EQUILlBRIUM OF DILUTE HYDROCHLORIC ACID AND GIELATIN. 313 XXXV.-The Eyuilibrium of Dilute Hydwclhi.ic Acid and Gelatin. By HENRY RICHARDSON PROCTER. IN an earlier paper (Koll.-chern. Beihefte, 1911, 2, 243) it has been shown that when gelatin jelly is immersed in a dilute acid, an equilibrium results which at a given temperature is dependent only on the ionisation and concentration of the acid, which determine not merely the volume of liquid absorbed, but the concentration of the anion in the jelly; and more or less empirical formulae were given connecting these with the concentration of the ionised acid. It was further pointed out that these formulae were consistent with the view that a hydrolysable and ionising salt* of gelatin was formed, and that the phenomena of swelling were simply dependent on the relation between the osmotic pressure of the ionising salt and that of the external acid solution. The object of the present paper is to indicate the precise nature of these relations, and to show that the formulEe there given, with some slight modification, can be fully explained and justified on the ordinary ionisation hypothesis. If this is the case, there seeins no reason for the assumption of more complicated and less verified theories dependent on surf ace-tension and other forces, and involving the unproved an3 rather gratuitms assumption of a two-phased structure of the jelly. The discussion of the present paper has been confined to the single case of gelatin and hydrochloric acid; but the theory proposed is quite general, and iE true in the particular case, must also be true (with different constants) of any other acid, and of other amphoteric proteins, so that its bearing, both on colloid chemistry .and on physiological theory, is very wide. The theory assumes that the jelly is a molecular network, in which the water, the acid, and the protein are within the sphere of each other’s molecular attractions, and theref ore homogeneous in the same sense as any other solution; and it discards the Butschli-van Bemmelen idea of coarse microscopic pores, although it is not denied that such two-phased jellies exist, and can be produced, and that the pores observed by these investigators had a real existence, probably due to the hardening agents with which their jellies were treated. 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 thought better to write “gelatin chloride ” simply. vor,. cv. Y Published on 01 January 1914. Downloaded by Aston University on 24/01/2014 06:54:41. View Article Online / Journal Homepage / Table of Contents for this issue
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EQUILlBRIUM OF DILUTE HYDROCHLORIC ACID AND GIELATIN. 313
XXXV.-The Eyuilibrium o f Dilute Hydwc lh i . i c Acid and Gelatin.
By HENRY RICHARDSON PROCTER.
IN an earlier paper (Koll.-chern. Beihef te , 1911, 2, 243) it has been shown that when gelatin jelly is immersed in a dilute acid, an equilibrium results which a t a given temperature is dependent only on the ionisation and concentration of the acid, which determine not merely the volume of liquid absorbed, but the concentration of the anion in the jelly; and more or less empirical formulae were given connecting these with the concentration of the ionised acid. It was further pointed out that these formulae were consistent with the view that a hydrolysable and ionising salt* of gelatin was formed, and that the phenomena of swelling were simply dependent on the relation between the osmotic pressure of the ionising salt and that of the external acid solution.
The object of the present paper is to indicate the precise nature of these relations, and to show that the formulEe there given, with some slight modification, can be fully explained and justified on the ordinary ionisation hypothesis. I f this is the case, there seeins no reason f o r the assumption of more complicated and less verified theories dependent on surf ace-tension and other forces, and involving the unproved an3 rather gratuitms assumption of a two-phased structure of the jelly. The discussion of the present paper has been confined to the single case of gelatin and hydrochloric acid; but the theory proposed is quite general, and iE true in the particular case, must also be true (with different constants) of any other acid, and of other amphoteric proteins, so that its bearing, both on colloid chemistry .and on physiological theory, is very wide.
The theory assumes that the jelly is a molecular network, in which the water, the acid, and the protein are within the sphere of each other’s molecular attractions, and theref ore homogeneous in the same sense as any other solution; and it discards the Butschli-van Bemmelen idea of coarse microscopic pores, although it is not denied that such two-phased jellies exist, and can be produced, and that the pores observed by these investigators had a real existence, probably due t o the hardening agents with which their jellies were treated.
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 thought better to write “gelatin chloride ” simply.
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swollen with water is treated with a strong acid, such as hydrochloric or sulphuric, the swelling becomes much greater than with water alone, but reaches a maximum at a very low concentration of the external acid, subsequently diminishing in a hyperbolic curve, as the concentration of the acid is further increased. This con- traction is obviously due to the anion of the acid, since it can be increased to almost complete dehydGation by the addition of its neutral salt; but the exact mechanism of the osmotic pressure is not easy to follow, since the jelly is in itself completely permeable both to the acid and its neutral salt, and their ions, and the explanation given in the paper quoted seems an incomplete one.
The fuller statement is that to satisfy the equation * of equality of products (Donnan and Harris, T., 1911,99, 1575; Donnan, Zeitsch. Elektrochem., 1911, 17, 572), the concentration of the free acid contained in the jelly must have a definite relation t o that of the ionised anion of the jelly-salt; and as the latter cannot diffuse from the jelly owing to the colloid nature of its cation, the equilibrium can only be reached by the absorption or expulsion of free acid and of water by the jelly. I n order to investigate these relations, it is necessary, not merely to determine the total chlorine contained in the jelly, as had been done in the earlier experiments, but to ascertain what were the relative proportions of ionised and of non- ionised chloride and of free acid in the jelly, and it became evident from the mathematical investigation of the equilibrium that the total chlorine and one of these being known, the others could be calculated.
The most obvious way of determining ionic concentrations is by means 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 briefly stated. First, it should have been obvious from the outset that the concentration-cell method, marvellously accurate as it is in the determination of the order of quantity of minute ionic concentra- tions, was quite unfitted t o deal with the massive differences of the same order of quantity which were concerned in the present problem. 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 in both phases, is, of course, in accordance with the mass-law, but the actual distribution of 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 sodium chloride and Congo-red ; whence H, x C1, = H, x GI,. This equation relates to the ionised portions only, and the non.ionised portions, i f any, will be related to the ionised according t o the ordinary mass-law equation, a x b=kc.
concentration cell, was not the actual concentration of the solution or jelly, but that of a non-colloid acid or salt solution with which i t would be in equilibrium, since Donnan’s “ membrane-potential ” a t a real or virtual surface mathematically equals and compensates any difference of potential between a colloid solution and its equilibrium acid or salt solution. This is obviously a point of fundamental importance with regard to the frequent use of the concentration cell in physiological investigations, and demands more complete proof than space allows here. The author therefore proposes to make this part of his work the subject of another paper; but it may be noted that means were devised for the approximate measurement of the membrane-potential, which, although only of a few millivolts, corresponded with large percentage differences in the present investigation.
Efforts were also made to solve the problem by conductivity measurements, but the results, although of considergable interest, and possibly of importance to the theory of colloid salts, failed t o give 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 colorimetric method with methyl-orange, which, within certain limits, gave useful results.
The method finally adopted rests on the fact that the influence of 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 of a salt and i b acid is influenced only by the “ common ” anion. I f therefore, sodium chloride is added to a jelly containing gelatin chloride and free hydrochloric acid, the ionisation is no doubt repressed, but the hydrolysis of tha gelatin salt is not affected, and the free acid is expelled with its associated water to almost com- plete dehydration by the osmotic pressure of the concentrated chlorine ion, and can be titrated in the expelled salt solution. The weight or volume of acid solution retained by the jelly can be easily ascertained, and is so small that even i f the assumption that its concentration is the same as that of the solution expelled is not quite accurate, no serious error is introduced by adopting it. The actual method of experiment was Bas follows. A quantity of care- fully purified thin bone-gelatin of known dry weight (usually 1 gram) was soaked in 100 C.C. of acid solution of known concentration in a stoppered bottle for forty-eight hours, a time which was shown to be sufficient for the attainment of practical equilibrium. The contents of the bottIe were then poured into a funnel provided with a finely perforated porcelain $ate, covered with a clock-glass, and
allowed to drain for two hours, the liquid being received in a graduated cylinder. The volume of the liquid, subtracted from 100 c.c., gives the volume of acid absorbed by the gelatin, and this can be further checked, if necessary, by the weight of the drained and swollen gelatin. By titration with alkali hydroxide and phenol- phthalein, the strength of the external acid is determined, and from its concentration and volume, the total acid absorbed from the gelatin is calculated. The swollen jelly is now returned to the stoppered bottle, and dry salt added in the approximate quantity necessary to produce a saturated solution. After repeated shaking, and standing f o r a t least twenty-f our hours, equilibrium is again established; the gelatin is shrunk to thin, horny plates, and a further portion of acid liquid can be separated by the draining funnel, containing the whole of t-he free acid with the exception of that in the small volume of solution (usually about 1.5 c.c.) re- tained in the jelly. If the quantity of solution is determined by volume, i t must not be forgotten that a saturated salt solution contains only 94 per cent. of its volume of water, but the effect on volume of the small quantity of acid present may be safely neglected. The acid salt solut,ion is titrated to determine its con- centration of acid, and the quantity is calculated t o the whole volume of solution absorbed.
We have thus the means of determining (a) the free acid unab- sorbed, which forms the " external solution " with which the jelly is in equilibrium; ( 6 ) the free acid absorbed by the jelly; and ( c ) the chlorine, ionised and non-ionised, combined with the jelly base. The sum of b and c can be further controlled by the titration of 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 with varying quantities of acid, and includes the whole of the results in the series of experiments t o which they refer, and are more concordant than would be expected from the comparative rough- ness of the method. Some of the results are given graphically on the curves, t o allow the reader to form a judgment of the trust- worthiness of the experimental data; but in many cases there is not room to insert the whole.
* I n the actual experimental work the weight of solution absorbed was taken as that of the volume, the increase of specific gravity by the acid being in most case negligible as compared with other sources of error ; and the total chloiine in the jelly is 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.
The lettered columns in roman type are observations. The numbered columns in italics are calculated from the observations as follows :
c x e d x 0'94
3 = 8 cc x 0.94
It is obvious that from these results two distinct series of curves can be calculated: those of the actual quantity of each associated with 1 gram o r 1 mol. of gelatin, and those of relative concentra- tions of the different constituenb of the jelly and its equilibrium acid solution; and these two sets of curves are not necessarily interdependent.
Taking first the question of quantities, the first problem is that of 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-extensive with the jelly itself; but tlie smallest weight which could exist in some ideal non-associating solvent, retaining its chemical structure
and reactive powers unaltered. It is obvious that the special characteristic of the colloid state is the tendency t o form associated groups of molecules, often of quite indefinite size (as in the case of suspension sols), which, osmotically, act as a single molecule or as a single ion. If it were practicable to isolate the pure saturated salt, the equivalent weight would be that combined with one atom of chlorine, and i t would only remain t o determine the valency of the base. This is, however, impossible, since gelatin is a very weak base, of which the salts hydrolyse readily, and, on account of secondary reactions, it is impossible so to concentrate the acid as to make hydrolysis negligible. All that we can obtain is a curve, of which the limit a t infinite concentration is the completely saturated 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 hydrolysis formula, which, as was shown by the author in the earlier paper already quoted (Zoc. cit . ) , is conveniently transformed into the
simple expression y = where x is the molecular concentration
or normality of the equilibrium-acid, k is the ordinary hydrolysis- constant, and y is the proportion of unhydrolysed salt to the total base present. Such a, curve, if the k is small, ascends a t first almost vertically, curves sharply as it approaches unity, and thereafter proceeds almost horizontally, reaching unity only when x beCOm6s infinite. I f the k be larger, the ascent is more gradual, and the curve rounder and more prolonged, so that it may still be far from unity within the limit of experiment, y having obviously a value of 0.5 when k=x.
The curve of gelatin chloride plotted from experiment, as will be seen by reference to Fig. 1, rises vertically a t first, with all the characteristics of a small k, but after turning sharply, continues t o rise throughout the limits of the experiment. Such a curve is that of a diacidic base, or dibasic acid, and is the sum of two curves, one of which is due t o the (usually small) k of the first valency, and the other to the larger k of the second. The expression therefore
X + k ’
X X becomes 9 = - + - and its limit is 2.* The experimental X+k, x:+h9’
curve is plotted Tor 1 &am of gelatin, whilst the expression is for
1 mol., and must obviously be multiplied by ___- *Oo0 to make i t
comparable with experimental results. There are thus three un- inol. wt.
* The curve of non-hydrolyecd gelatin given in n previous paper was calculated on purely theoretical ground? and on the assumption that gelatin was monacid, and the k then adopted of 0.005 was obviously a compromise between k, and k2.
knowns to be determined, the two k'sy and the molecular weight; and, although this might no doubt be done by three simultaneous equations from different points of the curve, I have preferred as more satisfactory, to adopt a method of approximation which apparently 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 is almost entirely dependent on the former, whilst the later part is
approximately 1 +-. If, therefore, the value of the curve a t x + k,
z = O * O l be assumed to be equal to the reciprocal of the molecular weight, and this be subtracted from the value a t x=O-25 , the
remainder, multiplied by the same reciprocal, will be the value due to the second term of the expression, and from these an approximate k, and k, can be calculated. I f these are now employed to correct the first calculations, a closer approximation can be obtained; and this can be repeated until the results are within the limits of experimental error. Fo r each single term,
k = - - x. With any approximate molecular weight, values for k, Y
and k, can be calculated which will give a curve agreeing with the experimental a t the two points taken, but unless the molecular weight is very nearly correct, the value of y will be noticeably wrong a t a third point, which is most advantageously taken near that of maximum curvature.
Since the molecular weight must be such as will give whole numbers of atoms in accordance with ultimate analysis, i t becomes easy to decide on the only possible weight within the limits of experimental error, and a (‘ rational ” formula is obtained.
The experimental curve in the present case is very accurately
X
X 1000 + 1.05 * 839 ’ +-- and t o this the curve X represented by
x + O 0013 in Fig. 1 has been calculated. This results in a probable ‘( rational ” formula for gelatin of C,,H,,O,,N,,, with a molecular weight of 839, which agrees with Schutzenberger’s o~7n determinations quite as well as his gener*ally accepted formula, C,,H.,,,O,,N,,, but is slightly 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 completely drying gelatin without decomposition. The hydrogen is, of course, the most doubtful number.
Formuls. Analyses.
Procter. - Schutzenberger. I p t t e n d e n C3,H,70,3W,, C7,1-J,,0,N,, Schiitzenberger. Mulder. and Solly.
It may be noted that Paal obtained a molecular weight of about 900 from freezing- and boiling-point methods (Ber., 1892, 25, 1202).
It must not, however, be assumed that the molecular weight of gelatin, from the physical point of view, is necesarily so compara- tively small. The weight calculGated from the previous experiments is merely that of the smallest quantity which can act as a chemical individual, and i t is not incompatible with the association of the colloid molecules in any way which does not affect their chemical combining powers; and, if the view of a molecular network is
correct, the whole jelly may be regarded in a physical sense as one enormous colloidal molecule dissociating a number of chlorine ions; whilst it is impossible t o say what degree of association may still exist after Iiquefaction.
Since the hydrolysis-constant of a salt of a weak base is the ionisation constant of water divided by that of the base, we can calculate the two basic constants of gelatin as concerned in the reaction, although i t may be probable that the two affinities are in themselves equal, and that the second only takes its lower value bec.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 10-3
0.5 x 10-l1, and Lund6n (loc. c i t . )
gives for leucine 7ca=1*8 x 10-10, and k b = 2 * 3 x 10-l2, and for glycine (aminoacetic acid), one of the principal constituents of the gelatin molecule, very similar figures, so that there is no interent improbability 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 by ordinates, the common concentrations of the external acid x, in which these are equal, will intersect on .a line passing through the origin a t an angle of 45O, and this will be the axis of a series of right-angled hyperbolas, corresponding with the different values of 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 C1 will lie, and if the concentration of one of these constituents is given, the equilibrium will be definitely determined. At any such point, the hydrogen and chlorine ordinates will enclose a rectangle equal in area t o x2, the chlorine being necessarily the greater from the ionisation of the gelatin chloride.
It is obvious that on the concentration of this ionised chloride the whole equilibrium depends, and if its relation to x can be determined, the problem is definitely solved. An experimental solution is given by the determination of the concentration of the free acid of the jelly, which is equal to its hydrogen abscissa. As the 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 the product of th6 hydrogen and chlorine ions must be the same in each case, or any difference which exists between the two must be compensated by an electric potential a t the interface. There is no evidence, experimental or theoretical, that the colloid gelatin
ion exerts any osmotic pressure, and, as an associated network, it should, theoretically, only act as a single molecule; but since the two sides of a rectangle are necessarily greater than those of a square of equal area, some surface-potential must exist, opposed in sign t o that shown by Donnan (Zoc. cit.) to be caused by the unequal concentration of the hydrogen and chlorine ions. Since the ionised chlorine is confined to the jelly by the attraction of its non-diff usible colloid ion, the adjustment of equilibrium between the jelly and the external acid can only take place by the passage inwards or outwards of hydrochloric acid and water, and if we suppose the jelly divided into separate volumes, each containing one of the constituents a t the common osmotic pressure, that of the acid will be of the same concentration as the external acid x, and will have an osmotic pressure of 22, since both hydrogen ion and chlorine ion are of x concentration, and the ionised chlorine, to be at the same osmotic pressure, must also have a concentration of 22, since the chlorine ion of the acid cannot be expelled without its attendant hydrogen ion.
Thus the x2 of the external acid is in oemotic equilibrium with the 2x of the jelly, and if we plot the concentration of the external acid as x, we must also plot the osmotic concentration as 4% t o maintain the same relation. Experiment shows that, measured in terms of x, the concentration of the ionised chloride is approximately 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,t the concentration of hydrogen ion in the jelly is algebraically
-'I,+ ~ c 1 , 2 + 4 x a and that of the expelled acid 2
but, graphically, all the concentrations are given by a simple con- struction, the proof of which is obvious. I f the C1' ordinate of x be produced vertically to an additional length of CVg, and a line be drawn through this point parallel with the axis of the hyperbola (that is, a t 45O), it will cut the hyperbola a t the common point of intersection of the IIC' and C1' ordinates of the jelly, the IT* ordinate of which, if produced, will cut the x vertical a t the tot.al Cl' concentration, and a horizontal line through the point where the (31' ordinate of the jelly cuts the axis of the parabola will cut the x vertical a t the hydrogen-chloride concentration of the jelly, whilst the difference between this and x will be the acid expelled. If continuous curves are drawn through these points for the different values of x, they will divide the diagram into
regions of free hydrogen chloride or hydrogenion concentration, and of ionised chloride, respectively, below and above the straighb line axis of x. Experimentally, the concentration of the ionised chlorine is obtained by dividing x2 by the concentration of free acid 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 the
FIG. 2.
0.05 0;lO 0.15 0.20 0.25 0.30 N.H'. X
total x . It will be seen that they practically coincide, and it may be concluded that the gelatin salt is almost wholly ionised, or, a t least, to an extent comparable with hydrogen chloride, for the incomplete ionisation of which no allowance has been made.
With regard to the correction, approximately 0.02, added to 2x under the squareroot sign, it may be noted that, putting x=O,
a 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 measurable chlorine-concentration being reached before any free acid is shown either by indicators like methyl-orange, or by the hydrogen con- centration cell. The probable explanation is that as gelatin is amphoteric, and, to some extent, ionises both H' and OH' in the neutral state, a small amount of neutral chloride can be forlr,ed in absence of any other free acid than its own; or, perhaps, in other words, that it must be brought to a neutral condition as compared with water before any hydrolytic production of hydrogen chloride can take place. This is in accordance with experiments quoted by Pauli (KoZL-Zeitsch., 1913, 12, 222), which prove that in neutral solution, gelatin and other proteins wander to the positive pole in elecikophoresis, and that a small amount of acid is necessary to bring them to a neutral condition in which they are unaffected by the current, whilst, with further additions of acid, their basic character preponderates, and they wander to the negative pole (probably as basic ions). The correction may thus be regarded as simply indicating the .amount of hydrochloric acid required before neutrality is reached.
It is obvious that, except for this small correction, the concen- trations are all purely mathematical functions of x, and therefore independent 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 that equilibrium still exists, although actual measurement, is complicated by the necessity of a membmne, and the much longer time required t o attain equilibrium than with the thin sheets of the present experiments; but, in the case of gelatin, neither concentration cells, conductivity, nor the experiments of G. S. Walpole on refractive index (Roll.-Zeitsch., 1913, 13, 241) show any break in the curves a t the melting point, .and, in all probability, the degree of associa- tion is still very large. Since such associated groups of ions must still be in equilibrium with their surrounding solution, they must also be associated with acid and water in the terms of the jelly equilibrium, and the suggestion is obvious that, whilst the true equilibrium-jelly is a homogeneous molecular solution, the .apparent aqueous solution is really a two-phased structure of associated colloid systems, surrounded by their equilibrium liquid. The same may probably be true of jellies made up with arbitrary quantities of water and acid, and may serve to explain some of the results of earlier investigators. Certainly, electrometric experiments made with such jellies, both by conductivity and by the concentration
cell, gave somewhat abnormal results; and it is clear that unless by chance the exact equilibrium mixture has been made, they must be in unstable equilibrium, and must tend to separate into equi- librium-jelly and its corresponding acid, possibly developing the Butschli 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 obtained curves identical in type with the swelling curve of acid gelatin, which probably can be explained by the varying quantities of water 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 the X + k x + k ’
theoretical quantity of non-hydrolysed gelatin divided by J 2. Obviously, if the q u a n t i t y of ionised chloride a t any point be divided by the corresponding concentration of the ionised Cl’, the quotient will be the volume of the jelly, and it is found that by dividing the calculated quantity of non-hydrolysed chloride which, it has been shown, is almost wholly ionised, by d 2 x + 0.02, a curve is obtained which agrees very closely with the smoothed curve of observed volumes, both in type and quantity. It is worthy of note that the above calculation takes no account of any solid rigidity or elasticity of the jelly, and it may therefore be presumed that these have no existence 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 the earlier paper of what was called “ acid fixed ” ; that is, of the excess of acid in the jelly over that contained in a n equal volume of the external solution. This is a well-defined quantity, rising rapidly with the concentration of the external acid to about 0.8 milligram- molecule for 1 gram of dry gelatin, formrng a slight maximum at about s=0*015 and a still less marked minimum a t about x=O*15, and again increasing, but only very slowly. The value is easily and accurately obtained by titration of the melted Jelly and of its equilibrium acid, but the curve is peculiar; and, a t the time, w-as incapable of definite explanation. It is now obviously the quantity of gelatin chloride less that of the free acid expelled. Calling Q the value of the quantity of non-hydrolysed gelatin chloride, c the concentration of the ionised chloride, and a that of the expelled acid, this is given by the (somewhat simplified)
expression Qc2, This accurately reproduces the peculiarities of
the experimental curve, but is very slightly too low in actual quantity, presumably because the theoretical expression assumes
total ionisation of the gelatin salt, and the consequent expulsion of a slightly larger quantity of free acid than actually takes place,
All the curves described are plotted in Figs. 1 and 2, together with the experimental results (so far as space allows), and the corresponding algebraical expressions are annexed ; and to facilitate experimental checking, the numerical calculated values f o r a number of values of x are also given in the following table.
Calculated Mathematical Curves for 1 gram of Gelatin. Quantity
Quantity Quan- excess of Con- un- Quan- tity OF C1 centra-
Nor- hydro- tity free in jelly Con- tion a t mahty 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.
The following are the forinuke used in calculation; the letters refer to the corresponding columns.
X - C1, + JCJg2 + 4x2 2
A = f + g = - 2 2
f d = b - e x i = x - f
a 9
8 = -. The dehydrating effect of salts having a common ion with the
acid 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 the same effect. Even numerically, so long as the salt solutions are dilute, it is probably sufficient to take account of the common ion only, using the same mathematical formulai! as with the acid alone, but with more concentrated solutions, the effect on ionisation a t least must be considered, and we can no longer assume that the colloidal salt is totally i o n i d .
It was shown in the earlier paper that when a salt with no common ion is introduced, as, for instance, sodium chloride into a 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 with the substances just named, in which the gelatin was shown by analysis to have combined with as much as 3 per cent. of .hydro- chloric acid derived from the sodium chloride. Similarly, in presence of large excess of sodium formate, hydrochloric would be replaced by formic in the gelatin salt, and this sort of reaction is not without bearing on some physiological problems.
The question whether the action of neutral salt solutions on gelatin falls under the aame theory still demands further study. It was shown in the previous paper (Zoc. cit.) that sodium chloride was abaorbed by gelatin from neutral solution with increased swelling, but was replaced and expelled by hydroch1o:ic acid, in presence of which the absorption of salt was negative. Neutral salta may combine with amphoteric proteins, either by the anion becoming attached to the amino- and the cation to the carboxy- group, or the whole salt may be attached t o the amino-group, a,p hydrogen chloride is to organic bases, by the nitrogen becoming quinquevalent; and the probable structure of the protein salt must be left t o more purely organic chemists to decide, since either would fulfil the requirements of the present theory.
Conclusions.-The swelling of gelatin in dilute acid solutions depends on the osmotic pressures and equality of products of a diacid ionisable salt of gelatin as a base, and of the external acid with which it is in equilibrium; and the ionisation-constants and molecular weight being known, all the other quantities are deter- mined. The method is general and applicable to other proteins and other acids.
The ionic concentrations in the jelly are all mathematical functiom of that of the equilibrium acid, and independent of the chemical nature of the gelatin or other protein.
While gelatin jelly in equilibrium with an acid is believed t o be a molecular solution, jellies and colloid solutions, in which the conditions of equilibrium are not fulfilled, are probably two-phased structures, and may exhibit the pores described by Biitschli and van Bemmelen.
PROCTER INTERNATIONAL RESEARCH LABORATORY, UNIVERSITY OF LEEDS.
