CONCEPTION OF HYDROGEN IONS IN CATALYSIS, ETC. 2187CCXXI. -An ExamzTmtioiz of tlbe ComeptioiL d' Hydi.0-yen Ions in Ccbtcdysis, Salt Fomaation, and Electro-lytic Conductioii.By ARTHUR LAPWORTH.['(LTt 1.WITH E. Fitzgerald the present author has shown that the additionof water to a liquid, such as alcohol, containing an acid leads to areduction in the number of hydrogen ions * present, and has found thatthe retardation of esterification and ester hydrolysis by water cannotbe explained by hydration of the intermediate products in the esterifi-* The term " hydrogeii iuri I ' ruf'ers tliroughout to the non-hydmtrd ion, or, inother words, to that supposed t o be responsible for hydriop catalysis2188 LAPWORTH : AN EXAMINA'I'ION OF THEcation process. Tbe Arrhenius view of the way in which water hydro-lyses the salts of weak bases was also found to be inadequate t o thecase.To obtain quite convincing evidence from esterification experimentsas to the non-validity of the latter asstiniption would be extremelydifficult, owing to complisation arising from the large number ofsubstances present.Experimental attack on a different line wasnecessary, and i t was therefore sought to determine, first, whetherhydrion cat,alyses, other than those already known, were affectedby water in a similar manner; secondly, if so, whether it would bepossible to obtain for examination a case in which the amount ofwater compared with that of the substance catalytically changedmight be made very small.The Transformation of Hydrazobenxene into Beneidine in AlcoholicSolution.This well-known change, which is brought about by acids, wasespecially interesting, because here the substance changed is not acarbonyl compound.A solution of this substance in absolute alcohol was divided intoquantities of 10 C.C.in test-tubes containing respectively 0, 0.2, and0.4 C.C. of water. To each was then added 5 C.C. of absolute alcoholt o which a little sulphuric acid had been added. Benzidine sulphatebegan to appear in the first tube in about five seconds, in the nextin forty seconds, acd in the last in eighty seconds. This observationwas frequently repeated under similar conditions, with results of thesame nature, showing that the effect of water on the catalysis ofhydrazobenzene in absolute alcohol is of the same order as its effecton catalysed esterification; the speed of change over a wide rangeis about inversely as the amount of water present.Fairly concordantresults are obtained if a standard tube is used to ensure a definitedegree of opalescence a t the point timed.The Bs.omination of Ketones.The bromination of carbonyl compounds has already been shown tobe catalytically accelerated by mineral acids, and in the case ofacetone the speed of the disappearance of the bromine is n measure OFa change in the ketone itself (Trans, 1904, 85, 31, et sep.).Solutions of a number of ket,ones, including acetone, menthone, andacetophenone in alcohol, were acted on by bromine in alcoholic solu-tion with hydrogen chloride as catalyst.I n all cases the speed withwhich a given quantity of bromine disappeared was nearly inverselCONCEPTION OF HYDROGEN IOXS IN CATALYSIS, ETC. 2189proportional to the concentration of water present when the quantityof water was more than one per cent. of the total weight.The following widely digerent, cases of hydrogen ion catalyses inalcohol had thus been shown to be affected by water in a similarmanner, namely, the decomposition of diazoacetic ester (Bredig andFraenkel, Ber., 1906, 39, 1756, et seq.), esterification of carboxylicacids (Goldschmidt), the change of .hydrazobenzene into benzidine,and the bromination of ketones. This suggested that a commonexplanation of them all is to be looked for, but hydration of the sub-stance undergoing catalysis still remained a possible, although asamemhat remote, one.The bromination of acetone appeared to offer a means of decidingthis point, for here a n enormous excess of the catalysed compound ascompared with the water could be employed.It has been shownthat the speed of disappearance of the bromine is a measure of thespeed of a change i n the acetone (compare Trans., 1904, 85, 31).Influence of Small Quantities of Water on the Velocity of Brominationof Acetone without Xolvent.A quantity of anhydrous acetone ( A ) was mixed with a little drybromine, and another quantity ( B ) with a few drops of sulphuric acid.After placing these in a thermostat at 25' for some time, portions of25 C.C. of A were then measured into 50 C.C.flasks containing varyingquantities OF water, also kept immersed in the thermostat, and subse-quently 25 C.C. of B were added,and the time elapsing between its additionand the complete disappearance of the bromine was taken. Thefollowing results were obtained ; the numbers given under in the thirdline are obtained by assuming the water value 0.10 for 50 C.C. ofacetone, a number calculable from the first and last observation.The experimental error in the time observation amounts perhaps toabout 10 seconds :Water = 0 0.1 0.25 0.5 0.75 1'00 gramsTime = 45 85 155 265 400 510 sees.Calc. = - 98 164 278 394 -A number of other experiments with this and other specimens ofacetone gave similar results, but different specimens differed slightlyin their water values, as was to be expected, since traces of moistureso greatly influence the speed. Experiments on a smaller scale withacetone, which had been prepared from the bisulphite compound andpurified with every care, gave results of the same order8190 LAPWVOR'PH : AN EXAMINATION OF THEPhenomena very similar to those observed in alcohol or acetoneare noticed in other oxygenated organic media, and markedretardation by water of acid catalysis occiirs to a greater or lessextent in ether, ethyl acetate, and other common Iiquids which dissolvewater. The different extent to which these respond is dealt withelsewhere.The suspicion that the effects noticed are due to impurities in thewater may be dismissed at once; these effects are so considerable thatin order that they might be caused by, say, an alkdi, it would benecessary to suppose the water to contain impossible quantit,ies of this.'i Mathenzahd I'reatment of the Question.Probably the main difficulty in obtaining acceptance of the view,t h a t the influence of water on catalysis by acids is accounted for bya reduction in the number of hydrogen ions, or, in other words, by adiminution of the available acid, lies in the initial difficulty i n demon-strating t h a t the conception is in accordance with the generalisations ofOstwald and his school, and in showing that i t can be applied t o t h efacts as readily as the original conception of Arrhenius, which, in i t sfirst form, is not consistent with the phenomena of acid catalysis,For this reason, and for the further consideration of variousaspects of the question, it will be necessary to develop, on strictlines, and first assuming the presence of bydrogen ions as the activecatalysts, an expression for the state of a monobasic acid, HR,in a mixture of basic liquids.Representing the amounts of eachliquid by the symbols W, TV', etc. respectively, those of their complexeswith hydrions as J, l', etc., and tho corresponding undissociatedcompounds as S, S', S", etc., the following expressions represent thest&e of equilibrium. No allowance in the general. expressions needbe made for a possible union between the bases, as this would simplyresult i n t,he introduction of more constituents of the series W,with corresponding additions to the series 8 and I. The symbolsS, S', etc.include the acid united with the solvents whether ionisableor not, and represents the total anions of the acid whether unitedto the liquids JV, W', etc., or not. Y is t h e volume occupied by thesystem, and A is the original amount of acid. All quantities areexpressed in gram-equivalents. Naturally, K, K2, etc. may be expectedto vary with a n alteration in the proportions of the solvent constituent,s,but will otherwise be constantCONCEPTION OF HYDKOGEN IONS IN CATALYSIS, ETC. 2191s = . (3') &'= I ' - K . etc,,/i. ' K'. P 'also(4) H + N K + ZZ + SS' = A ( where S I = I + I' + etc.).(5) IItz + I2 + SS= A (where S S = ,5'+ S" + etc.).Whence may be derived :(6) from (4) and ( 5 ) , S I + N=K.(7) from (2) and (2'),K JY Hence 21 = I--2S-, 1' = "'.K2K2. w' w ri,whereW tV JV' S- = - + - + etc. -+K2 L' K2 K'?(8) from (3)!IV v or, putting - =active maw, M, etc.from (2)'where(9) but from (6), (7), and (2),(10) By combining ( 5 ) , (l), and (S),(1 1) and introducing (9),L and for 1 gram.equivdent of acid2192 LAPWORTH: AN EXAMINATION OF THEConcerztration of Ifyd?*ogen Ions at IncfirLite Dilution.A t infinite dilution the term not containing Y must be neglected.(12) andA 11-2 fll + 1’&?or at in&zite dilution the hydrogen ions in solutions containing A grctnz-M equivalents of all acids have the same concentration, 8- beidg in-dependent of the acid and depending only on the nature of the solvent.This is in accordance with the well-known generalisation that themolecular activity of all acids as measured by their effect in invertingsucrose and hydrolysing esters tends towards a maximum value whichis the same for all acids.*lizRelation between Molecular Conductivity ctnd the Number ofHydrogen Ions.The conductivity is given by the sum of the number of the ions ofeach kind x its mobility:=Spul+p.lH+vR2T.w H W’ =p-+p’-+etc.+plH+vNfi,.v fry. v(13) :that is to say, the molecular conductivity is proportional to thenumber of hydrogen ions multiplied by a constant which dependsonly on the nature of the solvent. I n other words, the relationshipbetween the so-called degree of dissociation of an acid (as measured byits conductivity) and the hydrogen ions is independent of the nature ofthe acid.This is in agreement with, the generalisations of Ostwald andArrhenius, who have shown that the power of an acid to hydrolysemethyl acetate, or to invert sucrose, is the same for d l acids at thesame degree of dissociation as measured by electrical methods.** The generalisations, 3s thus stated, are not strict, bot the 1)oint insisted on isthat the expressions evolved as ahovp, are in Rgreemmt with the experimentalfacts to precisely the same extent as are those derived 113’ the application of theoriginal ionisation theory of acidsCONCEPTION OE’ HYDROGEN IOXS IN CATALYSIS, ETC.2193Variation of (( Degyee of Dissociation ’’ wit?& Kdunae of Solutio?~.The degree of dissociation, x, of an acid as at present measuredwhich, from the conductivity at voliime Vconductivity at intiiiite volume’represents the ratio =H a t vol.VH at intinite dilution’last paragraph = -Brit from (9) above,henceR x= -M1’A (from 11 above),RAx=- or R = A x (=x, when A = l ) . so thatXReplacing H i n the equation (10) by -_____ , a n d A by I ,8-+lKz2that is t o say, the foregoing view leads t o precisely the sameexpression as is applied at the present time t o the ‘‘ dissociation ”of weak acids as measured by their electrical conductivity, namely,where k is the “ dissociation constant.”x2 + xkv = kv,(15) This gives the dissociation constant of the acid :Mk = .---- 71 M - + B -- K , KK,2r* + 1or, in aqueous solution2194 LAPWORTH: AN EXAMINATION OF THEwhere M is the active mass of liquid water, and K is the ionicdissociation constant of the hydroxonium salt.It is clear from the preceding formula for k that the morestrong basic solvents (where - is large) mill.tend to minimise theinherent differences in potency between strong acids, so that i t may beanticipated that mineral acids which have nearly equal constants inwater will show very considerable divergencies in less basic solvents,such as ether or alcohol.I n order to demonstrate in a simple manner that this must be thecase, for the moment let the simplifying assumption be made that thedissociation constant OF the hydroxonium salts of strong acids is thesame, =K.14The above may be writtenI n the case of bases of the strength of water, the hydrogen ionshave been shown to be very few, that is, K2 is very small, and may beneglected in comparison with M .XK2is constant, and the intrinsic acidic affinity o r potency of t h ek acid, Kl, is therefore proportional to - - K - k’Taking two fairly strong acids, A and 6, with dissociationconstants in water nearly equal to that of salts, say, 0.95K and 0*9If,their relative intrinsic acidity is given by OSg5 - 0*90 -- - 19 and 90.05 and 0.1respectively. That is, whilst their true sfinities are in the ratio 2.11,their affinities in water appear to be only in the ratio 1.05.I n respect to this point, Goldschmidt and Sunde have shown (Ber.,1906, 39, 719) that, although picric acid appears nearly as powerfulas hydrochloric acid in aqueous solution, yet in alcoholic solu-tion it has only about one-tenth of the catalytic activity of thelatter.Similarly, picric acid and trichloroacetic acid differ far morein alcohol than in water, and similarly with di- and tri-chloroaceticacidsCONCEPTION OF HYDROGEN IONS IN CATALYSTS, ETC. 2195Hyholpsis of Sults in A Zcoholz'c und Siniikcr Media by rater.TVccter T'alue of Solvents.The effects of adding a small quantity of a relatively strong baseto a solution of an acid in a wedk base may readily be deduced fromthe general equation, providing certain conditions are known, as isperhaps the case where water is added t o a dilute solution of hydrogenchloride in absolute alcohol.It is known that in absolute alcohol the acid at N/10 dilutionexhibits already about 0.4 of its maximum conductivity, and thisfraction increases with addition of water t o a comparatively smallextent, so that for very small additions of water it may at n firstapproximation be assumed nearly constant.This fraction represents,according to the present conception, the proportion present as anions,SO thatIz K 2 XfM fP=4 2H =1 +--+K' I+ + ;';I +df,where M and li, refer to water, and ~11' and K', t o alcohol. AlsoIZ = x = measured degree of dissociation, and assuming that the velocityof esterification at any time is proportional to the active masses of thehydrogen ions, of the carboxylic acid, and the alcohol respectively, it- first time) :M'is given by the expression (neglecting 1 in comparisou with ~ ~- for theK'2where p is a new constant dependent on the nature of the carboxylicacid, and u is the active mass of this acid.This is in accordance with the observations of Goldschmidt andUdby (Zeitsch.yhysikal. Chem., 1907, 60, 735, et seq.) for the velocityof esterification of numerous acids by hydrogen chloride in alcoholand varying amounts of water, and their functions have the samesignificance.** For comparison, the cxlression used Ly these authors may be given hc1rc :d2L = J , ~ j j r c - ~ - "cll, r + 'L+&'( G . and S.) XT, 6, P', c, a-x, n+z.the corresponding symbols being :The fiiiictiori e (G. and S.) was shown to be probably proportional t o the nieasureddissociation of the catalyst, kr to depend on the nature of the carboxylic acid andof the alcohol, T to be independent of the nature of the carboxylic acid and todepend on the nature of the alcohol only2196 LAPWORTH : AN EXAMINATION OF THEIC?K ''This function -i-~ll', which iliis been termed the water value of thepure solvent, is identical with 3' iu the expression used by theseauthors, and is correctly interpreted by them as a hydrolytic con-stant.Their further conclusion, namely, that the general applicabilityof the formula is proof of the view that the alcohol forins the reactivecomplex ion, is, however, clearly incorrect, as the present mathematicalinvestigation shows that the same expression is obtained whether thereactive ion is formed from the alcohol or the carboxylic acid.The present author has found that this (' water value " may be deter-mined for a solvent by studying the effect of water on any of thecatalytic changes which have been mentioned, and also on the basis ofthe tinctomettic method, referred to later in this paper.Each method,however, gives a slightly different number for the '' water value," butt h i s is perhaps inevitable, owing, in part, to the fact that the concentrit-tion of catalyst is very different in different experiments, and alsothat i t is at present not easy to determine the influence of the sub-stance undergoing catalytic change. The values are of the sameorder, however, in each case, and to illustrate what kind of preliminaryresults have been obtained, the numbers for the " water value '' of50 C.C.of n specimen of nearly absolute alcohol may be given :Type of Acetone H y clrazoben zeii ecatalysis or test. Esterification. bromination. conversion. Tiiictometric.Water value ... ... ... 0.22 0.15 0'18 0'12Variation of the Velocity qf Psterijcntion in Alcohol witli Ahemtion inthe Amount of Cntulpst.Goldschmidt and Ud by (Zeitscli. physikd. Cliem., 1907, 60, 735) andKailan in numerous papers (iCionuteh., 1906, 27, 543, 997 ; Annalen.,1907, 351, 186, etc.) draw attention to the fact that in alcohol con-taining water, the velocity of esterification at constant volumeincreases more rapidly than the concentration of the catalyst. Thefirst-named authors consider that t h i s may be explained if theassumption be made that the alcohol forms the complex hydrions towhich the reaction velocity is proportional.I n order to ascertain whether this conclusion is a valid one, let oneof the complex hydrions in a mixture containing hydrogen chloride beselected, say I".We have I"= - and at constant volume it is obvious that an K",.V'increased amount of hydrogen chloride could never increase the amountof any of the free bases. K", and r a r e constant, so that 1" can onlyincrease more rapidly than the concentration of hydrogeu chloride iCONCEPTION OF HYDROGEN IONS IN CATALYSIS, ETC. 2197the same is true of the hydrogen ions. That is, '2 must be positivenegative. Differentiating the expression connecting the#Aand - dH2dA2amount of hydrogen chloride with the hydrogen ions,expression :which is always positive, so tlmt the dispropoj*tionntewe obtain theincrease in tlu?esteriJicatiora velocity cannot be due to any reccction which i s simplydependent on the mass of u, complex ?ydrion foiwied from the alcohol 01'carboxylic acid.Of the other individual substances which might be concerned, therelation between the undissociated compound, S", the base, jv", fin({the hjdrogen ions is :Any velocity which is proportional t o S" may (providing TV" doesnot diminish too rapidly with increase in the amount of catalyst, thatis, if V'' is a very weak base) increase more repidly than the amountof catalyst, forwhich is positive, providing Y is less than 2which must be very great.A ~ B increase in the velocity o f reactionproportionately greater than the increase in catalyst may inclicate thut a nundissocictted compound of the catalyst with the changing substance i s , inpart at lercsl, concerned directly in the formalion of the j n a l products.Xeulrul Sult Action.A similar reflection may apply to the acceleration by neutral saltsof reactions in which powerful acids in dilute solution take part. Theneutral salts must decrease the concentration of the hydrogen ionsthemselves, and also that of the complex ions of the changing substance,by converting them, on the one hand, into undissociated acid andundissociated compound. Itthat when '' dl " varies butvery weak,S" H.Rffrz = vis nearly constaat, say q.follows from the relations above discussedslightly, which is the case if the base i2198 LAPWORTII: AN EXAMINATION OF THE(1 8) Hence dS" = q.dlIh'.That is, ( 1 ) if S' is large coinpnred with HR, in other words, i f theacid is strong, the Iydrogen ions and tibe complex base iqdrions o ndisappearing will form mainly undissociated compounds of t?Le reactingbases ; on the other hand, (2) ay t?Le acid is weak, tiLen the ions will formmainly undissociated acid.(1) May account, in part, for the well-known stimulating effect ofneutral salts in catalysis by mineral acids, and the disappearanceof the hydrogen ions is in accordance with observations, such as thatof Walker and Wood (Trans., 1903, 33, 490j, that the degree ofhydroljsis of the salt of a strong acid with a weak base in aqueoussolution, as measured by its hydrolytic power, appears t o decrease onaddition of a neutral salt of the strong acid.(2) Accounts for the depressant effect produced by addition of theirneutral salts to solutions of weak acid.Preliminary Determinations by Tiizctometyic Processes of the RelativeBasic Aflniiies of Common Solvents.Whilst the majority of modern attempts to explain the phenomenaof catalysis by acids have been based on the attribution of a basiccharacter t o the reacting compounds, and, although esters have beenfound to retard esterification and to lower t o a slight extent theconductivity of an acid solution (Acree), i t is noteworthy that no simpletinctometric method, such as those applied in aqueous solutions to thedetermination of affinities of acids and bases, has been employed.Obviously, the experiments would have to be made in solvents withbasic atlinities of an order not greater than the substances experimentedwith, so that ~ a t e r , which is a much stronger base than alcohol, couldnot be used as a medium.I t was evident, too, that the indicatorrequired must be a weak base.It was foundthat in this medium a dilute solution of m-nitroaniline was suitablefor high concentration of mineral acid, and that one of aminoazobenzenewas better for small concentrations, N/100 or less. The red colour ofthe acidified aminoazobenzene solution was partly discharged on theaddition of minute quantities of water, and with the quantity of acidrequired to restore the colour to the original amount, was nearlyproportional to the amount of water present i f the alcohol itself wasassigned a small water value (50 C.C.of alcohol was equivalent to0.1 2 C.C. of water), so that hydrolysis of aminoazobenzene hydrochloridein alcohol much resembled esterification in alcohol, which servesexperimentally to connect the two phenomena by experiment.The results in ether, ethyl acetate, ethyl formate, and methyl alcoholThe first experiments made were in absolute alcoholCONCEPTION OF HYDROGEN IONS IN CATALYSIS, ETC. 2199were of the same character, except that these, in accordance with theirdifferent basic afinities, as seen below, had different wa.ter values.Apart from the fact that benzene, light petroleum, and carbon tetra-chloride do not dissolve water and are generally less useful as solvents,these liquids, as might be expected from their more nearly neutralcharacter, appear more suitable solvents for determination of therelative affinities of very weak bases.The author is much indebted to Mr.R. W. L. Clarke for conductingan independent series of measurements of the relative basic affinitiesof a number of common bases in several solvents. He reports asfollows :The results under the head A were carried out i n 99.65 per cent.alcohol with hydrogen chloride about 0-025N (with aminoazobenzeneabout 1 in 500,000 of solvent). Known quantities of the bases wereadded to the same amount of solution, and then the quantity of acidalcoholic hydrogen chloride required to impart the same tint t o eachwas introduced.Under B are given results in benzene with trichloroacetic acid, andunder C with carbon tetrachloride and trichloroacetic acid, used in5 per cent.solution as a maximum concentration. The relative basicaffinities were assumed to be proportional to the amount of acid useda t constant total volume. The numbers refer to equimolecular pro-portions, and the basid affinity of water. is taken as I, but that of ethylacetate is kept constant to link the three series together.Base.Carbamide ....................Water .......................Ether .........................Ethyl alcohol ..............Acetone.. ......................Ethyl acetate ..............."Methyl alcohol ...............A.B. C.17.5 - +1.0-- 0-13 0'12- 0.06 0.06- 0.055 0'0450-05 0 '05 0 '050.015 0.02 0'01- -The bases used were highly purified materials, and small quantitiesof impurities might conceivably bave made an appreciable differencein the series A , but could not very greatly affect B and C, where themolecular proportion of trichloroacetic acid was considerable.Specimens of ether, some dried by distillation over sodium andothers over phosphoric oxide, gave concordant results.* It is remarkable that, although methyl alcohol in these solvents appears to actas a specially weak base, yet in the liquid state (that is, when used as a solvent) i thas a water value much greater than ethyl alcohol, whether this be estimated tincto-metrically or otherwise (compare Goldschmidt and Udby, Zoc.cit., p. 755). This,among many other points, requires careful investigation.VOL. XCIII. 7 c 2200 LAPWORTH: AN EXAMJNATION OF THEI’urt 11.An Explanation of the Properties of Acids not Necessarily Involvingthe Conception of Hydrogen Ions.Proceeding from the usual standpoint that the catalytic activityand the salt-forming powers of acids are dependent on the hydrogenions, it has been shown in the preceding pages that the principalproperties of acid in aqueous and similar solutions may be fullyexplained, no matter what may be the actual concentration of thehydrogen ions in any given case. From a mathematical point of view,this must also be true if their concentration is always = 0 , and wouldlead to‘the conclusion that the properties of acids when dissolved insolvents containing bases may merely depend on (1) the extent towhich they combine with the bases present, (2) the manner in whichthey are partitioned between the bases, and (3) the degree to whichthe resulting salts are dissociated.The condition that the hydrogen ions are absent in the equationetc. E’ Po’ discussed is that K,=O, or unreal; it follows thatI Iare unreal, but that the products 5 K1 etc.are real. Call theseK9’ E;+, +’, etc. ; they represent the mutual propensities * of the bases for the+ 1 acid. Kl, --, etc,, are here unreal, because they are not exhibited 4until the base and the acid are brought into contact.As there is no necessity for supposing that the hydrogen ionsexist in any but infinitesimal concentration, it would appear moresatisfactory to revise the prevailing views of the nature of acids andbases, employing a convention of the above character, as this admitsof an advance from a, practical point of view.At present the functionof an acid which is regarded as the measure of its affinity is itsdissociation constant in water; this, however, depends on twodifferent real functions, namely, the affinity of the acid for thewater and the dissociation of the hydroxonium salt. It should not betoo difficult to separate these by experimental treatment.The new relations which arise by eliminating the incommensurablefunctions in the preceding formula, and which appear capable ofpractical application, may be tabulated here, and will be applicablewhether the hydrogen ions are real or not.* The term “affinity” has been used in other senses, and the function it is hereproposed to term L‘ propensity ” refers to the tendency of the acid and the base toyield a compound which is a perfect electrolyteCONCEPTION OF HYDROGEN IONS IN CATALYSIS, ETC.2201where x is the degree of dissociation of the acid as at present measured,31 the sum of the positive base ions, I" represents the amount ofany one of these, and R the gram-equivalents of the negative ionswhether united with solvent or not.k=---, ZMQ,M+ X - - + l li'where k is the dissociation constant as generally understood, and K isthe dissociation constant of the hydroxonium salts.(20)vx= ~ z'Q, v, X%+------- M+ LW+=f++ + l S-+1 (21)Kwhere V is the volume in C.C. containing one gram-equivalent of theacid.where EIR is the uncombined acidwhere X i s the sum of the amounts of all the undissociated salts andcompounds of the acid with the bases, and where 8" is the amount ofthese, derived from any one base.I n dealing with an aqueous solution, the sign 8 is, of course, omittedif no other base than water is present.The functions x and k are already known for many important acids.It should be possible to determine the amounts of the free acids andthe hydrated acids in their aqueous solutions a t known concentration.There will then be an experimental basis for the determination ofthe relative potencies, apart from the basic power of the solvent.Probably, however, it will be much simpler to deal with the problemfirst in non-ionising solvents, but in this case the undissociated ornon-conducting compounds of acid and base will probably be of themost importance.Bhsociation Constants of Acids.An interesting relation may be pointed out for the case of acids,Here in aqueous solution :where K is the dissociation constant of the hydroxonium salt.If, asappears probable, these salts are largely dissociated in the same way7 a 2202 CONCEPTION OF HYDROGEN IONS 1N CATALYSIS, ETC.as ammonium salts, then k may be neglected in the denominator inthe last equation if the acid is very weak; andthat is, for a weak acid, if its molecule is not hydrated in aqueoussolution, its dissociation constant is identical with its propensity forliquid water.(24) M+ = k,Application to the Case of the Hydrolysis of the Salt of a Weak Base.As measured by the catalytic activity of the solution of the hydro-chloride of a base, say carbamide, the connexion may be arrived a t asfollows :The water may be represented as W, the base, W', and the hydrolyte,W'.The velocity of hydrolysis of W" is mainly dependent on itscapacity to form the ions I". This is given by I" = R'"4" ~ that is,proportional to - (or when the substance catalysed is a very weakSM+ 'R8M+base and does not appreciably affect the state of the solutions) orproportional to =where M and + refer to water, and 111' M+ + M'+'and +' to the base W'.R in the case of dilute hydrochloric acidwhether a base like carbamide is present or not.Let 1 gram-molecule of the hydrochloride beapparent degree of dissociation, X , into base andI" where carbamide is presentI" where carbamide is absent - M+ + M'+'R -total amount of free ureavolume T, and as v AS M'=is nearly constantplaced in water, thefree acid is :M for dilute aqueousM4 X2solution remains nearly constant, X = ,or,+'+M+X=M+,JW+ @'(25) hence X 2 +--, Jf+ VX = H+ -V, or X 2 c kVX= kV.+ +This i s identical with the formula of Arrhenius (Zeitsch. pjlysikal. Chem.,1890, 5 , 16), and was found by Walker and Wood (Trans., 1903, 33,489) to apply to the case of carbamide hydrochloride, the dissociationconstant Tc being =* in the new measures.+'Walker and Wood find k=O*781 at 2 5 O when the volume isPutting H, the active mass of liquid water, as expressed in litres.1000 4' 1000 - 18 9becomes ~ : 0 ; 7 ~ = 71.1. That is, for hydrochloric acid, thTHE OXIDATION OF PHOSPHOROUS ACID BY IODINE. 2203propensity of dissolved carbamide is ‘71.1 times the propensity of liquidwater.Comparing this with the value in alcoholic solution, it appearsdthat liquid water has only one-fourth the basic affinity of waterdissolved in alcohol.The relations given in Part I1 of this paper will be true in practicewhether the reality or otherwise of free hydrogen ions is assumed.Jn conclusion, it must again be pointed out that the conceptionsintroduced in this and the preceding paper (this vol., p. 2163) have,for the most part, been used before. I n particular, the view that acids,unlike certain metallic hydroxides and salts, are not of themselveselectrolytes, is suggested in Lothar Meyer’s ‘‘ Modern Theories ofChemistry ” (Bedson and Walker’s translation, 1888 edition, p. 535),and attributed to Thomsen (1874). Lowry has recently drawn atten-tion to the great importance of the point.The only suggestion regarded as in any sense a novel one, is thatwater, when added to acids in less basic solvents, reduces the con-centration of the hydrogen ions, or, on a less hypothetical basis,diminishes the availability of the acid for salt formation. Even thisappears to be in a measure anticipated by Armstrong’s propositionthat substances which act as dehydrants will have a ‘‘ concentrating ”effect on others which are hydrated in aqueous solution.The author desires to express his indebtedness to the GovernmentGrant Committee of the Royal Society for a grant, which defrayedmuch of the cost of the experiments