EQUILIBRIA IN THE FORMOL TITRATION*

BY MILTON LEVY

(From the Department of Chemistry, New York University and Bellevue Hos- pital Medical College, New York)

(Received for publication, October 28, 1932)

The theory of the t’itration of weak acids and bases has been systematized on the basis of titration constants characteristic of the acids and bases and a constant (such as Kw) characteristic of the solvent and describing its behavior with strong alkalies. The usefulness of a knowledge of these characteristic constants is evident from the formidable literature which deals essentially with the behavior of acids and bases in water. The object of the present paper is to present data and an interpretation of them which may serve in an analogous way to systematize the behavior of certain of the monoamino acids in the form01 titration. Through postulated equilibria the data are reduced to character- istic constants independent of the amount of formaldehyde in the solution. These constants, with a knowledge of the behavior of the solvent, should place the form01 titration on a more satisfac- tory foundation than the present empirical one.

The form01 titration depends on more or less marked shifts of certain parts of the titration curves of the amino acids in the presence of formaldehyde. The relationship of these shifts to stoichiometry was recognized by Schiff (l), who showed that some amino acids in formaldehyde neutralized an equivalent of alkali if phenolphthalein was used as an indicator. Sorensen (2) applied the possibilities of the form01 titration as a quantitative method for the study of protein hydrolysis by acids, enzymes, etc. There is no need to emphasize the great usefulness of the method.

* A preliminary report was given before the American Society of Bio- logical Chemists at Philadelphia, April, 1932 (Levy, M., J. Biol. Chem., 97, p. xcii (1932)).

767

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768 Equilibria in Form01 Titration

Sijrensen (2) believed that the mixture of formaldehyde, amino acid, base, and water presented an equilibrium which he expressed in t,he equation :

COOH COOK / /

“\ +HCHO+KOH*R + 2 Hz0

\ NHz NC=Ha

The composition of the methylene compound was based on the substances which Schiff (3) had isolated from appropriate mixtures. Otherwise the equation and the existence of the equilibrium were based on the stoichiometry of the titration as it was affected by the formaldehyde concentration and the alkalinity of the end- point.

Harris (4) erroneously rejected this equation and interpretation because the titration of the amino acids in formaldehyde follows the Henderson-Hasselbalch equation (pH = pK + log cr/l -cy> at constant formaldehyde concentration. Application of the law of mass action to the Siirensen equilibrium leads to exactly this t,ype of equation (as will be shown below) under the condition noted and Harris’ rejection of the Sijrensen interpretation is not valid. As far as the shape of the titration curve is concerned, Harris’ experiments are consistent with the Siirensen equilibrium. Harris preferred to think of t,he system as dependent on a com- pound of the amino acid and formaldehyde having a dissociation constant differing from that of the original amino acid. While it is undoubtedly reasonable to assume that such compounds have definite hydrion dissociation tendencies, the assumption is of little use, alone, in accounting for a variation of the observed titra- tion constants with formaldehyde concentration. The additional assumption of an increase in the amount of t.he new acid with increasing formaldehyde concentration (Harris (5)) introduces into the equilibrium equations the acid corresponding to Sijren- sen’s methyleneamino acid salt. This has proved to be un- necessary in the derivation of the equations which we use to de- scribe the data presented in this paper. A sufficient assumption has been that formaldehyde combines with the amino acids only

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M. Levy

to the extent t,hat anions of the resultant compounds are formed.’

Derivation of equations including the presence of unionized formaldehyde compound is possible. Such equations show that when the amount of compound becomes appreciable the observed titration constants in formaldehyde no longer vary with the for- maldehyde concentration. This is not observed in our data, so that we may conclude for the range of formaldehyde concentra- tions included, the amount of un-ionized formaldehyde amino acid compound is not significant.

Our success in fitting the variation of the titration constants with the assumption of the formation of two simple compounds of amino acid anion and formaldehyde leads to the rejection of the importance of the variation of the dielectric strength of solvent produced by the addition of the formaldehyde (Harris (7)).

Besides Schiff (3), a number of other workers have isolated substances from mixtures of amino acids or their salts and for- maldehyde. (Among them are Franzen and Fellner (8), Krause (9), Bergmann a,nd coworkers (lo).) The compounds isolated do not seem to be particularly well defined. The possibility of the isolation of a particular compound depends on several factors besides its importance in an equilibrium between the various com- ponents of a system. The compounds are not of distinct value towards a formulation of the system involved in the form01 titra- tion, except that they support the existence of compounds formed from alkali, amino acids, and formaldehyde containing from 1 to 3 molecules of formaldehyde or its residue for each molecule of amino acid.

Zwitter Ionen and Formal Titration-Harris (11) (1930) uses the behavior of the amino acids in formaldehyde as a proof of the Zwitter Ion structure for amino acids. The logic involved in this proof may be stated without details in the form of the following syllogism. (1) The titration constants of amines are shifted towards diminished basicity in formaldehyde solutions. (2) The

1 Svehla (6) has shown by freezing point measurements that compounds are formed between amino acids and formaldehyde without the addition of alkali. These compounds are apparently not important in determining the behavior of the systems when alkali is added.

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770 Equilibria in Form01 Titration

NaOH titration constants only of the amino acids are diminished by formaldehyde. (3) Therefore the titrat,ions of amino acids with NaOH are reactions of the amino groups of the amino acids.

The acceptability of this syllogism would seem to depend on the interpretation of the term “titration constant.” If one accepts, as Harris does, the existence of formaldehyde-amino acid com- pounds whose’ dissociation constants may be measured in the form01 titration then one may accept this as a proof of the thesis that the NaOH titration constant represents a reaction of the amino group and not of the carboxyl group of the amino acid. But if the reaction is interpreted as SGrensen interprets it and as it is developed in the present paper then the titration constant becomes a composite which may be made to depend on the affinity of the amino acid anion (independently of its mode of formation) for formaldehyde and the hydrion dissociation constant of the amino acid as measured by the ordinary NaOH titration. It is therefore of no material consequence with what group the hydrion was previously associated and Harris’ argument reduces to an analogy with the validity of Bjerrum’s (12) original int,erpretation of the ampholyte constants.

The concept of Zwitter 1on is still satisfying but the proof of its reality must depend on a method t,he results of which can be interpreted in only one way. It may be pointed out that for a systematization of the knowledge of the thermodynamic behavior of acids and bases with respect to the hydrogen electrode the Bronsted (13) nomenclature allows completeness without involv- ing questions as to the structure of ampholytes and without requir- ing that certain constants be called acid constants and others basic constant’s in the old sense.

Theoretical

During our studies of the form01 titrat,ion we have developed the following t.heory of the titration which numerically acc0unt.s for the data on the basis of experimentally determined constants.

The following equilibria are postulated to determine the be- havior of the system.

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(1)

(2)

(3)

M. Levy

coo- coo- / /

“\ *R + H+

\ NH3f NH%

a b h

coo- coo-

/ /

R\ + CHzo =R\ NH, NH&Hz0

6 F d

coo- coo-

/ /

“\ + 2CHzO SR

\ NH2 NHztCHzOh

b F e

771

(4) K1 = ;

(5) K, = &

(6) Ka = &

Equations 4 to 6 are the corresponding equilibrium equations derived from the law of mass action. a, b, h, d, and F are concen- trations (used in place of activities) of the various ions and mole- cules below which they appear in the chemical equations. KI is the hydrogen ion dissociation constant of the amino acid. Kz and KS are association constants between the amino acid anion and 1 and 2 molecules of formaldehyde respectively.

If LY be defined as the fraction of the total amino acid present as one form or other of the anions, and complete dissociation of salts is assumed, Equation 7 results.

a (7)

bfd-l-e - = 1-a a

From Equation 7 and the equilibrium equations there may be derived Equation 8.

(8) pH = - log (KI + KIKzF + K,K#) + log a/l - a

The application of this equation to the form01 titration requires either that F be replaced by the exact relationship

(9) F=C -d-2e

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772 Equilibria in Form01 Titration

in which C is the formaldehyde added to the mixture or that an approximation be introduced. The use of the exact relation- ship leads to a complicated relationship and an approximation is readily available. If the total amino acid concentration is small compared to the formaldehyde concentration then d and e will be small compared to C and under these conditions it is permissible to neglect the amount of formaldehyde combined and to substi- tute for F in Equation 9 the total added formaldehyde.

Therefore at a constant and sufficiently high formaldehyde con- centration the first term on the right of Equation 8 becomes constant and equal to the pH at t,he mid-point of titration of the amino acid. This titration constant may be designa,ted pG, and defined by Equation 10.

(10) pGf = - log (K1 + K,KtF + KIKP)

The similarity of form between Equation 8 and the Henderson- Hasselbalch equation (pH = pK + log (~/l-a) may now be readily recognized.

Equation 10 may be transformed into a suitable form for graphic det,ermination of Kz and KS by taking antilogarithms a,nd rearrang- ing terms to obt,ain Equation 11.

(11) ( ) $+I +=K~+K~F=M 1

If the function M defined by Equation 11 be plotted against F then a straight line should result, the intercept of which is K2 and the slope KS.

At the higher formaldehyde concentration K3F2 becomes large in comparison to KtF, and as an approximation, the validity of which will vary from one amino acid to another, the terms K1 and KlK2F may be neglected in Equation 10 and Equation 12 results.

(12) pG, = - log KlK3 - 2 log F

The constant -log K1K3 may be determined from a plot of log F against pGf. Such curves reach or approach a slope of -2 as is expected from Equat.ion 12 and the intercept extrapolated on this slope is the value of -log K1K3.

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M. Levy 773

The addition of Equations 1 and 2 gives a modern equivalent of the Sorensen equilibrium. It is only necessary to place KS = 0 in Equation 8 to obtain the equations which would be applicable in this case. It is therefore seen that the Sorensen equilibrium leads to the form of the Henderson-Hasselbalch equation contrary to Harris’ (4) statement that it does not.

EXPERIMENTAL

In his earlier work Harris used an indicator method for the determination of pH but later showed that the hydrogen electrode could be used in formaldehyde solutions. The latter method has been used exclusively in obtaining the data in the present paper. We have also avoided the use of commercial formalin of qualita- tively and quantitiatively unknown composition.

The cell used consisted of a saturated KC1 calomel half cell, an agar KC1 bridge, and the solution containing a platinized platinum electrode; the solution and electrode were in a closed vessel through which hydrgoen passed. Temperature was controlled by means of an air thermostat at 30” and all solutions were brought to this temperature before use. The titrating reagent was added from a burette graduated at 0.01 ml. intervals. The potentials were measured by the use of the usual potentiometer and galvanometer.

While it is quite easy to detect the odor of formaldehyde over quite dilute solutions of formaldehyde, no evidence that significant quantities of formaldehyde were carried off in the hydrogen stream was obtained. No regular drifts of potential occurred on chang- ing the rate of bubbling and in some cases the hydrogen was first passed through a formaldehyde solution of the same concentration as that in the cell but this precaution seemed unnecessary within the limits of variation desired.

The amino acids were obtained from commercial sources or prepared in the laboratory, except for leucine which was kindly supplied by Dr. H. B. Vickery.

The formaldehyde was prepared by the dry distillation of para- formaldehyde. The gas was led through wide tubes into distilled water. The solution so obtained was filtered and the formalde- hyde content determined by oxidation with alkaline iodine (Ro- mijn (14)). The stock solution of formaldehyde approximated 10 M and after lo-fold dilution had a pH between 5 and 6. This was

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774 Equilibria in Form01 Titration

taken t,o indicate that formic acid was not present in significant quant,ities.

Formaldehyde neutralizes a certain amount of base in alkaline solutions. The correction or blank on the formaldehyde depends on the formaldehyde concentration. It was found unnecessary to correct any of the pGf, log F curves for this but in the titration with base at constant formaldehyde concentration the end-point is obscured in certain cases unless a formaldehyde blank is run. Since no data are given in this paper involving these blanks they are not presented here.

Results

Form of Titration Curve-The statements of Harris (4) that the form of the titration curve in formaldehyde is like that in water has been fully confirmed for a number of the amino acids at low amino acid concentrat.ions and at all formaldehyde concentrations dealt with. It is not felt necessary to present the actual data, as in the main they are simply a duplication of Harris’ results. These results are in conformity with Equation 8.

Variation of pG,--In order to follow the variation of the titra- tion constant in formaldehyde the following procedure was carried through. The amino acids were brought t.o the mid-points of the alkaline branches of their titration curves by the addition of the appropriate quant,ity of NaOH. The solution so prepared was placed in the titrat,ion vessel and the pH measured. This could be compared with the known titration constant of the amino acid. A formaldehyde solution of known concentration was added from the burette and the pH measured after each addition. The concentration of formaldehyde in the solution was calculated from the concentrat,ion in the titrating fluid and the volume added on the assumption that the volumes of the original solution and titrating solution were additive. Details were so arranged that the concentration of amino acid and its salt remained approxi- mately constant (within 10 per cent) throughout t.he titration. The pH measured at each formaldehyde concentration is equal to pGf. In Fig. 1 the values of pG, are plotted against the logarithms of’ the formaldehyde concen6rations slnd a smooth curve drawn through t.he points.

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M. Levy 775

An inspection reveals that these curves reach or approach a slope of 2 as the formaldehyde concentration increases (except proline in which the curve reaches a slope of 1). In the plot these portions of the curves have been extrapolated to log F = 0 and the constants (-log K&) of Equation 12 have been read. In the case of proline the intercept is equal to -log KlK2 of Equa-

FIG. 1. The variation of titration constant (pG/) with the logarithm of the formaldehyde concentrat.ion. Curve I represents glycine (0.005 M);

Curve II, or-amino-fl-phenylacetic acid (0.005 M); Curve III, leucine (0.01 M); Curve IV, glutamic acid (0.005 M); Curve V, phenylalanine (0.005 M);

Curve VI, tyrosine (0.002 M); Curve VII, proline (0.01 M). The dash lines represent extrapolations. [CH,O] is in mols per liter.

Con 8 and K3 is equal to 0. The values of these constants are given in Table I along with pKl and the pH of 99 per cent neutraliza- tion in 10 per cent formaldehyde calculated from the constants.

The constant, -log KIKs, is a practically useful constant since from it one may determine the titration constant at a given for- maldehyde concentration. The equation to which it applies is valid for the amino acids studied from about 2 M (6 per cent) for-

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776 Equilibria in Form01 Titration

maldehyde upward and therefore is applicable in the form01 titra- tion as usually carried out (5 to 20 per cent formaldehyde).

The proof of the validity of the entire theory developed in the theoretical section depends on the applicability of Equation 10 to the data. In Fig. 2 the function M of Equation 11 is plotted against the formaldehyde concentration F. The points fall reasonably well on straight lines and from these lines the slopes (KS) and intercepts (&) may be read. Many determined points have been omitted from the plot and in order to get the curves on one graph some portions of the curves have been omitted.

TABLE I

Form01 Titration Constants Based on the Relationship, pGf = -log K1K3 - 2 log (CH20), at 90’

Smino acid

Glycine.......................... &Phenyl-a-aminoacetic acid. Phenylalanine. Glutamic acid.. Leucine................. Tyrosine.........................

-

6.65 6.90 7.57 7.87 7.87 8.45

PKI (30’)

9.6 8.84 8.99 9.32 9.50 9.07

PG~ = ---log KlK2 -log (CH&)

-

I

pH of end- point (99 per cent neutral-

ized) in 10 per cent CHzO

7.6 7.9 8.6 8.9 8.9 9.5

Proline............................ 1 8.25 / 10.30 ) 9.7

We may conclude from the fit of the graph that the equilibria postulated in the theoretical section are justified in that they lead to a numerical equation which describes the data. A reservation is necessary in regard to glycine. There is evidence in this case that the formaldehyde compound is polymerized to a marked extent and the values of the constants are dependent to some ex- tent on the actual glycine concentration. We have in mind a further development of the theory to account for the behavior of glycine. In all the data presented in this section the amino acids have been at a concentration of 0.01 or 0.005 M and except for glycine no significant variation with amino acid concentration was observed.

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M. Levy 777

In Table II the values of Kz and KS for a number of amino acids are given as determined from Fig. 2. The presence of three con-

0 I I I I I I 1 2 [CHcO] 3 4

FIG. 2. Test of Equation 11, plot of M = f against F. Curve

1 represents glycine (0.005 M); Curve II, m-amino~&phenylacetic acid (0.005 M); Curve III, leucine (0.01 M); Curve IV, glutamic acid (0.005 M); Curve V, phenylalanine (0.005 M); Curve VI, tyroaine (0.002 M). [CHtOl = F is in mols per liter.

TABLE II

Form01 Titration Constants Referring to Equation 8

Amino acid

Leucine ..................................... @Phenyl-a-aminoacetic acid ................. Glutamic acid .............................. Phenylalanine. .............................. Tyrosine .................................... Glycine ....................................

K2

16 13 22 16 10 60

Ki

35 77 24 23 5

290 (0.01 M

only)

stants in Equation 8 is somewhat deceptive since one of them (K,) is independent of the measurements described.

For proline the variation of pG, is determined by the Sorensen equilibrium alone and the behavior of the system present in the

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778 Equilibria in Form01 Titration

form01 titration of proline can be accounted for on the basis of the hydrion dissociation constant of proline and an association constant of the proline anion and formaldehyde. This constant is Kz in the scheme derived above. This difference between proline and the true amino acids is no doubt significant for the structure of the formaldehyde compounds.

DISCUSSION

The significance of the results for the practical form01 titration will not be completely evident until a study has been made of the behavior of the formaldehyde solution with alkali alone. This behavior will determine the nature of the second factor involved in the determination of the end-point of the form01 titration. Thus while it might appear from the data presented that the titra- tion in formaldehyde would be most accurate at the highest possible formaldehyde concentration (lowest pGf) this conclusion is erroneous because of the nature of the blank titration. The most favorable formaldehyde concentration for the form01 titra- tion will undoubtedly prove to be a compromise between a low pGf, favored by high formaldehyde concentration, and a low blank favored by low formaldehyde concentration.

An important practical point is that the various amino acids have different characteristic constants for their equilibria with formaldehyde. This may become of importance in the titration of mixtures of amino acids such as appear in biochemical work. Ideally we would wish to titrate all of the amino acids in such a mixture but we cannot doubt that the best solution will again be a compromise.

The basic amino acids, lysine, histidine, and arginine, present complications due to the number of groups involved and their effect on one another. Data on their titrations in formaldehyde have been accumulated to some extent but presentation must await completion of the work. These amino acids will be particu- larly interesting because of their importance in determining the titration curves of proteins.

SUMMARY

A theory and equations describing the behavior of amino acids in the form01 titration have been evolved based on the following postulat.es.

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M. Levy 779

1. Only amino acid anions react significantly with formaldehyde. 2. Two types of new anions are formed, one involving 1 mole-

cule of formaldehyde per amino acid anion and the other 2. The equations developed have been applied to data and found

to describe the system adequately.

BIBLIOGRAPHY

1. Schiff, H., Ann. Chem., 319, 59 (1901); 326, 348 (1902). 2. Sorensen, S. P. L., Biochem. Z., 7, 45 (1907). 3. Schiff, H., Ann. Chem., 310, 25 (1900). 4. Harris, L. J., Proc. Roy. Sot. London, Series B, 97, 364 (1924). 5. Harris, L. J., Proc. Roy. Sot. London, Series B, 96, 500 (1923). 6. Svehla, J., Ber. them. Ges., 66, 331 (1923). 7. Harris, L. J., Proc. Roy. Sot. London, Series B, 104, 412 (1929). 8. Franaen, H., and Fellner, E., J. prakt. Chem., 96,299 (1917). 9. Krause, H., Ber. them. Ges., 61,136,542,1556 (1918); 62,1211 (1919).

10. Bergmann, M., Jacobsohn, M., and Schotte, H., 2. physiol. Chem., 131, 18 (1923). Bergmann, M., and Miekeley, A., Ber. them. Ges., 67, 662 (1924). Bergmann, M., and Ensslin, H., 2. physiol. Chem., 146, 194 (1925).

11. Harris, L. J., Biochem. .I., 24, 1080 (1930). 12. Bjerrum, N., 2. physik. Chem., 104, 147 (1923). 13. Bronsted, J. N., Rec. trav. chim. Pays-Bas, 42, 718 (1923); J. Physic.

Chem., 30, 777 (1926). 14. Romijn, G., 2. anal. Chem., 36, 19 (1897).

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Milton LevyTITRATION

EQUILIBRIA IN THE FORMOL

1933, 99:767-779.J. Biol. Chem. 

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