EQUILlBRIUM OF DILUTE HYDROCHLORIC ACID AND GIELATIN. 313XXXV.-The Eyuilibrium o f Dilute Hydwclhi.icAcid and Gelatin.By HENRY RICHARDSON PROCTER.IN an earlier paper (Koll.-chern. Beihefte, 1911, 2, 243) it has beenshown that when gelatin jelly is immersed in a dilute acid, anequilibrium results which a t a given temperature is dependent onlyon the ionisation and concentration of the acid, which determinenot merely the volume of liquid absorbed, but the concentration ofthe anion in the jelly; and more or less empirical formulae weregiven connecting these with the concentration of the ionised acid.It was further pointed out that these formulae were consistent withthe view that a hydrolysable and ionising salt* of gelatin wasformed, and that the phenomena of swelling were simply dependenton the relation between the osmotic pressure of the ionising saltand that of the external acid solution.The object of the present paper is to indicate the precise natureof these relations, and to show that the formulEe there given, withsome slight modification, can be fully explained and justified onthe ordinary ionisation hypothesis. I f this is the case, there seeinsno reason f o r the assumption of more complicated and less verifiedtheories dependent on surf ace-tension and other forces, and involvingthe unproved an3 rather gratuitms assumption of a two-phasedstructure of the jelly.The discussion of the present paper hasbeen confined to the single case of gelatin and hydrochloric acid;but the theory proposed is quite general, and iE true in the particularcase, must also be true (with different constants) of any otheracid, and of other amphoteric proteins, so that its bearing, bothon colloid chemistry .and on physiological theory, is very wide.The theory assumes that the jelly is a molecular network, in whichthe water, the acid, and the protein are within the sphere of eachother’s molecular attractions, and theref ore homogeneous in thesame sense as any other solution; and it discards the Butschli-vanBemmelen idea of coarse microscopic pores, although it is not deniedthat such two-phased jellies exist, and can be produced, and thatthe pores observed by these investigators had a real existence,probably due t o the hardening agents with which their jellies weretreated.It has been shown by the author (loc.cit.) that when gelatin* I t is most probable that this salt is a “ hydrochloride,” in the same sense as“ aniline hydrochloride,” but as other constitutions are possible, it has been thoughtbetter to write “gelatin chloride ” simply.vor,. cv. 314 PROCTER : THE EQUILIBRIUM OFswollen with water is treated with a strong acid, such as hydrochloricor sulphuric, the swelling becomes much greater than with wateralone, but reaches a maximum at a very low concentration of theexternal acid, subsequently diminishing in a hyperbolic curve, asthe concentration of the acid is further increased. This con-traction is obviously due to the anion of the acid, since it can beincreased to almost complete dehydGation by the addition of itsneutral salt; but the exact mechanism of the osmotic pressure is noteasy to follow, since the jelly is in itself completely permeable bothto the acid and its neutral salt, and their ions, and the explanationgiven in the paper quoted seems an incomplete one.The fuller statement is that to satisfy the equation * of equality ofproducts (Donnan and Harris, T., 1911,99, 1575; Donnan, Zeitsch.Elektrochem., 1911, 17, 572), the concentration of the free acidcontained in the jelly must have a definite relation t o that of theionised anion of the jelly-salt; and as the latter cannot diffuse fromthe jelly owing to the colloid nature of its cation, the equilibriumcan only be reached by the absorption or expulsion of free acid andof water by the jelly.I n order to investigate these relations, itis necessary, not merely to determine the total chlorine contained inthe jelly, as had been done in the earlier experiments, but toascertain what were the relative proportions of ionised and of non-ionised chloride and of free acid in the jelly, and it became evidentfrom the mathematical investigation of the equilibrium that thetotal chlorine and one of these being known, the others could becalculated.The most obvious way of determining ionic concentrations is bymeans of concentration-cells, and much time was spent in unsuccess-ful efforts t o solve the problem in this way. The work, however,has not been fruitless, and the causes of failure may be brieflystated.First, it should have been obvious from the outset that theconcentration-cell method, marvellously accurate as it is in thedetermination of the order of quantity of minute ionic concentra-tions, was quite unfitted t o deal with the massive differences ofthe same order of quantity which were concerned in the presentproblem. Secondly, it was proved that the apparent ionic con-centration of amphoteric colloid solutions, as determined by the* This equation, which states that the product H' x C1' must be equal inboth phases, is, of course, in accordance with the mass-law, but the actual distributionof H' and C1' depeuds on the thermodynaniic equation :6n R T log H,/H, = 8ia R T log CI,/Cl,given by Donnan and Harris (T., 1911, 99, 1575) for the analogous case of sodiumchloride and Congo-red ; whence H, x C1, = H, x GI,.This equation relates to theionised portions only, and the non.ionised portions, if any, will be related to theionised according t o the ordinary mass-law equation, a x b=kcDILUTE HYDROCHLORIC ACID AND GEL.4TIN. 31 5concentration cell, was not the actual concentration of the solutionor jelly, but that of a non-colloid acid or salt solution with whichi t would be in equilibrium, since Donnan’s “ membrane-potential ”a t a real or virtual surface mathematically equals and compensatesany difference of potential between a colloid solution and itsequilibrium acid or salt solution. This is obviously a point offundamental importance with regard to the frequent use of theconcentration cell in physiological investigations, and demands morecomplete proof than space allows here. The author thereforeproposes to make this part of his work the subject of anotherpaper; but it may be noted that means were devised for theapproximate measurement of the membrane-potential, which,although only of a few millivolts, corresponded with large percentagedifferences in the present investigation.Efforts were also made to solve the problem by conductivitymeasurements, but the results, although of considergable interest,and possibly of importance to the theory of colloid salts, failed t ogive information either so comuleto or so accurate as wits subse-quently obtained by a much simpler and apparently ruder method;and this was also true of a modification of Veley’s colorimetricmethod with methyl-orange, which, within certain limits, gaveuseful results.The method finally adopted rests on the fact that the influenceof one salt on the ionisation of another depends solely on the con-centration of their (‘ common ” ion.Hydrolysis depends, therefore,on the hydrion concentratioin only, whilst the mutual ionisation ofa salt and i b acid is influenced only by the “ common ” anion. I ftherefore, sodium chloride is added to a jelly containing gelatinchloride and free hydrochloric acid, the ionisation is no doubtrepressed, but the hydrolysis of tha gelatin salt is not affected, andthe free acid is expelled with its associated water to almost com-plete dehydration by the osmotic pressure of the concentratedchlorine ion, and can be titrated in the expelled salt solution.The weight or volume of acid solution retained by the jelly can beeasily ascertained, and is so small that even if the assumption thatits concentration is the same as that of the solution expelled is notquite accurate, no serious error is introduced by adopting it.Theactual method of experiment was Bas follows. A quantity of care-fully purified thin bone-gelatin of known dry weight (usually 1gram) was soaked in 100 C.C. of acid solution of known concentrationin a stoppered bottle for forty-eight hours, a time which was shownto be sufficient for the attainment of practical equilibrium. Thecontents of the bottIe were then poured into a funnel provided witha finely perforated porcelain $ate, covered with a clock-glass, andY 316 PROCTER : THE EQUILTHRlUi\I O Fallowed to drain for two hours, the liquid being received in agraduated cylinder.The volume of the liquid, subtracted from 100c.c., gives the volume of acid absorbed by the gelatin, and this canbe further checked, if necessary, by the weight of the drained andswollen gelatin. By titration with alkali hydroxide and phenol-phthalein, the strength of the external acid is determined, and fromits concentration and volume, the total acid absorbed from thegelatin is calculated. The swollen jelly is now returned to thestoppered bottle, and dry salt added in the approximate quantitynecessary to produce a saturated solution.After repeated shaking,and standing f o r a t least twenty-f our hours, equilibrium is againestablished; the gelatin is shrunk to thin, horny plates, and afurther portion of acid liquid can be separated by the drainingfunnel, containing the whole of t-he free acid with the exception ofthat in the small volume of solution (usually about 1.5 c.c.) re-tained in the jelly. If the quantity of solution is determined byvolume, i t must not be forgotten that a saturated salt solutioncontains only 94 per cent. of its volume of water, but the effect onvolume of the small quantity of acid present may be safelyneglected. The acid salt solut,ion is titrated to determine its con-centration of acid, and the quantity is calculated t o the wholevolume of solution absorbed.We have thus the means of determining (a) the free acid unab-sorbed, which forms the " external solution " with which the jellyis in equilibrium; ( 6 ) the free acid absorbed by the jelly; and( c ) the chlorine, ionised and non-ionised, combined with the jellybase.The sum of b and c can be further controlled by the titrationof the dehydrated jelly with alkali hydroxide, which with phenol-phth.alein as indicator, completely decomposes the gelatin sait.*The following table gives a series of such determinations withvarying quantities of acid, and includes the whole of the resultsin the series of experiments t o which they refer, and are moreconcordant than would be expected from the comparative rough-ness of the method.Some of the results are given graphically onthe curves, t o allow the reader to form a judgment of the trust-worthiness of the experimental data; but in many cases there isnot room to insert the whole.* I n the actual experimental work the weight of solution absorbed was taken asthat of the volume, the increase of specific gravity by the acid being in most casenegligible as compared with other sources of error ; and the total chloiine in the jellyis the sum of the uncorrected titrations of the expelled acid and the residual jelly.The free acid of the jelly as given in col. 1 of the table of experimental results is,however, corrected to allow for the portion of solution still retained by the jelly-W O d dc 0.2SSZ2" ,o3 422 3 d 8 8%+-la0.3000.2500.2000.2000.2000.1750.1500.1500.1250.1000.1000.0750.0750,0500.0500-0250-0250.0200.0150.0150.0150.0100.0100.0100.0080.006 --wO H u It 2: 623.2zss 2 $36 2b0.29500-24500.19450.19400-19250.16850,14350.14340.11800.10520.0944049300.06800.06660.05760*04200.04050.01720.01700.01220.01200.00770.00730.00320,00280.00250*0018 o.oc11DILUTE HYDROCHLORIC ACID AND GELATIN.- o E .3*kh 3%;sz .3$$2 -C19.9820.2222.1022.6820.5923.4824.2424.0024.3629.7526.3823.0929.1227.8534.0131.0736.4248.1340.4451.7251.8952.2057.9153.6858.4359.9048.7044.11E_ti 5I. ja" 2I n 1 5-d18.018.621.121.519.323.023.023.023.829.025.622.027.527.834.630.236.548.539.052.552.753.660.054.559.062.050.044.6 -_EjB $5 2 25s",m$22322e4.4053.6803.2453.3252.9252.9902.5552.5502.3 252.3101.7401.4801.3801.3051.4100.8451.0250.4150-3400.3000.3050~0000.1230.0250.0240.0230.0190.019 -f2.2221.9911.7501.7701.7851.7051.6201.6051.4901.4901-4451.4271.3101.3401.2701.2551.2001.0901.1551.1001.1151.0651.0350.8800.8250-8550.7350.590 -e +f6.6275.6714.9955.0954.7104.6954.1754.1553.6153.8003.1852.9072,6902.6452.6802.1002.2251.5051.4951.4001.4201.1551-1580.9050.8490.8780.7540.609 -EEple 3sg8 .E!i G P15.2024.2553-6153.7313-3203.2472.8652.8302.3142.5211.9071.6521.5551.3911.4740.9251.0880.4380.3750-3140.3200.0930.1260.0260-0250.0240.0200.020 --z &z .% *=5.2gg0--M21.4251.4161.3801.3641.3901.4481.3101-3251.3101.2791.2781.2551-1351.2541.2061.1751.1371.0671.1201.0861.10014621.0320.8790.8240.8540.7340.589 -30.26030.21040.16360.16450.16120.13830.11820.11800.08970.08470.07230.07160.05340.04990.04330.02980-02990.00910-00930*00610.00620.00180.00220*00050.00040.00040.00040*0005 -40-3320.2810-2260.2250.2290.2000.1 720.1730.1480.1280.1210-1260.0920.0950.0790.0680.0610.0310.0370.0270.0270.0220.0200.0170.0150.0150.0150.014 --%5 *g .2Sa ik= .Bn.2 o n0 .250.3340-2850.2320.2280.2300.2050.1 740.1750.1470.1310.1230.1210.0870,0890.0770.0590.0550.0330.0310.0250.0230.0330.0240.0210.0200.0160.0080.003 -31'760.7330.7160.7650.6950.7460-7380,6970.7140.7400.6710.5'950.7600.7100.7900.7210.7950.7460.6770.8070.7690.7970.7530.7350.7330,6850.7280-6040-560 -The lettered columns in roman type are observations. The numbered columns initalics are calculated from the observations as follows :c x ed x 0'943 = 8cc x 0.94It is obvious that from these results two distinct series of curvescan be calculated: those of the actual quantity of each associatedwith 1 gram o r 1 mol.of gelatin, and those of relative concentra-tions of the different constituenb of the jelly and its equilibriumacid solution; and these two sets of curves are not necessarilyinterdependent.Taking first the question of quantities, the first problem is thatof the determination of molecular weight. By this must be under-stood, riot the weight of the associated group of molecules, which,if the molecular network theory be correct., may be co-extensivewith the jelly itself; but tlie smallest weight which could exist insome ideal non-associating solvent, retaining its chemical structur318 PROCTER : THE EQUILIBRIUM OFand reactive powers unaltered.It is obvious that the specialcharacteristic of the colloid state is the tendency t o form associatedgroups of molecules, often of quite indefinite size (as in the case ofsuspension sols), which, osmotically, act as a single molecule oras a single ion. If it were practicable to isolate the pure saturatedsalt, the equivalent weight would be that combined with one atomof chlorine, and i t would only remain t o determine the valency ofthe base. This is, however, impossible, since gelatin is a very weakbase, of which the salts hydrolyse readily, and, on account ofsecondary reactions, it is impossible so to concentrate the acid asto make hydrolysis negligible. All that we can obtain is a curve,of which the limit a t infinite concentration is the completelysaturated salt, and before this limit can be predicted, the mathe-matical expression of the curve must be known.For a weak mon-acidic base, such a curve is yiven by the Ostwald hydrolysisformula, which, as was shown by the author in the earlier paperalready quoted (Zoc. cit.), is conveniently transformed into thesimple expression y= where x is the molecular concentrationor normality of the equilibrium-acid, k is the ordinary hydrolysis-constant, and y is the proportion of unhydrolysed salt to the totalbase present. Such a, curve, if the k is small, ascends a t first almostvertically, curves sharply as it approaches unity, and thereafterproceeds almost horizontally, reaching unity only when x beCOm6sinfinite.I f the k be larger, the ascent is more gradual, and thecurve rounder and more prolonged, so that it may still be far fromunity within the limit of experiment, y having obviously a valueof 0.5 when k=x.The curve of gelatin chloride plotted from experiment, as willbe seen by reference to Fig. 1, rises vertically a t first, with all thecharacteristics of a small k, but after turning sharply, continues t orise throughout the limits of the experiment. Such a curve is thatof a diacidic base, or dibasic acid, and is the sum of two curves, oneof which is due t o the (usually small) k of the first valency, andthe other to the larger k of the second. The expression thereforeX + k ’X X becomes 9 = - + - and its limit is 2.* The experimentalX+k, x:+h9’curve is plotted Tor 1 &am of gelatin, whilst the expression is for1 mol., and must obviously be multiplied by ___- *Oo0 to make i tcomparable with experimental results. There are thus three un-inol.wt.* The curve of non-hydrolyecd gelatin given in n previous paper was calculatedon purely theoretical ground? and on the assumption that gelatin was monacid, andthe k then adopted of 0.005 was obviously a compromise between k, and k2DILU'L'E HYDROCHLORIC ACID AND GELATIN. 319knowns to be determined, the two k'sy and the molecular weight;and, although this might no doubt be done by three simultaneousequations from different points of the curve, I have preferred asmore satisfactory, to adopt a method of approximation whichapparently is identical in principle with one described by Lund6n(Meddcl.R. Vetensk. Nobelinstitut, 1, No. 11).FIG. 1.Curves of quantity : 1 gram.N.Where k, is small and k, large, the earlier part of the curve isalmost entirely dependent on the former, whilst the later part isapproximately 1 +-. If, therefore, the value of the curve a tx + k,z = O * O l be assumed to be equal to the reciprocal of the molecularweight, and this be subtracted from the value a t x=O-25, the320 YROCTER : THE EG&UILlBRIUM OFremainder, multiplied by the same reciprocal, will be the valuedue to the second term of the expression, and from these anapproximate k, and k, can be calculated. I f these are nowemployed to correct the first calculations, a closer approximationcan be obtained; and this can be repeated until the results arewithin the limits of experimental error.For each single term,k = - - x. With any approximate molecular weight, values for k,Yand k, can be calculated which will give a curve agreeing with theexperimental a t the two points taken, but unless the molecularweight is very nearly correct, the value of y will be noticeably wronga t a third point, which is most advantageously taken near that ofmaximum curvature.Since the molecular weight must be such as will give wholenumbers of atoms in accordance with ultimate analysis, i t becomeseasy to decide on the only possible weight within the limits ofexperimental error, and a (‘ rational ” formula is obtained.The experimental curve in the present case is very accuratelyXX 1000+ 1.05 * 839 ’ +-- and t o this the curve X represented byx + O 0013in Fig.1 has been calculated. This results in a probable ‘( rational ”formula for gelatin of C,,H,,O,,N,,, with a molecular weight of839, which agrees with Schutzenberger’s o~7n determinations quiteas well as his gener*ally accepted formula, C,,H.,,,O,,N,,, but isslightly higher in nitrogen than the average of published analyses,as is shown by the following table. It is probable that the differ-ence may be accounted for by the extreme difficulty of completelydrying gelatin without decomposition. The hydrogen is, of course,the most doubtful number.Formuls. Analyses.Procter.- Schutzenberger. I p t t e n d e nC3,H,70,3W,, C7,1-J,,0,N,, Schiitzenberger. Mulder. and Solly.C...... 50.06 49.7 50.0 50.1 49.4H .... 6.79 8.8 6.7 6.6 6.80.. .... 24-79 25.2 25.0 25.0 25.1N .... 18.36 18.3 18.3 18-3 18.0It may be noted that Paal obtained a molecular weight of about900 from freezing- and boiling-point methods (Ber., 1892, 25, 1202).It must not, however, be assumed that the molecular weight ofgelatin, from the physical point of view, is necesarily so compara-tively small. The weight calculGated from the previous experimentsis merely that of the smallest quantity which can act as a chemicalindividual, and i t is not incompatible with the association of thecolloid molecules in any way which does not affect their chemicalcombining powers; and, if the view of a molecular network iDILUTE HYDROCHLORIC ACID AND GELATIN.321correct, the whole jelly may be regarded in a physical sense asone enormous colloidal molecule dissociating a number of chlorineions; whilst it is impossible t o say what degree of association maystill exist after Iiquefaction.Since the hydrolysis-constant of a salt of a weak base is theionisation constant of water divided by that of the base, we cancalculate the two basic constants of gelatin as concerned in thereaction, although i t may be probable that the two affinities arein themselves equal, and that the second only takes its lower valuebec.ause of the previous saturation of the first.0.6 x 10-14 - Since Icw =0*6 x 10-14 and Ic, = 1.3 x 10-3, kbl= -1.3 x 10-30.5 x 10-l1, and Lund6n (loc.c i t . )gives for leucine 7ca=1*8 x 10-10, and kb=2*3 x 10-l2, and forglycine (aminoacetic acid), one of the principal constituents of thegelatin molecule, very similar figures, so that there is no interentimprobability in those calculated.Turning from the question of quantities to that of concentra-tions, if we represent on a curvediagram the hydrogen-ion con-centrations by the abscism and those of the chlorine-ion byordinates, the common concentrations of the external acid x, inwhich these are equal, will intersect on .a line passing through theorigin a t an angle of 45O, and this will be the axis of a series ofright-angled hyperbolas, corresponding with the different valuesof x, and of which x2 will be the generating square; and on which,for each value of x, all possible solutions of the equation x3 = H x C1will lie, and if the concentration of one of these constituents isgiven, the equilibrium will be definitely determined.At any suchpoint, the hydrogen and chlorine ordinates will enclose a rectangleequal in area t o x2, the chlorine being necessarily the greater fromthe ionisation of the gelatin chloride.It is obvious that on the concentration of this ionised chloridethe whole equilibrium depends, and if its relation to x can bedetermined, the problem is definitely solved. An experimentalsolution is given by the determination of the concentration of thefree acid of the jelly, which is equal to its hydrogen abscissa.Asthe jelly is completely permeable to the ions of the external acid,it must be in equilibrium with it both osmotically and thermo-dynamically, that is, both the total concentration of ions and theproduct of th6 hydrogen and chlorine ions must be the same ineach case, or any difference which exists between the two mustbe compensated by an electric potential a t the interface. Thereis no evidence, experimental or theoretical, that the colloid gelati322 PROCTER : THE EQUILIBRIUM OFion exerts any osmotic pressure, and, as an associated network,it should, theoretically, only act as a single molecule; but sincethe two sides of a rectangle are necessarily greater than those of asquare of equal area, some surface-potential must exist, opposedin sign t o that shown by Donnan (Zoc.cit.) to be caused by theunequal concentration of the hydrogen and chlorine ions. Sincethe ionised chlorine is confined to the jelly by the attraction of itsnon-diff usible colloid ion, the adjustment of equilibrium betweenthe jelly and the external acid can only take place by the passageinwards or outwards of hydrochloric acid and water, and if wesuppose the jelly divided into separate volumes, each containingone of the constituents a t the common osmotic pressure, that ofthe acid will be of the same concentration as the external acid x,and will have an osmotic pressure of 22, since both hydrogen ionand chlorine ion are of x concentration, and the ionised chlorine,to be at the same osmotic pressure, must also have a concentrationof 22, since the chlorine ion of the acid cannot be expelled withoutits attendant hydrogen ion.Thus the x2 of the external acid is in oemotic equilibrium withthe 2x of the jelly, and if we plot the concentration of the externalacid as x, we must also plot the osmotic concentration as 4% t omaintain the same relation.Experiment shows that, measuredin terms of x, the concentration of the ionised chloride isapproximately dyz, but is more accurately expressed by J 2x + 0.02,the explanation of the small correction being discussed later.Calling the concentration of the ionised gelatin chloride C1,tthe concentration of hydrogen ion in the jelly is algebraically-'I,+ ~c1,2+4xa and that of the expelled acid2but, graphically, all the concentrations are given by a simple con-struction, the proof of which is obvious.I f the C1' ordinate ofx be produced vertically to an additional length of CVg, and aline be drawn through this point parallel with the axis of thehyperbola (that is, a t 45O), it will cut the hyperbola a t the commonpoint of intersection of the IIC' and C1' ordinates of the jelly, theIT* ordinate of which, if produced, will cut the x vertical a t thetot.al Cl' concentration, and a horizontal line through the pointwhere the (31' ordinate of the jelly cuts the axis of the parabolawill cut the x vertical a t the hydrogen-chloride concentration ofthe jelly, whilst the difference between this and x will be the acidexpelled. If continuous curves are drawn through these pointsfor the different values of x, they will divide the diagram intDILUTE HYDROCELORIC ACID AND GELATIN.323regions of free hydrogen chloride or hydrogenion concentration,and of ionised chloride, respectively, below and above the straighbline axis of x. Experimentally, the concentration of the ionisedchlorine is obtained by dividing x2 by the concentration of freeacid in the jelly, and that of the total chlorine by direct titration.Both are plotted in Fig. 2, but, the ionised is marked 0 and theFIG. 2.0.05 0;lO 0.15 0.20 0.25 0.30 N.H'.Xtotal x . It will be seen that they practically coincide, and it maybe concluded that the gelatin salt is almost wholly ionised, or, a tleast, to an extent comparable with hydrogen chloride, for theincomplete ionisation of which no allowance has been made.With regard to the correction, approximately 0.02, added to 2xunder the squareroot sign, it may be noted that, putting x=O324 PROCTER : THE EQUILIBRIUM OFa value of chlorine-ion concentration still remains equal to J0.02.This ionisation of chlorine in absence of an appreciable hydrogen-ion concentration is also confirmed by experiment, a measurablechlorine-concentration being reached before any free acid is showneither by indicators like methyl-orange, or by the hydrogen con-centration cell.The probable explanation is that as gelatin isamphoteric, and, to some extent, ionises both H' and OH' in theneutral state, a small amount of neutral chloride can be forlr,edin absence of any other free acid than its own; or, perhaps, inother words, that it must be brought to a neutral condition ascompared with water before any hydrolytic production of hydrogenchloride can take place.This is in accordance with experimentsquoted by Pauli (KoZL-Zeitsch., 1913, 12, 222), which prove thatin neutral solution, gelatin and other proteins wander to the positivepole in elecikophoresis, and that a small amount of acid is necessaryto bring them to a neutral condition in which they are unaffectedby the current, whilst, with further additions of acid, their basiccharacter preponderates, and they wander to the negative pole(probably as basic ions). The correction may thus be regarded assimply indicating the .amount of hydrochloric acid required beforeneutrality is reached.It is obvious that, except for this small correction, the concen-trations are all purely mathematical functions of x, and thereforeindependent of the chemical properties of the protein, and .applic-able to all substances capable of similar equilibria.If the tem-perature is raised so that the jelly melts, it can be shown thatequilibrium still exists, although actual measurement, is complicatedby the necessity of a membmne, and the much longer time requiredt o attain equilibrium than with the thin sheets of the presentexperiments; but, in the case of gelatin, neither concentration cells,conductivity, nor the experiments of G. S. Walpole on refractiveindex (Roll.-Zeitsch., 1913, 13, 241) show any break in the curvesa t the melting point, .and, in all probability, the degree of associa-tion is still very large.Since such associated groups of ions muststill be in equilibrium with their surrounding solution, they mustalso be associated with acid and water in the terms of the jellyequilibrium, and the suggestion is obvious that, whilst the trueequilibrium-jelly is a homogeneous molecular solution, the .apparentaqueous solution is really a two-phased structure of associatedcolloid systems, surrounded by their equilibrium liquid. The samemay probably be true of jellies made up with arbitrary quantities ofwater and acid, and may serve to explain some of the results ofearlier investigators. Certainly, electrometric experiments madewith such jellies, both by conductivity and by the concentratioDILUTE HYDROCHLORIC ACID AND GELATIN.325cell, gave somewhat abnormal results; and it is clear that unlessby chance the exact equilibrium mixture has been made, they mustbe in unstable equilibrium, and must tend to separate into equi-librium-jelly and its corresponding acid, possibly developing theButschli sponge-structure.I n this connexion, it is well to refer to the work of Pauli (Zoc.cit.) on the viscosity of acid protein solutions, in which he obtainedcurves identical in type with the swelling curve of acid gelatin,which probably can be explained by the varying quantities ofwater and acid associated with the gelatin molecules.It was shown in the earlier paper (Zoc. cit.) that the volume of -swelling was nearly proportional to - X + J; or - J x or to theX + k x+k’theoretical quantity of non-hydrolysed gelatin divided by J 2.Obviously, if the quantity of ionised chloride a t any point be dividedby the corresponding concentration of the ionised Cl’, the quotientwill be the volume of the jelly, and it is found that by dividing thecalculated quantity of non-hydrolysed chloride which, it has beenshown, is almost wholly ionised, by d 2 x + 0.02, a curve is obtainedwhich agrees very closely with the smoothed curve of observedvolumes, both in type and quantity.It is worthy of note that theabove calculation takes no account of any solid rigidity or elasticityof the jelly, and it may therefore be presumed that these have noexistence apart from the osmotic pressures of the jelly, or, a t least,tihat they are of negligible amount.Finally, a large number of determinations were given in theearlier paper of what was called “ acid fixed ” ; that is, of the excessof acid in the jelly over that contained in an equal volume of theexternal solution.This is a well-defined quantity, rising rapidlywith the concentration of the external acid to about 0.8 milligram-molecule for 1 gram of dry gelatin, formrng a slight maximumat about s=0*015 and a still less marked minimum a t aboutx=O*15, and again increasing, but only very slowly. The value iseasily and accurately obtained by titration of the melted Jellyand of its equilibrium acid, but the curve is peculiar; and, a t thetime, w-as incapable of definite explanation. It is now obviouslythe quantity of gelatin chloride less that of the free acid expelled.Calling Q the value of the quantity of non-hydrolysed gelatinchloride, c the concentration of the ionised chloride, and a thatof the expelled acid, this is given by the (somewhat simplified)expression Qc2, This accurately reproduces the peculiarities ofthe experimental curve, but is very slightly too low in actualquantity, presumably because the theoretical expression assume326 PROCTER : THE EQUILIBRIUM OFtotal ionisation of the gelatin salt, and the consequent expulsionof a slightly larger quantity of free acid than actually takes place,All the curves described are plotted in Figs. 1 and 2, togetherwith the experimental results (so far as space allows), and thecorresponding algebraical expressions are annexed ; and to facilitateexperimental checking, the numerical calculated values f o r anumber of values of x are also given in the following table.Calculated Mathematical Curves for 1 gram of Gelatin.QuantityQuantity Quan- excess of Con-un- Quan- tity OF C1 centra-Nor- hydro- tity free in jelly Con- tion a tmahty lysed total acid over Volume Concentra- centra- H'of gelatin C1 HCI eq.vol. of Concen- tion, tion ex-eq.acid. chloride. of jelly. of jelly. solution. jelly. tration If'. C!, . total Cl'. pel!ed.2. a. b. C. a. e. f. 8. h. a.0.001 0.520 0.522 0.002 0.481 35.0 0*00007 0.0149 0.0149 0.00090.002 0.725 0.737 0-012 0.615 46.8 0.00025 0.0155 0.0157 0.00180-006 0.952 1.023 0.071 0.750 54.7 0.0013 0.0174 0.0187 0.00370.010 1.066 1.283 0.219 0.754 53.3 0.0041 0.0200 0.0241 0-00580.015 1.114 1.494 0.380 0.747 49.8 0.0075 0.0223 0-0298 0.00750.02 1.142 1.664 0.522 0.732 46.6 0.0112 0.0245 0.0357 0.00880.03 1.176 1.965 0.789 0.720 41.6 0.0190 0.0283 0.0473 0.01090.05 1.216 2.467 1.251 0.710 35.1 0.0356 0.0346 0.0702 0.01440.10 1.279 3.440 2-161 0.714 27.3 0.0793 0.0469 0.1262 0.02070.15 1.330 4.253 2.923 0.718 23.5 0.1244 0-0566 0.1810 0.02560.20 1.375 4.987 3.612 0.743 21-2 0.1702 0.0648 0.2350 0.02980.25 1.415 5.662 4-247 0-758 19.6 0.2165 0-0721 0.2886 0.03350.30 1.452 6.318 4.866 0.773 18.4 0.2632 0.0787 0.3419 0.0368The following are the forinuke used in calculation; the lettersrefer to the corresponding columns.X - C1, + JCJg2 + 4x22A = f + g = - 2 2fd = b - e x i = x - fa98 = -.The dehydrating effect of salts having a common ion with theacid has not been dealt with experimentally in the present paper,since it is obvious that if the anion of the acid diminishes swelling,by increasing osmotic pressure and concentration, additional quan-tities of the same ion introduced as neutral salt must have thesame effect.Even numerically, so long as the salt solutions aredilute, it is probably sufficient to take account of the common iononly, using the same mathematical formulai! as with the acid alone,but with more concentrated solutions, the effect on ionisation a tleast must be considered, and we can no longer assume that thecolloidal salt is totally i o n i d DILUTE HYDROCHLORIC ACID AND GELATIN.32 7It was shown in the earlier paper that when a salt with nocommon ion is introduced, as, for instance, sodium chloride intoa solution of gelatin formate, a quadruple equilibrium is produced,in which each anion is in equilibrium with its own gelatin salt.This has been shown rather strikingly by a recent experiment withthe substances just named, in which the gelatin was shown byanalysis to have combined with as much as 3 per cent. of .hydro-chloric acid derived from the sodium chloride. Similarly, inpresence of large excess of sodium formate, hydrochloric would bereplaced by formic in the gelatin salt, and this sort of reaction isnot without bearing on some physiological problems.The question whether the action of neutral salt solutions ongelatin falls under the aame theory still demands further study.It was shown in the previous paper (Zoc. cit.) that sodium chloridewas abaorbed by gelatin from neutral solution with increasedswelling, but was replaced and expelled by hydroch1o:ic acid, inpresence of which the absorption of salt was negative. Neutralsalta may combine with amphoteric proteins, either by the anionbecoming attached to the amino- and the cation to the carboxy-group, or the whole salt may be attached t o the amino-group, a,phydrogen chloride is to organic bases, by the nitrogen becomingquinquevalent; and the probable structure of the protein saltmust be left t o more purely organic chemists to decide, since eitherwould fulfil the requirements of the present theory.Conclusions.-The swelling of gelatin in dilute acid solutionsdepends on the osmotic pressures and equality of products of adiacid ionisable salt of gelatin as a base, and of the external acidwith which it is in equilibrium; and the ionisation-constants andmolecular weight being known, all the other quantities are deter-mined. The method is general and applicable to other proteinsand other acids.The ionic concentrations in the jelly are all mathematicalfunctiom of that of the equilibrium acid, and independent of thechemical nature of the gelatin or other protein.While gelatin jelly in equilibrium with an acid is believed t obe a molecular solution, jellies and colloid solutions, in which theconditions of equilibrium are not fulfilled, are probably two-phasedstructures, and may exhibit the pores described by Biitschli andvan Bemmelen.PROCTER INTERNATIONAL RESEARCH LABORATORY,UNIVERSITY OF LEEDS