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

FIGURE 87.-The system sucrose, invert sugar, and water. MN, AC, and 09 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

All

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). 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) $519.

[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.

903232 O-50-25

By means of such equations, it is not only easy to calculate a table which is interpolated readily but also to obtain other special values not given in the table. Furthermore, values from the equation may be compared with observed data.

It is interesting to note that in most cases values calculated from these equations agree with Spengler's observed data better than they do with his graphic data; therefore, the use of such equations throughout the range of observed concentrations is justified. These equations are as follows:

100 purity

log10 At=2.6157X10-6X3-4.0185X10-X2+4.2567X10-2X-1.1979,

90 purity

log10 At=3.1013×10-X3-5.1209×10-X2+4.9574 × 10-2X-1.2622,

80 purity

log10 At=2.9431X10-X3-4.8211X10-4X+4.7512 × 10-2X-1.1533, 70 purity

logio At=3.3138X10-6X3-5.5257X10-X2+5.1177/10-2X-1.1305,

where At is the boiling-point elevation of the solution above that of pure water at a pressure of 1 standard atmosphere, and X is the concentration in percentage of solids.

Knowing the boiling-point elevation at 1 atmosphere (At780), the boiling-point elevation at another pressure (At,) may be calculated by means of the following equation:

At2 = At700 (T
(惡

760

L760

(110)

This is the same as eq. 127, the derivation of which is given on the following pages.

2. DEFINITION OF BOILING POINT

The boiling point of a liquid may be defined as the temperature at which its vapor pressure is equal to the pressure of the surrounding atmosphere [4]. If the liquid is considered as a solution of two substances, A the solvent and B the solute, then the total vapor pressure is equal to the sum of the partial vapor pressures resulting from A and B. If, however, the solute B is as nearly nonvolatile as sugar, the total vapor pressure is that arising from the solvent only and depends on the number of solvent molecules present in the vapor phase per unit volume.

3. RELATIONSHIP BETWEEN VAPOR PRESSURE AND
CONCENTRATION OF SOLUTE IN A LIQUID

According to the law of Raoult, a definite relationship exists between the number of molecules present in the vapor phase and the number of the same molecular species present in the liquid phase. The vapor pressure of a liquid, p, is proportional to o, the mole fraction of the liquid which exists in the form of the same molecular species as the vapor, or

p=kro.

(111)

If we consider the pure solvent by itself, in which case the same molecular species exists in both the liquid and vapor phases, then the mole fraction, zo, becomes unity, and we have the proportionality factor, k, equal to the vapor pressure, Po, or

Substracting both sides of eq 113 from Po, we have

(112)

(113)

(114)

(115)

However, by definition, zo is the mole fraction of solvent present

in the liquid, or

in which is the mole fraction of solute present in the solution, N refers to the number of moles of solute present which have the molecular weight of the solute, and No is the number of moles of solvent present which have the molecular weight of the solvent in the vapor state.

4. RELATIONSHIP BETWEEN VAPOR-PRESSURE LOWERING AND BOILING-POINT ELEVATION

From the definition of the boiling point, it is readily seen that, should the vapor pressure of the boiling solvent be lowered by the addition of a solute it will cease boiling until equilibrium is again established and the vapor pressure is raised to the same value it had before the solute was added. An increase in vapor pressure will be accompanied by a proportionate increase in the temperature or

in which T-To is the elevation of the boiling point of the liquid which takes place in reestablishing equilibrium between the vapor pressure of the liquid and the surrounding atmosphere, and dpo/dto is the rate of change of vapor pressure of the solvent with change in temperature.