If, finally, the solutions for direct and invert polarizations were made to volume at the same temperature but polarized at different temperatures, the direct polarization (if free from invert sugar) can be corrected to the temperature of the invert polarization by

P=P+0.00061 P(t'-t),

in which the coefficient includes the changes arising from the change of rotary power of sucrose and the expansion of the solution.

(e) EFFECT OF HYDROCHLORIC ACID

Many dissolved substances affect the rotation of invert sugar, the greater number elevating it to a higher negative rotation but some altering it in a positive direction. Hydrochloric acid is most commonly used as the inverting agent, and its effect has been shown to increase the negative rotation to a higher negative value. Jackson and Gillis studied this effect quantitatively and found that the negative rotation was enhanced as the concentration of acid was increased, the relation being precisely linear up to 1.3 N hydrochloric acid and approximately so up to 2.5 N. They confined their measurements to a single concentration of invert sugar, namely that formed by the inversion of 13 g of sucrose in 100 ml of solution. In their formula, R and Ro represent the rotation at 20°C of 13 g of inverted sucrose multiplied by 2, m the grams of hydrochloric acid, and N the normality of the acidified solution.

R-R-0.5407m-Ro-1.972N.

(38) If we select for a stock hydrochloric acid one having a normality of 6.34 (d20 1.1029),

R=R。-0.1250,

(39) in which v is the number of milliliters of 6.34 N acid in 100 ml of the solution polarized.

It is evident from these equations that the concentration of acid should be carefully regulated. Instead of the 5 ml of concentrated acid previously used, Jackson and Gillis recommended dilution of strong acid to 6.34 N or d420 1.1029. This constitutes a 1:1 dilution if the original concentrated acid contained exactly 38.8 percent of hydrochloric acid. As this is seldom the case, it is preferable to adjust the diluted acid to the concentration specified. This specification has been adopted by the Association of Official Agricultural Chemists [18]. Ten milliliters are used for inversion.

If in eq 39 the correction term which, evaluated for 10 ml of 6.34 N hydrochloric acid, becomes -1.25°, is applied, and if the experimentally determined values of R given in table 14 are then substituted, the equations can be solved for Ro, the rotation of invert sugar in the absence of acid. If no decomposition of invert sugar during the inversion reaction occurred, R。 would equal the rotation of pure invert sugar, or in other words, the Clerget divisor by the invertase method. For the acid inversion at 70° C, R。 becomes -31.75; for 60° C, -31.93; for room temperature, -32.03; and for 4°C, -32.08. The accepted value for invert sugar by invertase inversion is -32.10. Evidently in all methods of acid inversion, decomposition of invert sugar occurs, but to a diminishing extent as the temperature of inversion is decreased.

(f) EFFECT OF VARIOUS REAGENTS ON THE ROTATION OF INVERT SUGAR

An effect on the rotation of invert sugar similar to that of hydrochloric acid is produced by neutral salts. It is thus not because of its acidity that hydrochloric acid enhances the negative rotation of invert sugar, but rather because it, like many salts listed below, is a dissolved substance which, conceivably on account of its high degree of solvation, produces an effect similar to an increase in concentration.

Jackson and Gillis [3] studied systematically the effect of various reagents on the rotation of invert sugar. They derived the formulas given in table 14, in which R is twice the rotation in saccharimeter degrees of the half-normal solution, and m the weight in grams per 100 ml of the substance (anhydrous) whose effect is measured. ther but less detailed measurements are given in table 15.

Salt

TABLE 14.-Effect of salts on the rotation of invert sugar a

Fur

Equivalent depression

- In their original article, Jackson and Gillis used the value -32.00 for invert sugar in the absence of reagents. However, they determined merely the slope of the curves upon addition of reagents. The substitution of the correct value, -32.10, does not affect their measurement of the slope.

It will be recognized that the list of salts is far from comprehensive, but the data show clearly that relatively large variations in the rotatory power of invert sugar can arise as a result of the admixture of salts and furthermore that the anion produces unpredictable effects. Under the column headed "molecular depression" is given the depression caused by 1 mole of dissolved substance, and under "equivalent depression" that caused by the salt calculated to valence 1. A very rough similarity in the equivalent depression caused by the sodium, potassium, and ammonium salts seems to occur, 1 molecular equivalent depressing the rotation by 25° to 40° S. Further reference will be made to this relation under a discussion of Saillard's modification of the Clerget method.

Attention should be directed to the well-known effect of basic lead acetate on the rotation of invert sugar. This is probably due to a chemical combination of the basic lead constituent with levulose and illustrates the necessity of acidifying the direct polarization of a crude substance which contains invert sugar and which has been defecated TABLE 15.-Influence of various reagents on the rotation of invert sugar

with basic lead. Acetic acid, and probably many other weak organic acids, change the rotation of invert sugar in a positive direction.

(g) ROTATION OF SUGAR MIXTURES AND THE EVALUATION OF m

It has been shown above that the rotatory power of pure invert sugar increases in a negative sense with increase in concentration, and that for the analysis of pure sucrose the Clerget divisor must be increased by the quantity 0.0794 (m-13), in which m is the number of grams of sucrose taken in the sample for the invert polarization. The question now arises as to what the value of m is if the original sample contains invert sugar, organic nonsugars, or inorganic salts in admixture with sucrose. In general, sugar-cane products contain all four of these constituents, while beet products usually contain all except invert sugar.

Consider first the analysis of a mixture of sucrose and invert sugar. The essential condition of the Clerget method is that the rotation of the invert sugar in the direct polarization be the same as in the invert polarization. Jackson and Gillis [3, 9] showed that a given quantity of invert sugar in the presence of sucrose had a slightly lower negative rotation than it would have if all of the sucrose were inverted. However, since its rotation approached constancy more closely if the concentration of total sugar were unaltered than if the relatively large effects of dilution were introduced, they recommended that both direct and invert polarizations have the same concentration of the sample. This expedient was admitted by the authors to be a first approximation "since the problem of the rotation of mixtures was too large a one for a complete solution at that time." If now the plausible assumption is made that the rotatory power of sucrose is unaltered by admixture with invert sugar, its change of rotation upon hydrolysis would be from the positive rotation of sucrose itself to the negative rotation of invert sugar at the concentration of total invert sugar, which is the sum of the invert sugar formed by hydrolysis and the invert sugar originally present. Since the variations in the Clerget divisor are caused only by the variations of the specific rotation of invert sugar with concentration, the quantity m should represent the grams of total sugar in 100 ml of solution rather than the grams of sucrose."

Vosburgh [19] in a more general study measured the rotations of mixtures of sucrose, dextrose, and levulose and stated his results in an article which has been widely quoted and very frequently misquoted. Vosburgh summarized his conclusions as follows:

1. The specific rotations of glucose and fructose when mixed in equal proportions (invert sugar) are those which the sugars would have if each were present alone at a concentration equal to the total invertsugar concentration.

2. In mixtures of glucose and sucrose the specific rotations of the two are those which the sugars would have if each were present alone at a concentration equal to the total sugar concentration.

3. The relationship is only approximate for mixtures of fructose and sucrose, in which case the rotation is a little smaller (or larger numerically if negative) than that calculated upon its assumption.

7 This is a reversal of the recommendation of Jackson and Gillis, who substituted for m the grams of sucrose alone.

4. The polariscopic determination of the percentage of sucrose replaced by invert sugar gives slightly high results.

It should be noted that the statement in conclusion 1, which was confined to pure invert sugar and was not even applied to all dextroselevulose mixtures, has frequently in subsequent literature been extended to apply not only to all sugar mixtures but to all sugar-nonsugar mixtures. Conclusion 4, which concerns the Clerget analysis specifically, implies that conclusion 1 does not apply exactly to sucroseinvert sugar mixtures, the deviation amounting to about 0.4 percent, an error quite appreciable in Clerget analysis. This conclusion is in harmony with the previously described experiment of Jackson and Gillis, although the precision of analysis by the invertase method and by the compensation methods described in later paragraphs is closer than 0.4 percent. It should be recognized that the expedients suggested in this paragraph are recommended as approximations and are subject to alteration as knowledge of the rotations of sugar mixtures advances.

Zerban [20] in an extensive study of the analyses of complex sugar mixtures showed that satisfactory agreement of calculated and determined values of sucrose was obtained if "in these calculations the divisor corresponding to the total sugar concentration, and not that for the sucrose concentration, is used." In other words, m represents the number of grams of total sugars taken for inversion and made up to 100 ml after inversion.

In a further study Zerban prepared samples simulating cane molasses by combining accurately known quantities of its constituents, and here he found it necessary to assign to m the total weight of dry substance taken for inversion.

(h) INFLUENCE OF REAGENTS ON THE ROTATION OF SUCROSE

Sugar sirups of commercial importance frequently contain appreciable quantities of inorganic salts. Cane and beet molasses are essentially sirups in which, by removal of sugar, the salts have accumulated to such an extent that no further crystallization of sugar is possible. The presence of salts causes an alteration of the rotatory power of sucrose and, therefore, not only is the direct polarization of plant juices rendered uncertain, but both the direct and invert polarizations of the Clerget method are affected and the analytical results are made uncertain unless the change in the direct is the same as in the invert polarization.

In general, dissolved inorganic salts diminish the rotatory power of sucrose. For a few salts, Jackson and Gillis measured this depression and found it linear with respect to concentrations of salt ranging between 0 and about 4 g in 100 ml. They established the relations shown in table 16.

In the early literature [21] efforts were made to find some regularity between the depression and the molecular weight of the salt, and indeed the "molecular depression," that is, the depression caused by 1 g multiplied by the molecular weight, approached constancy for a few closely related salts, such as the chlorides of barium, strontium, and calcium. But molecular depression failed of constancy if applied more generally. Evidently in the relations listed above no constant molecular depression can be observed.

The depression caused by a given quantity of salt is, in dilute solution, a constant percentage of the rotation of pure sucrose quite regardless of the concentration of the latter. Thus Jackson and Gillis [22] showed by their own measurements and by calculation of the careful measurements of Browne [23] that 3.392 g of ammonium chloride produced the same relative depression on the rotation of sucrose, even when the concentration of the latter was varied between 5 and 52 g in 100 ml. When all rotations were calculated to 26 g of sucrose, the depressions were found to be the constant quantity 0.56° S. Similarly, 2.315 g of sodium chloride in 100 ml of a sucrose solution caused depressions of rotation which, when calculated to 26 g of sucrose, amounted to 0.62° S, quite regardless of the concentration of sugar.

Brown [24] extended these studies to very low concentrations of sugar and various salts, expressing this relation by the formula

Percentage of sugar=P+KPM,

in which P is the polarization, M the weight in grams of the salt present in 100 ml of the solution polarized, and K a constant which is characteristic for each salt. The following values of K were found mainly by measurement in very dilute solution, and with inevitable multiplication of error:

Brown thus agreed with Jackson and Gillis that the depressive effect of salt was the same relative fraction of the total polarization regardless of concentration. Hence the values of K can be determined at high concentrations where the errors are small and applied to the low concentrations of thin juice and other dilute sirups.

(i) METHODS OF COMPENSATION

The direct application of the Clerget method in unmodified form to low-grade cane and beet products frequently leads to the introduction of analytical errors which are due to the effects of impurities in such samples. Cane products usually contain, in addition to sucrose, invert sugar which in the case of molasses may amount to 30 percent or more of the total sugar. It is necessary that the rotation of this invert sugar remain unaltered in both the direct and invert polarizations. Mention has already been made of the necessity of observing both polarizations in the same concentration of substance in order to avoid the change in rotation caused by dilution. An additional source of error is introduced in the acid methods of inversion as a result of the