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in a bath at 70° C decomposition of invert sugar ensues as a result of too drastic conditions. Jackson and McDonald [15] have carried out the inversion in a 70° bath but have shortened the final period of heating from the prescribed 5 minutes to 3, 2, and 1 minute, respectively. In these measurements the value -33.00 for 5 minutes rose to a maximum of -33.08 at the 2-minute period. With this value included, all of the values in table 11 except the first represent twice the rotation of the inverted half-normal solution, the destruction of invert sugar after the completion of the inversion being avoided. It is evident that the rotation is definitely a function of temperature and that invert sugar is attacked by acid during the course of the inversion. Conceivably furanoid fructose, which has a transitory existence, is attacked by the acid, and increasingly so as the temperature rises.

TABLE 11.-Variation of twice the rotation of the half-normal invert-sugar solution with varied conditions of inversion

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The data in table 11 illustrate the importance of specifying the time and temperature of inversion for the standard values of the divisor and of adhering closely to the specifications in carrying out the analysis. For practical purposes there are three temperatures which require consideration. Room temperature is quite suitable if the precautions stated above are observed. For more rapid work the inversion can be effected in a bath regulated at either 60° or 70° C. At 70° there is a destruction of about 1 percent of invert sugar, and the analysis is incorrect unless such destruction occurs. It is quite possible to reproduce the value, -33.00, with relatively pure sugars, but the question arises whether in crude substances, which are heavily charged with inorganic salts of weak acids, the acid retains its activity. If by buffer action the activity of the acid is diminished, it is possible that the 1 percent of invert sugar is not destroyed and an error in the analysis would result, since the basic value of the divisor to be used at 70° requires that such decomposition occur. The same statements are of course true of the 60° inversion, but here only onethird of 1 percent of invert sugar must be destroyed. Moreover, such destruction occurs unavoidably during the process of inversion and not both during and after the inversion, as is the case at 70°.

These considerations make it appear that the 60° inversion advocated by Jackson and Gillis is preferable to that at 70°, but further experiments are required before a final decision can be made. It is true that at 60° many final molasses are not completely inverted in the specified period of time. Such samples would require either a prolonged time of inversion at 60° or an elevation of the temperature to 70°, and the value of the divisor under these altered conditions requires determination.

Until much additional work is done it appears advisable to employ alternatively three inversion temperatures, namely 70°, 60°, and that of the laboratory, and to use for each temperature the proper basic value of the divisor. Detailed methods are given on page 152. Walker [12] has devised a method of inversion which has the advantage of requiring a minimum of attention. In this method 75 ml of the solution used for the direct polarization is transferred to a 100-ml flask and heated in a water bath to 65° C. The flask is removed from the bath, and to the solution is added 10 ml of HCl (d20 1.1029). The solution is allowed to cool spontaneously in the air for 15 minutes or as much longer as may be convenient, made to volume, and polarized in the usual manner. The advantage claimed in addition to its convenience is that the maximum temperature coincides with the minimum quantity of invert sugar, and thus the destruction of levulose is diminished. Walker did not determine the basic value of the divisor, but Jackson and Gillis in a limited number of experiments found it in agreement with the value obtained by inversion at 60° C. It is, therefore, tentatively assigned a value of 133.18.

Low-grade products which were clarified by basic lead acetate suffered decomposition of reducing sugar during the period of heating as a result of the excess basic lead in the filtrate. Walker therefore advised, in these instances, the addition of 1 or 2 ml of acid to bring the solution to neutrality or slight acidity.

(b) VELOCITY OF INVERSION OF SUCROSE

The hydrolysis of sucrose, when catalyzed in dilute aqueous solution by acids, follows the unimolecular reaction formula

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in which R and R. are, respectively, the initial and final rotations, and R, is the rotation at the time t. Under any one set of conditions, k is constant during the course of the reaction but varies somewhat with the concentration of sugar and directly with the activity of the acid. An inspection of the chemical equation shows that two molecular species are involved in the hydrolysis, namely sugar and water. The amount of water which disappears is, however, in dilute solution. quite insignificant in comparison with the amount of water present in the solution, and it is for the reason that the concentration of water remains practically constant that the unimolecular formula applies. That the reaction is of second order becomes evident if reaction velocities of different concentrations of sugar are compared. Thus Jackson and Gillis found the velocity constant 0.002161 for 19.5 g in 100 ml of solution at 20° C, while Jackson and McDonald found, under the same conditions of temperature and volume concentration of acid, a constant of 0.003355 for 83.3 g in 100 ml. This large difference of 50 percent is probably due to increased activity of the hydrochloric acid as well as to the increased concentration of sucrose.

Jackson and Gillis [3] measured the velocities of hydrolysis of sucrose in the presence of 0.01, 0.10, and 0.7925 N hydrochloric acid for a concentration of 13 g of sucrose in 80 ml of solution, over a wide range of temperatures.

Arrhenius [13] proposed the hypothesis that some molecules in a reacting system contained sufficient energy to react, while some were inactive, and, if the system contained a constant amount of energy there would be an equilibrium between active and inactive molecules. Thus

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The displacement of the constant with temperature follows the van't Hoff equation

d log k Q
dt RT

in which Q is the energy of activation. If Q is constant over a wide range of temperatures, this equation can be integrated to the form

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in which T represents absolute temperature, and R is the gas constant. Jackson and Gillis applied this formula to their velocity-constant measurements with satisfactory agreement.

The data are computed to a usable form in table 12. These data are reproduced to serve as a guide for general use. They are applicable to a concentration of 13 g of sucrose in 80 ml and will deviate slightly for different concentrations of sugar.

TABLE 12.-Time required at various temperatures for 99.99-percent inversion in the presence of 0.01, 0.1, and 0.7925 N hydrochloric acid as catalyzer

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(c) INFLUENCE OF CONCENTRATION OF SUGAR ON THE CLERGET DIVISOR

The specific rotations of both dextrose and levulose vary with the concentration of sugar, and that of invert sugar likewise varies with concentration, as is shown by the Gubbe [14] equation

[a]2-19.447-0.06068p+0.000221p2,

in which p is the percentage of invert sugar. Thus the basic values of the Clerget divisor discussed above are valid only for a concentration of 13 g of inverted sucrose.

Herzfeld applied to the basic value of the divisor the correction 0.0676 (m-13), in which m is the weight of inverted sucrose in 100 ml

of the solution taken for the invert polarization. This value of the coefficient has remained in general use to the present day. Steuerwald found a slightly higher value, 0.0717. Herles found 0.067 and Sazavsky

0.0677.

Jackson and McDonald [15] have recently measured this coefficient by observing the polarization of a series of solutions prepared by dilution of an invert-sugar solution over a wide range of concentrations. By this procedure assurance was had that all variables such as those arising from the inversion reaction itself were eliminated, the only variable being that caused by dilution. Two series of measurements were made. In one series each solution contained 10 ml of 6.34 N hydrochloric acid in 100 ml, the condition which prevails in the acid Clerget method; in the other series no substance other than dextrose and levulose was present, the condition of the enzymotic method of analysis. The results are given in table 13. The respective coefficients are shown in the following formulas:

(0.634 N HCl) P'=— (32.265+0.07935S)

(Pure water solution) P' - (30.994+0.08241S)

in which P' is the rotation calculated to 26 g of sucrose, and S is the weight of sucrose in 100 ml of solution. The relation proved to be linear between 2 and 26 g of sucrose.

TABLE 13.-Measurement of the concentration coefficient of invert sugar

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(d) EFFECT OF VARYING TEMPERATURE ON THE CLERGET DIVISOR

The specific rotation of levulose varies considerably with the temperature of observation, while that of dextrose is very nearly independent of temperature. The specific rotation of invert sugar, and consequently the negative constituent of the Clerget divisor, are therefore functions of temperature. Clerget found that the divisor diminished 0.5° S for each degree increase of temperature above 20° C, and applied the correction-0.5t to his value 144.0, in which t is the centigrade temperature and 144.0 is the divisor extrapolated to 0° C. This does not imply that the value 144.0 is actually valid at 0°; it rather means that for relatively small deviations from 20° C, the correction is valid. If, as Zerban suggests, the basic value is defined as the reading at 20° C, the temperature correction becomes -0.5 (t-20). This value of the temperature correction has remained in general use to the present day. Tuchschmidt [16] in 1870 found

the value to be -0.50578t, but it is questionable whether the instruments available at that early date were capable of the precision required for so accurate a measure of the coefficient.

Zerban calculated from Vosburgh's observations that the coefficient for the half-normal (German) weight of sucrose would be -0.478 and for the quarter-normal weight, -0.466. Gillet [17] reported a value of 0.49 for the half-normal solution. Zerban states that the value -0.50 for final cane molasses at quarter-normal concentrations is considerably too high.

It is evident that considerable uncertainty attaches to the value of the temperature coefficient and that new careful measurements are urgently required.

The foregoing coefficients apply solely to the polarization of the inverted solution. Sucrose also has a definite, although small, temperature coefficient. The normal solution diminishes 0.03° S per degree increase of temperature, so that the negative temperature coefficients given above are to be increased to a higher negative value by 0.03° S when applied to the whole Clerget divisor. Pending further accurate measurements and general agreement, it appears necessary to use 0.53 for the temperature coefficient except in special instances where a different value is known to apply accurately.

In applying the Clerget divisor and its temperature coefficient to actual analyses, it is assumed that the solutions are made to volume and polarized at the same temperature, the saccharimeter wedges likewise being at this temperature. Zerban recommends that these readings be made at exactly 20° C in view of the uncertainty of the temperature coefficients. Evidently this difficult requirement can be met only by laboratories that have complete temperature control. It is urgent therefore that the temperature coefficients not only of the pure sugars, but also of the commonly occurring crude mixtures, be determined.

It frequently occurs that the two polarizations_differ slightly from each other in the temperature of observation. In such a case it is preferable to calculate the results from the temperature of the invert polarization alone and, whenever possible, to correct the direct polarization and the quartz wedges to this temperature. If the temperature of the wedges differs from that of the solution under observation, the reading can be corrected to the temperature of either solution by applying the temperature coefficient of quartz, namely 0.000148 per degree temperature per degree sugar. Since the effect of the coefficient is to lower the reading of the scale with increase of temperature, the apparent polarization is lower than it should be. Thus if a solution polarizes 100° S and the wedges are 1 degree centigrade higher than the solution, the reading must be increased by 0.015. Obviously these corrections need be made only for high polarizations and considerable differences in temperature.

If the solution for direct polarization is free from invert sugar, as is the case with beet products, and if made to volume and polarized at a temperature different from that of the invert polarization, it can be corrected to the temperature of the latter by

P=P+0.0003 P (t'—t),

in which t and t' are the temperatures of the invert and direct polarizations, respectively.

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