Part 15

=93. Influence of Strength of Solution and Time of Heating on the Inversion of Sucrose.=—As has been intimated, the strength of a sugar solution and the time of heating with hydrochloric acid are factors that must be considered in determining a formula for the calculation of sucrose by inversion. The Clerget formula holds good only for the conditions specified and these conditions must be rigidly adhered to in order to secure the proper results. This matter has been thoroughly studied by Bornträger, who also gives a nearly complete bibliography of the subject. As a result of his investigations it seems well established that the original Clerget formula is practically correct for the conditions indicated, Bornträger modifying it only by substituting in the formula 143.66 for 144. This is so nearly the same as the Clerget factor that it is not advisable to substitute it therefor. If, however, the inverted sugar solution be diluted to double its volume before polarization the factor proposed by Landolt, viz., 142.4, gives more nearly accurate results. If the hydrochloric acid be neutralized before polarization by an alkaline body, the character of the salt which is formed also influences, to a greater or less extent, the specific rotatory power of the solution. Hydrochloric acid itself also influences the rotation to a certain degree.

=94. Calculation of Results.=—The percentage of sucrose in a solution which has been polarized before and after inversion is calculated by an appropriate formula from the data obtained or is taken directly from tables. These tables are too long to insert here, and in point of fact the calculation can be made from the formula almost as quickly as the result can be taken from a table.

Two factors are commonly used in the calculations, one based on the supposition that a sugar solution polarizing 100° to the right will, after inversion, give a reading of 44° to the left, at zero temperature. In the second formula in common use the polarization to the left in the circumstances mentioned above is assumed to be 42.4, a number reached by Landolt after a long series of experiments. The principle of the calculation of the percentage of sucrose is based upon the original observation of Clerget to the effect that the algebraic difference of the two readings, divided by 144, less half of the temperature, will give the percentage of sucrose desired. The formula by which this is obtained is

a - b S = -----------. K - t ---- 2

In this formula a is the polarization on the sugar scale before inversion, b the polarization after inversion, K the constant representing the algebraic difference of the two polarizations of pure sugar at 0° and t the temperature of the observation. To K may be assigned the values 144 or 142.4, the one in more common use. In case the polarization, after inversion, is to the left, which is more commonly the case, the sum of the two readings is taken for a - (-b) = a + b; when both polarizations are to the right or left the difference is taken. S is the percentage of sucrose desired.

Example.—Let the polarization before inversion be +95 and after inversion -26 and the temperature 20°

95 + 26 Then S= -------- = 121 ÷ 134 = 90.6. 144 - 10

Substituting the value 142.4 for K, the result of the calculation is 91.4.

In high grade sugars, therefore, the difference in the results secured by taking the two values of K amounts to about 1 per cent of sucrose.

For a further discussion of the theory and practice of inversion the reader is referred to the articles of Herles, Herzfeld, and Wohl.

=95. Method Of Lindet.=—Courtonne recommends the method of Lindet for securing the inversion instead of the method of Clerget. Modified by Courtonne, the method is as follows:

Make two or three times the normal weight of sugar dissolved in water to a volume of 200 or 300 cubic centimeters, as the case may be. After thoroughly mixing proceed as follows:

First, to Obtain the Polarization Direct.—Place fifty or 100 cubic centimeters of the prepared solution in a flask marked at fifty and fifty-five or at 100 and 110 cubic centimeters, add a sufficient quantity of lead acetate to secure a complete clarification, make the volume to fifty-five or 110 cubic centimeters, shake thoroughly, filter, and polarize in a 220 millimeter tube.

Second, to Obtain the Rotation after Inversion.—Place twenty cubic centimeters of the original solution, in a flask marked at fifty cubic centimeters, containing five grams of powdered zinc. The flask should be placed in boiling water. Add, little by little so as to avoid a too rapid evolution of hydrogen, ten cubic centimeters of hydrochloric acid made of equal parts of the strongest acid and water. After the operation is terminated, cool to the temperature of the room, make the volume to fifty cubic centimeters, polarize, and determine the rotation. The volume occupied by the zinc which is not dissolved, will be about one-half cubic centimeter, hence the deviation should be multiplied by the factor 2.475 in order to get the true deviation which would have been produced by the pure liquor. We have then:

A = the deviation direct. B = the deviation after inversion. C = the algebraic difference of the deviations.

The amount of sucrose, therefore, would be calculated by the formula of Creydt,

C - 0.493A X = --------------; 0.827

for raffinose the formula would be

A - S Y = ---------, 1.57

in which S is the deviation due to the sucrose present. The solutions inverted in the manner described are absolutely colorless. There is no need of employing bone-black to secure the saccharimetric reading nor does it present any uncertainty. It is thought by Courtonne that this method will soon take the place of the method of Clerget on account of the advantages above mentioned. The method will be somewhat improved by adopting the following suggestions:

1. Instead of allowing any arbitrary number for the volume of the undissolved zinc, decant the liquid, after inversion, into another flask and wash repeatedly with hot water until all trace of sugar is removed from the flask in which the inversion took place.

2. Instead of polarizing in a 200 millimeter tube make the observation in a 500 millimeter tube, which will permit of the reading being made without any correction whatever.

=96. Inversion by Means of Invertase.=—Instead of using acids for the inversion of cane sugar the hydrolysis can be easily effected by means of a ferment derived from yeast. A complete history of the literature and characteristics of this ferment, together with a study of its properties and the various methods of preparing it, has been given by O’Sullivan and Tompson. In the preparation of invertase, the method found most effective is the following:

The yeast is allowed to liquify for at least a month in a fairly warm room without stirring. At the end of this time the surface is removed and any supernatant liquid poured away. The lower sedimentary part is thrown on a quick-acting filter and allowed to drain for two days. To the filtrate, alcohol of specific gravity 0.87 is gradually added to the extent of one and a half times its volume, with continued and vigorous stirring. The process of adding the alcohol and stirring should require about half an hour, after which the mixture is allowed to stand for twenty-four hours to allow the precipitated invertase to settle. The supernatant liquid is poured away and the precipitate washed several times on successive days by decantation with alcohol of 0.92 specific gravity. When the washings become nearly colorless the precipitate is thrown on a filter, allowed to drain, and immediately removed and mixed with a large bulk of alcohol of 0.92 specific gravity. The precipitate is again collected, mixed thoroughly with its own bulk of water, and some alcohol of 0.97 specific gravity, allowed to stand for a few hours and thrown on a filter. The filtrate contains the invertase.

=97. Determination of Activity of Invertase.=—The activity of a solution of invertase, prepared as above, is measured by the number of minutes required for it to reduce to zero the optical power of a solution of 100 times its weight of cane sugar at a temperature of 15°.5. In order to facilitate the action of the invertase, a trace of sulfuric acid is added to the solution. The manipulation is as follows:

Fifty grams of sucrose are dissolved in water and made to a volume of nearly a quarter of a liter and placed in a bath maintained at 15°.5. Half a gram of the invertase is added, the time noted, the solution immediately made up to a quarter of a liter and well shaken. The contents of the flask are poured rapidly into five beakers; the actual quantity in each beaker is not necessarily the same. To each of these beakers, in succession, are added the following amounts of decinormal sulfuric acid, viz., one-tenth, three-tenths, six-tenths, one, and one and four-tenths cubic centimeters. After an hour a small quantity of the solution is taken from beaker No. 3 and the reaction of the invertase stopped by adding a few drops of strong potassium hydroxid and the time of adding this reagent noted. This solution is then read in the polariscope and the percentage of sugar inverted is calculated from the formula C₁₂H₂₂O₁₁ + H₂O = C₆H₁₂O₆ + C₆H₁₂O₆.

The calculation of the amount of cane sugar inverted is based on the formula, (38.4 - d) ÷ 0.518 = p. In this formula d equals the divisions of the sugar scale read on the polariscope; p the percentage of cane sugar inverted; 38.4 the reading on the sugar scale of the original sugar solution and 51.8 the total number of divisions of the cane sugar scale that the polariscope reading would fall through if all the sugar were inverted. The observation tubes used in the polarization are only 100 millimeters in length. After stopping the action of the invertase with potassium hydroxid the solution is allowed to stand for some time before polarization inasmuch as the dextrose formed appears to assume the state of birotation and some time is required for it to reach its normal rotatory power. If the invertase be used in the alcoholic solution a sufficient quantity should be added to be equivalent to 0.01 of the sucrose present. The time which the contents of beaker No. 3 will take to reach optical activity is calculated in a manner described by O’Sullivan and Tompson, but too long to be inserted here. The five beakers mentioned above are examined in succession and the amount of sulfuric acid best suited to the maximum inversion thus determined. This quantity is then used in subsequent hydrolyses with the given sample of invertase.

The action of invertase on sucrose is very rapid at the first and becomes very much slower towards the end. At a temperature of 15°.5 it is advisable to let the solution stand for forty-eight hours in order to be sure that complete inversion has taken place. For this reason the method by inversion by means of invertase is one of no great practical importance, but it may often be useful to the analyst when the employment of an acid is inadmissible.