T H E DISSOCIATION CONS‘L’ANTS OF VERY WEAK ACIDS. 5 By JAMES WALKER and WILLIAM CORMACK. ALTHOUGH the dissociation constants of many hundreds of organic acids have been measured, chiefly by Ostwald and his pupils, the feeble inorganic acids have been practically neglected in this respect. We are, in consequence, without accurate knowledge of the relative strengths of such common acids as carbonic acid, hydrocyanic acid, sulphydric acid, and boric acid, either relatively to each other or to acetic acid, which may be taken as the typical “weak” organic acid with a definite afinity constant. It is the object of the present com- inunioation to supply the necessary data for filling up this blank. The Appccrcctus and Mode of Experiment. As most of the acids investigated were gaseous a t the ordinary tem- perature, a closed form of apparatus had to be devised, which would permit of the solutions being diluted to definite strengths without communication with the air.I n a vessel of the usual type, the loss of gas is very rapid, and accurate dilution is impossible. After several preliminary experiments, the principle finally adopted was that of the syringe. The electrodes were placed a t the bottom of a long tube provided with a piston, which, by its regulated withdrawal, could be made to suck into the tube a measured quantity of the water used for dilution. A sketch of the whole apparatus is given in Fig. 1. The principal tube A was 46 cni. long and 2.2 cm. in diameter. The stem P was made of a glass tube of external diameter only slightly smaller than the bore of A , and was closed at the lower end by a rubber stopper R, which formed the piston, and fitted closely to the walls of A .The external tube was closed at its lower extremity by a perforated rubber stopper provided with slits for the passage of the wires from the electrodes EE. These wires were soldered to copper wires WW, which made connection with the rest of the apparatus through the mercury cups MM, As the tube A was immersed in water for a t least three-fourths of its length in order that a constant temperature might be secured, great care had to be paid t o the insula- tion of the wires from the electrodes, as the conductivity of the water in the thermostat was much greater than the conductivity of the solu- tions investigated.The connections are shown on a larger scale in Fig. 2. The copper wires leading to the mercury cups were covered with gutta-percha, and, as an additional precaution, were surrounded by tight-fitting glass tubes throughout the whole length immersed in the water. The connections, together with the lower end of the6 WALKER AND CORMACK : THE DISSOCIATION tube and the stopper, mere embedded in paraffin wax, a shopt piece of wide rubber tubing being slipped over all before the parafin wax had set. When the apparatus thus protected was placed in ordinary tap water, no current between the wires could be detected with an induc- tion coil and telephone (compare Ostwald, Physico-chemicaZ Mensure- melnts, p. 222) if no liquid were inside the apparatus, The apparatus was filled in the following manner with the solution to be investigated, A bent tube Twas introduced into one of the holes in the stopper so that connection might afterwards be formed FIG.1. FIG. 2. with the measuring vessel N by means of a short piece of rubber tubing provided with a clip. The syringe was now inverted, and the piston withdrawn, so as to leave a little more than 20 C.C. clear space above it. By means of a pipette or burette, 20 C.C. of the liquid to be examined were delivered into the apparatus through the other hole in the stopper, which was then closed by a glass plug, the piston being thereafter forced upwards until the liquid reached the end of the tube 2'. The measuring tube N, which, together with the connection tube, had been previously completely filled with water, was now attached toCONSTANTS OF VERY WEAK ACIDS.7 T, communication between the two vessels being prevented by the pinch-cock C. Both the rubber tube and bent glass tube were chosen of narrow bore so as to prevent mixing of the liquids when the pinch-cock was open. The wliole apparatus was now placed in the upright position in a thermostat containing water a t 18", a t which temperature all measurements in this paper were made. The thermo- stat consisted of a tall enamelled cylinder of about 20 litres capacity, the outer vessel, of a steam steriliser being found very suitable. The mercury cups JfX were fixed in a coppey stage fastened to the rim of the thermostat. The measurements were made mi th induction currents and telephone in the manner described by Kohlrausch and Holborn (Leitvernzogen der EZelctroZyte).For the weakest acids measured, the electrodes were not platinised ; for stronger acids, like carbonic acid, they were platinised with Lummer and Kurlbaum's solution. I n order t o wash the electrodes free from conducting substances after platinisation, we first of all electrolysed a solut,ion of sodium acetate between them as recom- mended by Walker and Hambly (Trans., lS97, 71, 63), after which no difficulty was experienced in rendering them fit for use in a few hours by treatment with water. All the rubber parts of the apparatus were subjected t o the prolonged action of water before being used, and did not affect the conductivity of the purest water we employed during the time necessary for completing a series of dilutions. After the first me:rsurement of the conductivity had been made, the solution was diluted by the addition of 20 C.C.of water, which was admitted by opening the clip C and the stopcock of the measuring tube (a Schiff nitrometer), the piston being then carefully withdrawn until the level of the water in the measuring tube reached the 20 C.C. mark. The clip and stop-cock wcre then closed, and the diluted solu- tion thoroughly mixed by inverting the conductivity vessel several times. The mixing was effected by the glass float Pof approximately the same specific gravity as water. The apparatus was then replaced in the thermostat, and a reading of the conductivity made when tem- perature equilibrium had been established.The solution was again mixed and another reading taken. If this differed from the first, the operations were repeated until a constant value was obtained, which occurred, as a rule, in less than fifteen minutes. The dilution was now continued by the addition of another 20 C.C. of water in the manner previously described, the level of the water in the nihrometer now standing a t the 40 C.C. mark. I n this way, four t o five dilutions by successive increments of 20 C.C. could be made in little more than an hour, without the solution coming in contact with the air during the process.8 WALKER AND CORMACK : THE DISSOCIATION Prepccration of the Whter used f o r Dilution. We found no difficulty in obtaining a supply of water with a con- ductivity of 0.7 x 10-6 in Siemens units, at ISo, by three successive distillations, namely, with alkali, with phosphoric acid, and, finally, with- out the addition of any chemical.The last distillation is the most im- portant, and must be conducted in a room containing no volatile acids or alkalis, the atmosphere even of a well ventilated chemical laboratory being fatal to the preparation of water of the above quality. I n this last distillation, the water was condensed in a tin pipe, the end of which passed through the rubber stopper of a bottle which was further provided with a glass syphon tube and a long, narrow inlet tube for air. I n this bottle, the water suffered no deterioration in quality even when kept for several days. It is essential, if weak acids are to be investigated, that the conductivity of the water used for the prepara- tion and dilution of the solutions should not exceed the above value, otherwise errors of unknown magnitude are introduced into the deter- minations of the conductivity. The conducting power of water of the conductivity 0.65 x is due to dissolved carbonic acid almost entirely, and it will be shown in the sequel that the error thereby introduced into the conductivity of other weak acids is not only very small, but can be estimated and eliminated with moderate accuracy. Carbonic Acid.When carbon dioxide dissolves in water, the solution produced possesses a considerable electrical conductivity, indicating the forma- tion of the acid H,CO,. The conductivity of such solutions have already been measured by Pfeiffer (Ann.Phys. CAem., 1884, 23, 625) and by Knox (ibid., 1895, 54, 44). The solutions studied by Pfeiffer were prepared under pressure, and are therefore somewhat too con- centrated to be of service in fixing the dissociation constant of carbonic acid; the solutions invastigated by Knox, on the other hand, are suEciently dilute to permit of a constant being calculated, although Knox did not seek to perform the calculation himself. KLIOX’S results are given in the following table, the letters bearing their usual signification, namely : v-Dilution, or number of litres in which 1 gram-molecule is p = Molecular conductivity. rn = Proportion of acid dissociated. contained. nG k = Dissociation constant, or the value of the expression - ( I -m)v’CONSTANTS OF VERY WEAK ACIDS.9 I n cnlcu1:tting the dissoci;ited proportion, the molecular conduc tjivitJy of carbonic acid at infinite dilation mas made equal to 536 at 1 8 O , the data used in fixing this number being given below. ?J . 12-61 14.54 18.43 24.9 36.36 53.2 74.3 125 287 1099 p. A 0.731 0.78'3 0.877 1.025 1.233 1.487 1.756 2.300 3,520 7.540 711. 0.002 17 0 4 0 2 35 O.OO86 1 0.00305 0 -003 6 7 0.00443 0.00523 0.00684 0.01048 0.02244 IF. c) .0,37G 379 3iO 375 372 37d 3 'TO 377 386 469 The constancy of the expression k for a tenfold increase in the dilution leaves nothing to be desired. At the two greatest dilutions, the constant increases rapidly owing to the conductivity of the water used in preparing the solulions, for which no correction has been made in the calculation. Before beginning our own experiments on the conductivity of carbonic acid, we made a series of measurements on the conductivity of solutions of sodium hydrogen carbonate, in order to obtain the data necessary for the calculation of the conductivity of carbonic acid at infinite diiutiou.As i t was possible that the sodium hydrogen salt might undergo some degree of hydrolysis at the greatest dilutions we investigated, two series of experiments were made. I n one set, the solution was diluted with water in the usual manner by means of pipettes. I n the other set, the diluent employed vats a solution of carbonic acid, in order that the extent of hydrolysis might be reduced (compare Bredig, Zeit. p1ysik:aZ. Chem., 1894, 13, 214). Both sets yielded practically the same result, as indeed might have been ex- pected, the magnitude of the dissociation constant of carbonic acid indicating that the extent of hydrolysis of sodium hydrogen carbonate would not exceed a fraction of a per cent.even a t the greatest dilution we investigated. The molecular conductivities here, as throughout this paper, are expressed in Siemens units, a O*O2-normal solution of potassium chloride with molecular conductivity equal to 11 2.2 a t 1 So having been taken as the standard of reference. * The molecular conductivities in the abstract of Knox's paper (Zeit. physikal. Cheem., 1895, 17, 186) have been reduced to half the true value by an inadvertence in the recalculation ; the dissociation constant given there is consequently erroneous.10 WALIZER AND CORMAClZ : THE DISSOCIATION V.32 64 12s 256 512 P. 65.6 68.6 71.1 73.9 76-0 These numbers point t o a conductivity of 79.5 for sodium hydrogen carbonate a t infinite dilution (compare Bredig, Zoc. cit., 198). Sub- tracting from this total value the number 41.5 for sodium (Kohl- rausch), we are left with the value 38 for the ion HCO’,. To this we must now add the value 298 for the hydrogen ion (Kohlrausch), and thereby obtain the number 336 as the molecular conductivity of carbonic acid, H*HCO’, a t infinite dilution. The carbonic acid used by us was prepared from marble and hydro- chloric acid, and was washed by passing through two wash-bottles and finally a Geissler potash bulb all filled with pure water. The gas was then bubbled through water of minimum conductivity con- tained in a carefully cleansed bottle.To estimate the concentration of the solution thus obtained, we employed Pettenkofer’s method, the titrations being made with fortieth-normal solutions of bargta and hydrochloric acid. The following table gives the conductivity results for carbonic acid solutions prepared in this way : Caybonic acid, H2C0,, fvom mcwbke. 2). P- 911. k. 31.25 1.038 0.00309 0*0,306 62.5 1.475 0.00439 309 93.7 1.800 0.00536 308 125 2 -083 0 -00 6 20 309 Mean.. . . . . . . .0.0,308 As a very slight amount of impurity, say hydrochloric acid, would considerably affect the conductivity of a weak acid such as carbonic acid, another solution was prepared by passing the gas generated by the slow evaporation of solid carbon dioxide, first through pure water to wash it, and then through water of minimum conductivity.In this way, it was thought that the presence of all conducting impurities would be avoided. As the subjoined table indicates, practically the same numbers were obtained as for carbonic acid from marble.CONSTANTS OF VERY WEAK ACIDS. 11 Cwrboxic cccid, l12W3, jrom solid c a d m i dioxide. 21. lu. 111. k. 27.5 0.972 0 -00 2 8 9 0*0,305 55.0 1.368 0.00407 303 82.5 1.679 0*00500 304 110.0 1.930 0.005’75 302 Mean.. , , . , . . .0*0,304 The value of the constant ca,zulated from our experiments is thus about 20 per cent.. less than t’he value calculated from Knox’s numbers, corresponding to an actual difference in the conductivity of 10 per cent. I n view of the small conductivity of the solutions investigated, this difference cannot be said to be excessive, and is probably to be accounted for as follows.In the first place, the water which we used for the dilutions was of distinctly bett,er quality than that employed by Knox, the conductivity of which varied from 0.95 x lodG to 2.6 x 10-6, and was especially large for the most dilute solutions where its proportionate infliience is greatest. Thus at the dilution 125, the conductivity of the water amounted to 1 2 per cent. of the total con- ductivity of the solution. It is clear, therefore, that this alone might go a long way in accounting for the larger numbers obtained by Knox. The mode of measuring the concentration of the solutions was also different in the two cases. Whilst we used a chemical method for estimating the carbonic acid in the solutions examined by us, Knox determined the amount dissolved by measuring the pressure of carbon dioxide with which the solution was in contact, and then calculating from Bunsen’s absorption coeficient for 18’ by means of Henry’s law.Now Bunsen’s number may ‘be affected by an error of several per cent., as a reference to his paper (Liebig’s Annalen, 1855, 93, 1 ) will show, and it is by no means certain that Henry’s law is accurately true throughout the range of pressures considered. -We are theref ore dis- posed to adhere to our own numbers as being probably the more accurate, notwithstanding the satisfactory constancy of the expression k exhibited when Knox’s values are used in the calculation. Conductivity of Wuter Distilled in Air.On the assumption that Henry’s law was valid, and that the con- ductivity varied inversely as the square root of the dilution, which is very nearly the case for carbonic acid, Knox calculated what the con- ductivity would be if the water was saturated with carbon dioxide a t a pressure equal t o the partial pressure of the gas in atmospheric air. The result given in his paper, viz., 0.56 x 10-6 in reciprocal Siemens units,12 WALKER AND CORMACK : THE DISSOCIATION is, however, erroneous, owing t9 nn arithmetical error in the last equation (Zoc. c i t . p. 57). The correct number deduced from his data is 0.725 x 10-6. A more accurate value can be calculated from the dilution formula, f i t 2 k=- (1 - nqv' as follows. A t 1 8 O , the dilution of a solution saturated with carbon dioxide at a pressure of 760 mm.is, according to Bunsen's absorption data, equal to 24 litres. If the partial pressure of carbon dioxide in air is 0.0003 atmosphere, the dilution of a solution saturated a t this pressure will be 24/0*0003 = 80000. If, then, in the above equation we substitute 0*000000304 for L and SO000 for v, we obtain m=0.144, that is, 14.4 per cent. of the carbonic acid dissolved from normal air by pure water is dissociated into the ions H* and HCO',. From the degree of dissociation m we obtain the molecular conductivity p by multiplication with 336, the maximum molecular conductivity of car- bonic acid a t 1 8 O . From this value, namely, 48.4, we obtain the specific conductivity on dividing by the dilution in cubic centimetres, so that we have the conductivity 4S*4/80,000,000 = 0.605 x 10-6 for water which has been in contact with the atmosphere a t 18".It is highly improbable that Henry's law in an unmodified form can be applied with propriety to such a case as that discussed above. From the study of analogous cases, it appears much more likely that the con- centration of the gas in the air bears a constant ratio to that of the undis- sociatedportion of the dissolved gas, rather than to the concentration of the total dissolved gas. The dilution of the undissociated portion 1 - na thus becomes 80000, and the dilution of the whole gas dissolved 69000. Calculating in the same manner as above described, we obtain the value 0.65 x for the conductivity of water which has been in contact with air.If we use the const,ant derived from Knox's numbers, the values become 0.67 x and 0.71 x 10-6 for the un- modified and modified forms of application of Henry's law respectively. Kohlrausch (Zeit. phgsikal. Chem., 1894, 14, 321) found that water prepared in a vacuum and of conductivity 0.11 x gained in con- ductivity on being left in contact with the air until the value 0.60 x was reached. It is also stated by Kohlrausch and Holborn (Zoc. cit., p. 111) that the lowest conductivity obtainable for water dis- tilled in air is 0.65 x 10-6. It will be seen that these values are in excellent agreement with those calculated from our experiments, so that we may assume with confidence that carbon dioxide is the only substance in the atmosphere which confers conductivity on water.CONSTANTS OF VERY WEAK ACIDS.13 State of Carbon Dioxide in Aqueous Solution. I n what has been said above, it is assumed that all the dissolved carbon dioxide exists in the aqueous solution as carbonic acid, H,CO,. This is by no means necessarily the case, for a large proportion might exist in the solution as carbon dioxide without entailing any alteration in the apparent dissociation constant. We may suppose, for example, that only half of the dissolved carbon dioxide exists in the solution as H,CO, and its dissociation products K* and HCO’,. If v, as before, represents the volume in which 1 gram-molecule of the carbon dioxide is dissolved, irrespective of the condition it assumes in the dissolved state, the dilution formula becomes since the quantity of H,CO,, which was formerly 1, is now only 4.Now, in solutions of this strength which we investigated, m does not amount to more than 0.006, so that we can write the dilution formula in the form k nt2 - _ - V without sensible error. in the solution as H,CO,, this formula becomes If only half of the dissolved gas is contained We have therefore Ic’ = 2k. The real dissociation constant of the acid H2C0, would therefore, in this case, be twice the apparent dissociation constant, namely, equal to 0*0,608. I n general, if 1/n represents the fraction of the total dissolved carbon dioxide which exists in the solution as H,CO,, the dissociation constant for the acid will be nk, where k is the apparent dissociation constant calculated from our experiments.What is here stated holds good, however, only for moderate degrees of dilution and for moderate values of n, for as soon as nz becomes of dimensions approaching those of l/n, the simple formula can no longer be applied. We have assumed above that the proportion of the dissolved gas which remains as (30, is constant and independent of the dilution of the solution. This assumption is justifiable, since the active mass of the solvent water must remain sensibly constant for dilute solutions, and the quantity converted into H,CO, will therefore be proportional t o the quantity dissolved. It is possible, however, that t.he equi- librium is: between the CO, in solution and the wzdissocicctetl H,CO,, ilot14 WALKER AND CORMACK : THE DISSOCIATION the whole amount of H,C03 and its dissociation products.For moderate dilutions and moderate values of n, this latter assumption in no way alters the deductions given above. Since we obtain a constant value of 7c for dilutions up to 125 litres, the value of m cannot be very great-cannot, for instance, well be more than 5, for otherwise Ostwald’s dissociation formula would not be applicable in its simple form.. The agreement, too, between the actual and calculated values of the conductivity of water which has absorbed carbon dioxide from normal air points to the value of n, being small, probably not greater than 2. We may take it, then, as fairly certain that when carbon dioxide dissolves in water, at least half of the dis- solved substance exists in the form of the acid H,CO,. It is only the apparent dissociation constant which is of interest to US, however, for it is that which enables us to calculate the strength of carbonic acid in solution as an accelerator, as a conductor of elec- tricity, or as competing for a base against other acids.A knowledge of the real constant, and of the constant regulating the equilibrium, H,O + CO, = H,CO,, would be of undoubted theoretical interest, but for practical purposes and ordinary solutions, the apparent constant supplies us with all the information necessary for the treatment of problems likely to occur. IIyclrogeiz Su Zphide. I n 1885, Ostwald determined the conductivity of hydrogen sulphide, and found that it was very small. No constant can be calculated from his numbers, however, as at that date the influence of the quality of the water employed in making the solutions was insufficiently under- stood.We therefore made several determinations with the best water we could obtain, and with hydrogen sulphide as free as possible from foreign conducting matter. The hydrogen sulphide was prepared by the action of hydrochloric acid on a very concentrated solution of pure sodium sulphide, and was subjected t o no other purification than thorough washing with water, the final mashing taking place through water contained in a Geissler potash apparatus. If the hydrochloric acid is added at such LZ rate that the disengagement of hydrogen sulphide is slow and steady, the method gives a product of constant conductivity. The strengths of the solutions thus prepared were estimated by adding a measured quantity of the solution to a known excess of silver nitrate solution, filtering, and determining the amount of silver in the filtrate by Volhard’s method.The maximum conductivitly of hydrogen sulphide, treated as theCONSTANTS OF VERY WEAK ACIDS. 15 monobasic acid HoHS, was fixed by means of measurements of the conductivity of sodium hy drosulphide, NaHS (Walker, Pvoc. Roy. 8oc. Edin., 1893-4, 255). These measurements give 58 as the ionic rate for HS', and therefore 356 as the maximum conductivity for hydrogen sulphide at 18". H@rogen sulphide, H*HS'. V. F- m. k. 25 0.426 0.001 19 0*0,572 50 0.599 0~00168 568 75 0.731 0*00205 562 100 0.854 0*00240 577 125 0944 0-002G5 56s Mean.. . . . .0*0,569 Another similar set of experiments a t somewhat smaller dilutions gave the mean value 0*0,574, which is practically identical with the former result. Since the impurity in the water used for dilution is carbonic acid, the dissociation constant of which is known, it is possible to correct the individual values of the conductivity by using the dissociation equations for the separate acids. As Lthe correction in this case, however, is of very small dimensions, it may be neglected without sensible error. An example of the method of calculation employed in the correction will be given when the conductivity of phenol is under consideration. Hydrocyanic Acid. We are again indebted to Ostwald for measurements of the electric conductivity of hydrocyanic acid. H e found the conductivity t o be considerably smaller than that of hydrogen sulphide, but, as before, his numbers are not sufficiently accixrate to permit of the calculation of a dissociation constant, owing to the uncertain correction for the conductivity of the water employed as solvent.I n our experiments we used water of conductivity not exceeding 0.65 x lowG, and even with water of this quality experienced much difficulty in obtaining satisfactory solutions. The method me finally adopted for preparing solutions OF hydrocyanic acid was first t o prepare a liquid acid very nearly free from water, and then allow the vapour of this to pass slowly into the water of minimum conductivity, The liquid hydrocyanic acid was obtained by gently heating a mixture of potassium ferrocy anide nud glacial phosphoric acid with an equal bulk of wnher, and condensing the vapour in a cooled dis- tilling flask.When x sufficient quantity had been collected, the16 WALKER AND COHMACK : THE DISSOCIATION distilling flask mas disconnected from the generating apparatus and attached t o a delivery tube which dipped beneath the surface of the water used as solvent. As the conductivity of the hydrocyanic acid was very small, the solutions were made as strong as was consistent with the theoretical possibility of obtaining a constant value for the expression k. J t was found that non-platinised electrodes gave better results than those which had been platinised. Kohlrausch has shown that the molecular conductivity of potassium cyanide in concentrated solutions (normal and semi-normal) is inter- mediate between the molecular conductivities of equivalent solutions of potassium chloride and potassium iodide.As these two salts have practically the same molecular conductivity for infinite dilution, it was assumed that the conductivity of potassium cyanide would have a maximum value equal to 121.6, which gives 60 for the ion CN’ and 358 for the conductivity of HCN a t infinite dilution. The concentration of the original solution was determined with silver nitrate solution according to Liebig’s method. Hydrocyanic ucicl, H*CN’. V P nz k a 0.0183 0.00005 12 0*0,131 4 0.0262 738 133 8 0.0320 894 133 16 0.0365 1019 130 Mean.. . . . 0*0,132 Another set of experiments gave a mean value of 0*0,14, and several preliminary experiments gave still higher values.We have chosen the smallest value as being the most probable, owing to the fact that any possible impurity would increase the conductivity and thus the constant. The constant as it stands is probably still too high, for even the presence of the carbonic acid in air-saturated water would effect an increase of about 2 per cent. on the mean value. Boilic Acid. Kahlenberg and Schreiner (Zeit. physikuZ. Chem., 1896,20, 547) have shown that in all probability only one boric acid exists in solution, namely, H,BO,, and that in dilute solutions the only stable salt is of the type NaH,B03. From their conductivity numbers, it would appear that the maximum conductivity of the salt Na.H,BO3 is about 75.0 at IS0. Now this number is certainly too great, as Shields has provedCONSTANTS OF VERY WEAK ACIDS.17 that a decinormal solution of borax is hydrolysed to the extent of one- half per cent. The conductivity of the sodium hydroxide produced by the hydrolysis is much greater than that of an equivalent solution of the boric acid salt, so that we must make a deduction of at least 3 per cent. in order t o obtain an approximate value of the maximum con- ductivity of the non-hydrolysed salt ; this would lead to R value of somewhat more than 72. In order to check this result, we made a series of determinations of the conductivity of the salt at 18O, using a 0.025-normal solution of boric acid as dilution liquid in order to diminish the hydrolysis. From our experiments, we deduced the value 71.5 as the maximum conductivity of the salt NaH2B0,, supposing hydrolysis to be absent.This value would give 328 as the maximum conductivity of the acid H,BO, if the dissociation is into theions H* and H,BO',. The boric acid we employed in our experiments was thrice recrystal- lised from pure water in a platinum vessel, and the solution made up by weight. The electrodes used in the final experiments were not platinised, but platinisation did not seem to affect the accuracy of the method or alter the numbers obtained. Boric acid, H*H,BO',. 9. P- rn. k. 11.1 0-0450 0*0000137 0.081 70 22.2 0.0636 194 169 33.3 0,0783 239 171 44.4 0.089 1 272 166 Mean ............ 0'0,169 Another set of experiments yielded the mean value 0.08170. This constant is of the same magnitude as that for hydrocyanic acid, and a similar correction would have t o be applied to eliminate the effect of the conductivity of the carbonic acid in the water employed for dilution. Bock (Ann.Phys. Chem., 1887,30, 638) made some observations on the electric conductivity of boric acid solutions at lao, but the solu- tions he employed were stronger than ours, and the results he ob- tained do not yield a value for k which is even approximately constant. If, however, we take his most dilute solution, which is comparable with our strongest solution, we obtain the following : V. CC. m. k. This value is in excellent accordance with that obtained in VOL. LXXVII. C 8 0.0386 0.0000118 0.081 74 own experiments. our18 WALKER AND CORMACK : THE DISSOCIATION Phenol. Bader (Zeit.physikal. Chent., l890,6, 289) has given numerous data for the conductivity of the phenols and their substitution products. Many of the substitution products yield definite dissociation con- stants, but this is not generally the case with the simple phenols themselves. Thus he obtains for phenol, C,H,*OH, the following values at 25’ : 9. P* k. 60 0.23 077 100 0.41 120 Here the value of the expression k varies greatly, a fact which is possibly due to the character of the water employed in the dilutions. Bader gives no figures from which we can judge the quality of this water. As we suspected that Rader’s numbers for phenol were considerably too high, we determined the conductivity of as pure a solution as we could produce, A quantity of colourless crystallised phenol was shaken up in a stoppered cylinder with successive small quantities of pure distilled water in order to remove any conducting substance which the phenol might contain.A solution of this purified phenol was then made up by weight, the phenol being assumed to have taken up 26 per cent. of water, in accordance with the experiments of Alexkeff. 25 0.1 4 0*0,056 The results we obtained were as follows : t’ . Pa 10 0.0132 m. 0*000041 It will be seen that this value is only about one-tenth of that ob- tained by Bslder for the molecular conductivity under corresponding conditions of temperature and dilution. Rut this value must itself be too great. The specific conductivity of the water used to prepare the solution was 0.65 x 10-6, the specific conductivity of the solution being only twice this magnitude, namely, 1-32 x 10-6.We are not justified in assuming, however, that the conductivity of the phenol is equal to the difference of these two numbers, for if carbonic acid is the impurity present in the water, each acid will lower the dissocia- tion, and therefore the conductivity, of the other, so that the cor- rection will not be so large as at first sight appears. The mode of correction is as follows. For the maximum conductivity of phenol, we have the number 322 according to the rule established by Ostwald for organic acids. The degree of dissociation of the phenol solution is therefore 0.000041 if we take the uncorrected conductivity. The concentration of theCONSTANTS OF VERY WEAK ACIDS. 19 hydrogen ions is therefore one-tenth of this, namely, 41 x and this number is practically correct, since the hydrogen ions are responsible for at least seven-eighths of the conductivity, and the difference in the speeds of the carbonate and phenolate ions vanishes in comparison.The equilibrium in the case of carbonic acid is regulated by the equation (H ions) x (HCO, ions) - - - 3.04 10-7, (H,CO,) the quantities in brackets indicating concentrations in gram-molecules per litre. Now the total concentration of the carbonic acid dissolved from the air is 125 x 10-7 in the same units. If n is taken to repre- sent the concentration of the HCO, ions, we have thus the equation 41 x x ,n - = 3-04 10-7, (125 x lO-T)--n whence n = 9 x 10-7. The number of hydrogen ions coming from the carbonic acid in the water is therefore 9 x 10-7.This deducted from the total concentration of hydrogen ions leaves 32 x 10-7 as the con- centration of hydrogen ions derived from the phenol, so that this number also represents the concentration of the C,H,O ions. Now the product of the hydrogen and phenolate ions in the above solution must be equal t o the product of the same magnitudes for a solution of phenol in water free from carbonic acid. If d therefore represents the concentration of dissociated phenol in the pure solution, we have d2 = 41 x 10-7 x 32 x 10-7 d== 36 x 10-7, whence we obtain as the degree of dissociation of a pure decinormal solution of phenol, n = 0*000036 instead of the uncorrected value, Om000O4l. Using this corrected value, we find k = 0*0,13 as an approximate value of the dissociation constant of phenol, that is, about one-fortieth of Bader’s smallest value of k.Acetylene. Jones and Allen (Amer. CAem. J., 1896, 18, 1 ) give numbers for the conductivity of acetylene which are very much too high, probably as the result of some arithmetical error. The values they obtained when recalculated from equivalent into molecular weights indicate that acetylene is a stronger acid than acetic acid, which is certainly not the case. We made a single experiment in order to determine the magnitude of the conductivity of aqueous solutions of acetylene. The acetylene c 220 THE DISSOCIATION CONSTANTS OF VERY WEAK AClbS. was prepared from calcium carbide and purified by washing in suc- cessive bottles containing silver nitrate solution, the gas being there- after thoroughly washed with pure water.A small quantity of pure water was then saturated with the gas a t the atmospheric pressure. Since water dissolves about its own volume of acetylene a t the ordinary temperature, the dilution of the solution thus obtained would be approximately 23, a number which we confirmed by precipitating with ammoniacal silver nitrate, filtering, and titrating the excess of silver in the filtrate with ammonium thiocyanate. The conductivity of this solution was only one-fourth greater than that of the solvent water, and this slight rise might conceivably be due in great part to the presence of a trace of some conducting impurity. We must there- fore conclude that acetylene has very feeble acid properties, its dissociation constant being less, and in all probability much less, than that of phenol.Xurninar y . The following table contains the dissociation constants of the acids which we investigated, the constant of acetic atid being added for comparison : Acid. k x lolo. Acetic .............................. 180000 Carbonic ........................... 3040 Boric ................................. 17 Hydrocyxnic ........................ 13 Phenol ............................. 1.3 Hydrogen sulphide ............... 570 A better idea of the relative strengths of the acids, however, may be formed from the subjoined table, which shows the percentage dis- sociation of the acids in decinormal solution. The numbers for hydro- chloric and acetic acids are derived from the data given by Kohlrausch and Holborn (Zoc.cit.), the numbers for the other acids being calculated from the dissociation constants found by ourselves. Pewentage degree of dissociation in decinormcc! solution. Acid. Acetic ................................ Carbonic ................................ Boric .................................... Hydrocyanic.. ....................... Phenol ................................ Hydrochloric .......................... Hydrogen sulphide .................. 100 m. 91.4 1.30 0.1 74 0.075 0.01 3 0.01 1 0.0037YREPARATIOK AND PROPERTIES OF SOLID AMMONIUM CYANATE:. 21 These numbers, inasmuch as they are proportional to the avidities, give a practical indication of the strengths of the acids. Thus, if acetic and carbonic acid compete for a monacid base, all three sub- stances being in molecular decinormal solution, the base will be shared between the acids in the ratio 1.3 : 0.174, that is, the acetic acid will take eight parts of the base for one taken by the carbonic acid. Again, if carbonic acid and hydrogen sulphide compete in equivalent quantities for an equivalent of R base, the carbonic acid will take seven-tenths, and the hydrogen sulphide three-tenths. In the extreme case of hydrochloric acid competing against phenol in decinormal solu- tion, the phenol gets only 1 part in 22000. For acids weaker than acetic acid, the degrees of dissociation are in the ratios expressed by the above table for practically all dilutions, since they are, in fact, proportional to the square roots of the dissocia- tion constants. All the acids in the table have been treated as monobasic acids, so that molecular quantities are always considered, not equivalent quantities. We are justified in proceeding thus, for each acid in competing with mother acid for a n insufficient quantity of a base, behaves in the first instance as a monobasic acid. Possibly the assumption would not be quite accurate for the case of carbonic acid competing for a n equivalent of base against phenol, but where the polybasic acid is the weaker of the competing pair, the assumption is in every case justifiable. As to the probable accuracy of the numbers, it may be said that the conductivities and constants €or the weakest acids are undoubtedly somewhat too high. We are of opinion, however, that the error is in no case very considerable, for our results are in close agreement with the hydrolysis determinations of Shields (€‘Id. Mag., 1893, [ v], 35, 365), data now being available for the comparison of the two methods. A discussion of this connection between the conductivities of the weak acids and the extent of hydrolysis of their salts in aqueous solution will appear in another place. UNIVERSITY COLLEGE, DUNDEE.