in which C equals the weight of levulose in 100 g of water and t is the centigrade temperature. Such calculated points must be considered as approximations. The solubilities are given in table 138.

In order to encourage and facilitate studies on the crystallization of levulose, an extended table of concentration and supersaturation (table 139, p. 682) has been computed. These data are admittedly based on insufficient experimental work and must be considered purely tentative.

4. SOLUBILITY OF LACTOSE IN WATER

Lactose occurs in alpha and beta forms, the alpha form crystallizing with 1 molecule of water, and the beta in the anhydrous state. The transition temperature between the two forms is 92° to 93° C; below this temperature the alpha hydrate separates from a supersaturated solution, whereas the anhydrous beta form crystallizes at temperatures above.

Table 140, p. 690, published by Gillis [5], contains the experimental results of Hudson [6], Saillard [7], and Gillis [8]. The first two authors approached the saturation point from both supersaturated and undersaturated solutions. Hudson determined the amount of lactose present by evaporating the solution and drying the crystalline residue at 130° C. to constant weight. Saillard employed polariscopic and copper-reduction methods of analysis, which he standardized by drying the lactose on sand at 105° to 106° C. Gillis approached the saturation point by increasing the temperature of a solution in the presence of a solid phase until the disappearance of all crystals.

Hockett and Hudson [9] have found that when the alpha lactose hydrate is shaken for 10 minutes at room temperature with 10 times its weight of methyl alcohol containing from 2 to 5 percent of anhydrous hydrogen chloride, a crystalline phase separates. This is a molecular compound having the composition 5 a-lactose-3 ß-lactose.

5. SOLUBILITY OF SUGARS IN SUGAR MIXTURES

(a) THREE-COMPONENT SYSTEMS

The system: dextrose, lerulose, and water.-When a sugar is dissolved in an aqueous solution of another sugar, its solubility in the water of such a solution is in general diminished as a result of the salting-out effect of the second sugar. Thus Jackson and Silsbee [10], in a study of the solubility of dextrose in levulose solutions, found that while 100 parts of pure water dissolved 120.5 parts of dextrose (anhydrous) at 30° C, 100 parts of water containing 106.2 parts of levulose dissolved but 114.8 parts of dextrose. Compared with other systems described below, this is but a slight diminution of solubility. The solid phase in these equilibria is crystalline dextrose containing 1 molecule of water of crystallization.

Systematic data obtained by Jackson and Silsbee are given in table 142, p. 691, and plotted in figure 86. In this figure the point E represents the solubility of pure dextrose in water at 30° C, that is, 54.64 percent, the solid phase being a-dextrose hydrate. Curve EG shows the solubility of dextrose in the presence of increasing concentrations of levulose, while the straight line, EI, represents constant relations between dextrose and water. The departure of solubility. curve EG from EI is seen to be slight.

The line KL bisects the diagram, and is therefore the locus of all solutions in which the ratio of dextrose to levulose is unity. In other words, it is the locus of all invert-sugar solutions. At the intersection F of the line KL with the dextrose solubility curve EG we have the point which represents the composition of a solution which is saturated with dextrose and which contains 34.85 percent of dextrose and 34.85 percent of levulose. In other words, this point represents the "solu

EG is the saturation curve of dextrose in the presence of levulose determined experimentally. The dotted curves extending from the KJ coordinate are similar curves computed. The line KL is the locus of all invert sugar solutions. The intersections of the dextrose saturation curves with KL represent the compositions of invert sugar solutions saturated at the respective temperatures with dextrose. M, alfalfa honey; N, sage honey; 0, tupelo honey: P, Cuban honey. X's on the water-levulose line show the solubilities of levulose at 20°, 40°, and 55° C, respectively.

bility" of invert sugar, if "solubility" is understood to have the significance that a solution containing 69.7 percent of invert sugar is saturated at 30° C with respect to dextrose.

Since the salting-out effect of levulose is small, it is possible to compute without serious error the solubility of invert sugar at other temperatures by assuming a similar departure of the solubility curve from the straight line joining the point I with the solubility of dextrose in water at the respective temperatures. These computed solubilities are given in table 141, p. 691, and plotted as dotted lines in figure 86.

The data presented here represent the system after attainment of equilibrium. Equilibrium is approached very slowly even in the presence of abundant quantities of the solid phase. If the solid phase is not present, the solutions may remain supersaturated for long

periods. Honey is essentially a mixture of dextrose and levulose, with the latter usually in excess. Jackson and Silsbee [10] have calculated from the analyses of Browne [11] and Bryan [12] that all the honeys for which analyses were available were supersaturated with respect to dextrose. In those calculations, the small content of nonsugars was disregarded and the small quantity of sucrose was added arithmetically to the levulose, since the effects of these two sugars on the solubility of dextrose were approximately the same. Proceeding in this manner, they found that 92 American honeys analyzed by Browne had an average supersaturation coefficient of 2.42 at 23° Č

MN, AC, and 00 are saturation curves of sucrose in the presence of invert sugar. HP is the composition of invert sugar saturated with dextrose in the presence of sucrose. Pis the composition of a mixture of sucrose and invert sugar saturated with sucrose and dextrose at 30° C. RS represents the variation of P with temperature. Solid lines are experimental; dotted lines are computed.

with respect to dextrose and a ratio of levulose to dextrose of 1.19. The 72 imported honeys analyzed by Bryan had an average supersaturation of 1.90 and a ratio of 1.20. The points M, N, O, and P in figure 86 represent the composition of certain characteristic honeys. Points M, N, and O, by coincidence, lie on the line QR, Q being the composition of crystalline dextrose hydrate. If in any of these honeys dextrose starts to crystallize, say, for example, at 23.15° C, the solution becomes more and more impoverished with respect to this constituent, and its composition moves to the right on the line QR until it becomes

just saturated at R with respect to dextrose. For honey M, the relative quantities of the resulting phases are proportional to the lengths of the segments JM (solution) and MR (crystals). All honeys are probably supersaturated with dextrose, and the fact that they can be kept in fluid form for considerable periods of time is due to the sluggishness with which the sugars crystallize.

(b) SOLUBILITY OF SUCROSE IN INVERT-SUGAR SOLUTION

Van der Linden [13] first showed that the solubility of sucrose in the water of an invert-sugar solution was less than in pure water.

PARTS INVERT SUGAR IN 100 PARTS WATER

FIGURE 88.-The system sucrose, invert sugar, and water.

The solubilities of sucrose at 23.15°, 30.0°, and 50.0° C in the presence of varying amounts of invert sugar The solubilities are calculated to a constant water content. The lines AJ, MJ, and OJ are the loci of all solutions having a constant ratio of sucrose to water.

Jackson and Silsbee [10] measured these solubilities with precision at 23.15°, 30.0°, and 50.0° C. Their measurements are shown in table 143, p. 692, and plotted in curves OI, AC, and MN in figures 87 and 88. The salting-out effect is shown best in figure 88 in which, if no such effect occurred, the solubilities calculated to 100 parts of water would have followed the horizontal dotted lines.

As the concentration of invert sugar is increased, the saturation point of dextrose is ultimately reached, and at complete equilibrium

dextrose would crystallize from this system upon further increase of concentration of invert sugar. At this point the solution is saturated with both sucrose and the dextrose constituent of the invert sugar and is thus the concentration of maximum solubility which a mixture of sucrose and invert sugar can have. At 30° C this is plotted as point P in figure 87. The sirup of maximum solubility contains 33.57 percent of sucrose and 45.44 percent of invert sugar.

As shown in table 141, p. 691, the solubility of invert sugar varies considerably with temperature, and therefore the composition of the sirup of maximum solubility varies with temperature. This change in composition can be computed with fair approximation, and is plotted on the curve RS in figure 87, and is also given numerically in table 144, p. 692.

6. REFERENCES

[1] A. Herzfeld, Z. Ver. deut. Zucker-Ind. 42, 232 (1892).

[2] P. M. Siline, Bul. assn. chim, sucr. dist. 52, 265 (1935).

[3] R. F. Jackson and C. G. Silsbee, BS Sci. Pap. 17, 715 (1922) S437.

[4] R. F. Jackson, C. G. Silsbee, and M. J. Proffitt, BS Sci. Pap. 20, 613 (1926) S519.

[5] J. Gillis, Rec. trav. chim. 39, 677 (1920).

[6] C. S. Hudson, J. Am. Chem. Soc. 30, 1767 (1908).

[7] E. Saillard, Chimie & industrie 2, 1035 (1919).

[8] J. Gillis, Rec. trav. chim. 39, 88 (1920).

[9] R. C. Hockett and C. S. Hudson, J. Am. Chem. Soc. 53, 4454 (1931). [10] R. F. Jackson and C. G. Silsbee, Tech. Pap. BS 18, 277 (1924) T259. [11] C. A. Browne, Bur. Chem. Bul. No. 110 (1908).

[12] A. H. Bryan, Bur. Chem. Bul. No. 154 (1912).

[13] T. van der Linden, Arch. Suikerind. 27, 591 (1919).

XXIII. BOILING POINTS OF SUCROSE SOLUTIONS

1. GENERAL

When, for the purpose of controlling boiling operations, the concentration of a solute in a boiling liquid is to be determined, it is more conveniently found from the relationship existing between the boilingpoint elevation and concentration of dissolved substances than by direct determination. Heretofore, Claassen's [1] boiling-point elevation table for aqueous solutions of sucrose has been used in this manner throughout the sugar industry and in laboratories. His table has been subjected to some criticism [2], however, owing to the fact that his values, determined at a pressure of 760 mm Hg, do not take into account the effect of variations in pressure on the boiling-point elevation. As a result of this criticism, and at Claassen's own suggestion, Spengler, St. Böttger, and Werner [3] determined the boiling-point elevation of pure and impure sugar solutions at various concentrations under numerous conditions of pressure. From these observations they plotted curves and from the curves selected values of boilingpoint elevations corresponding to even values of Brix for each pressure and purity condition, from which they erected a table covering pressures ranging from 4 to 2 standard atmospheres and concentrations ranging from 15 to 90 percent of solids.

It was thought that for the purpose of constructing table 145, p. 694, it would be well to correlate Spengler's observed data by means of empirical equations rather than to use the graphic method.

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