ELECTROMETRIC DETERMINATION OF THE HYDROLYSIS OF SALTS. 41V.-The Electrometric Determination of the Hydi*olysis0 f Salts.By HENRY GEORGE DENHAM, M.A., M.Sc., 1851 Exhibition Scholar,University of New Zealand.Introduction.NUMEROUS methods have been employed for measuring the amount ofhydrolysis in salt solutions. Amongst the most important of thesemay be mentioned those depending on the determination of theinversion of sucrose, the hydrolysis of methyl acetate, electricalconductivity, lowering of freezing point, and distribution betweentwo solvents. These methods have been employed in the researchesof Ley (Zeitsch. physikal. Chern., 1899, 30, 193); Bruner (Zeitsch.physikal. Chem., 1900, 32, 133); Walker and Aston (Trans., 1895,67, 576) ; Bredig (Zeitsch.physikd. Chew,., 1894, 13, 289) ; Kahlen-berg, Davis, and Fowler (J. Arne?*. Chem. Soc., 1899, 21, l), andCarrara and Vespignrtni (Gnzzetta, 1900, 30, ii, 35.None of these methods is really satisfactory for the measurementof very small concentrations of hydrogen ions, and, although Bredigand Fraenkel (Zeitsch. Elektrochem., 1905, 11, 525) have recentlydescribed a new method whereby concentrations of hydrogen ionsdown to N/lOCO can be accurately determined, nevertheless thepresence of neutral salts produces a disturbing effect, thus renderingthe practical applicability of the method rather difficult.In the present paper, the hydrogen electrode has been used for thepurpose of determining the concentration of the hydrogen ions inaqueous salt solutions.This method is particularly suitable whenwe are dealing with very small concentrations, and it thereforepromised to be very useful in many cases when the methods hithertoemployed become difficult of application. It suffers, however, fromthe disadvantage that it cannot be employed in the case of the saltsof metals less ‘ I noble ” than hydrogen, nor in the case of multivalentcations (such as Fe”’) which are reduced by hydrogen to cations ofsmaller electrovalency, nor is the method admissible in the case ofsalts with reducible anions as NO,’, CIO,’. During the course ofthis work, papers have been published by Bjerrum, in which the samemethod has been employed in the study of solutions of chromiumchloride. Reference will be made to these later42 DENHAM : THE ELECTROMETRICThe Equilibrium Equations of Progressive Suit HpdrolysiS.I n dealing with the salts of multivalent cations, the hydrolysis mayoccur progressively in several stages, to each of which corresponddefinite equilibria.If aluminium chIoride is taken as an example, theprogressive stages of the hydrolysis may be represented by the threofollowing purely stoichiometric equations :. . . . . . . AICI,+H20 =AICI,(OH) + HCl (1)AICl, + 2H,O - AICl(OH), + 2HC1 (2)AICI, + 3H,O = Al(OH), + 3HC1 (3). . . . . . .. . . . . . .The mechanism of equation (1) may be represented by the twoionic equilibria :. . . . . . . . (AlC12)* +OH' z2 AIC12(OH) , (14H ' + O H = H , O . (4)(AICl,). + H,O AlCl,(OH) + H' ( W.. . . . . . . . .which may be combined in the simple equilibrium equation :. . . . . . .Denoting molar concentrations by square brackets, we have from(la) and (4) :. . . . . . . . [AlCli]. [OH'] = k,,[AlCl,(OH)] ( 5 )[He]. [OH'] = K, (6) . . . . . . . . . . . . .and therefore[AlCI,'] = ~[AlCl,(OH)][H'J . . . . . . . . . (7). K wIf we now make the simplifying assumptions that aluminiumchloride and hydrochloric acid are completely ionisad according t othe equations :AICJ, AICl,D+Cl',HC1 H'+Cl',and if v denotes the molar dilution of the "total" aluminiumchloride (hydrolysed and non-hydrolysed), and x the fractionalamount hydrolysed, it follows from the above equations and assump-tions that[AlCI,'] = 3, [H'] = [AlCl,(OH)] = E,whence from (7) we haveIt must be observed that LX denotes the fractional amount oDETERMINATION OF THE HYDROLYSIS OF snrs.43hydrolysis according to the first stage (equation l), and that thevalidity of the equations, [H'] = [AlCl,(OH)] = depends on theusually made assumption that the value of [N'] is very considerablygreater than the value corresponding to the dissociation of pure water.This "first-stage" hydrolysis is due t o the formation of therelatively undissociated basic salt, AICI,(OH), which may be regardedas the hydroxide of the complex cation (AlCl,').Let us now imagine a state of affairs wherein the hydrolysis corre-sponds to the stoichiometric equation (2), that is to say, to the forma-tion of the relatively undissociated basic salt, AlCl(OH),.Regarding the latter as the hydroxide of the complex cation AlCl",we might suppose that the second-stage hydrolysis would correspondto more dilute solutions, wherein the dissociation of the aluminiumchloride would proceed chiefly or largely according to the equation :AlCl, AlC1" + 2Cl".Assuming that the dissociation of the aluminium chloride accordingto this equation is complex, and denoting by z the fractional amountof hydrolysis according to equation (2), we obtainU'X 2z [AlCl"] = A-y-?, [hlCl(OH),] = -, [H ] = -.The second-stage hydrolysis being controlled by the equilibrium :AlCl" + 2(OH) z AlCI(OH), . .. , . . , . . (9)together with (6), yields the equations :[AICl"][OH']2 = kb,[AlCI(OH),] and[AlCl"] = %2, [AlCl(OH),].[H'],,Kwwhich, on the above assumptions, givesKw2- K2 . . . . . . . . . . . . (10). (-=K2- X2The third-stage hydrolysis corresponding to the stoichiometricAssuming complete equation (3) may be dealt with in a similar way.dissociation of aluminium chloride according to the equationand a hydrolysis controlled by the dissociation equilibrium :AICI, Al"'+3C1',Al"' + 30H' Al(OH),,[Al"'] = %3[Al(OH)s] . [H*l3,we have [Al'.'] . [OH']3 = kb3[A1(OH)3]Ku44 DENHAM : THE ELECTROMETRICI - % X 3s and therefore, since [Al***] = -:, [Al(OH),] = --, and [H 3 = -2) V V ,For .z chloride of a bivalent cation, the first-stage hydrolysis corre-sponds t o equation (S), and the second stage t o equation (10).I n the case of a sulphate of a tervalent cation, such as aluminium,the stoichiometric equations representing the progressive hydrolysisare :A12(S04), + 2H20 = A12(S04)2(OH), + H2S0,,A12(S04)3 + 4H20 = Al,(SO,)(OH), + 2H,S04,AI2(SO4), + 6H20 = Al,(OH), + 3H2S04.Corresponding to the first of these equations, we have the dissociationequilibrium :which leads toAl,(SO,)** + 20H' t Al,(SO,),(OH),,[AI,(SO4)"] [OH']2 = kh[AI2(SO4),(OH)21-Assuming complete dissociation according to the equations :H2804 = 2H' + SO,"A12(S0,), = A12(S04)iD + SO4",and putting x=fractional degree of hydrolysis, we obtain as theequation for the first-stage hydrolysis :(12).. . . . . . . . . . . - ~ - - - XI - K " 2 - K l .(1 -x)v' 4kblIt might be possible t o write the dissociation equilibria, also, asfollows :A12(S04), 2AlSO,'+ SO,"Also,' +OH' z2 Al(SO,)(OH),leading thus to the equations :[AISO,'] .[OH'] = kb,[AlSO,OH][AlSO,'] =$ [AlSO,OH] . [H'].K*2x [H'] =;, and 2x In this case, [Also,.] = u, [AlSO,OH] = -,thus the equation corresponding to the first-stage hydrolysis would be(1 3). G" ~- - - = K l . . . . . . . . . . . .(1 -X)V 2kb,X 2On this view, the corresponding stoichiometric equation wou Id be :Al,(SO,), + 2H,O = 2AI(SO,)(OH) + H2S0,DETERMINATION OF THE HYDROLYSIS OF SALTS. 45Corresponding to the second-stage hydrolysis, we get by similarreasoning the equation :--- x5 - Kw4 = K z . a . . .(1 - X)V* 256 kb2where ka, is the dissociation constant of the basic salt,dissociating into the ions AI,SO,"" and 40H'.stoichiometric equation :I n the case of the third-stage hydrolysis, it is possible to write theAl,(SO,), + 6 H,O = 2Al( OH), + 3H,so,.The hydrolysis in this case may be supposed to be controlled by thedissociation equilibrium,[Al"' ][OH']3=k~,[Al(OH),].Assuming a complete dissociation of A1,(S0,)3 .according to theequation :we arrive at the equation :Al,(SO,), = i?Al'** + 3SO,",where cz is the fractional degree of hydrolysis according to the aboveequation.I n the case of a sulphate of a bivalent cation, there is only one stageof hydrolysis possible, and to this corresponds a cubic equation in x ofthe same form as equation (10) or (12). Similarly, for the sulphate ofa univalent cation, the equation of hydrolytic dissociation is the sameas (8).I n attempting to test any of the equations given in the precedingparagraphs, three points must be borne in mind.I n the first place,certain simplifying assumptions have been made with respect to thenature and degree of the ionisation of the salts and acids involved.I n the second place, the stages of the progressive hydrolysis consideredmay not be sharply marked off, with the result that a superposition ofthe different equilibria may occur. Finally, the solubilities of thebasic salts or hydroxides may be overstepped, so that heterogeneousequilibria are produced. Furthermore, if, as very often happens, thebasic salts or hydroxides separate in the form of colloidal pseudo-solutions or suspensions, it may be expected that no definite equilibriawill be obtained.The second and third of these difficulties reside in the nature of thephenomena themselves, and cannot be surmounted.The first difficult06 DENHAM : THE ELECTROMETRICmentioned may, however, be obviated to a certain extent by intro-ducing suitable corrections. Thus in the preceding theory the totalconcentration of the acid that must be produced according to thestoichiometric mass-relationship has been identified with the concentra-tion of the hydrogen ion. This will, however, not in general be true,even for the highly dissociated mineral acids. In the case of thechlorides of chromium and aluminium dealt with below, a correction hasbeen made for the undissociated hydrochloric acid on the assumption thatthe percentage amount of undissociated acid would be the same as ina pure hydrochloric acid solution of the same total concentration ofchlorine ions. I n the case of the sulphate of aluminium, it has notbeen possible to apply a similar correction, owing to the want ofsufficiently secure data concerning the dissociation of the ion HSO,'.Appuratus and Metlbod of Measurement,The hydrogen electrode employed was constructed after the typedescribed by Wilsmore (Zeitsch.physikal. Chem,, 1900, 35, 296). Theother half-element consisted of a normal mercurous chloride electrode.The hydrogen and mercurous chloride electrodes were connected by asaturated solution of ammonium nitrate, which Abegg and Gumming(Zeitsch. Elektrochem., 1907, 13, 17) have recently shown to annul theliquid potential difference.The rest of the apparatus consisted of aslide-wire bridge, accumulator, cadmium cell, and Lippmann electro-meter. The temperature at which the experiments were carried outwas 2 5 O , const,ancy of temperature being secured by a suitable water-thermostat. The hydrogen used for saturating the electrode wasprepared from electrolytic zinc and pure dilute sulphuric acid, andpassed through a waahbottle containing an alkaline solution of potassiumpermanganate.The solutions were always prepared from conductivity water(1.2 x 10-6 to 2.5 x by siphoning the required quantity on to aweighed amount of the salt. The solutions were kept in steamed-out Jena flasks, and whenever they were kept for more than a daythey were protected with a soda-lime tube to guard against the entryof carbon dioxide.The potential of the hydrogen electrode is given by the formula :where rL = the potential of a solution of concentration [H'];r,, = potential for a solution normal in respect to H'-ion, andR, T, P have their usual significations. 111 accordance with theagreement of the Commission on Electrode Potentials of the GermanBunsen Society, under electrode potential is here understood positivDETERMINATION OF THE HYDROLYSIS OF SALTS.47potential of the electrode-positive potential of solution. If we takethe absolute potential of the normal calomel electrode as + 0.56 volt,we may (Wilsmore, Zoc. cit.) put 7ro= + 0.277 volt. The method ofcalculation employed may, for the sake of clearness, be brieflyillustrated by two examples :( a ) Table I, p.48.Cell measured, H2 1 m/32C6H;NH,C1 { NH,NO, I Hg,Cl, electrode.Observed E.M.F. = 0.4655 volt (in direction indicated by tbearrow). Hence potential of the hydrogen electrode = 0.56-0*4655 =RT 0.0945 volt, and therefore Fl~ge[H'] = 0.0945-0.277 =3- ---RTF - 0.1825. As T = 273 + 35 = 298, we have - x 2.3026 = 0.059,0.1825 and therefore log[H'] = - - whence [H'] = 0.000807. Since0.059 'complete hydrolysis mould produce a value of [H'] 'equal to 1/32(assuming complete dissociation of the hydrochloric acid), the per-centage hydrolysis is given by the equation lOOx = 0.000807 x32 x 100, whence lOOx = 2-58 (x =fractional hydrolysis).(b) Table (XII), p.57.Cell measured, H, I m/4A1,(S04)3 I NH,NO, I Hg2C12 electrode.Observed E.M.F. = 0-4354 volt,Potential of H,-electrode = 0.56-0-4354 = 0.1246 volt.Hence 0.069 log[H'] = 0*1246--0.277 = - 0,1524, whence [H'] =0 ~00261.Since the solution is one-fourth molecular normal with respect toaluminium sulphate, complete hydrolysis according to the stoichio-metric equation :Al,(SO,), + 2H20 = Al,(SO,),(OH), + H2S04,mould yield a one-fourth molecular normal solution of sulphuric acid.I f one assumes complete dissociation of the sulphuric acid into theions H' and SOL', the molar concentration of the hydrogen ionwould be 0.5. Hence the percentage hydrolysis according to theabove reaction is given by the equation :__lfAniline Hydrochloride.The hydrolysis of this salt has been very carefully determined byBredig (Zeitsch.plqsikal, Chena., 1894, 13, 289) and by Walker an48 DENHAM : THE ELECTROMETRICAston (Trans., 1895, 67, 576). [Bredig used the conductivity method,and found 2-61 per cent. hydrolysed for v3, at 25'. Walker used theinversion method, and found 4.5 per cent. for v8,, at 60°. A re-determination of the hydrolysis of this salt appeared to be a usefultest of the method employed in this paper.The salt used was purified by recrystallisation from a saturatedsolution in acetone, the solvent being removed by repeated washingwith ether. It was finally dried over potassium hydroxide and con-centrated sulphuric acid in a vacuum desiccator.I n the table below, as well as in all following tables, v denotes themolecular dilution, E.M.F. the measured electromotive force of thecell in volts, rrl the absolute potential of the hydrogen electrodefor that solution, [H'] is the hydrogen-ion concentration in gram-mols. per litre, and 100~: is the percentage hydrolysis calculated fora first-stage hydrolysis, unless the contrary is stated.TABLE I.Aniline Hydrochloride.Cell, H, I C,H,*NH,Cl 1 NH4N03 I Hg,Cl, electrode.21. E. M. F. TI * H' x lo2. 1oox. Kl x lo4.16 0.4567 0.1033 0.1138 1'82 0.2124 0.4609 0'0991 0'0966 2.32 0.2332 0.4655 0'0945 0.0807 2.58 0.21Mean ... ... ... ... 0.216Under Kl are tabulated the values of the constant calculated fromequation (S), ___ = K l , as deduced for a first-stage hydrolysis of asalt of this type.The hydrolysis for v32 amounts to 2.58 per cent., avalue agreeing extremely well with that found by Bredig tit the sametemperature and dilution, 2-61 per cent.X3(1 -x)vThe Apparent Heat of Dissocicttion of Anilz'nium Hydroxide.''The hydrolytic constant of aniline hydrochloride is calculated fromx2equation (a), --- - ",. If the dissociation of a normal electrolyte(1 - x)v KOis measured over n range of temperature not too great, i t is generallyfound to be practically independent of the temperature. Therefore,knowing XI, at 25' and the variation of K, with the temperature, oneshould be able to calculate x for any other temperature. But as Kwat 60' is nine times as great as at 2 5 O , i t follows that the hydrolysisof aiiline hydrochloride for vs0 at 60' would be 7.5 per cent., whilsDETERMIBATION OF THE HYDROLYSIS OF SALTS.49Walker and Aston (Zoc. cit.) found only 4.5 per cent. The conclusionmust be drawn that the dissociation constant of “anilinium hydr-oxide ” is not independent of the tempernture. An application ofvan’t Hoff’s equation,d log& - RTddt Q__should therefore give information regarding q, the apparent heat ofdissociation. On integrating between the limits TI, T2, we getlog& - Q (T - .T’) ----- &’ R yl’yl ’where &“, Kb’ are the dissociation constants of ‘‘ anilinium hydroxide ”a t the temperatures T” and T.If 5 is calculated from the percentage hydrolysis obtained byWalker and Aston at 60°, the value !& = 0.707 x 10-4 results; a tas0, 5’ = 0.216 x and from these results q is calculated to be2860 calories ; q here refers to the heat absorbed in the dissociationof “ anilinium hydroxide ” plus the heat absorbed in the hydration ofthe anhydrous aniline.KbZ bKbAmmonium ChEoride.The hydrolysis of this salt mas recently measured by Veley (Trans.,1905, 87, 26).The method he used was to boil the solution for anhour, and then determine the loss of ammonia by titration. The con-clusion was drawn that the hydrolysis of ammonium chloride must bevary small indeed.As usual, the salt was freed from any traces OF acid by repeatedrecrystallisation from conductivity water. A normal solution wasfirst used, and the potential registered by the hydrogen electrodeamounted to - 0.0049 volt after thirty minutes, but in an hour it hadrisen to 0.0066 volt.This steady increase in potential, and thereforein hydrogen-ion concentration, pointed to the loss of ammonia, audthis was conclusively proved by passing the escaping gas into a solu-tion of red litmus. I n orderto overcome this loss of ammonia, three washbottles were insertedbefore the hydrogen electrode, all containing a solution of the samestrength as was being measured, One washbottle was outside thethermostat, and two within. Thus when the hydrogen reached thesolution containing the electrode, it was already in equilibrium withammonia a t that temperature and concentration.The observed potential wasIt very quickly turned a decided blue.One other difficulty still remained,VOL.XCIII. 50 DENHAM : THE ELECTROMETRICfound to fall to a minimum, and then rise a little to a fixed, but higher,value. The steady fall to a minimum is duo to the gradual saturationof the electrode with hydrogen, and the subsequent rise can only bedue either to the electrode having been supersaturated or to anincrease in the hydrogen-ion concentration. The first possibility maybe left out of consideration, for in no other salt used did this occur.The increase in the hydrogen-ion concentration can be readilyexplained as being due to the adsorption of ammonia by the electrodefrom the film of liquid in contact with it, The potential registeredwould be that of the surrouhding film, and mould consequently be toohigh. The hydrogen and ammonia gases are occluded by the platinum,the former probably with a much greater velocity, and hence thelowest potential registered would, on this assumption, correspondvery nearly to the true potential. Slight evidence in support of thisi s furnished by the fact that the hydrogen-ion concentrations calcu-lated from the higher potentials are practically the same, althoughthe concentration of the solution has changed from N/2 to N/32 ; butthe hydrogen-ion concentrations calculated from the lower potentialsshow differences much more in accord with the behaviour of allknown hydrolysed salts, that is, with increasing concentration of thesalt there is an increasing hydrogen-ion concentration, but a decreasingpercentage hydrolysis. As it was a matter of very great difficulty toobtain values for the minimuzh potential when it changes so quickly, anumber of independent experiments were carried out, and the meanminimum potential recorded,TABLE 11.Ammonium Chloride.2).281632Cell, H, 1 NH,C1 I NH,NO, ('Hg2C12 electrode.h'. M.F. Tl* [H-] x lo8. 1002. Kl x l o p .05732 - 0'0132 1'233 0'00246 0.3005911 - 0'0311 0.604 0'00479 0.290.5998 - 0.0398 0.427 0'0068 0.290.6056 - 0.0456 0'340 0-oioa 0.360 '3 1-Mean, . . . . . . . . . . .X2 The constant K , is calculated from equation (8), ~ - L c y = K l , for afirst-stage hydrolysis of a salt with univalent anion. The experimentalerror arising from the adsorption mentioned has prevented moredilute solutions being examined, but enough has been done to showhow small is the hydrolysis of this saltDETERMINATION OF THE HYDROLYSIS OF SALTS.51The ratio €or the hydrolytic constants of aniline hydrochloride andammonium chloride is seventy thousand, that is, aniline is seventythousand times as weak a base as ammonium. Bredig (Zeitsch. physikal.Chem., 1895, 13,289) has found the dissociation-constant of ammoniumhydroxide to be 0.0023, and Abegg (Die elekt. Dissociation-theorie,Ahreus’ ‘‘ Vortrage,” 8, 183) gives the dissociation-constant of anilineas 4.9 x10-10. The ratio of the constant of ammonia to that of‘‘ anilinium hydroxide ” is 60,000. Since the hydrolytic constant ofaniline hydrochloride agrees so well with that found by Bredig, weare justified in concluding that the hydrolytic constant of ammoniumchloride is tolerably correct.Moreover, Noyes, in his report, ‘‘ The Electrical Conductivity ofAqueous Solutions ” (p.346), has calculated the per cent. hydrolysis ofammonium chloride (v = 100) to be 0.02 a t 1 8 O , whilst extrapolationfrom the above values (Table 11) gives 0.018 for this dilution a t 25’.Chromium Chloride.A great deal of work has been done on the green and bluemodifications of chromium chloride, Amongst others, the work ofGodefroy (Compt. rend., 1885, 100, 105) ; Peligot (Compt. rend., 1885,100, 105) ; Recoura (Ann. Chim. Phys., 1887, [vi], 10,39) ; Wernerand Gubser (Ber., 1901, 34, 1579), and Gubser (Inccug. Diss., Zurich,1900) may be mentioned.The work of these goes to show that theformula of both varieties is CrCI,,GH,O, but in the green chloride twoatoms of chlorine cannot be precipitated by silver nitrate, as they formpart of a complex cation. Recently, Bjerrum (Zeitsch. physikal. Chem.,1907, 59, 336) has shown that the blue chloride, when dissolved inwater, is hydrolysed, thus :CrCl, + H,O = CrCI,(OH) + HC1.The hydrolytic constant of the green salt is only about one four-hundredth that of the blue. The method used by him to measurethe hydrolysis was the determination of the potential of the hydrogenelectrode and conductivity measurements.Hydrolysis of the Greeya Chloride.-This chloride was preparedaccording to the method described by Recoura (Eoc. cit,) and Wernerand Gubser (Zoc.cit.),Bjerrum has very carefully examined the solution of the greenchloride, using an apparatus whereby he was enabled to obtain a poten-tial within two minutes, and a conductivity measurement in even lesstime. He has found that tho hydrolysis as indicated by the potentialobserved is at first much less than for the blue chloride, but thatthere is a rapid increase of hydrolysis in the first few hours.Unfortunately, the apparatus used in the present work was unsuitableE 52 DENHAM : THE ELECTROMETKlCfor obtaining readings in such a short time, for it required a t leastten minutes to obtain a constant potential. A more or less qualita-tive series of experiments with the green solution has therefore beencarried out in order to check Bjerrum's results.A solution of the green chloride was prepared and divided into twoparts, and to one was added a few drops of concentrated hydrochloricacid.These two samples were allowed to stand at the ordinary tem-perature. In sixteen hours, that which had not been acidified wasbluish-green, whilst the other remained green. I n three days, thelatter was still unchanged, but the unacidified sample was blue. Theaddition of the acid had evidently retarded the formation of the bluesalt from the green, consequently the change of the green into theblue must be attended by the increase of acid concentration throughan increase of hydrolysis.A solution of concentration vO4 was then prepared, and readingswere taken for two hours; t denotes the time in minutes since thesolution was made.TABLE 111.Cell, H2 I CrCI, (green) 1 NHI,NO, [ Hg,CI, electrode.v = 64.t.E. ill. F. =1 [H'] x lo2.20 0 '4545 0.1055 0-12440 0.4526 0.1074 0-133120 0.4458 0.1142 0.174TABLE IV.1.20354575105v = 16.E. af. F. "1.0'4355 0.12450.4268 0.13320.4220 0.13800'4180 0'14200'4180 0.1420[ I I ~ x 102.0.2600.3173.44105140-514TABLE V.V = 32.t. I$. ill. l? = I ' [EI'] x 10'.15 0.4559 0.1041 0.11732 0.4471 0'1129 0'16655 0,4368 0'1232 0'247These experiments all show that there is a rapid rise in the hydrogen-ion concentration, and, as the hydrolytic constant found by Bjerrumand by me for the blue chloride is very much larger than thDETERMINATIOK OF THE HYDROLYSIS OF SALTS.53approximate constant found by him for the green chloride, he is quitejustified in his conclusion that the rapid increase in hydrolysis is dueto a progressive conversion of the green chloride into the blue.Chromium Chloride (blue).The salt was prepared as described by Higley (J. Amer. Chem. Soc.,1904, 26, 613).TABLE VI._I_, --Cell, H, I CrCl, I NH4N0, I Hg,Cl, electrode.V. E. M. F. R1' [H'] x loy. [H'] x lo2. 1002.4 0'4234 0,1366 0.417 0510 2.028 0 '4332 0.1278 0'296 0.351 2'8116 0'4382 0'1218 0'234 0'269 4 3 032 0.4455 0.1145 0.176 0.19T 6'30'64 0'4523 0.1077 0.135 0.148 9'47TotalI n Table VI, ' I total [H']" refers to the concentration of thehydrogen ion after a correction has been made for the undissociatedhydrochloric acid, as already explained.Figure 1 shows x plottedas a function of v.9.48163264TABLE VII.1oox. K~ x 103. K, x 107.2'02 0.10 0'652'81 0'10 0.434 '30 0'12 0-406'30 0.13 0.319.47 0.15 0.270 '12-Mean.. . . . . . . . . . ,Here Kl refers to the constant calculated for a first-stageX2 hydrolysis from equation (8), ~ - -q; (1 - x)vand K2 has been calcu-x3 lated for a second-stage reaction according to equation (10) - --- ' (1 - x)v2'x here being, also, calculated for a second-stage reaction, 'that is,half the values tabulated above. Although Kl varies somewhat, itsvariation is much less than that of K,. Undoubtedly, therefore, themain reaction must be represented by the ionic equation :CrCI,' + H,O CrCI,(OH) + H',but probably the basic salt, CrCl(OH),, is also produced in the dilutesolutions as in the equation :CrCl" + 2H,O CrCl(OH), + 2H'54 DENHAM : THE ELECTROMETRICAt any rate, Bjerrum (Zoc.c;t.) has also noticed the rise in the constantin the dilute solutions. The percentages of hydrolysis given inTable VI are slightly larger than Bjerrum found, for his constantamounts to 0.98 x but consideringthe great influence a slight erroy in the E.M.F. exerts, the agreementmust be considered quite satisfactory.as compared with 1.2 xFIG. 1.105116 64 256Aluminium Chloride.This salt was prepared from a specimen obtained from Merck byprecipitating it from a saturated solution with hydrogen chloride.The salt was left for a month in a vacuum desiccator over potassiumhydroxide to remove any traces of adhering acid.Preliminary experiments with zinc sulphate, which will be describedlater, had already shown that a solution of this salt does not give thDETERMINATION OF THE HYDROLYSIS OF SALTS.55April 26 ............ 0.4485,, 27 ........... 0.4607,, 26 ............ 0.4537same hydrogen-ion potential from day to day, but that an extra-ordinary change in the hydrogen-ion concentration of the solutionoccurs. Thus it was important to determine whether the solutionof each salt examined gave a constant potential over a considerablenumber of days, proving that the solution was in a state of equili-brium. This was done in a I' time" experiment, wherein a quantityof a solution was siphoned from the main stock into the apparatusevery day, and its potential ascertained for a sufficient number ofdays to show that equilibrium had set in.It was not necessary to dothis in the case of the chromium salts, because it is known from thework of Richard and Bonnet (Zoc. ait.) and Bjerrum that the solutionsslowly change their hydrogen-ion concentrations until equilibrium isreached ; nor were '' time " experiments carried out with aniline hydro-chloride or ammonium chloride, for here there is no possibility of solidbasic salts or hydrates complicating the ionic reactions.The '' time " experiment for aluminium chloride showed that withintwenty-four hours a state of equilibrium is reached, as is shown in thefollowing table.TABLE VIII.April 27 ............ 0.4607,, 29 ............0.4606,, 29 ............ 0'4605Cell, H, 1 AlCl, I NH,NO, ,- 1 Hg2C12 electrode.All solutions in the following experimenk were therefore allowedto stand in the thermostat for twenty-four hours before measure-ments were made.TABLE IX.Aluminium Chloride.Cell, H, I AlCl, I NH,NO, I Hg2C1, electrode. + --TotalV. E. M. F. =I - [H'] x lo2. [H'] x lo2. 1OOz.16 0'4492 0'1108 0'1520 0-1750 2.832 0.4567 0'1023 0-1140 0.1270 4-0664 0.4655 0.0945 0.0807 0,0885 5'66100 0.4720 0.0880 0.0626 0.0679 6.79128 0.4741 0.0859 0.0577 0.0620 7'93Figure 1 shows x plotted as a function of v56U.163264100138DENHAM : THE ELECTROMETRICTABLE X.1002. K~ x 104.2-80 0.504-06 0.535.66 0.536.79 0'407-93 0.530 5 1-Mean.. , .. . . . . . . .XI is calculated from equation (8) for a first-stage hydrolysis,2 2 - Kl ; the value obtained clearly shows that the hydrolysis ( l - z q v -proceeds according to the ionic equation :AlCI,' + H,O t AlCI,(OH) + He.A comparison of the percentage hydrolysis of chromium andaluminium chlorides at similar dilutions shows that the chromiumchloride is, on the average, hydrolysed 1.6 times as much as thealuminium chloride. From these experiments, it would appear thatchromium is about 1.6 times as weak a base as aluminium,Compa&on of Results for AZuminium ChZo.r.ide.Kahlenberg, Davis and Fowler (Zoc. cit.) have found 2.2 per cent.hydrolysed in a sixth-molecular normal solution at 55.5'. Ley (Zoc.cit.), working at 9 9 * 7 O , where the hydrolysis is much greater, obtainedthe following results.TABLE XI.9.326412825 65121002.8-0413'2019'7028.2041-40K~ x 104.2'23 -13 -84'35.7Here x and Kl refer to a first-stage hydrolysis, the latter beingX2calculated from equation (8), -- (I - x ) v - =I*His results at 99.7" are roughly about twice those observed by theLey has made one determination of the hydrolysis of aluminiumHe found 13.5 per cent.Bruner (Zoc.cit.) worked at 40' and found at w4 3.3 per cent., at v8He is the onlyauthor at a lower temperature.chloride by conductivity methods at 25'.hydrolysed at v,,,~~.2.9 per cent., and at vS2 2.9 per cent, hydrolysedDETERMINATION OF THE HYDROLYSIS OF SALTS.57worker who has not found increasing hydrolysis of this salt ondilution.Recently, Bjerrum (Zoc. cit., p. 349) carried out a series of experi-ments on the hydrolysis of aluminium chloride a t 25O, using con-ductivity measurements. He says '( Ley hat fruher die Hgdrolyse desAluminiumchlorids in 3/1024-molarer Losung zu 4.5 pro cent.(alle Salzsaure frei = 100 pro cent.) berechnet. Dieses entspricht13.5 pro cent. Hydrolyse nach der Gleichung AlCI, + H,O =AlC1,OH + HCl. Ich finde 16.6 pro cent." Two misstatementsoccur here. Ley worked throughout (Zoc. cit.) with molecular solu-tions, and it was in a solution 1/1024-~noZecuZar normal that heobtained 13.5 per cent. hydrolysis; secondly, the solution in whichBjerrum records 16.6 per cent.hydrolysis is, according to his owntable, one containing 0.000326 of a gram-molecule, that is, v = 3069.These misstatements both appear to be due to confusion betweenmolecular normality and equivalent normality. Further comparisonof Bjerrum's results must be left over until the errors mentionedhave been corrected.A lw niiniunh SuZpha t e .The salt was obtained from Merck, and was freed from any tracesof acid by precipitating it from a saturated solution by the additionof alcohol.Just as in the case of aluminium chloride, there was a slightchange of hydrolysis in the '' time " experiment during the first day,but after that time the potential registered remained quite constantfor the next three days. I n the following experiments, the solutionswere kept twenty-four hours in the thermostat before measurementswere made.TABLE XII.Aluminium Sulphate.Cell, IT, I AI,(SO,), I NH,NO, I Hg,Cl, electrode.v.E. M. F. n,. [H*] x lo2. 1 0 0 ~ . Kl x 108. K X 10".4 0'4354 0'1246 0-261 0.522 0 -88 0.688 0'4439 0-1161 0.187 0.748 0'66 0.7116 0-4505 0'1095 0.145 1 *160 0 '62 0.8532 0'4541 0.1059 0'126 2-016 0*82 1.3064 o m r i 0'1016 0.106 3.492 0.98 1-86256 0.4672 0 *0928 0.075 9.600 1'48 4.00Figure (1) shows the variation of x with v. In the above table, Klx3 is calculated from equation (12), _____- - Kl , for a first-stage hydro-(1 - 4 v 2lysis of a salt of this type, The rise in the value of Kl from w2558 DENHAM : THE ELECTROMETRICpoints to the probability that with increasing dilution the second-stage hydrolysis is becoming increasingly important.The reactionfrom v4 to wC4 is represented by the stoichiometric equation :and by the ionic equation :but in more dilute solutions we have also :A12(S04), + 2H20 = A12(S04)2(0H)2 + H2S04,A12(S04)2" + 2H20 t A12(S04)2(OH)2 + 2H',A12(S04), + 4H20 = A1,(S0,)(OH)4 + 2H2S0,Al,(SO,)"" + 4H20 Al,(SO,)(OK), + 4H'.The constant g i n the above table has been calculated from equationP3), (ix-qj. This equation has been deduced on the assumptionthat the reaction is represented by the stoichiometric equation :A12(S04), + 2H20 = 2A1(S04)(OH) + H2S04,and the ionic equation :AISO,' + OH' Z Al(SO,)(OH).The constant K shows considerably more variation than does Kl,although in the concentrated solutions K is as constant as can beexpected for such concentrations.X2Comparison of Res2jts for Aluminium SuEphate.Bruner (Zoc.cit.) at 40' found 1.3 per cent. hydrolysed a t v12, 1.4 perLey (Zoc. cit.) at 99*7O found 8.9 per cent. at v256, and 5.4 per cent,Kahlenberg, Davis and Fowler (Zoc. cit.) at 55.5' found a hydrolysisof 1.56 per cent. for v12.Finally, Carrara and Vespignani (Zoc. cit .) measured the hydrolysisof this salt at 25' by the inversion of methyl acetate. The basis ofthis method is to compare the constant of the reaction for a salt withthat obtained for a dilute solution of an acid where the dissociation iscomplete, that is, where the hydrogen-ion concentration can beidentified with the total-acid concentration.Now these workers havecompared their constant for aluminium sulphate with that of sulphuricacid, both fifth-molecular normal, and thus obtained a percentagehydrolysis of 2.6. It is obviously incorrect to identify the hydrogen-ion concentration of a fifth-molar solution of sulphuric acid with thatof the total acid, and any such assumption must cause a very largeerror in the calculation, If the percentage hydrolysis is calculatedfrom the constant of aluminium sulphate and that obtained bythem for hydrochloric acid (v&, according to the equation, percent-cent, at v2,,, and 1.7 per cent. at v , ~ .at '128DETERMINATION OF THE HYDROLYSIS OF SALTS. 59age s the result is 0.81. But a fifth-molar solution of hydrogenKavachloride is only dissociated t o the extent of 80 per cent,, and on cor-recting for this the percentage is found to be 0.65.This agreesextremely well with the value 0.52 given in Table XI1 for v4.ThaElous Sulphate.The salt was supplied by Kahlbaum, and was not further purified.The solutions were all acid towards litmus, and owing to the sparingsolubility of the sulphate only a few solutions were examined.Although the solution vI6 was observed for several days, no changein the amount of hydrolysis was detected. Apparently the hydrolyticequilibrium is established immediately on preparing the solution.TABLE XIII.-+ ---Cell, H, 1 Tl,SO, I NH,NO, I Hg,Cl, electrode.v. E. M. F. A1. [H'] x lo2. 1002. Kl x lo?.16 0.4137 0-1463 0.609 4.87 0*1532 0'4213 0.1387 0.448 7.15 0'170.4309 0'1201 0.311 9 *95 0 -17 640.16-Mean... ... ... ...X The constant XI is calculated from equation (S), A, for afirst-stage hydrolysis of a salt with univalent cation; the value ofKl is practically constant, and this shows that the hydrolysis mustproceed according t o the ionic equation :T1' + OH' =. Tl(0H).(1 - x ) vNickel Xulphate.The salt was prepared from a specimen of Kahlbaum's by carefulrecrystallisation. The *' time " experiment again showed a variationin the hydrogen-ion concentration, although much less than observedin the salts of zinc, magnesium, thorium, and cerium60 DENHAM : THE ELECTROMETRICTABLE XIV.Nickid SUlphC6te ; v = 32.Cell, H, I NiSO, I NH,NO, I Hg,CI, electrode.Days. E.Af. F. Tl' [H.] x lo30 0.5031 0.0569 0.1861 0.4966 0'0634 0'2303 0.4962 0.0638 0.2444 0-5023 0-0577 0.1925 0'5003 0.0597 0.2076 0'4098 0-0602 0.211---- >The first column denotes the age of the solution in days.In the following series of experiments, in order to make the resultscomparable, the potentials were measured ten minutes after the solu-tions were made; but as the "time" experiment shows a slightvariation in the hydrogen-ion concentration, one cannot expect toobtain a satisfactory constant.Cell, H, I NiSO,4 0.5302 0'02988 0'5362 0.023816 0.5400 0.020032 0-5518 0-008264 0.5637 -0.0037v. 3.AI.F. r1.TABLE XV.+ --NH4N03 I Hg,CI, electrode.[H-] 104. ~ O O X . K, x 1012. K x 108.0.647 0.013 0-14 0.420.512 0.020 0-1 3 0.520'440 0.035 0.17 0.770.278 0.044 0.09 0 '620.175 0.056 0'04 0'49 -Mean... , , . . . . . . . 0 '1 123 Kl has been calculated from equation (12), -I-- - = Kr, for a first-stage hydrolysis of a salt of this type; ZC is the constant calculatedfrom equation (13), - = K.(1 - x)v222(1 -x)wThe first constant Kl is sufficiently satisfactory to show that thehydrolysis proceeds according to the ionic equation :Ni" + 20H' t Ni(OH),.The constant K is again satisfactory, although the equation fromwhich it is calculated lacks the possible theoretical foundation that ithas in the case of aluminium and chromium sulphates.Eahlenburg, Davis and Fowler (Zoc. cit.) have measured thehydrolysis of nickel sulphate (v4) at 55*5", and found 0.045 per cent.hydrolysed. This compares well with that quoted in the above tablefor the same dilution, namely, 0.013 per cent.a t 25DETERMINATION OF THE HYDROLYSIS OF SALTS. 61Cobalt Xulphate.This salt was prepared from a specimen of cobalt carbonate (freefrom nickel) by the action of sulphuric acid. The sulphate so formedwas three times precipitated from a strong solution by the addition ofalcohol. Finally, the sulphate was recrystallised from water. The" time " experiment was followed for five days, but the hydrogen-ionconcentration showed very little change from the value first obtained.TABLE XVI.-+ --Cell, H, I CoSO, I NH,NO, I Hg,Cl, electrode.7'. E. M. F. =1. [H'] x 104. 100s. li; x K x lo9.2 0.5487 0.0113 0.313 0.0031 0 * i 6 0.484 05590 0*0010 0.210 0.0042 0 *46 0 '448 0'5675 -0.0075 0,163 0.0065 0.43 0-5316 0'5762 - 0.0162 0.107 0'0085 0'24 0'4532 0'5798 - 0.0198 0.093 0.0149 0.32 0.69-Mean... . . . . . . . . , 0 '4439 I n table XVI, Kl is calculated from equation (12), ____- = Kl,for a first-stage hydrolysis of such a salt. The value of Kl is muchtoo high in the strongest solution, but for the others it is sufficientlysatisfactory to show that the ionic reaction is :(1-x)v2CO" + 20H' Co(OH),.X 2 Here, also, K, calculated from the equation (13), -~ = K, (1 -x)vgives a much better constant, and yet this equation again appears tolack a theoretical basis.Nickel Chloride.The salt was purified by careful recrystallisation. A solution ofmedium strength was measured for four days, and a decided increaseof the hydrogen-ion concentration took place within the first twenty-four hours, rising from 0.00014 to 0*00018.No change beyond thelimits of error occurred on the three succeeding days. I n the follow-ing experiments, all solutions mere therefore allowed to stand inthe thermostat for twenty-four hours before being measured.In order to obtain the hydrolytic constant, a concentrated solutionwas prepared and its strength determined by analysis ; other solutionswere prepared from this by dilution62 ELECTROMETRICCell, H29. 3. M. F.4 ' 4 0'49278.8 0'503.217.6 0.510935.2 0.5229DETERMINATION OF THE HYDROLYSIS OF SALTS,TABLE XVII.I NiCI, I NH,NO, ['Hg,CI, electrode."1. [H'] x lo3.1oox. K~ x 105.0.0683 0'290 0.127 0.360.0568 0.184 0.16 0.290'0481 0.132 0'23 0 '270.0371 0.086 0.30 0'300 *30-Mean.. . , . . . . . . . ,XZ The values under Kl are calculated from equation (8), ____-for a first-stage hydrolysis of a salt with a univalent anion. Thesatisfactory nature of the constant shows that the reaction is correctlyrepresented by the ionic equation :NiCl' + OH' Z NiCl(0H).(1 - x)v,Zinc Sulphccte.The salt mas purified by recrystallising it three times from con-ductivity water ; an analysis gave SO4 = 33.43 and 33.41, whilsttheory requires SO, = 33.40 per cent.The "time" experiment for this salt was, as usual, carried outwith every precaution against chance impurities ; but, although varioussolutions were measured daily for four weeks, yet no sign appeared ofan equilibrium having been reached, the h ydrogen-ion concentrationvarying irregularly from day t o day.A solution of zinc chloride showed an exactly similar phenomenon.Owing to the similarity between zinc and magnesium sulphates, i twas expected that a similar variation in the hydrogen-ion concentra-tion, that is, in the hydrolysis, would be met with.The variationwas again observed, but not to so marked an extent as in zincsulphate. The percentage calculated for magnesium sulphate of con-centration v32 from the mean hydrogen-ion concentration is 0.0023,agreeing well with that found by Carrara and Vespignani. Theyused a fifth-molecular normal solution, and found 0.0047 per cent. atthe same temperature.The '' time "experiment again showed that the hydrolysis is by no means aconstant quantity. The variations were not large, but yet quitemeasurable.Solutions of cerium chloride showed undoubted variations in thehydrolysis from day to day. The mean percentage for vep is 0.14,whilst Ley found 0.5 for the same dilution a t 90.7".Thorium sulphate (v= 64) has also been examined.The mean percentage for v64 is 46ATTEMPTED SYNTHESIS OF DINAPHTHACRIDINES 63Finally, it may be mentioned that cobalt chloride shows considerablevariation in solution ; the mean percentage for g32 is 0.17, and forVI6 0.1 1.The most probable explanation of the peculiar behaviour of thesesalts lies in the theory that the hydrolysis leads to a heterogeneoussystem, and that basic salts and hydrates are present in colloidalsuspension.Xunzmary.1. The preceding experiments have proved that the hydrogenelectrode can be used to determine the hydrolysis of salt solutionseven when the hydrogen-ion concentration is as low as 0.3 x (seeammonium chloride).2. The hydrolytic constant of ammonium chloride proves ammoniato be about 70,000 times as strong a base as aniline.3. The salts of chromium are hydrolysed about 1.6 times as muchas the salts of aluminium, and chromium may therefore be consideredabout 1.6 times as weak a base as aluminium.4. Nickel salts are more strongly hydrolysed than those of cobalt,and in this connexion it is significant that the electropotential ofcobalt is higher than that of nickel (Wilsmore, Zoc. cit.).5. The salts of zinc, magnesium, cerium, thorium, cobalt, and, to aslight degree, nickel show peculiar behaviour in so far as theirsolutions present a variable degree of hydrolysis from day t o day.I n conclusion, I wish to acknowledge my deep debt of gratitude toProfessor F. G. Donnan for his ever-ready assistance and kindlyencouragement during the course of these experiments.THE MUSPRATT LABORATORY OFPHYSICAL AND E LECTRO- CH E JI ISTRY,UNIVERSITY OF LIVERPOOL