SOLUBILITY RELATIOXSHIPS OF LACTOSE-SUCROSE SOLUTIONS I. Lactose-Sucrose Solubilities a t Low Temperatures BY PHILIP N . PETER*
A study of the solubility relationships of the several forms of lactose in pure solution and of the principles governing the separation of this sugar from such a solution has been made by Hudson.* In the presence of certain dissolved substances, however, i.e. sucrose, ammonia, etc., the rate of separation of the solid phase and other physical relationships of these solutions are materially altered. These phenomena are of significance in a consideration of the problem of lactose separation from heterogeneous mixtures, such as ice cream and condensed milk, wherein supersaturated states may exist. I n order to determine the extent of the deviation from the principles which hold for pure solutions a study of certain physical relationships of lactose solutions in the presence of sucrose and of other dissolved substances has been initiated. This first investigation deals with the determination of the solubility relationships of lactose-sucrose solutions a t low temperatures. During the past few years several papers which have a bearing on lactosesucrose solubilities in aqueous solution have been published. Jackson and Silsbee* present results and discuss the saturation relations in mixtures of sucrose, dextrose and levulose. Jenkins3 has determined the effect of various factors upon the velocity of crystallization of substances from solution, lactose being one of the substances used. Palmer and Dahle4 and Lucas and Spitzer5 have investigated lactose crystallization in sandy ice cream. Dahle6 further discusses the sandy ice cream problem and presents results showing the influence of glucose, gelatin and other substances upon the crystallization of lactose. Browne? states that sodium chloride, potassium acetate, and many other salts increase the solubility of sucrose and that “the presence of free alkali, and of different salts of the alkalies, increases the solubility of lactose in much the same manner as with sucrose.” It is questionable, however, whether these salts are present in sufficient quantity in lactose products to affect materially the solubility of this sugar. Leighton and Pete$ have done work upon the factors which influence the crystallization of lactose. Hunziker and Nisseng have investigated a t 50’ F and 65’ F the effect of sucrose and milk colloids upon the solubility of lactose. Before discussing the procedure and results embodied in this paper, which treats of the solubility determinations a t 0°C and -3’C, it is perhaps advisable to consider the properties of sucrose and of lactose which have a bearing on their solubility relationships. The very high viscosity of concentrated sucrose solutions a t low temperatures1° is evident from Table I. *Research Laboratories, Bureau of Dairy Industry, U. S. Department of Agriculture.
SOLUBILITY RELATIONSHIPS O F LACTOSE-SUCROSE
I857
TABLE I Viscosity of sucrose in aqueous solution Viscosity in centipoiaes
Temperature
"C
Per cent sucrose by weight 0
20
I5
1.7921 1.5188 1.3077 I . I404
20
I . 0050
3.804 3 . I54 2.652 2.267 I . 960
0
5 IO
40
14.77 11.56 9.794 7.468 6.200
60
238. 156. 109.8 74.6 56.5
This high viscosity does not in itself affect materially the final solubility value of lactose in sucrose solutions but it does cause considerable experimental difficulty and, in a study of solutions a t temperatures below their freezing points, it may so delay the normal equilibrium of the several phases that the correct value is obtained with difficulty. The influence of viscosity upon sucrose-lactose solubilities will be discussed more in detail in another section of this paper. Lactose, likewise, evidences certain properties which prolong tho time that is usually necessary for the determination of the solubility of a substance. The slow rate a t which equilibrium is attained1 is consequent to the existence in ordinary solution of two forms of lactose, namely, lactose hydrate and the P-anhydride. It is questionable whether a third form, a-anhydride, made by heating the hydrate crystals to I Z O O C , can exist in solution. The normal form of lactose, which has been prepared by crystallization from water a t ordinary temperatures, is lactose hydrate. In the presence of water this sugar dissolves to a definite value called the initial solubility,' and then is slowly converted into its equilibrium form, the P-anhydride. As this change proceeds more of the sugar (hydrate) dissolves until solution has reached completion. This value is spoken of as the final solubility. If the /%anhydride, formed by crystallizing lactose above the transition temperature, 93OC, be dissolved, the reverse change P-anhydride +lactose hydrate takes place. Thus solutions made from either form of lactose will exhibit the phenomenon of mutarotation and finally attain a constant value. This change may be measured in the polariscope. The rate a t which this equilibrium is attained is slow a t o°C, and increases with temperature; it is greatly accelerated by both hydrogen and hydroxyl ions, and the ratio of the rate of the reaction in 0.001 normal ammonium hydroxide solution to that in purewater is 2.4:1. At 75OC theequilibrium change is practically instantaneous and a t temperatures below 93'C when equilibrium has been attained the ratio of lactose hydrate to P-anhydride is approximately I :1.5. By some investigators, however, it is assumed that the complete reaction equation, which is quite similar to the equilibrium equation which has been formulated for glucose, is:
PHILIP N. PETER
1858
+
CizHnOn HzO a-anhydride
s CizH240n s Hz0 + CizHzzOii (hydrate)
P-anhydride
Observations of this mutarotation reaction of lactose show that the laws of dynamics that hold for a simple unimolecular change are followed; hence the first part of the complete reaction which is thought to occur on dissolving lactose hydrate, namely, a - a n h y d r i d e s h y d r a t e , must take place instantaneously. Likewise the equilibrium between these two forms must be preserved. That concentration, as well as temperature, has almost no influence on this equilibrium in solution is shown by the fact that there is no slow change in the rotatory power of milk sugar after dilution. In addition to the investigations previously mentioned Urechll and Trey1* have done work upon the influence of various substances on the rate of change of rotation of milk sugar. The latter in particular presents extensive data, covering a wide range of substances, on this mutarotation. Such observations are of special interest in relation to the rate of solution or of crystallization of lactose. Thus sodium hydroxide (o.oogN) and ammonia (o.osN) produce practically instantaneous equilibrium and in quite dilute solution these alkalies exert an accelerative influence on the rate of attainment of equilibrium. Hydrochloric acid in 0.4 normal solution establishes equilibrium quickly and in '0.04 normal solution accelerates the reaction. H-ions in equal concentration have less effect than OH-ions. Sucrose in a concentration of 1 7 grams per 100 cc. of solution exerts practically no effect. Very concentrated solutions a t low temperatures, which more nearly approximate the conditions found in partly frozen ice cream and in condensed milk, however, have a viscosity which is approximately one hundred times greater and possibly exert considerable influence on the rate of attainment of equilibrium and on the equilibrium ratio. In the measurement of lactose solubilities at oo C and lower, values obtained by Hudson show that it is necessary to agitate the solutions in contact with the solute for a considerable length of time, and for a much longer time than at higher temperatures, in order to insure saturation. Thus the velocity constants of solution obtained by Hudson and calculated by the formula
were found to be: oo, 0.0125; IS',
0.0664; 2 s 0 , 0.184.
Hudson obtained, both from supersaturation and undersaturation, values which were in reasonable agreement. The velocity constants determined by Trey were of a somewhat different order. His constanta were determined from the rate of change of the rotatory power of lactose solutions. It seems evident that the measurement of the constants by this change should give values in good agreement with
SOLUBILITY RELATIONSHIPS O F LACTOSE-SUCROSE
1859
those determined from the maximum rate of solution or rate of crystallization because the surface of the solid in rate of solution and rate of crystallization experiments is so large, the stirring so rapid (and the temperature being low) that the actual process of solution or crystallization takes place very much faster than the controlling equilibrium change which precedes it, as measured by polariscopic readings. Hence a measurement of the change in rate of rotation should by calculation give velocity constants of the same magnitude as by determination from measurements of the rate of solution or of crystallization. Trey, however, did not thus obtain values which can be said to be in reasonable agreement with those of Hudson. The constants of the former were calculated from the changing rotation values of lactose solutions according to the formula: log b - log (b-x) C =
t
Comparison of this expression with that used by Hudson will show that in reality they are equivalent formulae. The results of calculating the velocity constants of the two investigators to the same basis, giving the value of unity to the constant at o'C, are as follows: Rate of solution* OO..
IS'..
............
1.0
Hudson Rate of change of rotation 1.0
Trey Rate of change of rotation I .o
-. . . . . . . . . . . . . . . - . . . . . . . . . . . . . 8.57 . . . . . . . . . . . .I j.5 . . . . . . . . . . . . . . . 1 5 . 6 . . . . . . . . . . . . . I O .15 . . . . . . . . . . . . 5.3
5.85. . . . . . . . . . . . .
zoo. . . . . . . . . . . . . . 25'.
*or rate of crystallization.
It seems evident that the values of Hudson are the correct ones. Not only were his determinations by the two independent methods in satisfactory agreement, but the rotation velocity constants, whether determined from lactose hydrate or anhydride solutions, were shown to be of the same magnitude. Such a result is predicted by theory and was verified by Roux.13 The rotation values (velocity constants) of hydrate and anhydride solutions as determined by Trey were not in good agreement. Data have been obtained on the effect of sucrose and ammonium hydroxide on the magnitude of this velocity constant, the values being calculated from determinations made of the rate of crystallization of lactose from solutions containing these substances. This work will be presented in a later paper. In reviewing past work i t should be mentioned that the cryohydrate temperatures for the different forms of lactose as given by Hudson are of value in a study of lactose solubilities in partly frozen solutions. An excellent review of lactose and its properties is given by W'hittier.14
1860
PHILIP N. PETER
Experimental The 'solubility determinations were made by enclosing an excess of the solid sugar with the respective sugar solution in ground glass stoppered bottles of approximately 1 2 5 cc. capacity. By means of spring clips the bottles were fastened upon a motor-driven metal frame, which revolved in an elec-
F
FIQ.I Solubilities of lactose-sucrose solutions a t low temperatures. Curves A and C represent Solubilities a t 0°C Curves B and D represent solubilities at -3%
trically-operated temperature-controlled bath. This bath was a wateralcohol-glycerine mixture which had a freezing point of approximately - IO'C. The sugar solutions in which the solubility was to be measured ranged in concentration from 0.0% to approximate saturation and were, of course,
SOLUBILITY RELATIONSHIPS O F LACTOSE-SUCROSE
1861
cooled to the necessary temperature before being added to the solid phase. Analysis by a method later described gave the exact concentration of these solutions. A small quantity of vaseline was placed upon the ground glass stoppers in order to make the bottles water-tight. In all determinations a t o°C and below the solutions, in contact with an excess of the solid phase, were rotated for approximately 30 days. Duplicate samples were taken a t time intervals of 7 days. The viscosities a t low temperatures of some of the more concentrated sugar solutions were so high that equilibrium was but slowly attained. I n making the solubility measurements the bottles were removed from the metal frame and placed in a wire basket which was suspended in the bath. A short piece of rubber tubing was drawn over the end of a I cc. pipette and a small quantity of cotton was stuffed into it. Suction was applied a t the other end. The tip of the pipette was placed just below the surface of the liquid to be sampled and I cc. of the solution was withdrawn. The sample was placed in a tared weighing dish, the bottom of which was covered with a layer of asbestos. After being weighed, a small quantity of distilled water was added and the sample was evaporated to dryness a t I O ~ C . It was further dried to constant weight in a vacuum oven. From this weight calculated on a water basis (parts total solids to IOO parts of water) was subtracted, likewise on a water basis, the concentration of the original solution. Such a determination gives the solubility of a sugar in 100 parts of water, in the presence of a definite concentration of another sugar.
In determining the solubilities in partly frozen solution it was necessary to use other methods of analysis. In these instances the methods of the TABLE I1 Solubilities of lactose in water and in sucrose solutions Kind of solution
Temperature
Rater Sucrose in water I,
3,
11
I,
I1
t,
Water Sucrose in water lf
11
I1
JJ
>)
t,
Solubilities of Parts lactose to I O O parts water
0°C
11.94
O0C
10.85
ooc
9.96 8.45 6.03
0°C O0C -3 o c - 3OC -3oc -3oc -3OC
Lactose Percentage lactose
10.68 8.41 6.48
Solution used Parts sucrose Perto 100 parts centage sucrose water
18.26
Frozen
-
43. 89 82.62 171.84 -
9.1 7.55 6.2
5.97 3.98
43.2 82.4
2.70
122.8
5.5
2.14
151.2
4.42 2,Ij
14.15 28.54 43.24 61.80
28.37 43 ' 4 53 ' 63 58.9
1862
PHILIP N. PETEF
Association of Official Agricultural Chemists were employed. I n all cases i t was assumed that the form of lactose obtained on drying at 100' C was the anhydride. C. P. lactose and C. P. sucrose were used in this work.
TABLEI11 Solubilities of sucrose in water and in lactose solutions Kind of solution
Temperature
Water Lactose in water 11
11
11
11
1)
11
11
11
Water Lactose in water 11
11
11
11
71
,1
O0C ooc
ooc ooc ooc ooc -3 o c - 3OC
-3OC
-3 o c -3 o c
Solution used Parts lactose Perto xoo parts centage lactose water
-
-
2.40 4.88
1.72
7.32 9.43 1:0.82
2.40 4.2 6.1 8.2
.8j
2'57 3'29 3.76
-
.85 I.j o
2.18 2.89
Solubilities of Sucrose Parts sucrose Perto 100 parts centage water sucrose
181.69 180.23 178.8
64.5 63.8 63.0
177.75 177.48 176.36 179.0
62.4 61.9 61.45 64.2
178.5 175.0 174.0
63.j 62.7
175.5
61.9
62.1
Discussion The data shown in Tables I1 and I11 and the values plotted in Fig. I represent the solubility relationships of lactose-sucrose solutions a t o°C and -3OC. It will be seen that the solubility of lactose in nearly saturated sucrose solutions is reduced to approximately one-half of its value in water. Consequently it appears that in ice cream, and likewise in condensed milk, particularly if it be subjected to low temperatures, the water may be greatly supersaturated with respect to lactose. Doubtless in the freezing of ice cream and its subsequent storage in the hardening room, ab more and more water is converted into ice, a solution approximating saturation with respect to sucrose is obtained. Likewise the removal of water concentrates the lactose. These two factors tend to produce a solution which is highly supersaturated with lactose. Thether or not the lactose will separate is, however, dependent upon other influences. Unpublished results which have been obtained show that the crystallization of lactose from viscous sucrose solutions is very slow. Hence, although the solubility of lactose is considerably less a t the low temperatures of cold storage and the solution becomes supersaturated with respect to this sugar it will be seen that the very high viscosity a t these temperatures of concentrated sucrose solutions creates an influence which opposes and materially
SOLUBILITY RELATIONSHIPS O F LACTOSE-SUCROSE
1863
retards the separation of lactose. It may, therefore, require several weeks or even months for lactose to crystallize from solution. For this reason it was advisable that the solubility determinations described in this paper be made from undersaturation and not conducted in such a way that equilibrium was attained from supersaturation. Data by Jenkins3 serves to establish the above conclusion. He found that the determining factor which alters the velocity of crystallization is the viscosity of the solution. The relation is given by the expression Const. K = - n 0.59 where K is the velocity constant and n is the viscosity. It will also be seen that the presence of lactose has a slight effect on the solubility of sucrose. The two curves C and D which express this relationship cause the statements, with respect to the influence of viscosity upon the rate of crystallization of lactose, made in the preceding paragraphs, to appear more evident. Thus a solution which is approximately saturated with lactose can in turn become saturated with sucrose, and hence greatly supersaturate the solution with lactose, without the separation of the latter sugar during the interval of several weeks that the experiment is continued and the solution is agitated.
It thus appears that it is the viscosity of the solution and not the solubility of lactose which is the most important factor in controlling the separation of this sugar from concentrated sucrose solutions a t low temperatures. Since, however, the viscosity of saturated sucrose solutions falls sharply as the temperature increases above o°C, it seems very probable that with rising temperature the solubility of lactose will become the predominating influence upon lactose separation. The results in Table I11 have also been expressed as percentages in order that they may be plotted in a triangular diagram expressing the phase rule relationships of the lactose-sucrose-water system. Such a representation will be made in a later paper when the cryohydrate relationships of the solutions and a more extensive temperature range have been studied. Summary
The changes in the solubilities of lactose in sucrose solutions a t oo and -3'C are roughly inversely proportional to the concentrations of the sucrose and in approximatley saturated sucrose solutions this solubility is reduced to about one-half of the solubility value in water. Owing to the limited solubility of lactose in water a t oo and -3OC the solubility of sucrose a t these two temperatures is but little affected by the presence of lactose. The values bear an inverse relationship to the concentration of the lactose in solution.
1864
PHILIP N . PETER
Lactose in the presence of high concentrations of sucrose may be very supersaturated with respect to the solution and yet, because of the high viscosity, crystallize very slowly. The relationship of the above conclusions to the crystallization of lactose in several dairy products has been discussed.
References 1
C. S. Hudson: J. Am. Chem. SOC.,26, 1065 (1904);30, 960, 1767 (1908). R. F. Jackson and C. G. Silsbee: Technologic Papers of the Bureau of Standards, No.
259.
J. D. 3enkins: 3. Am. Chem. SOC.,47, 903 (1925). L. S. Palmer and C. D. Dahle. hlinnesota Agr. Expt. Sta., Ann. Rept. (1922) 6P. S. Lucas and G. Spitzer: Purdue University Agr. Expt. Sta. Bulletin No. 286, a
January (1925). C. D. Dahle: Ice Cream Trade Journal, 19, Xo. I O (1923). C. A. Browne: “Handbook of Sugar Analysis”, 709 (1912). a B. Leighton and P. S . Peter: Proc. \T70rld’s Dairy Congress,1, 477-495 (1923). 9 0. F. Hunziker and B. H. Sissen: J. Dairy Science, 9, No. 6, November (1926). 10 “Smithsonian Physical Tables”, I 56 (1923). 1’F. Urech: Ber., 15, 2130-2133 (1882). 1z H. Trey: Z. physik. Chem., 46, 620-719 (1903). W. Roux: Ann. Chim. Phys., (7), 30, 422-432 (1903). 1 4 E. 0. Whittier: Chemical Reviews, 2, No. I , April (I92j).
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