On the Rate of Solution of Casein in Solutions of the Hydroxides of the

ON THE RATE O F SOLUTION OF CASEIN I N SOLUTIONS OF T H E HYDROXIDES O F THE ALKALIES AND OF T H E ALKALINE EARTHS BY T. BRATLSFORD ROBERTSON

(From the Rudolph Sfireckels Physiological Laboratory of the University of California) In previous communications' I have shown that when casein is shaken or stirred up in a solution of a hydroxide of an alkali or of an alkaline earth, i t dissolves rapidly at first, but later, and especially after the solution has become acid t o litmus, with extreme slowness. It appeared of interest t o ascertain more precisely the time-relations of this phenomenon and their dependence upon the mass of casein or of hydroxide present in the mixture--upon the kind of hydroxide, etc. Accordingly the following experiments were undertaken. The casein which was employed was Eimer & Amend's " C. P. Casein nach Hammarsten," specially purified by washing in water, alcohol and ether according to the method described in a previous communication.' It was dried a t about 30' for about 1 2 hours, but not over H,SO,. Hence it contained traces of ether and a trace of water, too small t o affect the accuracy of the determinations, but of considerable importance to the success of the investigation. Perfectly anhydrous casein only sinks in and is wetted by water or watery solutions with extreme difficulty and hence was not suitable for the present purpose. The same preparation of casein was employed in all of the experiments enumerated in Tables I-XVII inclusive. A fresh preparation of casein was employed in the experiments enumerated in Table XVIII. A measured amount (usually IOO cc) of the fluid employed __

I T.Brailsford Robertson: Jour. Biol. Chem., 2, 317 (1907); 5 , 147 (1908); Jour. Phys. Chem., 13, 469 (1907). ' T. Brailsford Robertson: Jour. Biol. Chem., 2, 317 (1907).

378

T.Brailsford Robertson

as solvent was placed in a beaker of squat form and 400 cc capacity and was agitated by a flattened glass rod which was bent a t right angles, the plane of the horizontal arm being somewhat inclined to the vertical, so as to communicate an upward thrust to the rotating liquid. The horizontal arm of the stirrer was about 2 ' j 2 cm long and as near as possible to the bottom of the beaker; this was rotated at an approximately constant rate of about 1600 revolutions per minute by a small motor. While stirring, a weighed amount of the casein was dropped into the fluid. A t stated intervals samples of the mixture were almost instantaneously abstracted by means of a I O cc pipette which was provided with a rubber bulb. The samples were then very rapidly filtered through lightly-packed glass wool. The time occupied in filtration was never more than 30 seconds for the 5 and I O minute samples, or more than I minute for the later samples. The refractive index of the filtrate from each sample was then determined. Denoting the refractive index of the filtrate from any given sample by rz and that of the pure solvent by n - .n,

n,, the quotient ___ is the number of grams of casein 0.00152

dissolved in IOO cc of the solvent at the moment when the sample was extracted. The type of relation which was found to subsist between the time which elapsed after the introduction of the casein and the number of grams of casein dissolved in IOO cc of solvent is shown diagrammatically in Fig. I , in which the abscissae represent minutes and the ordinates the number of grams of casein dissolved in IOO cc of solvent. It will be observed that the rate of solution is at first very great, but that it very rapidly falls off. It does not fall to zero, however, that is, the curve does not appear to approach an asymptote but is rather of a parabolic form. Nor does this appear strange when we observe that although, after two hours' Using a Pulfrich refractometer which read the angle of total reflection accurately t o within I', and a sodium flame as the source of light. T. Brailsford Robertson: Jour. Phys. Chem., 13, 469 (1909).

Raie of Solution

Case& 379 li 14JG stir,ring, the rate of so1ution:of the caseinlisrvery small, yet the sohrent is still very far from being “saturated” with casein. The alkali-equivalent of I gram of casein, measured by neutralization of the excess of alkali by means of a strong acid,’ is about 11 X IO-‘ equivalent gram molecules hut the proportion of the casein actually dissolved to the amount of base present in the solvent was always, in these experiments, ever after two hours of stirring, very much less than this.’ of

k.~ bj

Fig.

I

The relation between the time of stirring and the quantity of casein dissolved does not appear t o obey any of the ordinary chemical reaction-or solution-velocity formulae. Noyes and Whitney3have shown that the rate of solution of a crystalloid is a t each moment proportional to the difference between the concentration at the moment and that required for saturation. This leads, for a constant rate of stirring and assuming that the surface’of the crystalloid exposed to the action of the solvent is approximately constant during the progress of the experiment, to the equation log

CL = Izt,

a-x

where a is the

concentration at saturation, x is the concentration of the dissolved crystalloid at time t and K is a constant. We can T.Brailsford Robertson: LOC.cit. It might be imagined that the solutions of the caseinates which are prepared by neutralizing the excess of base by a strong acid are “supersaturated” with respect to casein. I have, however, prepared a solution in this way containing 3 percent of casein in 0.0043 N KOH ( I g. of casein to 14 x IO-’ equivalent gram molecules of KOH) which has now been standing a t room temperature with toluol in a sealed glass vessel for over four months. I t is still perfectly stable and contains only a trace of precipitate, probably of paranuclein, derived from the casein by autohydrolysis. Noyes and Whitney: Zek’phys. Chem., 23, 689 (1897).

380


compute a in the above equation, for casein, from the known alkali-equivalent of casein ( I g. = I I x IO-^ equivalent gram moleeules of base) and from the known amount of alkali present in the solution employed as solvent. But a few trials suffice to demonstrate that the relation between time and amount dissolved, for casein, does not even approximately obey this formula. The rate a t which the velocity of solution falls off; the negative acceleration of the process; is far too great to permit of representation by this formula. Nor is any better agreement obtained if we insert, for the value of a, the actual number of grams of casein present in the mixture, or if, allowing for the diminution in the surface of the casein exposed to the action of the solvent, as solution proceeds, we endeavor to apply

dX

the relation

=

K(A - x)(B - x)'

where A is the number of grams of casein which the- amount of alkali present in the solvent is capable of holding in solution, B is the number of grams of casein actually present in the mixture, x is the amount of casein dissolved at any given moment, and K is a constant. The relation between the time of stirring and the amount of casein dissolved, however, does obey, very accurately, the relation x = Kt", where x is the amount dissolved after time t and K and m are constants which vary with the nature and concentration of the alkali-solution employed as solvent and with the total mass of casein present in the mixture. In the following tables are given the results of these experiments. The quantity of solvent employed was always roo cc and the number of grams of casein initially added to it was always 5 . For a reason which will shortly appear, no especial effort was made to maintain a constant temperature during the progress of an experiment, but a t the head of each table are given the temperatures of the mixture at the beginning and a t the end of the experiment. The temperature a t the beginning of the experiment is always placed first. In I n its integrated form, log

B(A-x) A(B --x) ~

=

Kt.

Rate of SolzLtion of Casein

381

the column headed “calculated” are .given the values of x calculated from the above formula, the constants K and m being determined from all of the observations by the method of least squares, employing for this purpose the form log,, x = m log,, t log,, K. The possible experimental error in the determination of the concentration of a casein solution by means of its refractive index is always fo.07 gram per IOO cc. It will be seen that the differences ( = A ) between the observed and calculated values of x are hardly ever greater, usually considerably less, than the possible error in the determination of the concentration of the casein in the filtrates. TABLEI Solvent: 0 . 0 0 2 18 N KOH. Temperature 24’-2 I O

+

Grams casein dissolved in roo cc solvent

Time in minutes

1

Found

0.45 0.51

5 IO

I

I

I

z:;:

30 60

0.71

I20

Calculated

0.46 0.51 0.61 0.68 0.75

+O.OI 0.00

-0.03

-0.03 +0.04

EA I TABLEI1 Solvent: 0.00435 N KOH. Temperature 25 I

K

=

0.578

- ~ _ _ _ _ - - _

-

Time in niin u tes

Found

-_ _-_

IOO

Calcdlated

0.78 0.89

30 60

0.76 0.89 I . 15 I .28

I20

1.35

I

5 IO

cc

I

1

---o.oI

m = 0.187

Grams casein dissolved in solvent ___

=

___

!

A

I

fo.02 0.00

-0.05

I . IO I . 25

-0.03

.42

f0.07

XA

= +O.OI


Grams casein dissolved in Time i n niinutes

-

5 30 60 I20

cc

solvent ___~___ Found

IO

io0

1.71 1.91 2.37 2.63 2.89

I I

iI

,

'

1

Calculated

1

1

1.72

I

A

So.01

,

i

$0.02

-0.05 2.61 2.94

-0.02 $0.05

i

I

I

EA

= $0.01

TABLEV Solvent: o.oo870N KOH. Temperature 18O-20~ .m = 0.146 K = 1.48 Time i n minutes

Grams casein dissolved in solvent

5

cc

__-___

I _

Found

IO

IOO

I .84 2.11

30 60

2.43

120

2.96

2.70

I

1

Calculated

,

,

A

Rate of Solution of Casein

383

TABLEVI Solvent: 0.01088 N KOH. Temperature m = 0.168 K = 1.64

-_ _ _ _ _

1

Tittie in minutes

Grams casein dissolved in roo cc solvent

i

1

Calculated

1

Calculated

1

I

Found

1 I

Found

2 I '-24'

-____

A

-

T.Brdilsford Robertson

384

TABLEIX Solvent: 0.01740 N KOH. Temperature K = 2.60 _ _ _ _ _I ~ ~ ~ _ _ Time in minutes

-,,

m = 0.153 -______________ ~

I

Grams casein dissolved in solvent Found

22 O

ICO

cc

1

,

A

I

1I

1

Calculated

I

I

+0.03 30 60

I

4.48 4.81 (5

$0.01 -0. I O

4.38 4.87

$0.06

-

EA

=

0.00

TABLEX Solvent: o.oo870N ",OH. Temperature K = 1.50 m = 0.141 Timein minutes

I ~

I____

__________-

Gram casein dissolved in solvent

___-____

__._.

Found

5 IO

30 60 I20

j ~

I

I

I

1

IOO cc

Calculated

2oo-z2

'

i I

A

I

I

1.84

1.88

i

2.11

2.07

I

+O. 04 -0.04

2.43

2.42 2.67 2.94

!

-0.01

, i

-0.03

2.70

2.89

'

+0.05

EA

= +O.OI

That is to say, at some undetermined time previous to this all of the casein present had been dissolved. Only the first four observations were used in computing the constants.


minutes

' Found

5

I

IO

30 60 I20

1

1.71 1.97 2.30 2.63 2.89

Calculated

1.73 1.94 2.32 2.60 2.91

385

I

I

I

+0.02

I 1 1

-0.03

1

$0.02

ii

$0.02

-0.03

ZA

=

0.00

L

T. Brailsford Roberison

386

I

Tiuie in

5 IO

30 60 I20

I1

I

'

1

Grams casein dissolved in loo cc solvent

2.77 3 . IO 3.63 3.95 4.35

A

+0.02

I

2.79 3.08 3.60 3.96 4.37

1

-0.02

-0.03

,

+O.OI $0.02

TABLEXVI Solvent: 0.01740 N Ba(OH),. Temperature zoo

Time in miuutes

i I

Grams casein dissolved i t 1 I C O cc solvent _ _ -~ - --FOUII~ Calculated

__

I

5 IO

30 60 I20

I .85 2.05

2.64 3.03 3.36

1

____-

1.84

-0.01

2 ,I O

+ O . 05 -0.04

2.60 2.98 3.40

-0.05 +O.

ZA

04

= -0.01


387

It is evident that equally concentrated solutions of KOH, NaOH, LiOH ana “,OH dissolve casein with about equal rapidity, while solutions of the hydroxides of the alkaline earths dissolve casein much more slowly, Sr (OH), dissolving the casein most rapidly, Ca(OH), more slowly and Ba(OH), more slowly still. This fact is perhaps of significance when viewed in the light of the facts that solutions of the caseinates of the alkaline earths become opalescent on heating, while those of the caseinates of the alkalies and ammonium do not,l that the caseinates of the alkaline earths will not pass through the pores of a clay filter, while those of the alkalies and ammonium readily do so,’ and that in these and in other ways the caseinates of the alkaline earths give evidence of being present, in their solutions, in the form of more bulky molecules than those of the caseinates of the alkalies and of ammonium under equivalent conditions. The amount of casein which is dissolved, in a given period of time, by a solution of KOH is, within the limits of accuracy of the determinations, directly Proportional to the concentration of the KOH-solution. This is very clearly shown in Table XVII, in which r denotes the ratio of the number of grams of casein dissolved to the number of equivalent gram molecules (multiplied by 100)of KOH present in the IOO cc of solvent employed. It will be observed that this ratio, for any of the given times, is very nearly ~ o n s t a n t . ~ A comparison of Tables IV and V at once shows that the temperature-coefficient of the velocity of solution is very small. The differences between the amounts of casein dissolved, after a given time, a t 18’--20’ and at 26’ are only double the possible error of the determination for the 5 - and IOminute periods and only equal to the possible error for the remaining periods. So far as the accuracy of the method employed enables us to decide, therefore, the temperature-

’ W.

A. Osborne: Jour. Physiol., 27, 398 (1901). W. A. Osborne: LOC.cit. A t “saturation” of the alkali with casein the numerical value of this ratio would be 9 1 . a


z

‘

0

1

2

1

Rate of SolzLtion of Casein

389

coefficient of the rate of solution, between the temperatures mentioned, is practically zer0.l This agrees with the results of my previous investigations, namely, that for temperatures lying between 20' and 36' the rate of solution of casein in solutions of the hydroxides of the alkalies is unaffected by temperature, while a t higher temperatures the rate of solution in solutions of the hydroxides of the alkalies is increased and the rate of solution in solutions of the hydroxides of the alkaline earths is diminished. This fact would, in itself, lead us to suspect that the process which determines the rate of solution of casein in solutions of hydroxides of the alkalies and alkaline earths is not chemical in nature. That the rate of solution of the casein is not determined by the velocity of a chemical reaction occurring exclusively in the liquid phase is also shown by the fact that the rate of solution of the casein is dependent upon the mass of casein initially introduced into the mixture. Were the rate of solution of the casein dependent solely upon the velocity of a reaction between casein and the alkali, taking place in the liquid phase, then since, in the presence of undissolved casein, the liquid would always be saturated with casein, the rate of solution should be independent of the mass of undissolved casein. We are led t o conclude, therefore, that the processes which determine the velocity of solution occur, in part at all events, either within or at the surfaces of the suspended particles of undissolved casein. The relation between the amount of casein dissolved in a given time and the mass of casein initially added t o the solvent is shown in Table XVIII and graphically in Fig. 2. The temperature of the mixtures was, in all of these experiIt will be seen that the rate of solution inments, 20'. creases, at first somewhat rapidly with the mass of casein added to the solvent, later more slowly. -

It was for this reason, of course, that no special effort was made t o maintain a constant temperature during the progress of the experiments T. Brailsford Robertson Jour Biol. Chem , 5 , 147 (1908).

T . Brailsford Robertson

390 __________ ____

Grams casein added to zoo cc of solvent (0.010 N KOH)

‘

________________ ____ ____~_ 2.5

11

I

I

5 .o

1‘

12.5

1

15.0

_ _ _ _ _ _ _ _ _ _ _ _ _ ~ ~

-

Grams Grams GC :#S: G I s Grams Grams dissolved dissolved dissolved dissolved dissolved dissolved

Time in minutes

2.24 2.36

5 IO

B‘

2.76 3.28

I

3.28 3.82

3.68 4.22

1

3.68 4.22

3.82 4.60

Grams casein in mixture

Fig. 2

The relation x = Kt” is, it is of interest to observe, the same as that found by Cameron and Bell2 and later confirmed by Ostwald from the investigations of Goppelsroeder, s to subsist between the amount of fluid absorbed by a column of sand or of a strip of filter-paper and the time during which the fluid has remained in contact with a portion of its surface.* The values of the constants are also of the same order of magnitude as those found in these investigations. It is possible, therefore, that the rate of soltition of the casein is primarily That is to say, a t some undetermined time previous to this all of the casein introduced.into the solvent had been dissolved. Cameron and Bell: Bulletin No. 30, p. 50, Bureau of Soils, U. S. Dept. of Agriculture, 1905; Jour. Phys. Chem., IO, 658 (1906). a Wo. Ostwald: z Supplementheft zur Zeit. Kolloidchemie, 1908,20, der F. Goppelsroeder. “Neue Kapillar- und kapillaranalytische Untersuchungen” Verhandl. Naturforsch. Gesellsch. zu Basel, Bd. XIX, Heft 2, 1907. 4 According to Cameron and Bell, Jour. Phys. Chern., IO, 658 (1906), this formula can be derived from the formula of Poiseuille for the flow of liquids through capillary spaces.


'

391

determined by the rate at which the particles are penetrated and wetted by the solvent, the processes of chemical reaction between the alkali and the casein and of diffusion of this compound into the liquid phase taking place at relatively great velocities. It is, perhaps, not surprising that the factor which determines the rate of solution of casein should be the velocity with which it is wetted by the solvent, while that which determines the rate of solution of a crystalloid is the velocity with which the dissolved substance diffuses through a thin layer of saturated solution in immediate contact with the surfaces of the crystals. A crystal is only wetted upon its external surface, and the wetting, naturally, takes place instantly. A particle of casein (or, in general, of the solid or semi-solid phase of any colloid) is, however, comparable in structure with a sponge; the surface which may be wetted by the solvent is, per unit volume very much larger than that of a crystal and the solvent must, in wetting this surface, transverse a relatively immense network of minute capillary pores. Under such conditions the time occupied in wetting the surfaces of the particles may m7ell be great compared with the time required for the dissolved substance to diffuse from these surfaces into the solvent, or with the time required for the accomplishment of the union between the protein and the alkali in the solvent. Conclusions I . If casein be stirred at an approximately constant rate in solutions of the hydroxides of the alkalies or of the alkaline earths, the amount dissolved is connected with the time which has elapsed since the casein was introduced into the solvent by the equation x = Kt"', where x is the number of grams of casein dissolved, t is the time, and K and m are constants which depend upon the concentration and kind of hydroxide-solution employed as solvent, and upon the total mass of casein in the mixture. 2. The rapidity of solution is, within the limits of the accuracy of the determinations, unaffected by temperature,

392


for temperatures ranging between room-temperature and 300. 3. Equally concentrated solutions oi the hydroxides of potassium, sodium, lithium and ammonium dissolve casein a t approximately the same rate. Solutions of the hydroxides of the alkaline earths dissolve casein much more slowly, Sr(OH), dissolving it most rapidly, Ca(OH), more slowly, and Ba(OH), more slowly still. 4. The amount of casein dissolved by a solution of KOH in a given period of time is directly proportional to the concentration of the KOH. 5 . The rapidity with which casein is dissolved by a given solution of a hydroxide of an alkali increases with the mass of casein present in the mixture. At first the increase in the velocity of solution with increasing mass of casein is rather large, but as the mass of casein is still further increased, the increase in the rapidity of solution is less. 6 . Having regard to the smallness of the temperaturecoefficient of this phenomenon, to the dependence of the rate of solution upon the total mass of casein present, and to the identity of the form of the equation x = Kt" with that which expresses the relation between the amount of a liquid absorbed by a column of sand or a strip of filter paper and the time, it is suggested that the factor which determines the rate of solution of casein in solutions of the hydroxides of the alkalies and of the alkaline earths may possibly be the velocity with which the casein particles are penetrated and wetted by the solvent.

On the Rate of Solution of Casein in Solutions of the Hydroxides of the

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