The invert reading was multiplied by 11/10. The percentage of sucrose was calculated by the formula

in which D is the algebraic difference between the two corrected polarizations and t is the centigrade temperature.

Browne [2] modified the Clerget method by allowing the solution to invert overnight at room temperature and making it to a volume of 55 ml at the completion of the inversion. It was pointed out that as the result of three factors a contraction in volume of about one-third of a milliliter occurred in the original method. The diminution in volume is caused, first, by the contraction which all sucrose solutions undergo during inversion and which for 13 g of sucrose in 55 ml is about 0.25 ml; second, the elevation of temperature caused by dilution of 5 ml of concentrated hydrochloric acid; and third, by the evaporation of water during the inversion. The advantage claimed by the author is that the invert solution, being but slightly diluted, can be observed with practically the same precision as the solution for direct polarization and with no great multiplication of errors, as is the case in methods in which the invert solution is more highly diluted. This advantage is lost, however, if the invert solution in the alternative methods is observed in a 400-mm column.

Browne found the percentage of sucrose to be expressed by the formula 100D

S=

in which the parenthetical term multiplied by 0.01 in the denominator is the correction of the divisor for concentration of sugar. If the concentration of sucrose is diminished from 26 to 25 g, the parenthetical term becomes roughly 5.19 and the concentration coefficient 0.052 for 1 g of sucrose. This value is considerably lower than the prevailing value 0.0676, and quite at variance with the revised value, 0.0794, of Jackson and McDonald discussed in a later paragraph.

Jackson and Gillis [3] showed that under the conditions prescribed by Browne inversion is complete in 8 minutes at 60° C.

In 1888 Herzfeld [4] devised the modification of the Clerget method which has remained in use to the present day. He observed the direct polarization in the usual manner, employing the normal weight of sucrose. He then took the half-normal weight (13 g) in 75 ml of solution, added 5 ml of hydrochloric acid (38 percent or 1.188 specific gravity), and warmed the solution to 67° to 70° C in from 2 to 3 minutes. The solution having attained the prescribed temperature, he kept it as near 69° C as possible for 5 minutes, when it was quickly cooled, made to a volume of 100 ml at 20° C, and polarized at the same temperature. Being that of a half-normal solution, the reading was multiplied by 2. Under these conditions he found the Clerget formula to be

The basic value of the Clerget divisor in the above formula, 142.66, is defined as the algebraic difference between the rotation of the normal pure sucrose solution at 20° C (i. e., +100) and twice the rotation of 13 g of inverted sucrose in 100 ml at 20° C, corrected to 0° C by the term +0.5t. The actually measured value, free from the uncertainty of the value of the temperature coefficient, is 132.66 at 20° C.

The basic value of the divisor has been the subject of numerous investigations with different results. Herzfeld, in his original publication, adopted the value 132.66 at 20° C, but apparently the actual measurement was made by Dammüller [5]. Later investigators have invariably obtained higher values: Walker [6], 132.78; Tolman [7], 132.88; and Steuerwald [8], 133.05. Jackson and Gillis computed that by the Herzfeld procedure the destruction of invert sugar caused a lowering of the rotation by 0.15 to 0.20° S, which, deducted from their recalculated value, 133.18, left a resultant rotation of -33.03 to -32.98.

In 1920 Jackson and Gillis [3] published the results of a careful series of measurements in which they inverted sucrose solutions at 60° C instead of 70° C in order to avoid the destruction of invert sugar. They made their measurements at a somewhat higher concentration than the half-normal solution in order to utilize such standard quartz plates as were available, thus eliminating the errors of graduation of the saccharimeter scale. They were consequently obliged to correct their observed rotations for the higher concentration of sugar, using for this purpose the then prevailing value 0.0676 per g departure from 13 g of sucrose per 100 ml. Recent experiments have shown that this coefficient is considerably too low and that a recalculation of the Jackson and Gillis value for the rotation of the half-normal weight is necessary. Thus their originally announced value, -33.25, now becomes -33.18 at 20° C.

Subsequent to the publication of the Jackson and Gillis measurements, but previous to the appearance of the German translation of the same article [9], Herzfeld published a posthumous work of Schrefeld [10], whose experiments were made in 1910 to 1912. Schrefeld dissolved the half-normal weight of sucrose in 75 ml of water and added 5 ml of concentrated hydrochloric acid (sp gr 1.19). Inserting a thermometer in the sugar solution, he immersed the flask in a water bath having a temperature of 70° C, and agitated it until in 2%1⁄2 to 2% minutes the solution had reached a temperature of 67° C. From this moment he allowed it to remain in the bath for exactly 5 minutes, during which time the temperature gradually rose to 69.5° C. The flask was removed and cooled rapidly to 20.0° C and the solution made up to 100 ml. Polarization measurements were made at 20° C. As a mean of seven concordant polarizations, Schrefeld found the rotation of the half-normal solution multiplied by 2 to be -33.00. This value has not been officially adopted by the International Commission for Uniform Methods of Sugar Analysis but has been widely used and has been verified by Browne. Zerban and coworkers under similar conditions found -32.97; Spengler, Zablinsky, and Wolf [11], -33.02; and Jackson and McDonald, -32.99. Thus the basic value, 133.00 at 20° C, for inversion under the Schrefeld conditions must be considered a well-established constant. It has been adopted officially by the Association of Official Agricultural Chemists.

Jackson and McDonald have experimentally corroborated the recalculated value -33.18 of Jackson and Gillis and have extended their measurements to include values obtained after inversion at several other temperatures. The Arrhenius formula, 37, evaluated by Jackson and Gillis, and discussed further on page 133 permits a calculation of the velocity constant of inversion at any desired temperature in the presence of 0.7925 N hydrochloric acid. With the aid of this equation, Jackson and McDonald [15] calculated the time required for 99.99-percent hydrolysis at 49° and 35° C, respectively, and measured the rotation of the half-normal solution. They found the value 33.25 for both temperatures.

Many analysts advocate inversion at room temperature as a safe means of avoiding decomposition of invert sugar. Formula 37 enables us to calculate the velocities of inversion and times required for 99.99-percent inversion at the temperatures which may be expected in uncontrolled laboratories. These periods of time vary considerably with small changes of temperature, as is shown in table 10. While the velocities of many reactions double themselves with a rise of 10 degrees in temperature, the velocity of inversion of cane sugar increases more than fourfold between 20° and 30° C. Thus room-temperature inversion is safe only if such variations of temperature as inevitably occur are known to the analyst and are considered in calculating the time required for complete hydrolysis. It appears from table 10 that 24 hours is insufficient for hydrolysis at 20°C, that 16 or 17 hours for overnight inversion at 30° C is excessive, and that serious decomposition of invert sugar can result. Evidently room-temperature inversion must be carried out with considerable discretion.

TABLE 10.-Time required for inversion of sucrose at room temperature by 0.7925 N hydrochloric acid

For room-temperature inversion the value of the negative constituent of the Clerget divisor adopted by the Association of Official Agricultural Chemists is -33.20. Jackson and McDonald [15] have measured this constant with care by inverting the half-normal weight of sucrose in a thermostat which maintained a constant temperature within a few hundredths of a degree. The times of inversion were calculated by formula 37 for temperatures varying from 20° to 25° C. The mean value found for the rotation of the half-normal solution was -33.29.

In recapitulation, table 11 shows the values of twice the rotation of the inverted half-normal solution. All of these measurements except the first one at 70° C were made with care to avoid the destruction of invert sugar after the completion of the inversion. Jackson and Gillis showed that when sucrose is inverted by the Herzfeld method

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

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 (do 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

in which Ro 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.