosphoric were found to be effective, but acetic acid had no appreciable influence (in fact it gives the same effect as the strong acids, but after a much longer time). As an example we cite some experiments with nitric acid at 15 C. Time of A -x , ^ g_ I loff A Reaction (Min. ). Quant . Sugar. log A x ' ~ t g A - x ' 65.45 45 56.95 0.0605 0.00134 90 49.45 0.1217 0.00135 150 40.70 0.1981 0.00132 210 33.70 0.2880 0.00137 270 26.95 0.3851 0.00142 The time law proposed by Wilhelmy leads to the expression log A - log (A - x) = Kt, where t is the time of reaction, x the quantity of trans- formed sugar after that time, A the quantity of sugar present at the beginning and K a constant. The for- mula expresses very well the progress of the process; it has been confirmed later by a great number of in- vestigators. It is possible to invert the cane sugar without the addition of acids at higher temperatures, e. g., in auto- claves above 100 C. Of course this process goes on also at low temperatures but so slowly that it cannot conveniently be measured. The same process is also promoted by an enzyme called invertase, which is pro- duced by yeast cells. It was believed for a long tune, according to experiments performed by V. Henri, that this process obeys another time law than that relating to inversion by means of acids. Hudson has shown 9 114 THEORIES OF SOLUTIONS. that the exceptional behavior, found by Henri, de- pends upon the abnormal rotatory power (the so-called mutarotation) of the components of invert sugar, when they are recently formed. The values of x, i. e., the transformed quantity of sugar, were therefore, in Henri's determinations, affected by great errors. It is possible to avoid this error by adding a trace of alkali to the solution of invert sugar, which very rapidly reaches its end value of rotating power under such circumstances. When these measures are taken, the change of cane sugar by means of invertase goes on according to the same law as if it were promoted by acids. This observation is very important as it shows again that the supposed difference in action of organic products (enzymes) and inorganic substances (acids) is not a real one. It is to be hoped that the correspond- ing irregularity found by Henri, his pupils, and others in the transformation of other sugars, will also disap- pear on closer investigation. This has already been proved by A. E. Taylor regarding the hydrolysis of maltose by means of maltase and that of starch with salivary amylase. That the inversion caused by means of acids goes on regularly depends upon the destruction of mutarotation by acids, which is not quite so rapid as that of alkalies, but still sufficient to prevent serious disturbances. The said hydrolysis is also caused by ultra-violet light. Most reactions, especially hydrolytic ones, pos- sess the same peculiarity as the inversion of cane-sugar in that they are catalyzed by hydrogen or hydroxyl ions (i. e., by the presence of acids or bases) and by special enzymes. High temperature or ultraviolet light act VELOCITY OP REACTION. 115 in the same manner. In the yeast cells there is another enzyme, zymase, which carries the process further when cane-sugar has been transformed to glucose. Zymase transforms it to alcohol and carbonic acid; probably lactic acid is an intermediary stage. On the other hand Duclaux showed that glucose in the presence of potassium hydrate or ammonia (i. e. hydroxyl ions) in sunlight gives alcohol and C02. If Ba(OH) 2 was used as the alkali the process went on only as far as the formation of lactic acid, which by the means of potas- sium hydrate and sunlight could further on change to alcohol and C0 2 . Buchner and Meisenheimer found that sunlight is not absolutely necessary. They boiled inverted cane-sugar with strong KOH and thus pro- duced alcohol without sunlight. Nencki and Sieber stated that glucose with 0.3 per cent. KOH gives lactic acid after 10 days at 35-40 C. Hanriot continued this process by boiling calcium lactate with calcium hydrate and obtained alcohol, just as Duclaux by means of sunlight. We have here a number of reactions, namely: 1) CuH^On + H 2 O = C 6 H 12 O 6 + C 6 H 12 6 (catalyzer cane sugar water glucose laevulose H-ions or invertase or light). 2) CeH^Oe = 2CH 3 CHOHCOOH (catalyzer OH-ions glucose lactic acid or light or yeast). 3) C 3 H 6 3 = C 2 H 6 OH + C0 2 (catalyzer OH-ions or lactic acid alcohol carbonic acid light). Evidently in Duclaux's experiments with Ba(OH) 2 116 THEORIES OF SOLUTIONS. the process was brought to a relative standstill because of the slight solubility of the barium lactate, when this intermediary product had been formed. Other hydrolytic processes of very high importance, which are accelerated by hydroxyl or hydrogen ions and by special enzymes, namely trypsin and pepsin, are the so called digestive processes. The most important natural process, namely the formation of sugar from carbonic acid and water by the means of the catalytic action of the chlorophyll in the green parts of plants, probably takes place through a previous formation of formaldehyde, HCOH, and oxygen (O 2 ) from CO 2 and H 2 0. It has recently been found possible to reproduce this photochemical process without the help of living organisms (D. Berthelot, Stoklasa). In many cases the process itself produces a substance which accelerates it. Thus for instance if we dissolve copper in nitric acid, nitrous acid i formed, which accelerates the solution. Therefore if we put pieces of copper in, say 10 per cent., pure nitric acid, the copper is at first very slowly attacked; but the velocity of reaction increases so that after a tune the reaction is violent, giving rise to a strong current of gas-bubbles. Such a process is the inversion of cane-sugar without acids at high temperatures. The cane sugar itself has a weak acid reaction, but its hydrolytic products, glucose and still more laevulose have much stronger acid properties as Madsen found. Therefore the reaction goes on with accelerated velocity, until finally very little cane-sugar is left, so that the process becomes complete by degrees. Such an "autocatalytic" process is also the saponification of an ester, e. g., ethyl acetate by means VELOCITY OF REACTION. 117 of water. At first the hydroxyl ions of the water pro- duce saponification just as bases. The product, acetic acid, diminishes the quantity of the hydroxyl ions, so that the process goes on more slowly. But the hydro- gen ions of the acetic also cause a saponification al- though they are not so active as the hydroxyl ions (they act 140 times less), and when they have increased to a sufficient number the process is accelerated after it has passed through a minimum, when the hydrogen- ions are 140 times as many as the hydroxyl-ions. This reaction has been studied by Wijs, who found that the experiment wholly confirmed the theory. Even the common growth of organisms, e. g., bacteria, has been regarded as such an autocatalytic process. If bacilli, e. g., coli bacilli, are inoculated into a solution, containing their nourishment with a certain quantity of oxygen over it, and the whole is shaken so that oxygen is continuously carried to the bacilli, these are first increased in number, each independent of the others, so that the number of bacilli increases according to an exponential function, which as the curve shows is suddenly broken down, when the oxygen or nourishment begins to be nearly consumed. This phenomenon has been studied in my laboratory by Mr. Thor Carlson. The growth of a single organism shows similar pecu- liarities. To begin with the increase, measured by weight, becomes greater and greater, then it is nearly constant, and thereafter decreases. A very important case of reactions which are ham- pered by their own reaction products has been studied by me. If ammonia acts upon ethyl acetate, which is supposed to be present in great excess so that its quan- 118 THEOEIES OF SOLUTIONS. tity may be regarded as constant, then the velocity of reaction is proportional to the number of hydroxyl ions present. The progress of the reaction is followed by means of the conductivity of the ammonium acetate formed. Now the number of hydroxyl ions is almost inversely proportional to the quantity of ammonium acetate already formed and therefore the velocity of reaction is also inversely proportional to the said quan- tity. This leads to the differential equation dx K(A-x) dt' x ' r ' where A is the quantity of ammonia present from the beginning, x the quantity of ammonium acetate formed, K a constant and P the quantity of ethyl acetate which may also be regarded as a constant. When x is small compared with A we obtain: xdx = KAPdt or integrated: x 2 = 2KA .P.t. This formula tells us that the reaction proceeds so that the quantity of ammonium acetate is proportional to the square root of the time and also of the quantities of ethyl acetate (substrate) and reagent (ammonia). The truth of this premise is seen from the following figures, found for 0.66 n. ethyl acetate at 14.8 C. t zobs. x calc. 17.3 Vf t x obs. x calc. 17.3 Vj 1 17.5 19.4 17.3 10 51.2 51.3 54.7 2 25.5 25.2 24.5 15 59.6 59.7 67.0 3 30.7 30.6 29.9 22 67.5 68.6 81.1 4 34.7 34.9 34.6 30 74.5 74.7 94.7 6 41.5 41.7 42.4 40 80.7 80.7 109.4 8 47.0 46.9 48.9 60 88.2 88.2 134.0 VELOCITY OF REACTION. 119 The time i is given in minutes, x in per cent. The column 17.3 V t agrees well with x obs., until this exceeds 50 p. c. After that the x calculated found according to the exact integral of the last differential equation holds good. The said rule that the transformed quantity is pro- portional to the square root of the acting quantity and time is called Schiitz's rule and holds for a great number of reactions in physiological chemistry, amongst others digestion by means of pepsin or of trypsin, the hydro- lytic action of Upases on fats, etc. As an instance some figures given by Schiitz may serve for the quantity formed in the action of different quantities of pepsin at 37.5 C. on the same quantity of egg-albumen, freed from globulin. Quantity of Pepsin P. 1 4 9 16 25 36 49 64 Quantity of peptone found _ 9.4 20.6 32.3 45.4 55.2 65.0 76.0 85.3 10.8 Vp 10.8 21.6 32.4 43.2 54.1 64.9 75.7 86.5 Experiments regarding the influence of time are given by Sjoqvist for peptic digestion, by Stade for the lipo- lytic action of gastric juice and by others. The agree- ment with the exact formula is in most cases very satisfactory. In this case the expression Pt enters into the final formula. Therefore the same quantity of reaction- product is produced by the enzyme quantity q in 1 hour as by the quantity 1 acting during q hours on the same quantity of substance. In many investigations of a physiological-chemical nature, it is easy to determine a certain point of decomposition, e. g., when milk coagulates, when peptization, i. e., liquefaction of gels I 120 THEORIES OF SOLUTIONS. is reached, etc. In such cases it is generally stated that the necessary time is inversely proportional to the quantity of enzyme adapted to the experiment. I have laid so very great stress upon the fact that we may find Schiitz's rule to hold good for simple inorganic processes, also because at an earlier stage it was maintained that this rule was peculiar to the action of ferments in contradistinction to catalyzers, which are not prepared by living organisms. The deduction of this rule indicates that it is applicable, as soon as one of the reaction products reacts with the catalyzer, so that the free quantity of this substance is nearly in- versely proportional to the quantity of reaction pro- ducts. The deduction has also given a formula which holds for any magnitude of the transformed quantities whereas the rule of Schtitz is not reliable for higher values of x than about 50 per cent. As we have seen before, Williamson explained the pe- culiar action of catalyzers by stating that they give inter- mediary products of reaction from which the catalyzer is formed again in a later chemical reaction. Thus for instance, according to Williamson, the sulphuric acid in the formation of ethyl ether from alcohol at first gives ethyl sulphuric acid C 2 H 5 HSO4, which thereafter reacts with alcohol to give back sulphuric acid and form ether. The two steps of this reaction are the following : 1) C 2 H 5 OH + H 2 S0 4 = C 2 H 5 HS0 4 + H 2 0, 2) C 2 H 5 HS0 4 + C 2 H 6 OH = C 2 H 6 OC 2 H 8 + H 2 S0 4 , or taken together: 2C 2 H 5 OH = C 2 H 5 OC 2 H 6 + H 2 0. VELOCITY OF KB ACTION. 121 In reality the process is a dehydration of the alcohol and depends upon the binding of H 2 to the sulphuric acid. Therefore the process is very much retarded when a considerable quantity of water has been formed. This process has been investigated by Kremann. He found that reaction 1 goes on rather rapidly at moderate temperatures and in the absence of water, the constant of reaction being 0.00112 at 40 and 0.0044 at 51, corresponding to an increase in the proportion 1 to 3.63 in an interval of 10 C. The velocity constant of the formation of C 2 H 5 HSO 4 is about 1.7 times greater than that of its decomposition. In aqueous solution the velocity constants are about 50 times less (investigated for the decomposition of C 2 H 5 HS04) and their increase in an interval of 10 C. about as 1 to 1.99. Hence we conclude that the reaction is hampered in a high degree by the presence of water and that in the higher degree the lower the temperature is. Reaction 2 is inappreci- able at low temperatures and can only be investigated above 100 C. Its velocity sinks very rapidly with the increase of the water formed. Its rate of increase with temperature is in about the proportion of 1 to 2.35 in an interval of 10 C. at 117.5. The velocity of the total reaction is determined by the slow one, i. e., the second one, of the two partial reactions. In any case Kremann has shown that Williamson's theory of the formation of ether is correct. The said process is a very complicated one. There are some other compound processes, which show a greater regularity. Amongst those the radioactive changes, which are independent of temperature and concentration, have been very closely studied, especi- 122 THEORIES OF SOLUTIONS. ally by Rutherford. In some cases, as with the radio- active deposit from actinium emanation, the velocity of reaction characteristic of the two consecutive proc- esses are very different from each other, the actinium A being decomposed to 50 per cent, hi 35.7 minutes, whereas the corrresponding time for actinium B is 2.15 minutes. Then the total process except at the very beginning may be regarded as a reaction going on with the velocity of the first reaction. In other cases as with the decay of the excited activity from radium emanation there are products, radium A, radium B, and radium C, which do not differ so very much from each other in their rate of decay, the correspond- ing times being 3, 21 and 28 minutes respectively. In this case the total decay, measured by means of the emitted (0 or) 7 rays, which accompany the decom- position of radium C, gives totally different time curves, according to the time during which the radioactive deposit has been formed. Through a thorough exam- ination of the different possible cases, the different proc- esses have been separated from each other and the rate of decay for each of them determined. Probably the effect of catalyzers depends in most cases, just as in the case of the formation of ether, on their entering into intermediary chemical reactions from which they are regenerated hi later reactions. In some cases as with platinum sponge, or with cata- lyzers in suspension the effect is probably due to an adsorption of the reagents on the catalytic agent. It is well known that van't Hoff introduced the notion monomolecular, bimolecular, etc., reactions according to the number of molecules which, represented by the VELOCITY OF KEACTION. 123 chemical equation react upon each other, and for each of them a certain equation of reaction is character- istic. In many cases, especially when the number of the reacting molecules is great, the experimental re- sults agree better with an equation of reaction corre- sponding to a lesser number of reacting molecules than is expressed be the chemical equation. In such cases an explanation of the seemingly abnormal behavior of the reaction has been found by the supposition that the investigated reaction is composed of two or more partial reactions of which the slowest one corresponds to the equation found experimentally. The hypothesis made has in some cases been verified experimentally. As has been known from the times of the alchemists, temperature has a very great influence in hastening chemical processes. This was also stated by Wilhelmy, when he investigated the inversion of cane sugar. He found that the velocity of reaction increases nearly exponentially with temperature. The same was stated by Berthelot for the formation of ester from an alcohol and an acid, a reaction which*, being one of the first examined rather closely, has played a preponderating role in this chapter. The formula, representing the velocity k of reaction is then: *;*, = * 10* " Berthelot has himself said that the experiments were not sufficient in number for ascertaining if his formula is correct. The values given by him are Temp. Jb(obs.) k (calc.) B 8 0.0004 0.0004 85 0.074 0.0456 0.0281 100 0.17 0.115 0.0307 170 8.50 8.50 0.0243 124 THEORIES OF SOLUTIONS. The value of B decreases with rising temperature and this is the case for most processes studied hitherto. I therefore in 1889 examined the different determinations available at that time and found that another formula gives good results, viz. : d log k A . . , Ti- To . . . ~dt = T~ 2 ' s 1= TT + s where A is a constant and T designates absolute tem- perature. This formula, as well as that of Berthelot, is a special case of one proposed by van't Hoff and containing both the two terms occurring in the two formulas above. dlogjc _ A dt = T2 + tf- I found that the formula with only A/ T 2 corresponds very well and hi most cases better with the experi- mental results of different investigators than the em- pirical formulae proposed by these investigators do. It has a theoretical meaning and must be preferred to formulae containing a greater number of empirical constants, as does the formula of van't Hoff. Van't Hoff called attention to a rather remarkable circumstance, namely that the increase in the value of k for 10 degrees is in most cases about in the pro- portion 1 to 2 or 1 to 3. But there are rather great exceptions; thus the decomposition of phosphoreted hydrogen PH 3 into its elements accelerates very much more slowly with temperature, namely in the propor- tion 1 to 1.2 for an interval of 10 degrees. But it must here be remarked that the observations are made (by Kooy) at 256 and 367 respectively, so that if my formula VELOCITY OF REACTION. 125 is accepted the quotient increases to 2.5 at 27 C. The same remark may be made regarding the gas reaction studied by Smits and Wolff: 2CO = C0 2 +C, which according to the chemical equation ought to be bimolecular, as 2 molecules of CO are necessary for the reaction, but which is found to be monomolecular. This is explained by assuming two consecutive reactions of which the first has a much smaller velocity than the second, namely: 1) CO = C+0, 2) CO+0 = C0 2 . The velocity of this reaction is found to increase in the proportion 1 to 1.42 for 10 between 256 and 340. Reduced to 300 abs. ( = 27 C.) the increase reaches 1 to 3.53 for 10 C. The extreme values of the said proportion amongst the processes cited by van't Hoff seem to be shown by the two reactions which have been studied more than any other, namely the in- version of cane sugar and the saponification of ethyl acetate by hydroxyl ions with the values 1 to 4.0 and 1 to 1.77 at 27 C. This latter value differs rather much from that which holds for the saponification of esters by means of acids. The temperature coefficient of these reactions was determined by Price. The propor- tion reduced to 300 absolute and a 10 interval is about 1 to 2.35 for ethyl acetate and does not differ much for the other esters. The experiments of Kremann give about as high values of the said proportion as that found for cane sugar, namely 1 to 4.1 for the formation of CjH 6 HS0 4 126 THEORIES OF SOLUTIONS. in the absence of water and 1 to 4 for the formation of ethyl ether from C 2 H 5 OH and C 2 H 5 HS0 4 . In aqueous solution the first proportion sinks to 1 to 2.5 all figures reduced to 300 absolute. (The experimental error is in these cases rather great.) At low temperatures the increase goes on very rapidly with temperature. Thus Plotnikow found for the said proportion at 90 1 to 6.2 for the reaction C 2 H 4 + Br 2 = C^EUBrz. If the said figure is reduced to 300 absolute it gives the proportion 1 to 1.97. Therefore van't Hoff 's rule, stating that the order of magnitude of the increase of velocities of reaction in an interval of 10 is always the same for ordinary re- actions, is much nearer to the truth if all values are reduced to the same temperature, e. g., to 300 absolute. We may express this rule more simply in other words by saying that the constant A of the formula above (p. 124) is of the same order of magnitude for different reactions. We find for cane sugar and ethyl acetate saponified by bases or by acids 12,820, 5,580 and 8,700 respectively. There are some very remarkable exceptions to van't Hoff s rule. The first is the decay of radioactive sub- stances, which is independent of the temperature so that A = 0. The second is the solution of metals in dilute acids. Ericson Aure'n determined the velocity of reaction when zinc dissolves in 0.1 normal hydro- chloric acid. He found that it increased only 3 per cent, when the temperature rose from 9 to 50 C. This increase falls absolutely within the experimental VELOCITY OF KEACTION, 127 errors. In more concentrated solutions of the acids a greater increase in the velocity of reaction with temperature is observed, according to the experiments of Guldberg and Waage. The velocity of reaction at 18 compared with that at in hydrochloric acid was found by them to be for 1.3n. HC1 1.58 2 n.HCl 1.68 2.671. HC1 1.70 4 n.HCl 2.44 8 n. HC1 3.25 Spring dissolved iceland spar with natural surfaces of cleavage in 10 per cent. HC1 (about 3-normal) and found that the velocity of reaction increases to about double its value in 20 degrees (at 25 C.). This figure agrees very closely with that found for the solution of zinc in hydrochloric acid of the same strength. If the crystals were cut with surfaces parallel with or per- pendicular to the chief axis the rate of increase with temperature was higher (about as 1 to 3 between 15 and 35) but rather irregular. Recently I investigated the velocity of the solution of the active deposit from actinium emanation in water and 0.001 normal acetic acid at 15 and at 62 and found no appreciable difference at the two temperatures. The photochemical reactions are only to a very insignificant degree dependent on the temperature in regard to their velocities. Thus for instance the ratio of increase in an interval of 10 was found to be for the following reactions (the table is taken from Plotni- kow's Photochemistry). Polymerization of anthracene 1 to 1.21 Oxidation of quinine by means of chromic acid ... 1 to 1.06 128 THEORIES OF SOLUTIONS. Reaction of chlorine on hydrogen 1 to 1.21 Reaction of oxalic acid with ferric chloride 1 to 1.01 Reaction of oxygen on hydriodic acid 1 to 1.39 Transformation of styrol to metastyrol 1 to 1.36 Oxidation of dioxide of sulphur with oxygen. . . .1 to 1.20 Reaction of oxalic acid and mercuric chloride. . .1 to 1.12 The photographic process with silver bromide gelatine 1 to 1.00, to 1 to 1.03 The reaction evidently depends upon the absorption of the active light rays, which alters very little with temperature. Another peculiarity which is without doubt connected with the low coefficient of temperature is that the photochemical processes behave as if they were monomolecular. Thus Bodenstein observed that hydriodic acid, which at high temperatures is decom- posed according to the equation: 2HI = H 2 + I 2 which reaction is in fact found to follow the laws valid for bimolecular reactions, nevertheless on decomposi- tion by means of light at low temperature obeys the equation: HI = H + I, i. e.j behaves as a monomolecular reaction. From this we conclude that each molecule of HI independently of other similar molecules is decomposed by the light waves. These tear asunder the molecules by the intensity of their vibrations, whereas at high temperature bonds connecting the atoms H and I in the molecule HI are weakened, so that a dissociation takes place at first after the impact of another molecule of HI, when there is an opportunity for the atoms H and I to combine with another atom of H or I respec- tively. VELOCITY OF KEACTION. 129 Another exception to the rule of van't Hoff is found in the spontaneous decomposition of certain enzymes or similar substances such as hsemolysins. These latter are subject to an exceedingly high influence of tem- perature. Thus for instance Madsen and Famulener found for a hsemolysin contained in blood serum from a goat a value of A = 99,200, corresponding to an in- crease in the velocity of reaction in the proportion 1 to 2.6 per degree at 50.* A little less was the influence of temperature on the destruction of tetanolysin and vdbriolysin, A being 81,000 and 64,000 respectively. The destruction of 2 per cent, solutions of rennet, pepsin, invertase and trypsin also possess very high values of A, namely 45,000, 38,000, 36,000 and 31,000 respec- tively, corresponding to a doubling of the effect in a rise of the temperature of 1.5, 2, 2.1 and 2.4 degrees at about 60. On the other hand the reactions of these substances with other substances usually agree approximately with the saponification of ethyl acetate by means of bases in regard to then* hastening by temperature. Sometimes they give rather low values of A, for instance the inversion of cane sugar by means of invertase has a value of A = 4,500 between 20 and 30, 5,500 between and 20 (Euler and Beth af Ugglas) and the precipi- tation of egg-white by means of precipitin only 3,150. It is well worth noting that different vital processes such as the assimilation hi plants, the respiration of plants, the cell division in eggs possess nearly the same * This circumstance may, as Madsen remarks, be of use for the human body. After the toxin has entered the blood, the temperature rises sometimes 2-3 degrees fever temperature and the poison is destroyed about 10 times more rapidly than without the fever-heat. 10 130 THEORIES OF SOLUTIONS. value of A (between 6,000 and 8,000) corresponding to an increase in the proportion of about 1 to 2 for a rise of temperature of 10 C. Regarding these enzymatic and life-processes the literature is collected in Immunochemistry by S. Arrhenius. LECTURE VIII. CONDUCTIVITY OF SOLUTIONS OF STRONG ELECTROLYTES. As we have seen above, Kirchhoff as early as 1858 applied thermodynamics to equilibria in solutions. From the change of solubility with temperature he calculated the heat evolved at solution according to the equation of Clapeyron. Thus he found for one gram of ammonia gas at 20 214 cal. and for one gram of sulphur dioxide at 20 97.7 cal., using Bunsen's figures for the solubility of these gases. These calcu- lated heats do not agree very well with those deter- mined calorimetrically by Julius Thomsen, namely 494 cal. for 1 g. NH 3 and 120 cal. for 1 g. S0 2 . Kirchhoff demonstrated that analogous considerations of the vapor tension of salt solutions lead to determination of the heat of solution of the salt and the heat of dilution of its solutions. Regarding this latter point he showed that the experimental evidence, that at high dilutions of salts a further addition of water has no thermal effect, leads to the conclusion that the relative lowering of the vapor tension of salt solutions does not change with temperature, which rule had been demonstrated experimentally by von Babo. This work was continued by Guldberg in 1870 and by van't Hoff (1885) who introduced his law on the analogy of solution and evaporation. These deductions concern the heterogeneous equilib- 131 132 THEORIES OF SOLUTIONS. rium between a gas or a solid substance in equilibrium with its solution. Much more important are the homo- geneous equilibria. Horstmann had deduced the laws of these for the gaseous state and these are of course according to van't Hoffs law applicable also to di- lute solutions. Berthelot and Pean de S. Gilles had in 1862-1863 investigated the equilibrium between an alcohol, an organic acid and their products of reaction, water and ether. The reaction was allowed to take place either hi a gaseous mixture or in a liquid, to which was in some cases added benzene or acetone. The results of this classical investigation regarding a homogeneous equilib- rium were calculated in 1877 by van't Hoff and in 1879 independently by Guldberg and Waage. They found that for the combination of 1 molecule of ethyl alcohol with n molecules of acetic acid and m molecules of water, the following equation holds good: (m + x)x = 4(1 x)(n x) } where x is the number of alcohol and acid molecules transformed into x molecules of ethyl acetate. This is exactly the form of equation which holds for the gaseous state and according to van't Hoff's law also for the dis- solved state. Another example was the determination of the dissociation of nitrogen peroxide N 2 4 into 2NO 2 . This equilibrium takes place as well in the gaseous as hi the liquid state, in the latter case diluted with some organic solvent, such as chloroform. In such experi- ments of Cundall (1891) the rate of dissociation was determined colorimetrically. The experiments agree very well with the gas laws, as Ostwald proved a little later. CONDUCTIVITY OF STRONG ELECTROLYTES. 133 These applications of the theoretical laws were rather few, until Ostwald in 1888 demonstrated the applica- bility of Guldberg and Waage's law of equilibrium hi the electrolytic dissociation of weak acids, which work was completed some years later by Bredig's work on the weak bases. The experimental material regarding more than 200 weak acids and more than 40 bases was absolutely unrivalled and the evidence of the dissocia- tion theory was generally regarded as indubitable. But on the other hand we remember that Planck had at the same time as Ostwald tried to apply the gas laws to the electrolytic dissociation of salts without success. The same may be said regarding the strong acids and bases. For all these so-called strong elec- trolytes van't Hoff gave an empirical formula, namely: a is the degree of dissociation and v is the volume hi which one gram-molecule of the strong electrolyte is dissolved, K is a constant. Instead of the exponent 2, which is demanded by theory, van't Hoff introduced the exponent 1.5 which accords much better with the experiments in these cases. As there now exists a much greater number of electrolytes belonging to this class, than to that which obeys the gas laws, it has been rightly said that this deviation from the gas laws is really the weak point in the electrolytic dissociation theory. But for just this case by the help of a great number of rather simple empirical rules we are able to calculate the equilibria for these substances with a great degree of accuracy. As these play a very im- portant role in nature, as well in the waters of the 134 THEORIES OF SOLUTIONS. sources, rivers, seas and oceans, as in the humors of the animal bodies or of the plants, I will enter a little closer upon this chapter. The calculation of the dissociated part is performed very simply by taking the quotient of the molecular conductivity of the solution hi question and that of the same electrolyte in infinite dilution, i. e., the limit value to which the molecular conductivity tends with increas- ing dilution. This limit value may be written as the sum of two components, the one valid for the anion and the other for the cation. These values are determined by means of the migration numbers first determined by Hittorf and later unproved by different investigators. They have at 18 the following values (according to Kohlrausch). K 64.6, NH 4 64.2, Na 43.5, Li 33.4, Ag 54.3, Rb 67.5, Cs 68, Tl 66.0, H 315, HBa 55.5, y 2 Mg 46.0, HZn 46.7, J^Pb 61.3, F 46.6, Cl 65.5, Br 67.0, 1 66.5, N0 3 61.7, C10 3 55.0, COOH 45, CH 3 C0 2 33.7, OH 174, HSO* 68.4, SCN 56.6. For organic ions Ostwald and Bredig have given a great number of measurements, which indicate that the conductivity generally decreases with the increasing number of atoms contained in the ion. The conductivity of the different ions depends on the solvent and its temperature. An increase of the tem- perature augments the conductivity, so that that of the less conducting ion increases in a higher propor- tion than that of the better conducting one, i. e., the different conductivities approach each other with in- creasing temperature as is seen from the following figures calculated from the experiments of Noyes and his pupils: CONDUCTIVITY OF STRONG ELECTROLYTES. 135 Ion Temp. 18 100 156 218 281 306 C. K 64.6 206.5 312 412 502 560 Na 43.5 154.5 242 347 467 520 NH* 65.2 207.5 315 428 Ag 52.3 183.5 295 402 501 549 ^Ba 53.4 201.5 325 462 656 784 ^Mg 55.9 177.5 287 427 H 313.5 642.5 772 852 877 864 Cl 65.5 207.5 313 413 503 560 H 2 P0 4 24.5 87.5 158 NO 3 63.5 183.5 275 378 464 516 HSO 58.2 248.5 403 653 958 1165 CH 3 C0 2 34.6 130.5 208 313 413 474 OH 173 339.5 593 713 These figures are very instructive. The ion Ag which at 18 C. has six tunes less conductivity than the H-ion reaches nearly 64 per cent, of the conductivity of H at 306. The acetate ion CH 3 C0 2 has five times smaller conductivity than the ion OH at 18 but reaches about 44 per cent, of it at 218. Also minor differences as between K and Na diminish at higher temperatures as well as the proportion between the conductivities of chlorine or N0 3 and CHsCC^. An exception to this rule is found for the bivalent ions, which probably tend to reach double the value of that for monovalent ions, with increasing temperature. HS0 4 has already reached this value at 306, but the barium ion has at 306 only attained a value about 50 per cent, higher than that of the monovalent ions. A peculiar property is that the dissociation diminishes with increased temperature, which is also true for most weak acids. The non-dissociated part (1 a) follows a rule enunciated by Ostwald, namely that in not too concentrated solutions of equivalent strength it is proportional to the product v&i of the valencies Vi and 136 THEORIES OF SOLUTIONS. v z of the two ions. Noyes gives the following instruc- tive table of (Ia) expressed in per cent.: Type Eq. per Lit. 18 100 156 Obs. Calc. Obs. Calc. Obs. Calc. KC1* 0.04 12 12 15 15 17 17 KC1 0.08 15 14 18 17 21 20 BaCl 2 , KjSOi 0.08 28 28 34 34 40 40 MgS0 4 0.08 55 56 68 68 81 80 Type Eq. per Lit. 218 281> 306 Obs. Calc. Obs. Calc. Obs. < :ak KC1* 0.04 20 20 25 25 31 31 KC1 0.08 25 24 31 32 39 38 Bad,, K,S04 0.08 51 48 65 64 74 76 MgS0 4 0.08 93 96 The exponent in the equilibrium formula, which by van't Hoff has been calculated to 1.5 was according to Noyes' experiments variable between 1.4 and 1.5 with an average value of 1.46. With the aid of this formula of the equilibrium it is possible to calculate the degree of dissociation at any concentration. Noyes also stated a rule found by myself, namely, that the dissociation of each of two salts with a common ion hi a mixture is just as great as the dissociation of each salt itself would be, if the concentration of the common ion were the same as in the mixture (the rule of isohydric solutions). An analogous rule may be used for a mixture of any number of salts. This rule has a higher degree of exactness than those given above. With the aid of these simple rules it is possible to calculate the degree of dissociation for salts in general. Very significant is the rule that the exponent in the equilibrium formula is the same for all salts, inde- pendently of the number of ions into which they decom- pose. * For the strong monovalent acids, HC1 and HNOs, and for the bases, NaOH and Ba(OH) 2 , the quantity (1 a) is only about half as great as for the salts of the same type. CONDUCTIVITY OF STRONG ELECTROLYTES. 137 The conductivity of the ions depends also in a high degree on the solvent medium. Thus for instance the conductivities at 18 in 0, 50, 80 and 100 p. c. solutions of alcohol are the following: Per Cent Alcohol. K Na NH 4 H OH 65.3 44.4 64.2 318 174.9 50 21.8 17.0 95.8 80 18.4 14.0 17.9 50.2 26.1 100 21.5 14.5 20 32.1 16.5 Cl (C,H.),NH, Salicylat. Acetate. CH a CNCOO I 65.9 36.1 32 38.3 36.5 66.7 23.2 12.0 14.0 22.6 17.1 12.2 11.3 12.2 14.0 19.1 23.8 12.6 12.6 12.4 15.0 27.5 Most of these determinations were made by Godlewski, that regarding OH by Hagglund. All the ions, except H and OH, possess a minimum of conductivity at a certain concentration of the alcohol. This minimum is found at different percentages of alcohol; for Cl, I, K and Na at about 85 per cent., for the salicylate ion at about 75 per cent, and for the cyanacetate ion at about 70 per cent. Probably this minimum depends upon the decrease of the fluidity with decreasing strength of the alcohol until it reaches 40 per cent., where the fluidity has its minimum at 18. Evidently the minimum of conductivity does not coincide with that of the fluidity, but there is another factor which has a still greater influence. The figures for H and OH hi pure alcohol are very interesting, their conductivities being of the same order of magnitude as that of other ions. The hydrogen ion has also in alcohol the greatest conductivity, but is not very much superior to iodine and chlorine; one might expect this position of the hydrogen according to 138 THEORIES OF SOLUTIONS. its low atomic weight. The hydroxyl-ion falls far below all the ions consisting of simple atoms and also, curiously enough, below NH 4 . This circumstance, as well as the strong increase in the conductivity of the H- and OH-ion with the addition of small quantities of water, in spite of the increased viscosity, indicates that the exceptionally great conductivity of these two ions hi water is probably due only to the fact that they are the two ions into which water is electrolytically decomposed. According to Godlewski's figures the conductivities of Na, K and Cl in alcoholic solutions containing from to 100 per cent, alcohol are the following at 18 C. : Per Cent. Alcohol. Cl Na Mean. H H Obs. Red. OH Fluidity. Bed. 1 1 1 1 318 318 174.9 1 10 0.766 0.781 0.766 0.771 234.6 307 0.689 20 0.583 0.605 0.559 0.582 188.7 324 0.476 30 0.473 0.516 0.449 0.479 147.7 308 0.381 40 0.401 0.427 0.361 0.396 120.1 303 0.348 60 0.354 0.379 0.334 0.356 95.8 269 0.354 60 0.307 0.339 0.303 0.316 75.9 240 0.375 70 0.275 0.317 0.299 0.297 62.2 209 0.431 80 0.261 0.312 0.282 0.285 50.2 176 91.6 0.510 90 0.261 0.307 0.288 0.285 40.6 143 0.625 100 0.363 0.324 0.329 0.339 32.1 95 48.7 0.831 The conductivity of the three monovalent salt ions sinks at first rapidly, reaches 50 per cent, at about 28 per cent, alcohol, 33.3 at about 56 per cent., then sinks slowly to a minimum of about 28 per cent, at 85 per cent, alco- hol and then rises again to about 34 per cent, at 100 per cent, alcohol. If we correct the values of Godlewski for H tabulated under H obs. by dividing them by the mean values giving the conductivity of monovalent mono- atomic salt ions, we might expect to find a constant value CONDUCTIVITY OF STRONG ELECTROLYTES. 139 if the influence of alcohol were the same on the H-ion as on K, Na and Cl, but, instead of that we get the figures under H red. These last figures remain nearly constant until 40 per cent, of alcohol are added they decrease slowly, but only to the extent of 5 per cent, and thereafter they sink with a mean value of 32 units (10 per cent.) for each step of 10 per cent, of alcohol added until 90 per cent, of alcohol is reached. There- after for the last 10 per cent, of alcohol the decrease is not less than 48 units (15 per cent.). The few figures for OH, treated in the same manner, give a decrease between 80 and 100 per cent, of alcohol, which is nearly in the same proportions as the corresponding decrease for the figures under H red. This observation may be explained in the following manner. The wandering of the ions is hampered by their collision with molecules (of water or alcohol). The ions H and OH behave exceptionally in water because when, for instance, an H-ion hits a water molecule HOH on its OH-side it may unite with the OH and set the H-ion of the water molecule free so that it may continue to carry away positive electricity. It is just as in the Grotthuss' chain, except that it is not necessary that the molecules turn around. If another ion than H or OH hits the water molecule, the effect of an exchange with the H or OH in a water molecule would be the same as a decomposition of the water into H- and OH-ions, which would be accompanied by a rise of the free energy, which is impossible. As the alcohol acts as an entremely weak acid, i. e., may give the ions H and C 2 H 5 0, perhaps the high conductivity of H in alcohol may be partly explained by this circumstance, 140 THEORIES OF SOLUTIONS. but in all cases its superiority over other ions is so small that the ability of the alcohol-molecules to separate into their ions must be regarded as rather insignificant compared with that of the water molecules. For the sake of comparison I have added to the above table the figures of the relative fluidity of alcoholic solu- tions. It has long been maintained that the conduc- tivity is proportional to the fluidity. The change of both with temperature for weak salt solutions is very nearly the same, the fluidity increasing by about 2.4 per cent, per C. at 20, which is very nearly the average temperature coefficient of the conductivity of dilute salt-solutions. Therefore G. Wiedemann, Bouty and F. Kohlrausch were inclined to regard these two temperature coefficients as identical and to maintain that the increase of the conductivity is due to the increase of the fluidity, which was further explained by the supposition that the ions were covered with a layer of water molecules and that this complex moved in the water. The main difficulty with this hypothesis was that the conductivity of acids and of bases increases much less, about 1.6 and 2.0 per cent, per C. from 18 C. on, respectively. The increase in the conduc- tivity is here less than that of the fluidity. The same is valid for the salts. According to Noyes the values of the conductivity and that of the fluidity are at the temperatures 18, 100 and 156 the following, if that at 18 is taken as unity. A at 18 18 100 156 Fluidity (p 1.000 3.717 5.894 HC1 379 1.000 2.243 2.863 NaOH 216.5 1.000 2.743 3.856 Ba(OH) 2 222 1.000 2.905 3815 CONDUCTIVITY OF STRONG ELECTROLYTES. 141 A at 18 18 100 156 KC1 130.1 1.000 3.183 4.805 NaCl 109.0 1.000 3.322 5.092 AgN0 3 115.8 1.000 3.168 4.921 NaCH 3 C0 2 78.1 1.000 3.648 5.761 BaN 2 O 6 116.9 1.000 3.294 5.133 K 2 SO 4 132.8 1.000 3.426 5.388 As is seen from these figures the fluidity increases more rapidly than the molecular conductivity A of extremely attenuated solutions, which are considered here. This behavior seems to be general, as soon as the solvent is not too much changed. The trivalent La-ion forms an exception according to Johnston, the quotient A// increasing from 640 to 675 in the interval, 18 to 156. The same is the case for bivalent ions as J/Ba and ^S0 4 as is seen from the figures by Noyes given above. Also in the table above for small additions of alcohol (not exceeding 40 per cent.), the fluidity de- creases much more than the conductivity of the ions Cl, Na and K. I have proved the same to be valid for small additions of different organic substances to water. The different electrolytes are not influenced in the same degree and therefore I have divided them in four groups: (1) strong acids and bases, (2) salts of two monovalent ions, type KC1, (3) salts of monovalent cations with divalent anions, type K 2 S0 4 , (4) salts of divalent cations with monovalent anions, type BaCl 2 . The experimental results are given in the following table in which (A 1) gives the increase of the viscosity and a the increase of resistance in per mille at 25 on exchange of water to the quantity of 1 volume per cent, of the solution for the following substances, so that the volume remains the same. 142 THEORIES OF SOLUTIONS. Fluidity, lit Group. 2nd Group. 3rd Group. 4th Group Acetone 19 15.6 16.2 19.0 16.7 Methyl alcohol 21 16.2 17.5 19.2 18.0 Ethyl ether 26 16.3 19.9 21.4 20.9 Allyl alcohol 26 18.8 21.2 21.1 Ethyl alcohol 30 18.8 23.4 25.1 23.9 n-Butyl alcohol 30 18.4 22.6 27.9 24.1 Isoamyl alcohol 31 17.2 21.6 27.3 26.7 n-Propyl alcohol ...32 19.5 27.8 27.0 Isobutyl alcohol.... 33 19.5 24.4 28.0 26.5 Glycerol 33 20.5 22.7 26.0 25.0 Isopropyl alcohol... 36 20.3 25.6 27.7 26.9 Dextrose 40 22.9 Galactose 40 23.2 Mannite 43 25.0 Cane sugar 46 24.4 29.9 33.4 30.9 With weak acids or bases and slightly dissociated salts, such as sulphates of divalent metals, etc., the dis- sociation is perceptibly diminished by even very small additions of organic substances. Then it happens that the conductivity changes in a higher degree than the fluidity. Walden, on the other hand, investigated the molecular conductivity of extremely dilute solutions of tetraethyl- ammonium iodide for 26 different solvents and found that it was proportional within 5 per cent, to the fluidity, as is indicated by the following table (valid for 25 C.). ij A AT; Acetone 0.00316 225 0.711 Acetonitrile 0.00346 200 0.692 Acetylchloride 0.00387 172 0.666 Propionitrile 0.00413 165 0.682 Ethyl nitrate 0.00497 138 0.686 Methyl alcohol 0.00580 124 ' 0.719 Nitromethane 0.00619 120 0.743 Methyl rhodanide 0.00719 96 0.690 Ethyl rhodanide 0.00775 84.5 0.655 Acetyl acetone 0.00780 82 0.640 CONDUCTIVITY OF STBONG ELECTROLYTES. 143 Acetic acid anhydride ....... 0.00860 76 0.654 Epichlorhydrine ............ 0.0103 66.8 0.688 Ethyl alcohol .............. 0.0108 60 0.648 Benzonitrile ................ 0.0125 56.5 0.706 Furfurol ................... 0.0149 50 0.745 Diethyl sulphate ............ 0.0160 43 0.688 Dimethyl sulphate .......... 0.0176 43 0.757 Nitrobenzol ................ 0.0182 40 0.728 Benzyl cyanide ............. 0.0193 36 0.695 Asymmetric ethyl sulphite . . .0.0238 26.4 0.628 Ethylcyanacetate .......... 0.0250 28.2 0.705 Salicylaldehyde ............ 0.0281 25 0.703 Fonnamide ................ 0.0321 ca. 25 0.802 Anhydride of citraconic acid .0.0338 22.5 0.760 Anisaldehyde ............... 0.0422 16.5 0.696 (Glycol ..................... 0.1679 ca. 8 1.32) (Water ..................... 0.00891 112.5 1.00) This value is not valid for the monovalent ions Cl, Na and K in ethyl alcohol at 18; the product \ij in this case is only 0.407 instead of 0.648. rj is the vis- cosity, i. e., the inverse value of the fluidity. Hence the limit values of the conductivities of extremely diluted solutions are not in a constant proportion, as has also been stated by Dutoit and Rappeport. In the table regarding the conductivities of ions the propor- tion between this magnitude in alcoholic and in aqueous solution is: for OH 0.094, H 0.101, NH 4 0.312, Ace- tation 0.324, Na 0.324, K 0.329, (C 2 H 5 ) 2 NH 0.352, Cl 0.363, Salicylation 0.394, Cyanacetation 0.411, I 0.412 (Cf. p. 137). It must be remarked that these figures are not in good agreement with those given by Dutoit and Rapp- eport. The discrepancies may serve as a proof of the difficulty of the measurements in non-aqueous solutions. The ions OH and H behave quite excep- tionally, and OH in a higher degree than H which 144 THEORIES OF SOLUTIONS. may perhaps, as stated, be explained as due to a weak electrolytic dissociation of the alcohol molecules into H and C 2 H 5 0. Dutoit and Duperthuis investigated the relation between fluidity and conductivity of Nal in different solvents at different temperatures. They found the following values of the limit value M. at and the values of 17/1. at and at 60, where 77 is the viscosity : Ethyl Propyl Isobutyl Isoamyl Pyri- Ace- Alcohol. Alcohol. Alcohol. Alcohol, dine. tone. p* at 27.95 11.85 5.48 4.49 42.10 12.75 17^ at 0.495 0.453 0.441 0.374 0.573 0.502 Woo at 60 0.457 0.443 0.397 0.269 0.562 0.517 (at 40) In all cases observed, except for acetone, ^ sinks with increasing temperature, which indicates that the conductivity changes less with temperature than the fluidity, just as for water, according to Noyes, and as for small additions of organic substances to water. Schmidt and Jones found 77^ for KI to be (at 18) 0.72 in methyl alcohol, 1.32 in glycol and 2.10 in gly- cerol, which is the order of 17 in the three cases. Con- sequently the viscosity or the fluidity changes in a higher proportion than the conductivity. Quite recently Walden has investigated the conduc- tivity of salt solutions in different organic solvents at rather great intervals of temperature. He found that the conductivity can not be expressed as a linear function of temperature, as is done in most cases. The curve, which gives the conductivity as a function of the temperature as abscissa approaches the abscissa axis asymptotically, when the temperature sinks down towards the absolute zero. The same is true CONDUCTIVITY OF STRONG ELECTROLYTES. 145 also for the fluidity. The extrapolation formula which leads to a value zero as well for the conductivity as for the fluidity at a temperature above absolute zero, and which has for instance been used by Kohlrausch for determining this temperature for aqueous solutions to about 30, fails absolutely at low temperatures. This had also been found for aqueous solutions of H 2 S0 4 , CaCl 2 and NaOH by T. Kunz in 1902. Green and Martin and Masson investigated the conductivity /z tt of HC1, KC1 or LiCl in water with the addition of cane sugar, so that the fluidity (/) changed in about the proportion 1 to 23. They found that a formula /* = &/", where & is a constant, gives good results, n is found to be 0.5 for HC1 and 0.7 for KC1 or for LiCl. In other words the conductivity changes much more slowly than the fluidity, especially for the acid, which agrees wholly with the behavior of aqueous solutions, when the fluidity changes with temperature. Similar experiments have been made by Pissarshewski and Schapowalenko on solutions of KAgC 2 N 2 and KBr in methyl or ethyl alcohol, mixed with different quantities of glycerol. The /*, increases at 25 about in the proportion of 1:400 and 1:200 respectively if the solvent changes from pure glycerol to pure methyl and ethyl alcohol respectively, whereas w^ instead of being constant simultaneously decreases in the pro- portion 3.5:1 and 3.7:1 respectively. This corresponds to a value of n about 0.8 and 0.75. At 45 the value of n increases by about 0.05. A similar rule seems to hold also for fused electro- lytes according to Goodwin and Mailey. They examined nitrates of lithium, sodium, potassium, and silver 11 146 THEORIES OF SOLUTIONS. at temperatures up to 500. The conductivity is not strictly proportional to the temperature, but increases less and less rapidly as the temperature rises. The product rj\ at different temperatures is nearly constant for KN0 3 , K 2 Cr 2 7 and mixtures of KC1 and NaCl, but decreases (just as for aqueous solutions) with rising temperature by 10 per cent, for LiN0 3 between 250 and 300, by 4.2 per cent, for AgN0 3 between 250 and 350 and by 6.4 per cent, for NaN0 3 between 350 and 450. The conductivities of fused salts have also been measured by Arndt and Gessler, from whom the follow- ing table with some slight extrapolations indicated by brackets is reproduced. The conductivity is given in reciprocal ohms per cm. length and cm. 2 cross-section. TempC 500 600 700 800 900 1000 1100 CaCl 2 1.90 2.32 2.66 (2.86) KC1 2.19 2.40 2.61 KBr (1.55) 1.75 1.95 (2.15) KI 1.39 1.64 Nal 2.56 2.70 2.83 (2.97) AgCl 4.20 4.48 4.76 4.98 5.14 AgBr 3.02 3.18 3.34 3.50 3.68 Agl (2.40) 2.52 2.64 2.72 NaPOs 0.30 0.55 0.80 1.05 1.30 1.54 B 2 O S 7.10-e 21.10-' 46.1Q- NaCl 3.34 3.66 (3.98) SrCl 2 1.98 2.29 2.57 The conductivity increases very regularly and rather slowly with temperature except for B 2 O 3 , the dissocia- tion of which evidently increases very rapidly with temperature. The conductivity of KC1 or NaCl is very nearly proportional to the absolute temperature, that of KI and KBr increases a little more rapidly, still more that of NaP0 3 , CaCl 2 and SrCl 2 , that of Nal CONDUCTIVITY OF STRONG ELECTROLYTES. 147 and the silver salts more slowly. The conductivity of mixtures of equal quantities of CaCl 2 and SrCk is very nearly equal to the mean value of the conduc- tivities of the two components. For mixtures of KC1 and NaCl the conductivity was a little less (1.5 to 3 per cent.) than calculated according to the said rule. For mixtures of NaP0 3 (x per cent.) and B 2 3 the following values were observed at 900 (d is density, c concentration in gram equivalents per liter, A equiva- lent conductivity, t\ viscosity): X 0.5 1 5 10 25 50 100 d 1.520 1.522 1.552 1.585 1. 655 1.820 2.115 2.144 c 0.075 0.15 0.78 1. 62 4.46 10.35 21.0 A 0.67 1.55 16.4 49.5 7;A 74.3 73.3 73.8 74.3 The product TjA is very nearly constant. From this result the authors conclude that probably the NaP0 3 is nearly totally dissociated into its ions. Goodwin and Kalmus also found TjA for fused PbCl 2 , PbBr 2 and K 2 Cr 2 O 7 , nearly independent of temperature and thence concluded that fused salts are subject to a high degree of electrolytic dissociation. The concentration and equivalent conductivity at 900 of some salts is given below: Salt KC1 NaCl CaCl, SrCl a BaCl a c 19.7 25.3 36.2 34.0 30.5 A 123.5 144.5 64.1 58.2 56.1 The molecular conductivity, which for CaCl 2 , SrCk and BaCl 2 is 2A, is of the same order of magnitude for the five fused salts. A great number of investigators have found that in some cases solutions behave so "abnormally" that the molecular conductivity instead of increasing de- 148 THEORIES OF SOLUTIONS. creases with dilution. For aqueous solutions this ir- regularity has been observed with highly diluted solu- tions of strong acids and bases and is explained as due to the presence of traces of impurities, especially carbonic acid, hi the distilled water, used for the dilu- tion. A similar explanation seems impossible in most of the other cases observed with solvents other than water and they were therefore sometimes considered as a proof of the insufficiency of the theory of electro- lytic dissociation. A clew to the understanding of these " abnormities " was found by Steele, Mclntosh and Archibald, who investigated the conductivities of solutions of organic substances such as ethyl ether and acetone, hi HC1, HBr and HI. They made it probable, that some molecules, two or three, of the dissolved substance combine with one molecule of the solvent to form a salt-like conducting compound. According to the law of chemical equilibria the number of con- ducting molecules d minishes with increasing dilution. Hence the increased dissociation of the conducting molecules with increasing dilution may be more than compensated by their increasing decomposition. The said authors also applied this idea to similar cases observed before by other investigators. Similar observations were made by I. Wallace Walker and F. Godschall Johnson on solutions of KC1, KI and KCN in acetamide. They also observed the migration of the ions 'n these cases and found that combinations of the salts and the solvent occurred. Some very instructive similar observations have been made by Foote and Martin. They found the following values of the molecular conductivity /z at 282 C. for solutions of 1 gram-molecule in V liters of HgCl 2 : CONDUCTIVITY OF STRONG ELECTROLYTES. 149 V= 2 5 15 20 30 MforCsCl 70 51 48.5 44 AiforKCl 81 62 45.7 43.4 38.5 H for NHiCl 64.5 46.5 M forNaCl 61.5 43.8 31.3 28.0 /iforCuCl 70 42 26 24 CuCl 2 is soluble but does not increase the conductivity of the solvent. Determinations of the freezing point of the solutions indicated that the depression was normal. It was therefore necessary to suppose that molecules of, e. g. t the composition HgCl 2 . NaaCk were formed which dis- sociate into the ions Na and NaHgCL The presence of similar double salts and complex ions in solutions have been ascertained in many different ways, as for instance the solubility of HgCl 2 or HgI 2 hi solutions of KC1 or KI, the freezing point of such complex solutions, the diminution of the catalytic influence of KI on H 2 O2 on addition of HgI 2 , the distribution of HgI 2 between a solution of KI in water and benzene. They are very well known in crystalline form. This is a good example of the applicability of the hypothesis of Steele, Mcln- tosh and Archibald. Another series of interesting measurements of ab- normal dissociation has been given by Walden and Centnerszwer for solutions of potassium iodide in sulphur diox de. They found: y= 0.5 1 2 4 8 16 32 M =38.2 42.9 44.9 42.0 35.6 37.0 41.3 7 = 64 128 256 512 1,024 2,048 M=48.3 57.5 70.4 86.7 105.5 126.0 At first M increases in the normal manner, then de- creases until a minimum 35.6 is reached at V = 8 and thereafter increases very rapidly again. 150 THEORIES OF SOLUTIONS. This field was in a high degree elucidated by Franklin and his pupils. They investigated solutions of a great number of salts in ammonia and organic amines. As an example I give the figures for the solution in NH 3 of ammoniacal zinc nitrate ZnN 2 6 + 4NH 3 at 33.5. 7= 0.999 1.539 1.961 2.520 3.051 3.891 7.717 M=98.8 103.6 102.0 99.48 97.34 93.42 86.52 7 = 15.25 30.10 59.46 117.6 182.2 358.0 707.2 M =86.30 94.78 105.8 124.3 136.0 160.8 191.0 Similar cases, with first a maximum, thereafter a minimum and then a normal increase is found for solutions of copper nitrate, potassium mercuricyanide and potassium amide in ammonia and silver nitrate in methylamine. In other cases (e. g., AgN0 3 , LiN0 3 , NH 4 N0 3 or KI in NH 3 ) the first maximum disappears and is replaced by an inflexion point and thereafter an interval of nearly constant values of /*. In still other cases, e. g., trimethylsulfonium iodide, metamethoxy- benzenesulfonamide, orthonitrophenol, trinitraniline, the behavior was just the same as the normal one in aqueous solutions. The first increase at low values is due to a rapid increase in the flu dity on addition of ammonia, the maximum with the following decrease is due to forma- tion of molecular complexes. It is noteworthy that this maximum is most obvious just for solutions of salts of heavy metals, which as early as 1859 were found by Hittorf to contain complex ions, especially in organic solvents (ethyl and amyl alcohol). They are also known to give complex salts with ammonia. After the minimum, the quantity of ammonia is so great that its concentration may be regarded as nearly constant; CONDUCTIVITY OF STRONG ELECTROLYTES. 151 then the concentration of the conducting compound of ammonia and salt is nearly proportional to the quantity of salt and the conductivity increases in a regular manner. Two different compounds occur in these cases, one containing a less percentage of ammonia and a better conductor (in high concentrations of the salt), and one combined with a greater quantity of NH 3 and a poorer conductor (at greater dilutions). The abnormality with the minimum may then simply be due to the greater friction of the more voluminous 4ons rich in NH 3 as compared with that of the ions com- bined with smaller quantities of ammonia, just as the friction of organic ions increases with their complexity. A Russian chemist A. Ssacharow investigated solu- tions of NH 4 I, Lil, AgN0 3 and two bromides of amides in aniline, mono- and dimethylaniline and observed some cases in which /* decreased with increasing dilu- tion. Evidently these solutions are very nearly related to those observed by Franklin. After the interesting and wide-reaching investigations of Franklin similar older observations of Kahlenberg and Ruhoff regarding the abnormal conductivity of solutions of silver nitrate in amylamine are easily understood. The assertion made by these authors, that these abnormal conductivities are incompatible with the dissociation theory, is therefore eliminated. Even in fused electrolytes complex salts are formed, which must be taken into account hi calculations re- garding their conductivities. Thus R. Lorenz in experi- ments regarding the migration of ions found that in molten mixtures of PbCl 2 and KC1 there exist com- pounds 2PbCl 2 . KC1, PbCl 2 . 2KC1 and PbCl 2 . 4KC1. 152 THEORIES OF SOLUTIONS. One of the most experienced investigators regarding non-aqueous solutions, the Italian chemist Carrara, comes to the final conclusion that the same laws are valid for these solutions as for the aqueous ones and that the conclusions of the dissociation theory are applicable and can explain all seeming discrepancies hi the one case as well as in the other. Another of the most experienced men hi this field, Walden, has expressed the same opinion in nearly identical words. LECTURE IX. EQUILIBRIA IN SOLUTIONS. THE simplest chemical equilibrium is that between a gas and its solution hi a fluid, which is expressed by Henry's law, discovered hi 1803. This law states that at a given temperature the concentration of the ab- sorbed gas hi the fluid phase stands in a constant proportion to that of the gas in the gaseous phase. For highly soluble gases as NH 3 or C0 2 the law is not exact. A similar law was enunciated by M. Berthelot and Jungfleisch for the partition of a dissolved substance between two liquid phases for instance iodine between bisulphide of carbon and water for which they found (at 18 C.) Gram I in 100 c.c. water per cent. 0.041 0.032 0.016 0.010 0.009 Gram I in 100 c.c. CSa per cent. 17.4 12.9 6.6 4.1 0.76 Ratio 1:424 1:403 1:412 1:410 1:400 If the iodine is present hi so great quantity that it is not wholly soluble in the two fluids, concentrated solu- tions are formed and the ratio is equal to the quotient between the solubility of iodine in water and that in bisulphide of carbon. This remark was made by Ber- thelot. Through experiments regarding the freezing point of solutions it has been proved that a substance, dissolved in two different solvents, generally possesses different molecular weights in the two cases. In such circum- 153 154 THEORIES OF SOLUTIONS. stances the simple law of Berthelot and Jungfleisch does not hold. Nernst improved it by attaching the con- dition that the law is true for only the same kind of molecules. If for instance benzoic acid in water con- sists (chiefly) of simple molecules C 6 H 6 COOH and in benzene (chiefly) of double molecules (C 6 H 5 COOH) 2 , then the chemical equilibrium prevails: 2C 6 H 5 COOH (in water) ; (C 6 H 5 COOH) 2 (in benzene) and the law of Guldberg and Waage demands: (concentration in water) 2 = constant (concentration in benzene). This also agrees well with experience as indicated by the following figures (valid at 20). Cone, in water d 0.097 0.1500 0.1952 0.289 (g. in 100 c.c.). Cone, in benzene Cj = 1.05 2.42 4.12 9.7 Constant =C2:cx =110 108 108 116 For more dilute solutions the number of electrolytically dissociated molecules in the aqueous solution and of simple molecules in the benzene solution increases, and the equilibrium cannot be calculated in the simple manner given above, but a closer analysis is necessary. The equilibrium is also disturbed by the circumstance that a small quantity of water is soluble in the benzene and vice versa, and this quantity depends on the con- centration. The said law has been of great use in determining the partial pressure of a dissolved substance in a solvent, which itself possesses a perceptible vapor pressure, for instance of water in ethyl ether, further for determining equilibria, for instance between NH 3 and NH 4 OH in aqueous solution. If namely this is shaken with chloroform, the NH 3 molecules are divided EQUILIBRIA IN SOLUTIONS. 155 between the water and the chloroform, but the NH 4 OH molecules occur only in the aqueous solution. Moore used some figures of Dawson and MacCrae in which the concentrations were the following, c concentration of ammonia in the aqueous phase, Ci concentration in the chloroform phase, x concentration of NH 3 in3he aqueous phase, y concentration of NH 4 OH in the aqueous phase, the concentration of the ions is so small that it might be omitted. The temperature is written under t. t 10 c 0.3917 0.01352 x 0.213 15.8 0.178 0.836 20 0.3917 0.01588 0.251 15.5 0.141 0.560 30 0.3917 0.01846 0.285 15.4 0.106 0.372 The ratio y : x is here constant at a given temperature and the determination of x is therefore not possible simply by changing c. Therefore experiments at dif- ferent temperatures were necessary. According to the law of van't Hoff regarding the change of equilibrium with temperature it is possible to determine the change of the ratio of y/x with temperature, if we know the heat evolved on the addition of NH 3 to H 2 so that NH 4 OH is formed. Moore made it probable that x : d does not change with temperature which is found to be true in this and similar cases, i. e., that no perceptible heat is evolved, when in the experiment NH 3 passes from an aqueous solution to a chloroform solution. This gives a means of determining the ratio y : x. (Moore started from a little different premises and therefore did not find x : Ci absolutely constant.) As is seen from the table above the ratio y : x decreases rapidly corresponding to a heat of hydration of am- monia equal to 7,190 calories. The dissociation con- 156 THEORIES OF SOLUTIONS. stant was found to be about k = 5.10- 5 at 20 in the equilibrium equation ky = 2 2 , where z is the concentra- tion of the ions NH 4 and OH. This constant k is evidently (1 + fe) : fcz times greater than that found if instead of the concentration y of NH 4 OH, as is gener- ally done, is put the concentration x + y of NH 3 and NH 4 OH together. The law of partition also enables us to determine the molecular weight of substances hi solid solution. For instance thiophene is soluble hi solid and in liquid benzene and the partition coefficient is independent of the concentration, from which we conclude that its molecular weight is the same hi both cases. Other experiments have been carried out with partition of ethyl ether between water and solid naphthalene and it was found that the molecules of ether in naphthalene correspond to double the magnitude of that given by the chemical formula. Another instance of the use of the partition law is found in studying the distribution of substances be- tween cells, e. g., bacteria or blood-corpuscles and the surrounding solutions. In this manner I have found that ammonia or acetic acid or saponine possess the same molecular weight in water and hi red blood- corpuscles. We can not decide if the said reagents are united with some substance in the blood-corpuscles but we know that in every molecule of the compound just as much of the reagent is present as in one molecule of it in the surrounding solution. That they are bound to some substance in the blood corpuscle is to a certain degree probable because their concentration in it is between a hundred and a thousand times greater than in EQUILIBRIA IN SOLUTIONS. 157 the liquid in which it is suspended. The same is true for the absorption of so-called agglutinins in just those bac- teria which are sensitive to them and of so-called im- mune-bodies in red blood-corpuscles. In these two cases a high degree of specificity prevails so that only a certain agglutinin is in a higher degree absorbed by a given bacterium, e. g., coli-agglutinin by Bacterium coli, cholera-agglutinin by cholera-vibrions and a certain kind of red blood-corpuscles takes up a given immune- body, namely corpuscles from that species of animals, by the injection of whose corpuscles in the veins of another animal the immune-body in question has been produced. This specificity can scarcely be understood without supposing a chemical reaction of the cell-content with the reagent. In this case the compounds formed con- tain only two thirds as much of the reagent, as a mole- cule of it in the surrounding fluid. It was urged by the school of colloid chemists, that the equation of equilibrium in this case: A = K . C - 67 , where A is the concentration of the absorbed substance, C its concentration in the surrounding fluid, indicates that an adsorption phenomenon prevails here. This might be true for a small variation of C, but in the present case the equation holds for so great variations of C as in the proportion 1 to 300 or more of which there is no example in the adsorption phenomena, except perhaps at very small concentrations, where proportionality rules between A and C. The most important of all equilibria between dis- solved substances is that proved for weak acids by 158 THEORIES OF SOLUTIONS. Ostwald. The law of mass action does not only hold for weak monobasic acids as acetic acid, but as well for weak di- or poly-basic acids, such as tartaric acid or citric acid. These acids are so weaK that only one of the hydrogen ions is dissociated off from each molecule, or at least the molecules from which two hydrogen ions are dissociated away are so small in number that they may be wholly neglected. But still there were some among the weak acids, such as the amidobenzoic acids, picolic acid, etc., for which the so-called dissociation constant in the equation of equilibrium is not constant but changes rather rapidly with dilution. Ostwald himself supposed that perhaps the explanation ought to be sought for in the circum- stance that these acids may also act as weak bases, so that a salt-like compound might be formed from the two molecules of the acid. Such substances which may act as acids towards bases or as bases towards acids, are called amphoteric electrolytes. The simplest of them is water, which dissociates into the hydrogen ion characteristic for acids and the hydroxyl ion characteristic for bases. Most of these substances are amido acids, in which one hydrogen atom of an acid is replaced by the group NH 2 or a pyridine residue or something similar. Also some hydrates of metals are amphoteric, e. g., those of lead, aluminium, zinc, chromium, arsenic, beryllium, tin, tellurium, germanium. These last substances have the formula R . O . H, which gives H-ions as well as OH- ions. The amino acids possess the formula NH 2 RCOOH of which a part is united with H 2 to OH . NH 3 - RCOO . H just as a part of NH 3 is bound to H 2 0, EQUILIBRIA IN SOLUTIONS. 159 thereby giving NH 4 OH. The molecule OH . NH 3 - R . COO . H is the amphoteric electrolyte; it may dis- sociate off hydroxyl-ions from its NH 3 side and H-ions from its COO-side. It may even give off both and then be regarded as an "inner salt." Bredig was the first to study these interesting substances and he in- duced his pupil Winkelblech to continue this investiga- tion. They used the conductivity and the hydrolysis of the salts of these electrolytes to determine the dis- sociation constants of the two sides of these molecules. These researches were carried much further by James Walker, who gave the method for rationally calculating the degrees of dissociation and conductivities of these substances. Finally Lunde*n has performed an elab- orate experimental work and written a monograph regarding them. As an instance I reproduce the fol- lowing table regarding meta- and ortho-aminobenzoic acid (at 25). META-AMIKORENZOIC ACID. v. a.106 d.105 fclQScalc. *.10&ob. 64 11.8 159.0 1.12 1.12 128 11.4 77.0 0.87 0.88 256 10.7 36.2 0.81 0.84 512 9.6 16.2 0.88 0.91 1024 8.2 6.8 1.02 1.07 OBTHOAMINOBENZOIC ACID. v. 0.106 d.106 Jfc.lOcalc. UO&obs. 100 21.4 24.7 0.69 0.69 200 17.6 10.1 0.80 0.81 500 12.5 2.8 0.92 0.93 1000 9.2 1.0 0.98 1.02 In these tables a represents the concentration of the H-ions, d that of the molecule in question with the ion OH thrown off (the number of the OH-ions present is determined by the circumstance that the product of 160 THEORIES OF SOLUTIONS. the concentration of the H-ions with that of the OH- ions is constant = k w , e. g., 0.31.10- 14 at 10, 10- 14 at 25, 5.5. 10- 14 at 50), v is the volume in which one gram- molecule is diluted, and k is the apparent dissociation constant calculated from the conductivity under the supposition that the two acids behave as other acids. The meta-acid was measured by Winkelblech and cal- culated by Walker, the ortho-acid was measured and calculated by Lunde"n. It is obvious from the tables, that the "dissociation constant" k is not constant, but also that this agrees wholly with theory. The dissociation constant is really double, one for the hydrogen-ions, called k a (the sub- stance regarded as an acid) and one for the OH-ions, called k b (the substance regarded as a base). These two constants were: for the meta-acid k a = 1.63.10- 5 and k b 1.23.10- 11 , for the ortho-acid k a = 1.06.10- 5 , k b = 1.37.10- 12 . They are therefore much stronger as acids than as bases. The observed k is rather smaller than the real k a ', the amphoteric character lowers the dissociation of H-ions from the molecule. The meta- acid is stronger than the ortho-acid both as an acid and as a base. Rather remarkable is the fact that the concentration of H-ions for the meta-acid is nearly constant between v = 64 and v = 256, this is character- istic especially when k b exceeds very much the value of k w , the ion-product of water at the same temperature. For a value k a = 10- 5 and k b = 1,000& W Walker has calculated that a does not sink more than from 9.99. 1CM to 9.44. 10- 5 between v = 1 and v = 100, whereas d simultaneously sinks from 8,330.10- 5 to 79.10- 5 . If k a = k b the amphoteric electrolyte is neutral, i. e., EQUILIBRIA IN SOLUTIONS. 161 there are just as many H- as OH-ions in the solution. In this case the degree of dissociation is independent of the concentration and may be rather high, e. g. y for k a = 10- 7 the degree of dissociation is 0.667, for k a = 10- 9 only 0.019 (no such substance is yet known). Most amphoteric electrolytes measured are stronger as acids, exceptions are : acetoxim k a = 6.0. 10- 13 and k b = 6.5.10- 13 at 25, k a = 9.9.10- 13 and k b = 19.0.10- 13 at 40 and histidin k a = 2.2.10- 9 and k b = 5.7.10- 9 at 25. The albuminous substances, such as albumine from eggs or blood-serum, globuline, etc., seem also to be more acid than basic substances, they give salts more easily with bases than with acids. The same is the case with their decomposition products leucin, glycin, and alanin, for which k a is about 100 times greater than k b) and still more for tyrosin, leucylglycin, alanylglycin and glycylglycin, which are about 1,000 times stronger as acids than as bases. The peptones and still more casein are very decided acids, on the other hand the prota- mins, investigated by Kossel, are of a basic nature. Robertson has made some interesting applications of the theory of amphoteric electrolytes on albuminous substances. The chief objection, which could be made to the elec- trolytic dissociation theory at first glance, was the follow- ing. If two substances are mixed with each other, they may generally be separated from each other by means of diffusion. In this manner it was for instance possible to prove experimentally that sal-ammonia, NH 4 C1, is in the gaseous state partially decomposed into ammonia NHs and hydrochloric acid, HC1 (v. Pebal). But it had never been observed that the ions, into which a 12 162 THEORIES OF SOLUTIONS. salt is supposed to be decomposed, may be separated through diffusion. This behavior depends on the cir- cumstance that the ions of a salt, e. g., NaCl, are charged with enormous quantities of electricity of opposite sign, Na with positive, Cl with negative electricity to the extent of 96,550 coulombs per gram equivalent. If therefore Na and Cl separated from each other, power- ful electrical attractions between the Na and the Cl atoms would carry them back to each other, as I re- marked in my inaugural dissertation. The two ions therefore move together in equivalent quantities through the fluid, as if no dissociation took place. The diffusion of salts shows a certain parallelism with their conductivity, i. e., with the mobility of their ions as has been especially emphasized by Long and Lenz. This question could not be cleared up, before it was regarded from the point of view of the dissociation theory, which was done by Nernst in his well-known investigation on the mechanism of the diffusion phenomenon. There he proves that the rate of diffusion is equal to the driving osmotic pressure divided by the sum of the frictions of the ions determined by means of experiments on their conductivities. In this manner he calculated the coefficients of dif- fusion and found them in very good agreement with the values determined experimentally. Later on Oholm has worked out this chapter with the best of success. It may be remarked here, when we deal with the physical applications of the dissociation theory, that Nernst, proceeding further along the same lines calcu- lated the electromotive forces, which arise through the unequal diffusion of the ions in so-called concen- EQUILIBRIA IN SOLUTIONS. 163 tration cells, which had been before treated thermo- dynamically by Helmholtz. In this case the powerful charges of electricity, which in a free solution hinder the unequal diffusion of the two ions, are carried away by means of unpolarizable electrodes dipping into the unequally concentrated parts of the solution and connected metallically with each other. The results found by Nernst by means of his kinetic views agree wholly with those arrived at by Helmholtz. Nernst's theory has been unproved by the work of Planck and still more by the recent work of Pleijel, who has solved the problem in its entirety and removed the mathematical difficulties which hindered its complete solution at an earlier stage. The theoretical study of the phenomenon of diffusion has led to a conclusion which seems very paradoxical. If hydrochloric acid diffuses in water, its diffusion con- stant is found to be 2.09 at 12 C., which also agrees very well with the theory of Nernst. If instead of using pure water for the diffusion, I take a solution of sodium chloride, I might expect that the molecules HC1 moved, i. e.j diffused more slowly in that medium than in water because of the increase of the viscosity on addition of Na- Cl. But instead of that an increase of the constant of diffusion is observed. For instance into a cylindrical vessel was poured a layer of 1 cm. height of 1.04 n HC1 and over it was placed pure water to a height of 3 cm. The diffusion constant was found to be 2.09 at 12. In another experiment 0.1 n NaCl was used instead of water, so that at the bottom of the cylin- drical vessel was a 1 cm. high layer 1.04 n in regard to HC1 and 0.1 n in regard to NaCl and over it were placed 3 cm. of 0.1 n NaCl. 164 THEORIES OF SOLUTIONS. The diffusionconstant was now 2.50. According to Nernst's theory I calculated 2.43. In 0.67 n NaCl the constant was still higher 3.51, calculated 3.47. Many analogous experiments with results agreeing with the dissociation theory were performed with nitric and hydrochloric acid, caustic potash and soda. The explanation is that when the H-ions (i. e., the acid) diffuses hi pure water they must drag the (about 5 times) more immobile Cl-ions with them in equivalent number. If now Na-ions are distributed in the same fluid, these ions are carried back in the opposite direction of the diffusing H-ions because of the electric forces which hold back the H-ions and pull on the Cl-ions in the direction of diffusion (upwards hi the experiments). The driving back of the Na-ions partly neutralizes these electric forces, so that therefore the H-ions are not so strongly held back nor the Cl-ions pushed up as in pure water. Therefore the H-ions diffuse more rapidly and that in a so much higher degree as the Na-ions are more numerous relatively to the H-ions. The maximal velocity which the H-ions may reach at 12 is that corresponding to no hindrance from electrical forces and gives a diffusion constant 6.17. With 0.52 n HC1 and 3.43 n NH 4 C1 I reached a value of 4.67 in- stead of theoretically calculated 5.72. It must be borne in mind that at these high concentrations the degree of dissociation of the HC1 is diminished, which is not taken into consideration, and therefore the observed dissociation constant is smaller than the calculated one determined with the supposition that the electrolytic dissociation is complete. This phenomenon is a so-called salt action, which can EQUILIBRIA IN SOLUTIONS. 165 not be explained, if we suppose the molecules of the diffusing acids or bases and the added salts not to be dissociated into electrically charged ions. It is a real proof of the electrolytic dissociation hypothesis. As we have seen above, Guldberg and Waage, hi their theoretical investigation of 1867, supposed that foreign subtances, such as salts, alcohol, etc., exert a certain influence on reactions without actively taking part in them, and they introduced into their formulae different terms to account for this action. It was especially the velocity of reaction which was found to depend on the foreign substances. They found experi- mentally that some of the substances accelerate the reaction (e. g., NH 4 C1 the solution of zinc in HC1); others retard it (e. #., ZnCl 2 in the same reaction). Van Name and Edgar found that KI increases the rate of solution of metals by means of iodine. Through this introduction of new terms the equa- tions of Guldberg and Waage lost their simplicity and the many empirical constants in them allowed the ar- rangement of a good agreement between theory and experience but thereby the correctness of the theory was not subject to a convincing proof. Therefore at a later stage they threw away the many terms and coefficients having reference to the foreign substances and the simple law, which now carries their name, was the excellent result. It is, of course, not exact for higher concentrations or if great quantities of foreign substances are added. But nevertheless it has been proved that the salts exert a certain influence which is sometimes very great especially on the velocity of reaction. This may as 166 THEORIES OF SOLUTIONS. we now know be of rather different kinds and it was therefore quite natural that Guldberg and Waage were not able to disentangle this complicated riddle. The simplest case is the action of a sulphate such as potassium sulphate on sulphuric acid. Then a part of the acid is bound and the acid sulphate is formed. Therefore the catalytic action of the sulphuric acid is diminished by the addition of neutral sulphates. Spohr found that 1 n H^SO* at 25 has a reaction con- stant equal to 21.34 hi inverting cane sugar. On adding 0.5 n K 2 S0 4 the constant decreased to 16.07 (i. e., by 24.7 per cent.), on adding 1 n K 2 S0 4 the constant was only 11.56 (decrease 45.8 p. c.). Quite different is the action on strong monobasic acids. The velocity of inversion by means of 0.25 n HBr was by Spohr found equal to 9.67; an addition of 0.5 n KBr or 1 n KBr increased the constant to 12.18 (26 p. c.) and 15.48 (60.1 p. c.) respectively. This pe- culiar action will be treated in the next lecture (p. 179). The greatest action is exerted on weak acids (e. g., acetic acid) by their salts (e. g., sodium acetate). In this case, if we have 1 gram-molecule of acetic acid with the degree of dissociation a and n gram-molecules of NaCH 3 COO with the degree of dissociation in V liter solution, the following equilibrium holds: - a) V where K is the constant of dissociation (1.8.10- 5 ) for acetic acid at the temperature used (25). a is very small (less than 1 p. c.), rather near unity. 1 a is very nearly constant (as 1). The greater n is, the less is a and the velocity of reaction, which is nearly pro- EQUILIBRIA IN SOLUTIONS 167 portional to a. I found the following values of the velocity of reaction, p, when V = 4: n= 0.05 0.1 0.2 0.5 1 10V observed =0.75 0.122 0.070 0.040 0.019 0.0105 10/> calculated = 0.74 0.129 0.070 0.038 0.017 0.0100 This peculiarity can scarcely be explained without the help of the dissociation theory, which, as is seen from the good agreement between the observed and calculated values, agrees very well with experience. This influence of foreign ions on the degree of dis- sociation also plays an important r61e hi chemical equilibria. Such a one is the equilibrium which takes place on mixing equivalent quantities of two acids and of a base. The stronger acid takes the greater part of the base. According to the theory of Guldberg and Waage the coefficient of partition, the so-called avidity, ought to be proportional to the square root of the relative strengths of the acids, as measured by means of their catalytic action, and Ostwald tried to verify this theorem. But if a strong acid and a weak one compete, the influence of the ions of the salts and of the strong acid diminishes the degree of dissociation of the weak acid in a high degree, whereas the dissocia- tion of the strong acid is nearly undisturbed. The consequence is that the weak acid appears much weaker than according to Guldberg and Waage's theory, which did not consider the dissociation of electrolytes. An exact calculation taught me that the avidity of an acid is not proportional to the square root of its catalytic action, i. e., its degree of dissociation, but very nearly to this action itself, and this theoretical deduction was cor- roborated by previous experiments by Ostwald as the 168 THEORIES OF SOLUTIONS. following table giving the fractions of the bases (NaOH, KOH and NH 3 ) taken by the two acids indicates. Observed. Calculated. Nitric: dichloracetic 0.76 : 0.24 0.69 : 0.31 Hydrochloric: dichloracetic . .0.74 : 0.26 0.69 : 0.31 Trichloracetic: dichloracetic. .0.71 : 0.29 0.69 : 0.31 Dichloracetic: lactic 0.91 : 0.09 0.95 : 0.05 Trichloracetic: monochlora- cetic 0.92 : 0.08 0.91 : 0.09 Trichloracetic: formic 0.97 : 0.03 0.92 : 0.08 Formic: lactic 0.54 : 0.46 0.56 : 0.44 Formic: acetic 0.76 : 0.24 0.75 : 0.25 Formic: butyric 0.80 : 0.20 0.79 : 0.21 Formic: isobutyric 0.79 : 0.21 0.79 : 0.21 Formic: propionic 0.81 : 0.19 0.80 : 0.20 Formic: glycolic 0.44 : 0.56 (?) 0.53 : 0.47 Acetic: butyric 0.53 : 0.47 0.54 : 0.46 Acetic: isobutyric 0.53 : 0.47 0.54 : 0.46 This is one of the best proofs of the usefulness of the dissociation theory, for any theory which does not suppose that the acid molecules are dissociated, gives calculated figures, which are nearly proportional to the square roots of those given above. Water is partly electrolytically dissociated. There- fore it reacts with salts, dissolved in it, and hydrolyzes them partially. For salts of a strong acid or base with a weak base or acid the degree of hydrolysis increases nearly proportionally to the square root of the dilution, as was also shown by Shields and others. For salts of weak acids with weak bases the peculiar fact is deduced theoretically that if the dilution is not extremely great, the degree of hydrolysis remains nearly independent of the dilution. This was also found by Walker for anilinacetate, the hydrolysis of which did not increase more than from 54.6 per cent, to 56.9 per cent., when the volume, in which one gram-molecule of anilinacetate was dissolved, increased from 12.5 to 800 liter. EQUILIBRIA IN SOLUTIONS. 169 Now Hantzsch drew the conclusion from some of his experiments that salts of aliphatic nitrocompounds and of isonitrosoketones behave abnormally in regard to hydrolysis and supposed, that this circumstance was due to a transformation of the reacting acids or bases into then* so-called pseudo-forms. This assertion does not conform to the theory of electrolytic dissociation. A little later also Hantzsch in collaboration with Ley found on closer examination that the isonitrosoketones do not at all disagree in their hydrolytic properties with the dissociation theory. The same was the result of an investigation by Lunde*n regarding the aliphatic nitro-compounds. A certain difficulty for the dissociation theory seemed to arise from an investigation of Wakeman regarding the conductivity of weak acids hi mixtures of alcohol (up to 50 p. c.) and water. These acids acetic, cyanacetic, glycolic, monobromacetic and orthonitro- benzoic obey, in aqueous solution, the law of mass action. Wakeman found that the dissociation con- stant of the same acids in mixtures of alcohol and water decreases with increasing dilution, which would then be in contradiction to the dissociation theory. The same was also found for cyanacetic acid in a mixture of water and acetone. The result of Wakeman seemed corroborated by an investigation by Lincoln on the same subject. But nevertheless their observations seem to have suffered from some grave systematic experimental error. God- lewski made very careful measurements on just the same acids as Wakeman and found that these weak acids follow the demands of the dissociation theory in all 170 THEORIES OF SOLUTIONS. mixtures from pure alcohol to water. He found the following dissociation constants multiplied by 10 5 for the following acids (at 18) : Alcohol, percent.... 10 20 30 4050 60 70 80 90 100 Salicylic acid l&k... 100 95 83 57 3218 11 4.6 1.8 0.57 0.013 Cyanacetic acid 10*& 370 360 210 192 120 76.5 57.3 29.2 10.7 2.5 0.05 Bromacetic acid 10A; 138 131 85 58 3520.510.2 5.7 1.7 0.43 0.015 The dissociation constant at first decreases slowly, when alcohol is added, then more rapidly and when the quantity of water is only 70 to 80 per cent., the dis- sociation constant diminishes quite suddenly on further addition of alcohol. The order of the acids in regard to their strength is not the same in alcoholic as in aqueous solution. The dissociation constants in alcohol are about 10,000 times smaller than in water. The most violent attack on the modern theories or especially on that of van't Hoff is found in a memoir of Kahlenberg. He determined the osmotic pressure of solutions of cane sugar in pyridine, separated from pure pyridine by a membrane of caoutchouc, which is permeable to pyridine but not to cane sugar. He found that his measurements did not at all agree with the gas laws for solutions. These measurements were re- peated by Cohen and Commelin. They found the experiments connected with extremely great difficulties, which had caused very great errors in Kahlenberg's measurements. He was therefore not at all authorized to draw the conclusions, cited above, from them. The theories of the analogy between the gaseous and the diluted state of matter and of the electrolytic dis- sociation have been tried with perfect success in so many cases and found to be of such great use as well EQUILIBRIA IN SOLUTIONS. 171 for the chemical as for the physical and even the biological sciences, that van't HofFs words of 1890 regarding the electrolytic dissociation theory that it had become nearly a fact are still more valid now than 20 years ago. The same is of course true for van't HofPs theory itself which is indissolubly connected with the dissociation theory. LECTURE X. THE ABNORMALITY OF STRONG ELECTROLYTES. THE great difficulty in the application of Guldberg and Waage's law to the equilibria between ions and non-dissociated salts (acids or bases) lies, as has been said above, hi the great deviation of the strong elec- trolytes, which furthermore are of the greatest impor- tance hi nature and the industries. A very great num- ber of attempts have been made to explain this devia- tion, but none of them has to this day been crowned with success, and I therefore give only a short review of them. They may be grouped chiefly under the four following headings: 1. Theories introducing a correction regarding the change of the ionic friction with dilution. 2. Theories introducing a correction for the electric attraction of the charges of the ions. 3. Theories regarding the influence of foreign sub- stances on the osmotic pressure (the so-called salt- action). 4. Theories regarding the binding of water to the ions. As we have seen above, the friction of the ions is, if not precisely proportional to, yet very closely related to the viscosity of the surrounding solution. Now for all aqueous solutions of salts, except those of NH 4 , K, Rb and Cs amongst those examined the viscosity increases with the concentration. If we corrected the 172 ABNORMALITY OF STRONG ELECTROLYTES. 173 conductivity for the viscosity, we would, in the most cases, obtain a by far higher degree of dissociation than that calculated in the usual way and this correction would make the discrepancy still greater than before. The deviation takes place according to an empirical law found by van't Hoff (cf. p. 133), namely, that the dissociation constant in the equation of equilibrium increases nearly proportionally to the square root of the concentration of the ions. After a correction the " constant" would increase still more rapidly with con- centration for very dilute solutions, below 0.1 normal, the correction would be of very small importance. Yet Jahn advocated a theory that the ionic friction increases very markedly with dilution, e. g., by about 13, 10 and 8 per cent, for K, Na and H ions, when they are diluted from 0.0334 normal solution to infinite dilution. With- out further explanation, this hypothesis to which we come back a little later, seems inadmissible. The ions are supposed to move quite freely in the solutions and therefore to exert an osmotic pressure equal to that of an equal number of common molecules, and this hypothesis is in accord with the observations regarding freezing and boiling points of solutions. Now if a positive ion tried to fly out from a solution, e. g., into superposed water it would be held back by the negative charge of the rest of the solution and hence the osmotic pressure would be less than if the ions were wholly free. This diminution of the osmotic pressure would for each ion be the greater the less the distance between the ions, i. e., the greater the concentration was. Now the equation of equilibrium indicates (for salts of two monovalent ions, such as KC1), that 174 THEORIES OF SOLUTIONS. where the osmotic pressure of the ions is indicated by o iy that of the non-dissociated salt with o., and K is the constant of dissociation. Now o i is supposed to be proportional to the concentration c t of the ions, but according to the electrostatic attraction theory it ought to increase more slowly. If it were proportional to c< - 75 , we would find again the rule found by van't Hoff. In reality it increases according to another law and does not fit very well with the experimental determina- tions. The greatest objection to this theory is, that it would demand a decidedly smaller lowering of the freezing point, especially in not too small concen- trations, than that calculated from the determinations of the conductivity. The deviation from the theoretical law is in the opposite direction and increases with con- centration. For small concentrations, e. g., up to 0.2 normal for KC1, 1 have shown that theory agrees with experiment, if the degree of dissociation is calculated as proportional to the molecular conductivity. The said electrostatic theory has been developed by v. Steinwehr, Liebenow, Malmstrom and Kjellin. As early as in 1788 Blagden stated in an excellent in- vestigation that the freezing points of aqueous solutions in general are proportional to the concentration. But in some cases, e. g. y for H 2 S0 4 , K 2 C0 3 , etc., he observed that the lowering of the freezing increases more rapidly than the law of Blagden indicates. In other cases the increase was less than according to the law. The same was found by Riidorff in 1861, and stated by De Coppet in 1871, and afterwards by many others. Where the lowerings were less at high concentrations ABNORMALITY OF STRONG ELECTROLYTES. 175 than according to Blagden's law, this could easily be explained as due to the dissociation which diminishes with increasing concentration. But when the theory of ionization was applied, the more common deviation in opposite direction remained unexplained. Rudorff supposed that the said salts, which give a too great lowering of the freezing point hi concentrated solutions, bound a certain part of the water as water of hydration, e. g., CaCl 2 bound 6H 2 0, so that the whole quantity of water was not used for the dilution. This correction helps only if we consider the concentration as the number of salt-molecules in 100 g. of water or in 100 molecules of water and of salt, and not, as is common, in gram-molecules per liter. The idea of Rudorff was carried out on a large scale by H. C. Jones and his pupils, with due regard to the dissociation. From these determinations it was calculated that hydrates were formed with very many molecules of water, e. g., the chlorides and nitrates of bivalent metals with about 18, the corresponding salts of trivalent metals with 24, glycerol with 12, cane sugar and fructose with 6 molecules of water. Of course the simplest case is that where no dissocia- tion takes place, i. e., with non-electrolytes. These were investigated by Abegg, who found that in many cases these substances give an increasing molecular lowering of the freezing point with increasing concentra- tion; in other cases the deviation from Blagden's law was in the opposite direction. Some very accurate experiments regarding the os- motic pressure of solutions of cane sugar and glucose were performed by Morse and his collaborators and by 176 THEORIES OF SOLUTIONS. Berkeley and Hartley. They were struck by the nearly strict proportionality between osmotic pressure and cpncentration if this was taken according to Raoult's directions, i. e., in gram-molecules dissolved in 100 g. of water. But Sackur showed that this strict propor- tionality occurred only at about 20 C.; at C. it was necessary to suppose a binding of water to the molecules of sugar (as is already seen from Abegg's work). Sackur calculated the osmotic pressure p from the data of observations with the help of a modification: p(v - b) = RT of van der Waals's well-known formula, already used by Noyes. v is the volume and T the absolute temperature of the solution containing 1 gram-molecule, R is the gas-constant (1.985 cal.) and b the so-called co volume. b is just as great as the volume of the dissolved sugar at 23 C. (6 = 0.093 for dextrose and 0.20 for cane sugar) but it is greater at (0.16 and 0.31). He found the following values of 1,000 6 at 0. Methylalkohol Mol. 1,000 6. Weight ..32 50 Glycerol Mol. Weight. 92 1,000 &. 106 Ethylalkohol 46 72 Chloral 1475 125 Acetone . .58 55 Dextrose. . . . .180 160 Acetamide . . 59 58 Fructose 180 210 Ethylformate . . . Methylacetate . . ..74 140 ..74 81 Saccharose . . .342 305 In general 6 increases with the molecular weight and the lowering of temperature. Difficulties arise because sometimes there is found a deviation from van't Hoff s law even in very dilute solutions (e. g. f hi Abegg's figures), and Noyes in some cases found negative values of 6, especially in non-aqueous solutions. ABNORMALITY OF STRONG ELECTROLYTES. 177 The question of the formation of hydrates in solu- tions has been treated in a masterly manner by Wash- burn in a monograph to which I refer for further in- formation. A very interesting phenomenon has been discovered by Svedberg. He investigated the validity of the gas laws for suspensions of gold or mercury (particles of 58.10- 6 and 142.10- 6 mm. diameter respectively) and arrived at the peculiar result that these suspensions in extreme dilutions (3,700.10 6 and 1,500.10 6 particles, respectively, per cubic centimeter) obey the law of Boyle, but that in 10 and 15 times respectively greater concentrations then* osmotic pressures are about 1.5 and 2 times respectively greater than theory demands. Here there is no question of the impossibility of explain- ing these deviations by supposing the formation of hydrates, the quantity of water bound to the few par- ticles of metal would under all circumstances be abso- lutely insignificant. Tammann measured the osmotic pressure of cane sugar solutions to which he had added 0.91 mol. normal solution of copper sulphate. This solution was on the outside of the cell; in its interior was a solu- tion of IQCeNeFe. He found the osmotic pressure of the sugar to be 1.30 to 1.58 times greater than the theoretical value (for solutions containing 0.04 to 0.06 gram-molecule per liter). Hence the osmotic pressure of the cane sugar was increased by an average of 40 per cent, through the presence of the copper sulphate. Experiments on the freezing point of similar solutions and those containing no copper sulphate gave similar results. The same was the case with solutions of isobutyl alcohol in the presence of 13 178 THEORIES OF SOLUTIONS. Other experiments were performed by Abegg, who measured the osmotic pressure by the aid of diffusion with the same results as Tammann. He found that salts (NH4N0 3 and NH 4 C1) diffuse from an aqueous solution which contains a little quantity of alcohol (2 normal) into an aqueous solution equally concentrated in regard to the salts, without alcohol. The presence of the alcohol was therefore found to increase the osmotic pressure of the salt. Evidently this is the same phe- nomenon as that termed salting out of substances from water. Quite recently Rivett has examined this peculiar- ity. He investigated solutions containing salts and cane sugar and found that if the described increase in the lowering of the freezing point is attributed to the increase of the osmotic pressure of the cane sugar this increase is proportional to the product of the quantity of the salt and that of sugar present. The least influence was produced by barium nitrate which hi 0.5 equivalent normal solution increased the osmotic pres- sure of the sugar by only 4 per cent., the greatest by lithium chloride which in 0.5 equivalent normal solu- tion gave an increase of 30.5 per cent. Similar experi- ments were made with ethyl acetate with similar results (changing between 10 per cent, for barium ni- trate and 30 per cent, for sodium chloride hi 0.5 equiva- lent normal solution). Further experiments are necessary for ascertaining if an increase in the osmotic pressure of the salt or of the cane sugar, respectively, or of the ethyl acetate or both (which is probable) has taken place. These experiments remind very much of the influence ABNOKMALITY OF STRONG ELECTROLYTES. 179 of salts on the velocity of reaction of acids acting upon cane sugar or ethyl acetate. This velocity is increased to a high degree, about 30 per cent, on adding a 0.5 equivalent normal chloride or nitrate (for inversion of cane sugar) whereas an addition of methyl or ethyl alcohol or even of a weakly dissociated electrolyte such as acetic acid or chloride of mercury has no, or only a very small, influence. For the action of salt on the saponification of ethyl acetate by means of acids the effect is less, about 12 per cent, for 0.5 n chlorides and only 4 per cent, for 0.5 n nitrates. In saponification by means of bases the action is very small and different in different cases, sometimes negative. The action is proportional to the concentration of the salt. Moreover, the dissociation of weak acids is increased by the addition of neutral salts, which indicates an increase in the osmotic pressure of the non-dissociated part of the acid by the presence of the salt. The solubility of different substances such as gases, e. g. y H 2 , 2 , CO, N 2 , NO, or organic substances, e. g., ethyl acetate and phenylthiocarbamide, hi water is diminished by the addition of salts but not of non- dissociated substances, which may be explained as due to an increase of the osmotic pressure of those sub- stances by the presence of these salts. Washburn has given a review of this action. All these phenomena indicate that the osmotic pres- sure of a substance is in a high degree dependent on the presence of foreign substances especially of salts in the solvent water. Attempts have been made to explain this action through the binding of water to the salts, but the success attained has been very moderate. On the other 180 THEORIES OP SOLUTIONS. hand it is clear that if the ions act so as to increase the osmotic pressure of non-dissociated substances, the dissociation constant of salts may be increased by the presence of its own ions, i. e., by its own concentration, which explanation I proposed in 1899. This hypothesis has been taken up by Partington. He concludes, from the great ionizing influence of free ions hi gases, that there exists a similar influence of free ions in liquids and shows that a formula deduced from the ionization of salts from this idea agrees well with experience. Of course there is no doubt that electrolytes in solu- tion bind water. Jones showed that in solutions con- taining sulphuric acid and water dissolved hi acetic acid, molecules of the composition H 2 S0 4 + H 2 0, H 2 S0 4 + 2H 2 and probably H 2 S0 4 + 3H 2 O, exist, which are yet dissociated hi a high degree. Heydweiller, who investigated the specific weight of different solu- tions of salts hi water, expressed his results by the formula: A. = A.i + .(!- i), where i is the number of ions (hi gram ions) and (1 i) is the number of undissociated molecules hi one gram- molecule. A, is the change of density through the addition of the salt, divided by its concentration. A t is evidently a constant from which the density of the ions and B t one from which the density of the undis- sociated molecules may be calculated. This latter density was found sometimes to agree with that of anhydrous salts not only for salts which do not crystallize with water, e. g., for KN0 3 , KC10 3 , AgN0 3 , but also for salts which bind water strongly such as ABNORMALITY OP STRONG ELECTROLYTES. 181 LiCl, CaI 2 , etc. In other cases it agreed with the density of known hydrates such as Na2S0 4 + 10H 2 0, NaBr + 2H 2 0, CaCl 2 + 6H 2 0, MgCl 2 + 6H 2 0, CuS0 4 + 5H 2 0, BaCl 2 + 2H 2 0, MgS0 4 + 7H 2 0, etc. In some cases the hydrates indicated in this manner seem to contain more water than the solid salt hydrates which are stable at the same temperature, but generally the inverse is true. We may therefore say that the non-dissociated parts of dissolved salts are hydrated to about the same degree as the salt in the solid state at the same tempera- ture (under normal conditions). The constant A, gives the density of the ions. Of course there are always two ions present, one positive and one negative, and A, is therefore of a strictly additive nature. As these "density modules" of the ions are of a high practical value also, I reproduce them here (for equivalent weights) : Positive ion: H NH| Li Na K Rb Cs Ag Density module -1.25-0.94-0.31+1.35 2.16 6.52 10.59 9.70 Positive ion: ^Mg KCa HSr ^Cu HZn ^Cd KBa ^Pb Density module: 1.36 2.04 4.38 4.06 4.67 5.48 6.5310.37 Negative ion: OH CNS C 2 H 8 2 F Cl Br I Density module: 3.37 2.88 3.14 3.08 3.01 6.67 10.31 Negative ion: N0 8 C10 8 I0 8 ^C0 3 HS0 4 ^CrO 4 Density module: 4.56 5.78 16.04 4.92 5.51 6.53 A ty the sum of the two modules of a salt's ions, is always greater than B t , the corresponding quantity of the undissociated salt. Therefore we conclude that ionization is combined with a contraction of volume. This is also well known in other cases. For instance if a base is neutralized with an acid, both in highly diluted solutions, the whole action consists, as has been said above, in a combination of the hydrogen ions of 182 THEORIES OF SOLUTIONS. the acid with the hydroxyl ions of the base. The accompanying expansion Av is dependent on tempera- ture t in a rather complicated manner as is indicated by the table t 10 20 30 100 110 120 130 140 C. Ay 20.9 20.1 19.2 18.7 18.7 20.0 22.5 25.4 25.7 c.c. The peculiar behavior that a minimum occurs between 30 and 100 depends upon the occurrence at low temperature in the water of so-called ice mole- cules together with the real water-molecules. The ice- molecules have a greater volume than the water mole- cules, therefore the volume of neutralization is greater at than at 30. Otherwise the neutralization volume Av would without a doubt increase continually with increasing temperature. These figures are found for the neutralization of NaOH with HC1. Ostwald investigated the neutralization of different strong acids with KOH and NaOH and found the following neutralization volumes: Acid HN0 3 HC1 HBr HL AyforKOE 20.0 19.5 19.6 19.8 average 19.7 Ay for NaOH 19.8 19.2 19.3 19.5 " 19.5 There is still a little difference between the figure for KOH and NaOH. If it is real or depends upon experi- mental errors is difficult to decide. In the neutralization of weak acids Ostwald found a much lower Aw. This depends upon the almost wholly undissociated state of these acids. The expan- sion on neutralization is here equal to the difference between the expansion due to the combination of the two ions OH and H to form water and that, which oc- curs when the weak acid is formed from its ions. ABNORMALITY OF STRONG ELECTROLYTES. 183 Now this latter may be determined from the change of the electrolytic dissociation with change of pressure. Fan jung therefore determined the conductivity of weak acids under high pressures, up to 500 atm., and therefrom calculated the volume of dissociation of these acids, and by subtracting that from the neutrali- zation volume of strong acids with KOH or NaOH he calculated the neutralization volume of the weak acids and compared his results with those found directly by Ostwald. His results are reproduced below: SubiUnce. Volume of Neutralization. Obs. (Ostwald). Calc. (Fanjung). Formic acid 7.7 c.c. 8.7 Acetic acid 10.5 10.6 Propionic acid 12.2 12.4 Butyric acid 13.1 13.4 Isobutyric acid 13.8 13.3 Lactic acid 11.8 12.1 Succinic acid 11.8 11.2 Maleic acid 11.4 10.3 The agreement is as good as might be expected con- sidering the difficulty of the experiments. Ostwald also determined the neutralization volume of ammonia with strong acids and found it to be 26 c.c. at 15 C. This observation indicates that in the electrolytic dissociation of ammonia an expansion of 6.4 c.c occurs, which seems at first not to be in accord with the general fact that dissociation is followed by contraction. But we remember that at 15 C. am- monia consists of 59.4 per cent, of NH 3 and 40.6 per cent, of NH 4 OH (cf r. page 155) . The dissociation process may here be regarded as consisting of two combined proc- esses, the formation of NH 4 OH from the 59.4 per cent. NH 3 and a corresponding quantity of water and then 184 THEORIES OP SOLUTIONS. the dissociation of NH 4 OH into NH 4 and OH. This latter process may be accompanied by a contraction if the first process causes an expansion of more than 6.4 c.c. It seems peculiar that dissociation is accompanied by contraction, although such examples are known the simplest is perhaps that ice has a greater volume, but probably more complex molecules, than liquid water, or that a contraction occurs on mixing ethyl al- cohol and water. Drude and Nernst gave the follow- ing explanation. The free energy of a charged par- ticle, such as an ion, is the less the greater the constant of dielectricity in its surroundings. The dielectric constant of water is very high and increases with its compression. Now the free energy tends to a mini- mum, therefore the water has a tendency to contract in the neighborhood of the ions. This contraction is sometimes so great that the volume of the solution is less than that of the water contained in it. Such a contraction on ionization has also been observed by Carrara and Levi on dissolving electrolytes in methyl or ethyl alcohol or urethane, and by Walden on dis- solving iodide of tetraethylammonium in different solvents. In this latter case it was always nearly the same, namely 13 c.c. Another explanation of this fact has been given, namely that the ions may bind water and this binding might well cause a strong contraction. This idea that the ions bind water might be elucidated by studying the relative conductivity of the ions and especially if the ions carry water with them in electrolytic experi- ments. Kohlrausch had through the close coincidence of the temperature variation of fluidity and electric ABNORMALITY OF STRONG ELECTROLYTES. 185 conductivity of salt solutions been led to the hypothesis that the ions are surrounded by an "aqueous atmos- phere." The idea was developed by Bousfield who applied Stokes' law to the mobility of ions in their solutions. The friction of a little sphere against the surrounding medium is proportional to the viscosity of that medium and the radius of the moving sphere. Now the atomic volume of Li, Na, K, Rb and Cs increases from the first to the last. We might there- fore suppose that Li should move more easily than Na and that more easily than K in a very dilute solution, the viscosity of which may be considered equal to that of water. In reality this is the order of the rate of diffusion of these metals (9.5 for Li, 7.3 for Na, 4.9 for K, 4.7 for Rb and 4.6 for Cs) in mercury, but the order of the mobility of the corresponding ions in aqueous solutions is the inverse, which peculiar circum- stance has ever attracted attention as being difficult to understand. Bousfield calculated the radii of dif- ferent ions, which according to Stokes' law ought to be characteristic of them hi order that they should possess the conductivity really observed. I give below a reproduction of Bousfield's table, in which Ii 8 is the conductivity of the ion in question at 18 C. and r its radius at three different temperatures, namely 2, + 18 and + 38 C., that of the hydrogen ion at 18 C. taken as unity, a is the temperature coefficient of I at 18. For a comparison I have introduced into the table under the headings l k and t 10 8 the values of the conductibilities of the ions and their temperature co- efficients multiplied by 10 4 at 18 according to Kohlrausch (Praktiscne Physik., llth ed., 1910). 186 THEORIES OF SOLUTIONS. Kohlrausch has given some other figures regarding these magnitudes, which I also give here because of their great usefulness. They are: Ion. Ik Cs Tl %Ca 68 66 51 H ;cd > 16 Ra 58 Br I 67 5CN 56.6 BrO 8 46 a t .104 212 215 247 2. 15 5 539 \ 215 2 21 Ion. IO 4 C1O 4 ( :no a CH 5 Oj I /^OrO *4 / ^C,0 4 Ik . . . 48 64 47 31 72 63 at.10* 231 r Ion. fo a. 10*. at 2. at + 18. at + 38. Ik' ' ifc.10*. H 318 154 0.801 1.000 1.196 315 154 OH 174 179 1.541 1.828 2.078 174 180 NO 3 61.8 203 4.57 5.145 5.59 61.7 205 I 66.4 206 4.28 4.79 5.17 66.5 213 CIO, 57 207 4.99 5.58 6.01 55 215 Cl 65.4 215 4.41 4.86 5.16 65.5 216 Rb 67.9 217 4.29 4.68 4.96 67.5 214 K 74.6 220 4.53 4.91 5.17 64.6 217 NH4 63.7 223 4.64 4.99 5.23 64 222 J^SO 4 . . . . 69 226 4.31 4.61 4.80 68.4 227 Ag 54.7 231 5.50 5.81 6.00 54.3 229 }/ Sr 53 231 5.68 6.00 6.19 51.7 247 F ... . 45.5 232 6.63 6.99 7.20 46.6 238 I0 3 33.9 233 8.91 9.38 9.65 33.9 234 CaHsOz 34 236 8.95 9.35 9.58 35 238 HBa 57 239 5.38 5.58 5.68 55.5 239 Yz Cu 49 240 6.27 6.49 6.60 46 Yz Pb 61.5 244 5.05 5.17 5.22 61 240 Na 43.5 245 7.15 7.31 7.37 43.5 244 YL Mg 46.0 255 6.93 6.91 6.84 45 256 i^Zn 46 256 7.00 6.91 6.82 46 254 Li.. . 33.4 261 9.68 9.52 9.33 33.4 265 HCO 3 70 269 4.72 4.54 4.39 The temperature coefficient of the fluidity of water at 18 is 251. 10- 4 , therefore r increases with temperature for those ions which have a smaller a, decreases for ions with a>251.10- 4 . The table is therefore arranged according to the magnitude of a. A great difficulty at first arises in supposing that the radii of the ions ABNORMALITY OF STRONG ELECTROLYTES. 187 increase with temperature in such a high degree as indicated above (the cubic temperature coefficient of expansion of fluids seldom reaches 0.001 and the linear coefficient of expansion is only a third of that magni- tude) . It is therefore, according to Bousfield's hypothe- sis, necessary to suppose that the ions bind more and more water the higher the temperature rises. As an example we cite the estimate of Bousfield that one molecule of NaOH at attaches 19.9, at 20 22 and at 40 25.7 molecules of H 2 0. This conclusion does not at all agree with our experience regarding the hydration of solid salts, which always decreases with rising temperature,* nor is it in accordance with the electrostriction theory for the dielectric constant of water decreases rapidly with increasing temperature. The Li-ion with its aqueous envelope ought to be eight times as great as that of the Rb-ion or the Cs-ion (/is = 68) ; it ought then to bind a very great number of water molecules. The K-ion, which seldom enters into solid salts with crystal water, ought to bind a rather great number of water molecules in order that the com- plex should get a greater radius than the Rb- or Cs-ion. (The atomic volume of these metals hi the solid state is for Li 13.1, for Na 23.7, for K 45.5, for Rb 56, and for Cs 71 cubic centimeters.) In the same manner the F-ion has a greater volume than the Cl-ion and this exceeds the I-ion. Otherwise the ions possess in general the less mobility the more composite they are, as Ostwald at first showed for ions of organic acids, and Bredig for the corresponding ions of bases. * An exception from this law has been related by Koppel for sulphate of cerium (Zeitschrift fur anorganische Chemie, 41, 377 (1904)). It is well worth a reinvestigation. 188 THEORIES OF SOLUTIONS. The work of Bousfield leaves us in ignorance of the precise quantity of water which is attached to each ion, it only indicates that it ought to be very great. This want has been removed by the more recent work of Buchboeck, Washburn and Riesenf eld and Reinhold. It is possible to decide if water is dragged with the ions if they wander in a non-aqueous medium which is diluted by addition of water. The main parts of the liquid are not altered but in the neighborhood of the electrodes the transported water is deposited and may be determined according to the method of Hittorf. Nernst, Garrard and Oppermann were the first to use this method. They dissolved boric acid in the solutions to be examined, and determined if the concentration of the boric acid changed during the passage of the current. The analytical method used was not exact enough to allow evident conclusions. The same was the case with some later investigators in this field until Buchboeck took up the problem. He used mannite and resorcine as indicators. He electrolyzed hydro- chloric acid, which after the experiment was removed from a sample of a given volume by means of silver carbonate and consequent treatment with sulphureted hydrogen to remove traces of silver, after which the mannite or resorcine present was determined by evapo- rating and weighing. Washburn used arsenious acid, raffinose or saccharose as indicators and determined the concentration of these latter simply by measuring the rotatory power of the solution before and after the electrolysis. Of course it is necessary to know that the indicator is not carried forward by the current in the same ABNORMALITY OF STRONG ELECTROLYTES. 189 manner as colloids. Indeed there are some experi- ments by Coehn which seem to indicate such a trans- port of cane sugar and probably raffinose behaves hi the same manner. In all cases Washburn stated that with his experimental arrangements no such effect could be observed. The indicators should also not unite with the dissolved salts and enter into complex ions, nor enter into reaction with substances deposited at the electrodes through the electrolysis. For this latter purpose unpolarizable electrodes of silver with a coating of silver chloride were used and the elec- trolytes were chlorides (of H, Li, Na and K). The concentration of the indicator always increased in the neighborhood of the anode, whereby a transport of water in the direction of the current is indicated. The effect is a differential one. If the two ions migrate with the same velocity and carry each the same number of water molecules, then the concentra- tion of the water will not change. Therefore we must make a hypothesis regarding the number of water molecules transported by the one ion in order to deter- mine the number of water molecules transported. If it is supposed that the chlorine-ion does not carry any water, Washburn's figures give the following values for the positive ions: H + 0.28 H 2 0, K + 1.3 H 2 0, Na + 2.0 H 2 0, Li + 4.7 H 2 0. If we suppose that Cl carries one molecule of water, we must, as is easily seen, add to the 0.28 molecule of water combined with the H-ion, as calculated above, a quantity inversely proportional to the relative veloc- 190 THEORIES OF SOLUTIONS. ity, i. e., in this case 65.5 : 315 = 0.2 (cfr. p. 134, Washburn gives the ratio 0.185). The corresponding figures for K, Na and Li are according to Washburn 1.02, 1.61 and 2.29. Thus for instance if we suppose that the chlorine-ion carries six molecules of water, then the Li-ion carries 4.7 + 6.2.29 = 18.5. It is clear that this transportation of water has in- fluenced the concentration of the solutions in which Hittorf and his successors determined the migration of ions. At extreme dilution this difficulty disappears, for then the change of the relative concentration of ^'the water through its transportation becomes inappreciable. Now there has been worked out by Denison and Steele a new method for directly measuring the velocity with which the ions proceed by means of optical re- actions which they cause. These investigators, for instance, passed a current through three solutions of LiCl, KC1 and KCH 3 C0 2 , so that the slower ion Li or C 2 H 3 02 followed the more rapidly moving ion K or Cl respectively in the direction of then* movement. Then no mixing of the solutions occurred and their boundary surfaces remained sharp and could be deter- mined by a telescope through the change of the refrac- tive indices in them. These boundary surfaces move with the same velocity as the ions K and Cl in the middle portion of the conducting solution. This method is independent of the concomitant transporta- tion of water. From his own experiments Washburn determined the ratio of migration of the positive ion according to the chemical method used by Hittorf, then corrected it with regard to the transportation of the water and ABNOBMALITY OF STRONG ELECTROLYTES. 191 compared it with the results of Denison and Steele. He found for 1.25 normal solutions of KC1 and NaCl at 25 the following values: Hittorf a Method. Corrected. Denison-Steele's Method. KC1 0.482 0.495 0.492 NaCl 0.366 0.383 0.386 The figures of Denison and Steele are properly valid for 1 n solutions at 18, but the difference between these solutions and 1.25 n at 25 is in this regard in- significant. This confirmation of the correctness of Washburn's views and determinations seems very valuable, other- wise one would not have been quite certain that a part of the sugar or raffinose or arsenious acid had not wandered also, as negative ion-compounds of alkaline salts with sugar are well known, and may, to a small extent, exist in aqueous solution. Even Washburn could not with the means at his disposal decide how great a quantity of water is at- tached to the ions, but only that Li carries more water than Na, Na than K and K than H, and that there is certainly a transportation of water with the ions. The order of the ions Li, Na and K is the same as that of their solid salts hi regard to their capacity for binding water. A new step was taken by Riesenfeld and Reinhold. They combined the methods of Washburn and Bous- field. If in a salt ak composed of the anion a and the cation k, these two ions contribute to the conduc- tivity with the fractions w a and (1 w? a ) and if the anion carries A molecules and the cation K molecules of water, then the number x of water molecules transported 192 THEORIES OF SOLUTIONS. to the anode, accessible to analysis after the passage of 96,550 coulombs is as is easily seen: w a A - (1 w a ) K = x. From the change of the migration rate n a) as deter- mined by Hittorf, with concentration it is possible to determine x, as Washburn pointed out, for n a = w a + x/a, if 1 equivalent of salt is dissolved in a molecules of 0.5Z o.so 0.40 0.75 O.Z 0.4 0.6 0.8 10 10 ABNORMALITY OF STRONG ELECTROLYTES. 193 water. In the accompanying diagrams the variation of n a with concentration (c = 55.5/a for dilute solu- tions) is represented. Further, Biesenfeld and Reinhold supposed that the number of water molecules combined with an ion is so great as we have seen BousfiehTs figures indicate that this number is generally very high that the volume of the ion with accompanying water is propor- tional to this number. In this case the velocities of the ions are inversely proportional to the radii of these volumes, i. e., to the cube root of the accompanying number of water molecules A and K. Hence as x is known we have two equations for determining A and K, and we may calculate both of them. Riesenfeld and Reinhold now calculated the number of water- molecules attached to the 8 ions entering into the electrolytes HC1, KN0 3 , AgN0 3 , CdS0 4 and CuS0 4 , for which x is relatively well determined. From these figures they calculated seven values for the number of H 2 molecules bound to the ion Cl by comparing its conductivity with those of the seven other ions. They found values varying between 16 and 24 with an average value of 21. With the aid of this value and the known conductivities of the ions they found the following numbers of water molecules accompanying each ion: Ion: ....................... H K Ag ^Cd HCu Na Li Number of H 2 O-molecules: ....0.2 22 37 55 56 71 158 Ion: ....................... OH y 2 SO< Br I Cl NO 3 C1O 3 Number of H 2 0-molecules: .... 11 18 20 20 21 25 35 It is of course impossible to suppose that a lithium-ion is chemically bound to 158 molecules of water. It is perhaps bound to one, two or three molecules of water 14 194 THEORIES OF SOLUTIONS. as the solid salts LiCl + H 2 0, LiBr -f 2H 2 and Lil + 3H 2 0, or if we reserve one H 2 for the anion, the Li-ion may be bound to about 2H 2 0. It is proba- ble that hi the solution there occur Li-ions bound to 1 to 3 molecules of water. The motion of a complex molecule H 2 Li H 2 may be estimated to cause about double the effort of dragging Li alone. There- fore the mobility of Li is only about one half of that of Cs, which moves the most rapidly of all monovalent ions. In this case we except the ions H and OH of the water HOH itself on grounds cited above (cf. p. 134). The friction of the Na-ion 1/43.5 = 0.023 lies about midway between that of Li (1/33.4 = 0.03) and that of Cs (1/68 = 0.0147). Hence we conclude that the Na- ions are on an average bound to about one molecule of water. The other monovalent ions are bound to greater or less quantities of water, which as averages generally are fractions lying between zero and about two. With rising temperature the number of water molecules bound to the ions dissociate off; they then approach the limit value, which is characteristic for ions without "ionic water." Therefore the molecular conductivity of dif- ferent monovalent ions converge towards a common value with rising temperature. The bivalent ions ought to converge to double this value, as Noyes has also stated for S0 4 . Now Washburn has found that Li drags with it about 5 molecules of water which at first seems to conflict with the assertion that on an average Li has only two molecules of "ionic water." But as is well known from the doctrine of the fluidity a small particle moving in water carries with itself a rather thick "water envelope." ABNORMALITY OF STRONG ELECTROLYTES. 195 The molecules of water, with which the moving par- ticle collides, also get a pull in the direction of the moving particle and are carried with it. Evidently the number of water molecules dragged in this manner increases with the complexity of the ion and therefore also with the number of ionic water molecules. That only a very small number of water molecules is bound to the ions is evident from then* very marked individuality in moving through the water, especially if we consider the influence of the temperature on the mobility. The number of water molecules dragged with the ions may of course be considerably greater. An inspection of the values given by Bredig regarding conductivities of organic ions consisting of a great number of atoms, shows that their conductivities are roughly inversely proportional to the third root of the number of atoms contained in the molecule. This behavior corresponds to the law of Stokes. The hydration of a dissolved substance increases with dilution. Therefore we should also suppose that the average number of ionic water molecules increases with dilution. The conductivity of the ions decreases very rapidly with the increasing number of ionic water molecules. Therefore the degree of dissociation calcu- lated from the conductivity does not change so rapidly with dilution as we might expect if we did not consider the diminished mobility at high dilutions. The idea of Jahn (cfr. p. 173) may therefore be considered right, if it is combined with the idea of hydration which is undoubt- edly right. I regard this change of mobility and the salt effect as the chief factors which disturb the validity of Guldberg and Waage's law hi its application to strong electrolytes. LECTURE XI. THE DOCTRINE OF ENERGY IN REGARD TO SOLUTIONS. THE free energy of a dissolved substance is according to van't HofTs law just as great as the free energy of the same quantity of matter in gaseous form per gram- molecule, i. e., A = RTlo&p-RTlog e p a (1) where R is the gas constant 1.985 cal., T the absolute temperature and p the osmotic pressure. This formula indicates the work done in compressing one gram-mole- cule of a gas from the pressure p a to the pressure p. If p a is put equal to 1 then log, p a = and A=RTlo&p (la) According to the definition of free energy, A is therefore in this case the free energy of the said mass of gas, if the free energy of the same mass of gas at normal pres- sure, e. g., one millhn. mercury is taken as zero, from which the free energy is counted. If we have to calculate the change of free energy on evaporating a liquid, we consider that the work done in lifting a piston of cross-section s cm. square, loaded with p kilograms per cm. square, i. e. y with a total load of ps kilograms, through a height h is psh pv where v is the volume passed through by the piston. 196 THE DOCTRINE OF ENERGY. 197 If we allow the vapor to lift the said piston, the volume v is filled with saturated vapor. If th e evaporated quan- tity is one gram-molecule, the work done is: pv = RT. By this quantity the free energy of the said unit quan- tity of liquid exceeds that of the same quantity of vapor, i. e., gas. A similar calculation may be made regarding a solid or liquid substance and its solution in, e. g., water, in which case the work may be done by lifting a piston, loaded per cm. 2 with a weight equal to the osmotic pressure of the saturated solution, permeable to the solvent (water), but not to the dissolved body, and separating a satu- rated solution over this body from a layer of pure solvent. Of course all these deductions regarding the free energy A are based upon the assumption that we deal with such small concentrations that the laws for ideal gases are valid. Similar expressions referring to the pressure are used for gas-reactions because they generally take place at constant pressure and because the pressure is generally the quantity observed. The same expression should be used for solutions if their condition was character- ized by theb: osmotic pressure. But the osmotic pres- sure is very difficult to measure and instead of that we use the concentration c in defining the state of solu- tions. We therefore transform the equation given above by introducing in the expression of A the for- mula of Boyle-Gay-Lussac : p = cRT. (2) We now reckon the free energy from a certain concen- 198 THEORIES OF SOLUTIONS. tration c a , which is connected to p a through the equa- tion: p a = c a RT. (2a) Introducing the said values of p and p a into equation (1) we find: ). (3) If we put c a equal to the unit of concentration usually one gram-molecule per liter, we get: A = RT log, c. (3a) Let us consider an equilibrium between a weak acid, which obeys the law of Guldberg and Waage, and its two ions. If their concentrations are Ci and 02, then the so-called dissociation constant is K = of/Ci. We wish to calculate the work done in the electrolytic dis- sociation of one gram-molecule of the acid of unit con- centration into its two ions also of unit concentration. For this calculation we make use of the circumstance that an equilibrium exists if the concentration of the acid is Ci and that of each of its two ions GZ. In other words no work is done if we transform a certain quantity of the acid of the concentration Ci into its ions when their concentration is c% or vice versa. Then the work to be calculated consists of three parts: (1) The work done in the dilution of one gram-molecule of the acid from the concentration 1 to the concentration Ci A! = RT (log, 1 - log. ci). (2) The work done in transforming the said mass of the acid of the concentration Ci into solutions of its two ions, each of the concentration c% at constant vol- ume. This work is zero. (3) The work of condensing THE DOCTRINE OF ENERGY. 199 the two solutions of the ions from the concentration Cz to the concentration 1 (the original volume). This work is The total work done is: A = Ai + A 3 = RT (2 log. 02 - log. Ci) = RT lo&K. (4) As K is generally a very small fraction, A is generally negative, i. e., the ions possess in normal solution an excess of free energy above that of the acid in normal solution. If we have an acid in double the normal so- lution and it is dissociated into its ions to the extent of 50 per cent. this condition is nearly realized for tri- chloracetic acid at 25 then the free energy is zero, for an equilibrium exists between the undissociated acid and its two ions, all three in normal concentration, so that no work is necessary for carrying the process in the one or the other direction. In this case the dissocia- tion constant is 1. The expression above is due to van't Hoff. Evidently it is very easy to calculate A, if we know K, and van't Hoff did that with the help of the deter- minations of Ostwald. He found for instance at 25 C. for acetic acid A = 3,240, for formic acid A =] 2,510, for propionic acid A = 3,320, for trichlor- acetic A = + 60, etc. The free energy or affinity A is bound to the quantity of heat U developed in a reaction by the following equation, which is easily deduced from the second law of thermodynamics: U- A-T dA - U " A i dT " 200 THEORIES OF SOLUTIONS. If we know A, or K at a given temperature and U for all temperatures, then we may calculate K for any temperature from the last equation, which was given by van't Hoff. But we know A at absolute zero, for there according to the last equation U = A. Then knowing U we may determine A. If we develop A in a series in the neighborhood of absolute, we get We need only two terms of T if we do not consider temperatures too far from absolute. Using the last equation we find the following expression for U: This equation states that (dU:dT) at absolute is absolute zero, i. e. y U does not change with temperature hi the neighborhood of absolute zero. This seems to be nearly true. Einstein has recently given a theory ac- cording to which the specific heats of substances vanish at absolute zero, therefore also the so-called molecular heat, i. e., the product of the specific heat by the molec- ular weight is zero. This theory has lately been in a high degree confirmed by the measurements of Schimpff and Pollitzer. Now the change of U with tem- perature depends on the difference of the molecular heats of the reacting substances on the two sides of the sign of equality in the chemical equation expressing the reaction. If now the molecular heats are zero, then it follows that their differences will also be zero. The determinations of Schimpff and Pollitzer were carried out only with solid substances. The said regu- THE DOCTRINE OF ENEEGY. 201 larity is certainly only to be regarded as a first approxi- mation for systems in which gases or solutions enter. A has a maximum (or minimum) when dA/dt = v B + 2CT = 0, i. e., at an absolute temperature T, which is T = - B/2C. As we shall see this temperature is positive, i. e., occurs, because B and C have (hi the cases examined below) opposite signs (cfr. fig. 5, p. 212 ). At the same temperature A t and U t are equal, for if I put A t = A + BT + CT* = U t = A - CT\ I find BT = - 2CT 2 , i. e.,T = - B/2C. At this point we also find: dU/dt = - 2CT = J5, i. e., the tangent to the C7-curve at this remarkable point is parallel to the tangent of the A-curve at the point zero. The A- and Z7-curves cut each other at two points, at T = and at T = - B/2C. In the temperature interval between these two points they do not separate much from each other, but from there they diverge more and more rapidly the higher the temperature rises according to the prevalence of the term CT* in A above BT. In U the term - CT 2 determines the variation, which goes in the opposite direction to that of A. Other interesting points are those in which A t and U t = 0. For U t = we have A n - CT 2 = V T.. = i/ZTC 202 THEORIES OF SOLUTIONS. and for A t = 0, we find A + BT + CT* = v T a = - B/2C The examples of solutions given below give a positive value of T u because A and C are of the same sign. A does not reach zero for weak electrolytes, for which it may be calculated with sufficient accuracy. In order to elucidate these important theorems, I have calculated the free energy of two solutions, one prac- tically not dissociated, namely of boric acid, and the other dissociated to a high degree. The figures are taken from the tables of Landolt-Bornstein, third edition, t is temperature in C., T absolute tempera- ture, c concentration (gram mol. in 1000 gm. H 2 0). BORIC ACID, HjOsB = 62. A = -7519+34.02T-0.025T 2 . t T e:2 logc:2 A obs. Alcaic. Diff. dAldt U 273 0.1562 -0.8064 -86-94+8 -5656 20 293 0.3164 -0.4997 + 318 + 301 +17 20.2 -5372 40 313 0.5523 -0.2579 + 686 +680 +6 18.4 -5071 60 333 0.8352 -0.0679 +1019 +1037 -18 16.7 -4778 80 353 1.288 0.1101 +1368 +1376 - 8 17.4 -4404 100 373 2.062 0.3144 +1793 +1794 - 1 16.2 -4041 dA/dt is nearly constant and decreases a little with increasing temperature. Thereby C receives a negative sign, and consequently in this case B a positive one. A is negative. These signs of A , B and C are, as we shall see later, those generally found. Where A , B and C do not come out with these signs we may suspect that the observations are affected by some rather great errors (or the temperature interval is insuf- ficient for determining A , B and C with accuracy). As U = A CT 2 , the numerical value of U decreases THE DOCTRINE OF ENERGY. 203 with rising temperature. That B is positive depends upon the fact that the solubility always increases at low temperatures. The solubility is, according to the negative sign of A , as we shall see below always vanishing in the neighborhood of absolute zero. The change of A and U with temperature is given for H 3 3 B, Ca(OH) 2 and (C 2 H 5 )20 in the accompanying diagram. [10000 1*5000 fisiffil! +300 S^rigPZrisiift. 100 200 FIG. 4. 30O 400 We now take a very interesting example, in which U is positive at common temperature, i. e., in which heat is developed on solution, namely the solubility of Ca(OH) 2 . CALCIUM HYDRATE Ca (OH) 8 =74. t T C logc TTobs. TPcalc. Diff. dWIdt U U.2.62 273 0.0234 0.3691-2 -1910 -1885 -25 + 627 + 1643 40 313 0.01856 0.2688-2 -2331 -2332 + 1-9.6 +1799 + 4714 80 353 0.01196 0.0779-2 -2938 -2942 + 4 -14.3 +3130 + 8200 150 423 0.00446 0.6497-3 -4356 -4380 +24 -19.1 +5845 +15314 RT log, c = W = -3100 + 18.17 - 0.05T 2 . As in the example given above the formula with three constants represents the observations surprisingly well, 204 THEORIES OF SOLUTIONS. and within the limits of experimental errors. Just as in the previous case A is negative, i. e., the substance is absolutely insoluble at extremely low temperatures which in reality are not accessible for experiments. B is positive, i. e., the solubility increases to begin with, which is a necessary consequence of what has been said regarding the insolubility at abs., and C is negative, i. e., the numerical value of the heat of solution (if negative as hi normal cases) decreases with rising tem- perature (or increases if positive as for Ca(OH) 2 ). As A and C always have the same sign U is zero at a certain temperature; in the two examples given above this point lies at 548 abs. (= 275 C.) for boric acid and at 249 abs. (= - 24 C.) for Ca(OH) 2 . The point at which A has its maximum value and is equal to U lies for boric acid at 680 abs. (= 407 C.) and for calcium hydrate at 220 abs. (= - 53 C.). These temperatures are inaccessible experimentally as well for the calcium hydrate as for the boric acid. The calcium hydrate hi saturated solution is disso- ciated electrolytically to a degree of 81 per cent. There- fore its osmotic pressure is 2.62 tunes greater than if the molecules were simple. In order to correct for this peculiarity van't Hoff introduced the coefficient i, so that the constant R has 2.62 times greater value than for gases and undissociated substances. Hence also the A and U should be multiplied by this factor. If this is done we find at 18 C., the heat of solution (IT) equal to 2,930, whereas Thomsen found experi- mentally 2,800, a very good agreement. For boric acid Berthelot found -17= 5,600, whereas the calculation above gives 5,400, which is also in good agreement within the experimental errors. THE DOCTRINE OF ENERGY. 205 I have found only a single class of dissolved sub- stances, for which the rule that A and C are negative and B positive does not hold. This class is fluids, which are only partially immiscible with water. As these substances are also highly interesting from other points of view, I have calculated three typical exam- ples, namely ethyl ether, 2-4-6 trimethyl pyridine and phenol. For ether the solubility in the investigated interval decreases with rising temperature, for phenol it increases steadily and for trimethylpyridine it at first decreases and thereafter increases. The solubility c is given in gram-molecules per kilogram. ETHYL ETHER, C 2 H 6 OC 2 H5 = 74 (KLOBBIE). t T e - 3.5 269.5 1.63 +20 293 40 313 60 333 80 Iog 10 c dWldi 0.2123 17 +4812 W obs. W calc. Diff. 262 260 + 2 0.857 0.9329-1 - 90 - 90 -15.0 +3756 0.597 0.7762-1 -320 -321 + 1 -11.5 +2787 0.48 0.6810-1 -485 -483 - 2 - 8.3 +1753 353 0.368 0.5667-1 -699 -587 -112 -10.7? + 653 W= RT log a c = 10,623 - 60T + 0.08T 2 . 2-4-6 TRIMETHYL PYRIDINE, (CH 3 ) 3 C 6 H 2 N = 121 (ROTHMTTND). Crit. Point 5.7. c log 10 c t T 10 283 0.6404 0.8065-1 20 293 0.2819 0.4500-1 40 313 0.1593 0.2021-1 80 353 0.1428 0.1547-1 120 393 0.1537 0.1866-1 IT obs. TFcalc. Diff. dWldt U - 250 - 607 +357 +3746 - 737 - 753 + 16 -48.6 +3342 -1141 -1104 -137 -20.2 +2495 - 25 - 5.6 + 628 - 11 -1364 -1461 -1349 -1450 - 2.5 -1461 160 433 0.2417 0.3832-1 -1221 -1339 +118 + 6.0 -3772 180 453 0.3024 0.4806-1 -1075 -1098 + 23 + 7.3 -5013 W = RT log, c= 9,352 - 55T + 0.07T 2 . PHENOL, C 6 H 6 OH = 74 (ROTHMUND). Crit. Point 68.8. t T e Iogi c 273 0.761 0.8816-1 20 293 0.898 0.9534-1 40 313 1.044 0.0188 50 323 1.296 0.1125 60 333 1.828 0.2644 65 338 2.402 0.3805 W TPobs. TFcalc. Diff. dWldt U -148.3 +174 -322.3 + 5508 - 62.1 - 71 - 11.1 + 4.3 + 983 + 26.9 + 16 + 10.9 + 4.5 - 3859 +171.2 +190 - 18.8 +14.4 - 6408 +426.5 +424 + 2.5 +25.5 - 9022 +622.4 +584 + 48.4 +39.2 -10572 RT log. c=35,328-238T+0.4T 2 . 206 THEORIES OF SOLUTIONS. The points for which U is zero are 364 absolute (91 C.) for ether, 365.5 (92.5 C.) for trimethylpyri- dine, which also results from the minimum of c at that point, and 299.1 (= 26.5 C.) for phenol. This last point does not agree with the observations, for nothing indicates a minimum of c at that point, but as we see, we cannot speak of an agreement between the calcu- lation and observation below 20 C. The same is true for the temperature above 60 for ether (perhaps this is partly due to errors of observation) and below 20 C. for the trimethylpyridine. The point, where A W + 2T has its minimum value and A = U falls at 362 (= 89 C.), 379 (106 C.) and 295 (= 22 C.) for the three substances. This point is clearly visible for tri- methylpyridine and for phenol. For ether this point lies above the temperatures examined. U is for ether 4,500 cal. at common temperature according to an observation by Le Chatelier. The agreement is satisfactory. It is evident that the ground for the abnormal behavior of these substances lies in the very great positive value of C, i. e., d?A/dP in the examined interval of temperature. As is seen from the figures of dA/dt, d 2 A/dt 2 is by no means constant in this interval, and it is therefore not to be expected that a constant value of C will allow an ex- trapolation. This is exceedingly clear for phenol, and the observations regarding the other two substances leave no doubt that an extrapolation with a constant value of C cannot give reliable results. These obser- vations fall in the neighborhood of the critical points of these mixtures and it is well known that the simpli- fied formulae of van't Hoff, in which the volume of the fluid is omitted are not applicable in the neighborhood THE DOCTRINE OF ENERGY. 207 of the critical point. We shall later see this assertion exemplified. Hence we ought not to draw conclusions regarding the values of A , B and C for these substances from the formulae given above, which are only inter- polation formulae. The great value of C causes an abnormally high negative value of B and this in its order gives rise to the wholly abnormal positive value of A . But still one regularity remains, namely that A and C are of the same sign and opposite to that of B. In other words U passes through zero at some point and the U- and A -curves intersect at some point (above absolute zero). But we should not draw any conclu- sions regarding the real values of A , B and C from these experiments. Van't Hoff has determined a great number of heats of solution from observations regarding solubility and compared them with observed data. This list of sub- stances is the following (U expressed in great calories): Stance. So.uWH* ,n P M C.n, Succinic acid ..... 2.88 at 0, 4.22 at 8.5 6.7 6.9 Salicylic acid ..... 0.16 at 12.5, 2.44 at 81 8.5 8.0 Bcnzoic acid ..... 0.182 at 4.5, 2.19 at 75 6.5 6.8 Amyl alcohol ..... 4.23 at 0, 2.99 at 18 2.8 3.0 Anilin .......... 3.11 at 16, 3.58 at 55 0.1 0.7 Phenol .......... 7.12 at 1, 10.2 at 45 2.1 1.4 Mannite ......... 15.8 at 17.5, 18.5 at 23 4.6 4.9 Mercuric chloride. 6.57 at 10, 11.84 at 50 3.0 2.7 Boric acid ....... 1.95 at 0, 2.92 at 12 5.6 5.2 Van't Hoff also introduced for these substances, which are nearly perfect non-conductors, a magnitude i, similar to that spoken of above for calcium hydrate. As this magnitude i depends upon the dissociation of the substances, i = 1 + (n - IK 208 THEORIES OF SOLUTIONS. where n is the number of ions, into which the electro- lyte dissociates and a is the degree of dissociation, and a in all these cases is practically equal to zero, I have recalculated the figures, putting i = 1. In reality they have not changed much. Van't Hoff has also given figures for some electro- lytes which are dissociated to such a degree that we must take i as greater than unity, as for Ca(OH) 2 above. The influence of the dissociation is easily understood in the case of gases. If the gas does consist of just the simple molecules, indicated by its chemical formula, we may substitute RT.c for p where c is the concentra- tion. But if every one of the molecules, represented by the formula, is split up into i molecules (ions) then the pressure is i times greater than that calculated from the formula p = RTc. It is easy to see from the deduction of the formula above, that the same is valid also for solutions, namely that we must multiply c by i, in order to get correct values. That is what we have done above for^calcium hydrate, in which case i may be taken as a constant. But in other cases, especially where the solubility increases with temperature, as in normal instances this is not permissible but we ought to tabulate A = iRT (1 -f log, ic). Van't Hoff supposed that i is constant and found a good agreement between the observed and the calcu- lated figures. Probably a revision of the figures will also verify the ideas of van't Hoff; at present it may suffice to indicate, how the recalculation has to be performed. I reproduce only some few figures calcu- lated by Noyes, regarding silver salts, showing an excellent agreement with the figures observed by Goldschmidt. THE DOCTRINE OF ENERGY. 209 Salt. AgC.H.O, AgC 3 H s O t AfC 4 H T O, Heat of solution obs 4,613 3,980 2,860 Heat of solution calc. . . 4,562 3,928 2,836 I now come to the most interesting case regarding the energy of solutions, namely the change of free energy on electrolytic dissociation and the simultaneous evolution of heat. We shall see that the circumstances are very similar to those observed in the solution of substances. We begin with examining some substances which have been accurately investigated in a rather great interval of temperature, and thereafter consider other substances, which have not been measured so thor- oughly. In his great Carnegie-Institute memoir, which I have so often cited, Noyes gives some figures for the dis- sociation constants of water, acetic acid, ammonia and phosphoric acid, at different temperatures in a rather great interval, so that they may well serve as instructive examples of the variation of affinity of electrolytes. The interpolation formulae used for representing the A -values are for Water; H + OH = H 2 0; A = 21420 + 29.91T - 0.0857 72 . Acetic acid; H + CH 3 C0 2 = CH 3 C0 2 H; A = - 5360 + 14.66T - 0.06157 72 . Ammonia; NH 4 + OH = aNH 4 OH + (1 - a) (NH 3 + H 2 0); A = - 8625^+ 32.63T 7 - 0.08517 72 . Phosphoric acid; H + H 2 P0 4 = H 3 P0 4 ; A = - 1955 + 11.97 7 - 0.0446T 2 . It is interesting to see how well these interpolation formulae represent the observations. I therefore give 15 210 THEORIES OF SOLUTIONS. below the observed and the calculated values of A. The next column contains the difference A obs , - A CQic . After this the value of dA/dt calculated from ^ O bs. is tabulated. 7 gives the temperature hi C., T is the absolute temperature. WATER. t T A obs. A calc. Diff. dAldt 273 -18780 -18795 + 15 18 291 -19070 -19064 - 6 16.1 25 298 -19190 -19181 - 9 17.1 100 373 -21000 -21010 + 10 24.1 156 429 -22850 -22987 +137 33.04 218 491 -25440 -25783 +343 41.77 306 579 -31160 -30801 -359 65.00 ACETIC ACID. t T ^1 obs. A calc. Diff. dAldt IS 291 - 6306 - 6300 - 6 100 373 - 8446 - 8446 26.1 156 429 -10330 -10391 + 61 33.7 218 491 -12940 -12990 + 50 42.0 306 579 -18150 -17486 -664 59.2 AMMONIA. t : T A obs. A calc. Diff. dAldt 273 - 6058 - 6056 - 2 18 291 - 6337 - 6331 - 6 15.5 25 298 - 6463 - 6456 - 7 18.6 50 323 - 7002 - 6962 - 40 21.6 75 348 - 7612 - 7573 - 39 24.4 100 373 - 8302 - 8284 - 18 27.6 128 401 - 9066 - 9217 +151 27.3 156 429 -10202 -10283 + 81 41.3 218 491 -12894 -13113 +219 43.4 306 579 -18610 -18147 -463 64.9 PHOSPHORIC ACID. t T A obs. A calc. Diff. dAldt 18 291 - 2638 2629 - 9 25 298 - 2761 2749 -12 17.6 50 323 - 3181 3178 - 3 16.8 75 348 - 3689 3665 -24 20.3 100 373 - 4208 4203 - 5 20.8 128 401 - 4860 4876 +16 23.3 156 429 - 5585 5623 +38 25.9 THE DOCTKINE OF ENERGY. 211 The temperature interval is not so very great for the observations on H 3 P0 4 ; therefore this example is of much less value than the other series. At high tem- peratures the differences between the observed and calculated values increase, which may perhaps be due to the difficulty of these observations, perhaps also to the circumstance that the higher members in the inter- polation formula have been omitted and probably to both of these circumstances. The great negative values of these differences at T = 306, compared with the positive values at the nearest temperatures T = 156 and T = 218, indicate that the coefficient D of the omitted term DT 3 is negative, i. e., of the same sign as C. From this it also follows that the numerical value of C given above is a little too high. All the four interpolation formulae are of the same type, the values of A and of C are all negative, the B values are positive. Very remarkable is the circum- stance that whereas the four values of A are rather dif- ferent (in the proportion 11 to 1), the values of B do not change so much (only in the proportion 2.8 to 1) and still less is the variability of C (only as 1.9 to 1). The characteristic point, where A has its maximum value, and where the A- and {/-curves intersect, lies at the following absolute temperatures (at double this temperature A has the same value as at T = 0) : for H 2 0; T = 176 (t = - 97 C.) for CH 3 C0 2 H; T = 119 (t = - 154 C.) for NH 3 ; T = 192 (t = - 81 C.) for H 3 P0 4 ; T = 134 (t = - 139 C.) i. e. 9 about 150 to 80 degrees below the freezing point of water. 212 THEORIES OF SOLUTIONS. The other characteristic point, where U = 0, and consequently the dissociation is at its maximum, lies: for H 2 at T = 502 (t = 229) for CH 3 C0 2 H at T = 295 (t = 22) for NH 3 at T = 318 (t = 45) for HsP0 4 at T = 209 (t = - 64) It is easy to calculate the heat of dissociation from the variation of K with temperature. In drawing a curve through the points representing U as a function of temperature it is easy to find the temperature, where U = 0. This point will of course agree with that calculated above and I actually find from the curves the values T u = 502 for water T u = 295 for acetic acid and T u = 318 for ammonia. The zero point of U for HsPCX lies 64 degrees below zero of the thermometric scale and is therefore not accessible experimentally. l-JQOOO 400 600 FIG. 5. The great value of these observations depends upon their proximity to the zero of absolute temperature. THE DOCTRINE OF ENERGY. 213 The interval of observed temperatures is about as great as that below C. It is therefore probable that the formulae will give nearly right results also below C. and down to the neighborhood of absolute zero. I have given a graphic representment of the formulae for water hi the accompanying curves and in these I have also introduced the values of U calculated directly from Noyes' figures. If the [/-curve had not a horizontal tangent at T = 0, the value of dA/dt would have an infinite value at the same temperature. In other words, the A curve ought there to run vertically and make an extremely sharp bend. This is not probable although not quite impossible. 1*15000 J+WOVO tsooo - 000 JOOOO ZOO 400 FIG. 6. 600 There are very few cases in which the A values are so accurately determined so near to the absolute zero and within so great an interval as just these. Only the A 214 THEORIES OF SOLUTIONS. values for transformation of vapor into water may compare with them, and to which I therefore wish to refer for a comparison. Here A = RT (1 + log, p). Of course the value of A depends on the units hi which p is expressed, for instance, millimeters of mercury or at- mospheres. If, as generally done, p is given in milli- meters, which unit I also use below, then A expresses the maximal work obtained in transforming steam at 1 millimeter pressure to water in a reversible way and at constant temperature. t FLUID WATER WATEB VAPOR. W = RT log, p = - 11394 + 46.74T - 0.00927T 2 . T p obs. p calc. W obs. W calc . Diff- dWIdt -20 253 0.96 1.00 - 25 - 12 - 13 273 4.579 4.58 + 825 + 825 - 42.5 50 323 92.17 90.6 + 2,901 + 2,887 + 14 41.5 100 373 760 760.3 + 4,911 + 4,909 + 2 40.2 150 423 3,581 3,581 + 6,870 + 6,869 + 1 39.2 200 473 11,625 11,639 + 8,788 + 8,789 - 1 38.4 250 523 29,843 29,101 +10,695 +10,665 + 30 38.1 300 573 67,620 59,020 +12,650 +12,495 +155 39.1 350 623 126,924 90,440 +14,550 +14,127 +323 37.9 As is seen from these figures the agreement is excellent at 0, 100, 150 and 200, and sufficient at - 20, 50 and 250. At higher temperatures the difference between observed and calculated values increases rapidly. This peculiarity is evidently due to the omission of a term DT 3 , where D has a positive sign. The proximity of the critical point (365 C.) is without doubt the cause of these irregularities (cf. p. 207). The attempt to give the formula without D a so great interval of validity as possible has brought about that the effect of D has partially been attributed to C which therefore is a little greater than in reality. To compensate for THE DOCTRINE OF ENERGY. 215 this at low temperatures, , which is of opposite sign to Cj has also been taken a little too small and that has again caused a value of A , which is a little greater than in reality. Yet the error in A is probably not greater than about 180 calories, i. e., without appreci- able importance. Differences of this order of magni- tude may also be possible in the values of A Q for the dissociation of electrolytes, but the errors in B/C and A fC are probably still less, so that an appreciable deformation of the curves is excluded. It is noteworthy that if we designate p in another unit, e. g., 1,000 mm. Hg, then RT log, p decreases with RT log. M/m where M/m is the ratio of the new and the old unit, i. e., here 1,000. The decrease of A would then in this case be 1.985.T.2.3026 log. M/m = 13.71 T. In order to abolish the term 48.74T 7 in the expression for A it would therefore suffice to designate the pressure in a unit which is 1000, where m = 48.74 : 13.71 = 3.555, i. e., 4.62.10 10 times greater than 1 mm. Hg. Of course this unit is of no practical value, at least at present. A similar remark may be made regarding the dis- sociation constant of the electrolytes. If I use a unit, which perhaps is more consistent with the absolute system C.G.S. than the gram-molecule per liter, namely, the gram-molecule per cubic centimeter, all the values of K diminish in the proportion 1,000 to 1. Therefore A decreases by 13.71 T 7 ., i. e., the coefficient B decreases in its absolute value by 13.71. The magnitude of the coefficient B is here not so great as for the evaporation of water, therefore it is not necessary to change the units so much to get rid of the term BT. As units of volume should be taken instead of liter 216 THEORIES OF SOLUTIONS. for ammonia 0.0725 cubic millimeter, for acetic acid 0.617 cubic millimeter, for phosporic acid 2.5 cubic millimeter. Instead of increasing the unit of volume in the said proportion we may diminish the unit of mass in the same proportion with the same result. It is very easy to construct the curves thus trans- formed. It is only necessary to draw the tangent of the A -curve at the point T = and to count the A- values from an axis going through the origin parallel to this tangent. Then the formulae for A and U are A = Ao + CT 2 + DT* + ET* + . . ., U = A Q - CT 2 - 2DT 3 - SET* . . .. At low values of T we may omit the higher terms in- cluding T 3 and T 4 and then the condition, demanded by Nernst for condensed systems, namely, that the A- and 17-curves shall be related to each other as object and image in a mirror is true. But as soon as the higher terms T 3 , etc., can no longer be neglected, which happens in the cases investigated above, at tempera- tures above 150 to 250 degrees, then the similarity of the two curves is spoiled. There is no better proof of the small physical impor- tance of the coefficient B than that it may be reduced to zero or given any value by changing the units of meas- urement. Therefore it is clear that an assertion that B is zero at the absolute zero would have very little mean- ing in this case. The case is somewhat different if in the homogeneous equilibrium between gases or dissolved substances the number of molecules does not change through the transformation or if we work with pure substances as in studying the dissociation of water or, THE DOCTRINE OF ENERGY. 217 better said, with substances the concentration of which cannot be changed at constant temperature. But even in this case as we have seen above with water, there is no probability that the A -curve runs horizontally at T = 0, although special cases may agree rather well with this condition. This seems, for instance, to occur with some condensed systems, for instance with the transformation of rhombic sulphur into monoclinic as studied by Broensted. A Q and C are not dependent on the adopted unit of pressure or concentration; the same is evidently the case with U. The formula for the free energy A on transforming water vapor at 1 millimeter pressure into fluid water has the same form as the formulae for the free energy on transforming ions of normal concentration into un- dissociated substances of the same concentration. But the constants are very different, so that the temperature where A has its maximum value occurs at first at 2,520 absolute, where of course these simplified calculations have no real meaning. Even the temperature where U vanishes is very high, it is calculated to 836 C. The said temperature occurs much sooner because of the positive value of D. As a matter of fact U is zero at the critical point 638 abs. On evaporation A goes through zero just at the point where the vapor pressure is equal to the arbitrarily chosen unit (here it is 1 millimeter and this pressure is valid at about 20C. ; if we had chosen 1 atmosphere A would have passed through zero at exactly 100 C.). An inspection of the curves giving A and U as functions of T shows that in the case of evaporation the part of the curves between and 600 abs. corresponds only to the part of the A- 218 THEOEIES OF SOLUTIONS. and U- curves for electrolytic dissociation, which lie between about and 40 abs. By differentiation we find : dA dU B + 2CT /. B dt ' dt - 2CT /. , \ "\ 1 "2CT/' If we know dA/dt and dU/dt at a given temperature (not too high), we may easily calculate B : 2C, which is the temperature where A has its maximum (or minimum) value and the U- and A-curves intersect. In his inaugural dissertation Lund6n has calculated all available values of dA/dt and dU/dt at 25 C. = 298 abs. With the aid of his table we calculate the follow- ing values T m of the absolute temperature of A max . 298 absolute does not lie very high, so that probably the errors hi the value of this temperature T m are not so very great, perhaps some 30 C. Lunden also gives the values of A and U at 25; it is rather interesting to see how far they have diverged from each other from the point of equality T m . With Lunden, I have divided the material into three groups. The first contains bases, the second acids, which dissociate with absorp- tion of heat, and the third those with production of heat at 25 C. Through the subtraction of the heat of disso- ciation of a weak acid from that of water we obtain the heat of neutralization of this acid with a strong base. In an analogous manner the heat of neutralization of a weak base with a strong acid is obtained and also the change of free energy on neutralizing the said sub- stances. In the neutralization of weak acids with weak bases it is necessary to take the A and U values for both substances into consideration. In Lundn's work these THE DOCTRINE OF ENERGY. 219 neutralization data are tabulated, essary to reproduce them. I do not find it nec- FREE ENERGY AND HEAT IN IONIZATION PROCESSES AT 25 C. A U dAldt dUldt Water -21,450 -13,450 -27 + 50 Bases: Orthoaminobenzoic acid -16,220 -10,220 -21 + 52 Pyridine ....-11,840 - 7,780 -13.5 + 35.5 2, 4, 6 Trimethyl pyridine . .... - 9,110 - 5,510 -12 + 77 Ammonia ....- 6,440 - 1,160 -17.5 + 58 Acids with negative heat of diss. : . Boric acid ....-12,570 - 2,960 -32 + 12 p-Nitrophenol - 9,750 - 4,840 -16.5 + 21 Orthoaminobenzoic acid . . . .... - 6,780 - 3,270 -12 + 38 Aminotetrazol - 8,420 - 4,600 -13 + 55 Cinnamic acid .... - 6,070 - 400 -19 + 31 Benzoic acid ....- 5,690 - 200 -18.5 + 42 Nitrourea (at 20) ....- 5,600 - 3,700 - 6 +100 m-oxybenzoic acid ....- 5,560 - 100 -18.5 + 26 m-nitrobenzoic acid ....- 4,720 - 400 -14.5 + 38 Nitro-urethane ....- 4,470 - 2,900 - 5 + 65 Salicylic acid ....- 4,060 - 800 -11 + 44 Acids with positive heat of c lias.: Acetic acid .... - 6,450 + 110 -22 + 31.5 Ortho toluylic acid ....- 5,320 + 1,310 -22 + 30 Ortho chlorbenzoic acid .... - 3,920 + 2,240 -20.5 + 35 Ortho iodbenzoic acid .... - 3,900 + 2,660 -22 + 23 Ortho nitrobenzoic acid .... - 3,000 + 3,180 -20.5 + 29 Ortho bromcmnamic acid. . . .... - 2,510 + 3,280 -19.5 + 28 ' B m A. JB C Water 0.46 137 -21,420 +29.9 -0.085 Orthoaminobenzoic acid ....0.60 179 -17,770 +23.2 -0.084 Pyridine ....0.62 185 -13,070 +31.2 -0.087 2, 4, 6 Trimethyl pyridine . . ....0.84 250 -11,980 +48.2 -0.060 Ammonia ....0.70 209 - 8,625 +32.6 -0.085 Acids with negative heat of diss.: Boric acid ..-1.67(-497) - 4,750 -20.2 -0.02 p-Nitrophenol ....0.21 63 - 7,970 + 4.5 -0.035 Ortho aminobenzoic acid . . . 0.68 203 - 8,930 +26.2 -0.064 220 THEORIES OF SOLUTIONS. C2. 298 m Aminotetrazol 0.76 226 Cinnamic acid 0.39 116 Benzole acid 0.56 167 Nitrourea (at 20) 0.94 277 m-oxybenzoic acid 0.30 89 m-nitrobenzoic acid 0.62 185 Nitro-urethane 0.92 274 Salicylic acid 0.75 223 Acids with positive heat of diss.: Acetic acid 0.30 89 Ortho toluylic acid 0.27 80 Ortho chlorbenzoic acid 0.41 122 Ortho iodbenzoic acid 0.05 15 Ortho nitrobenzoic acid 0.30 89 Ortho bromcinnamic acid. . . .0.30 89 12,800 +42.2 5,020 + 12.0 6,460 +23.2 18,350 +93.5 3,980 + 7.7 6,060 +23.4 1,258 +59.7 7,360 +33.1 5,360 +14.6 3,160 + 7.8 2,980 +14.4 770 + 1.0 340 + 5.6 890 + 8.6 0.092 -0.052 -0.070 -0.167 -0.044 -0.064 -0.109 0.074 0.062 -0.050 -0.059 -0.039 0.049 0.047 These figures give a hint to many rather interesting conclusions, which will be more obvious if we smooth away the extremes by taking average values. These are for the three groups: Water. n A V A-U dAldt 1 -21,450 -13,450 -8,000 -27 ; . 4 -10.925 - 6,168 -4,157 -16 Acids with neg. U:. 10 -6,112 -2,121 -3,991 -13.4 Acids with pos. U:. 6 -4,183 +2,130 -6,313 -21 2G 298 Water 0.46 Bases: 0.69 Acids with neg. U: .0.61 Acids with pos. U: .0.27 T m 137 206 182.3 81 -21,420 -12,861 - 7,819 - 2,250 +29.9 +33.8 +32.3 + 8.7 dUldt +50 +55 +46 +29.4 C -0.085 -0.080 -0.077 -0.051 I have excluded the boric acid, which behaves quite differently from other acids, in taking the mean values. All the bases possess a negative value of U] they may therefore be compared with the corresponding acids. Although the heat of dissociation is about three times as great for the bases as for the corresponding acids, THE DOCTRINE OF ENERGY. 221 the value A-U is of nearly the same magnitude for the two groups. The values dA : dt and dU : dt are also not very far from each other in the two groups; therefore the same holds true for the two values of J5/2C.298 and T m (the difference here reaches 12 per cent.). For the acids with negative U (at 25) the value A U is 55 per cent, greater than in the foregoing two groups, dA/dt is about 1.5 times greater and dU : dt on the other hand only 0.6 of the mean value of the two fore- going groups. A consequence of these last two circum- stances is that T m lies about 113 lower for the last group than for the two first ones. At this temperature A and U coincide and diverge at higher temperatures, therefore it seems quite natural that A-U shall be less for the two first groups, where the distance from T m to the temperature of measurement is only 104 degrees, than for the third group for which the corresponding distance is 217 degrees. Evidently this circumstance as well as the low value of A is connected with the positive sign of U at 25 C. for this last group. At higher temperatures other acids will come over to the third group, thus for example m-oxybenzoic acid already at 29 and benzoic acid at 30. The numerical values of A , B and C decrease continuously from the first to the third group, A in the greatest proportion, C in the least. The most pronounced regularity is that dA : dt is negative and dU : dt positive for all substances exam- ined, and that for all (except boric acid, which is very difficult to determine accurately because of its extreme weakness) the numerical value of dU : dt exceeds that of dA : dt. A consequence of these regularities is that 222 THEORIES OF SOLUTIONS. T m for all examined electrolytes has a positive value below 298 (the temperature of observation = 25 C.). The two highest values for nitro-urea and nitro-urethane fall at + 4 and + 1 C., after these comes trimethyl- pyridine with 23 C., then there is a long distance of 24 and 27 C. respectively to the next two, aminotet- razol and benzoic acid. It must therefore be regarded as characteristic for the weak acids and bases, including water, that they possess A- and ^/-curves which inter- sect two tunes, not only at T = 0, but also at a higher temperature, and that they diverge from that tempera- ture, so that dA : dt is negative, dU : dt positive and numerically greater than dA : dt. Water has its place just in the middle of the two groups. A great part of the figures given above are deduced from determinations made by Lundn, the acids from aminotetrazol except acetic acid are deter- mined by other authors. If we now compare the values of T m according to the measurements of Noyes and those of Lunden, we find a certain difference; for water 176-137, for acetic acid 119-89, for NH 3 192-209. These differences are of course due to experimental errors, I am inclined to lay a great value on LundSn's determinations of ammonia, but for the other sub- stances the determinations of Noyes seem preferable. The phosphoric acid belongs to the second group of acids, its dissociation into ions is accompanied by an evolution of about 1,600 cal. at 25. Its T m lies higher (at 134) than that of those acids in general (81). I suppose according to Noyes' measurements that the values of T m deduced from the figures given by Lunden are a little too low, but on the whole this difference is of minor importance. THE DOCTRINE OF ENERGY. 223 We have seen before that: and U = - RT* d These equations are sufficient for the determination of A at any temperature if we know U at all temperatures. For then we know A and d log* K : dt, i. e. y the varia- tion of A with temperature. The old problem of the thermochemists, to determine the affinity, is therefore theoretically solved by means of these equations, given by van't Hoff. But practically, there are rather great difficulties, which depend upon our lack of knowledge of the values of U, the heats accompanying chemical processes at all temperatures and especially very low or very high ones. A certain theoretical interest is attached to the vicinity of absolute zero. Of course aqueous solutions do not exist in the neighborhood of this temperature, so that the consequences of our equations cannot be verified there. There A is negative and therefore T log, K is negative and has a definite value; f or T = log, K becomes negative and infinite, i. e., K = 0. The dissociation disappears totally at absolute zero. Ions cannot exist at absolute zero, just as the vapors of liquids on simi- lar grounds do not exist in the neighborhood of abso- lute zero. It is of a certain interest to remark that the regu- larities are much more prominent with the process of evaporation than with that of solution or of ionization. In the first case we have the important rule of Duhring, and its modification by Ramsay and Young, as well 224 THEORIES OF SOLUTIONS. as its consequence, the rule of Trouton. It would be rather difficult to find something similar for the solu- bility or the dissociation of electrolytes. Regarding the free energy on evaporation I have found that the coefficient B is nearly a constant, about 44 for all substances. The curves representing A therefore run very nearly parallel to each other. As we have seen above for the three groups of electrolytes there is a certain parallelism between the magnitude of the constants A , B and C, so that they are greater for the bases and least for the acids with positive heat of dissociation. But it would give very absurd results if one supposed that this rule were applicable for the comparison of two electrolytes chosen at random. On evaporation the regularity is much more obvious al- though not complete. On the other hand the multiplicity and variation of the phenomena is much greater in electrolytic dissocia- tion and they therefore have a greater attraction for the student who wishes to learn all possible combinations appearing in the central problem of physical chemistry, namely that regarding chemical equilibria. This prob- lem is classical here in the world-renowned Yale University, where one of the greatest thinkers in natural philosophy, the immortal Willard Gibbs, has devoted his genius to the investigation of chemical equilibria. At the close of my lectures I feel deeply that I need to tell you how thankful I am for the great kindness you have always shown me and for the permanent interest with which you have taken part in my lectures. I hope that you will have found how considerably American THE DOCTRINE OF ENERGY. 225 scientists have contributed to the most modern progress of physical chemistry. I am quite convinced that the development will go on still further hi that direction, and I am glad to say that we expect very much from the excellent work of American colleagues with their open mind, their unrivalled experimental skill and their practical sense. 16 BIBLIOGRAPHICAL REFERENCES. INTRODUCTION. J. Willard Gibbs: Trans. Connecticut Acad., 3, 109-249 and 343-524 (1874-1878). German translation by Ostwald: Thermodynamische Studien (1892). A. A. Noyes and G. V. Sammet: Zeitschrift fur physikalische Chemie, 41, 11 (1902). Emil Baur: Themen der physikalischen Chemie, Leipzig, Akademische Verlagsges. m. b. H., 1910. W. Ostwald: Lehrbuch der allgemeinen Chemie, Leipzig, Engelmann, 1885 and 1887, 2d ed., 1891, 1893, 1896-1902, 1906 (not finished). W. Nernst: Theoretische Chemie, Stuttgart, Enke, 1893, 6th ed., 1909. LECTURE I. M. Berthelot: Les origines de Talchimie, Paris, Steinheil, 1885. M. Berthelot and F. 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Cohen: Ibidem, 33, 57, 1900; 50, 225, 1905. W. Hittorf : Wiedmann's Annalen d. Physik u. Chemie, 4, 409, 1878. Cf. S. Arrhenius, Bihang t. K. Vetenskapsakademiens Handlingar, T. 8, No. 14, p. 19, 1884. Ostwald's Klassiker, No. 160, 1907. 226 BIBLIOGRAPHICAL EEFERENCES. 227 W. Ostwald : Die wissenschaf tlichen Grundlagen der analytischen Chemie, Leipzig, Engelmann, 1894, 3d ed., 1901. H. Dixon: Trans. Roy. Soc., 175, 617, 1884. Journ. Chem. Soc. Lond., 49, 94 and 384, 1886. H. B. Baker: Journ. Chem. Soc. Lond., 61, 728, 1892; 65, 611, 1894. D. K. Zavrieff: Journ. Soc. phys.-chim. russ., 4%, 36, 1910. F. Beilstein: Handbuch der organischen Chemie, 3d ed., 2, 79, 1896. H. Goldschmidt: Zeitschr. f. physikalische Chemie, 60, 728, 1907. Zeitschr. f. Elektrochemie, 14, 581, 1908; 15, 10, 1909. Cfr. Arrhenius: Theorien der Chemie, 2d ed., p. 202, Leipzig, Akad. Verlagsges., 1909. LECTURE II. B. Richter: Anfangsgrunde der Stochyometrie oder Messkunst chy- mischer Elemente, Breslau, 1792-94. H. 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ABEGG, 175, 176, 178 Alexejew, 31 Amagat, 69 Anaximenes, 1 Arago, 77 Archibald, 148, 149 Aristoteles, 2, 4, 5 Arndt, 146 Arrhenius, 52, 60, 87, 88, 101, 108- 111, 124, 127, 130, 136, 156, 164, 167, 180, 202, 218 Aure"n, 126 Avogadro, 20, 21, 34, 35 BABO, VON, 131 Baker, 14 Bartoli, 107, 108 Barus, 43 Baur, xix Bechhold, 44 Begeman, 30 Bellati, 76 Bender, 96 Berkeley, Earl of, 176 Berthelot, D., 116 Berthelot, M., 87, 102, 109, 123, 132, 153, 154, 204 Berthollet, 9, 10, 11, 18, 75, 76 Berzelius, 19, 103, 112 Biltz, 50 Bizio, 76 Bjemim, 31 Blagden, 174, 175 Bodenstein, 128 Bodlander, 43 Boltwood, 25 Boltzmann, 20, 79, 84, 89 Bousfield, 185-187, 191, 193 Bouty, 140 Boyle, 4, 5, 86, 177 Bredig, 37, 46, 49, 111, 133, 134, 159, 187, 195, Broensted, 217 Broglie, de, 31 Brown, 22 Buchboeck, 118 Buchner, 115 Buetschli, 51 Buffon, 7 Bunsen, 131 Burton, 43 CAHOURS, 83 Carlson, 117 Carnot, 82 Carrara, 152, 184 Cauchy, 26 Cavendish, 17 Centnerszwer, 149 Chappuis, 65 Clapeyron, 82, 131 Clausius, 20, 79, 91, 106-108 Coehn, 40, 189 Cohen, 13, 170 Commelin, 170 Coppet, de, 174 Cotton, 38 Coulomb, 112 Cundall, 132 DALTON, 18-20, 34, 35 Dawson, 155 Debray, 82 Democritus, 5 Denison, 190, 191 De Vries, 85, 86-88, 98 Dewar, 25 Ditte, 87 Dixon, 14 Drude, 184 Du Bois Reymond, 56 Duclaux, 115 Diihring, 223 Duperthiis, 144 Dutoit, 143, 144 EDGAR, 165 Ehrenhaft, 22, 23, 27-33 Einstein, 23, 24, 31, 40, 200 Empedocles. 1 Erfle, 26 Euler, 129 FAMULENER, 129 239 240 INDEX OF AUTHORS. Fanjung, 183 Faraday, 25, 27 Favre, 94, 95 Fink, 49 Fontana, 55 Foote, 148 Franklin, 150,151 Freundlich, 45, 48 GARRARD, 188 Gassendi, 5, 34 Gay-Lussac, 20, 35, 74-77, 86, 91, 103, 104, 106-108 Geiger, 25, 30 Gessler, 146 Gibbs, Willard, xvii, 70, 83, 84, 87, 224 Gladstone, 96 Godlewski, 137, 138, 169, 170 Goldschmidt, 15, 208 Goodwin, 145, 147 Gore, 14 Gouy, 22 Graham, 37 Green, 145 Grotthuss, 105, 139 Guldberg, 77-84, 87, 109, 127, 131-133, 165-167 HAGGLUND, 137 Hannot, 115 Hantzsch, 169 Hartley, 176 Helmholtz, H. v., 27, 84, 87, 108, 163 Helmholtz, R. v., 30 Helmont, van, 3, 17 Henri, 113, 114 Henry, 56, 87, 153 Heraclitus, 1 Hess, 96 Heydweiller, 111, 180, 181 Hittorf, 14, 134, 150, 188-192 Homfray, Miss, 63, 64, 67, 68 Horstmann, 77, 78, 83 Hudson, 113 ISAAC HOLLANDUS, 3 JACOBSON, 48, 49 Jahn, 96, 173, 195, Jellet, 87 Johnson, 148 Johnston, 141 Jones, 144, 175, 180 Jungfleisch, 87, 153, 154 KAHLENBERG, 151, 170 Kalmus, 147 Kirchhoff, 81, 131 Kjellin, 174 Klein, 10 Klobbie, 205 Kohlrausch, 96, 109, 111, 134, 140, 145, 184-186 Kooy, 124 Koppel, 187 Kossel, 161 Kremann, 121, 125 Kunckel, 4 Kunz, 145 LADENBURG, 32, 33 Landolt, 96 Landsteiner, 71 Latley, 30, 31 Lavoisier, 8, 9, 17 Le Chatelier, 4, 18, 22, 84, 87, 206 Lemery, 5 Lenz, 162 Levi, 184 Lewis, 70 Ley, 169 Lincoln, 169 Linder, 45 Loewenstein, 10 Lorentz, 26, 30 Lorenz, 151 Loschmidt, 30 Lowitz, 55 Lunden, 159, 160, 169, 218, 222 MADSEN, 116, 129 Mailey, 145 Malikow, 31 Mallard, 10 Malmstrom, 174 Marignac, 82 Martin, 145, 148 Masson, 145 Maxwell, 20, 79 McCrae, 155 Mclntosh, 148, 149 Meisenheimer, 115 Mendelejew, 80, 81 Michaelis, 71 Millikan, 28, 30, 31 Moore, 155 INDEX OF AUTHORS. 241 Moreau, 31 Morse, 175 Monton, 38 Muller v. Berneck, 46 NABL, 30 Nencki, 115 Nerast, xx, 154, 162-164, 184, 188, 216 Newton, 6, 7, 74, 112 Noyes, xix, 134, 136, 140, 141, 144, 176, 194, 208, 209, 213, 222 , 52 Oholm, 162 Ohm, 106 Olympiodoros, 3 Oppermann, 188 Ostwald, xx, 14, 21, 22, 26, 87, 109-111, 132-135, 158, 167, 182, 183, 187, 199 Oudemans, 96 PARACELSUS, 4 Partington, 180 Payen, 55 P6an de St. Gilles, 132 Pebal, 161 Pellat, 30 Perrin, 22-27, 31, 32, 36, 39 Pfeffer, 85, 86 Picton, 45 Pissarshewski, 145 Planck, 26, 30, 32, 33, 89, 111, 133, 163 Plato, 2, 5 Pleijel, 163 Plotnikow, 126, 127 Pollitzer, 200 Price, 125 Proust, 9, 18 Przibram, 28-32 RAMSAY, 63, 223 Raoult, 82, 87, 98-100, 110, 176 Rappeport, 143 Rappo, 51 Rayleigh, 26 Re'aumur, 6 Regener, 25, 31, 33 Regnauld, 22 Reicher, 111 Reinhold, 188, 191, 193 Reuss, 40 Richarz, 30 Richter, 9, 17 Riesenfeld, 188, 191, 193 Rivett, 178 Robertson, 161 Rontgen, 96, 98 Rona, 71 Rosenstiehl, 77 Rothmund, 205 Roux, 31 Rudorff, 82, 174, 175 Runoff, 151 Rutherford, 25, 30, 122 SACKUR, 176 Sainte-Claire-Deville, 93 Sammet, xix Saussure, de, 55 Schapowalenko, 145 Sche"ele, C., 18 Sch