Part 47

In a mixture of the two sugars under the conditions mentioned and at a temperature of 0° the angular rotation observed is -15°.15 equivalent to 43.37 divisions of the cane sugar scale.

The + rotation due to the dextrose is 14°.53. Therefore the total negative rotation due to levulose at 0° is 15°.15 + 14°.53 = 29°.68. Hence the gyrodynat of levulose at 0° and in the degree of concentration noted is readily calculated from the formula

29.68 × 100 [α]°_{D} = - ------------ = -108.24. 2 × 13.71

Since at 88° (circa) the mixture of levulose and dextrose is neutral to polarized light, it follows that at that temperature the specific rotatory power of levulose is equal to that of dextrose, viz., 53°.

The total variation in the specific rotatory power of levulose, between zero and 88°, is 55°.24. The variation for each degree of temperature, therefore, of the specific rotatory power of levulose is equal to 55.24 divided by 88, which is equal to 0.628. From these data it is easy to calculate the specific rotatory power of levulose for any given temperature. For instance, let it be required to determine the gyrodynat of levulose at a temperature of 20°. It will be found equal to 108.24 - 0.628 × 20 = 95.68. The required rotatory power is then [a]²⁰ °_{D} = -95°.68.

In these calculations the influence of the presence of hydrochloric acid upon the rotatory power of the levulose is neglected.

Since the variation in angular rotation in the mixture at different temperatures is due almost wholly to the change in this property of the levulose it follows that the variation for each degree of temperature and each per cent of levulose can be calculated. Careful experiments have shown that the variation in the rotatory power of levulose between 0° and 88° is represented by a straight line. For 13.71 grams per 100 cubic centimeters the variation for each degree of temperature is equal to 43.37 ÷ 88 = 0.49 divisions on the cane sugar scale, or 15.15 ÷ 88 = 0°.1722 angular measure. If 13.71 grams of levulose in 100 cubic centimeters produce the deviations mentioned for each degree of temperature, one gram would give the deviation obtained by the following calculations:

For the cane sugar scale 0.49 ÷ 13.71 = 0°.0357 and for angular rotation 0.1722 ÷ 13.71 = 0.01256.

The above data afford a simple formula for calculating the percentage of levulose present from the variation observed in polarizing a solution containing levulose, provided that the quantity of levulose present is approximately fourteen grams per 100 cubic centimeters.

Example.—Suppose in a given case the difference of reading between a solution containing an unknown quantity of levulose at 0° and 88° is equal to thirty divisions of the cane sugar scale. What weight of levulose is present? We have already seen that one gram in 100 cubic centimeters produces a variation of 0.0357 division for 1°. For 88° this would amount to 3.1416 divisions. The total weight of levulose present is therefore 30 ÷ 3.1416 = 9.549 grams. In the case given 26.048 grams of honey were taken for the examination. The percentage of levulose was therefore 9.549 × 100 ÷ 26.048 = 36.66 per cent.

If it be inconvenient to determine the polarimetric observations at temperatures so widely separated as 0° and 88° the interval may be made less. In the above case if the readings had been made at 20° and 70° the total variation would have been only ⁵⁰/⁸⁸ of the one given, viz., 17.05 divisions of the cane sugar scale. The calculation would then have proceeded as follows:

0.0357 × 50 = 1.785.

Then, 17.05 ÷ 1.785 = 9.552 grams of levulose, from which the actual percentage of levulose can be calculated as above.

With honeys the operation is to be conducted as follows:

Since honeys contain approximately twenty per cent of water and in the dry substance have approximately forty-five per cent of levulose, about 38.50 grams of the honey should be taken to get approximately 13.8 grams of levulose.

In the actual determination the calculations may be based on the factors above noted, but without respect to the degree of concentration. If half the quantity of dextrose noted be present its specific rotatory power is only reduced to about 52°.75, and this will make but little difference in the results. In the case of honey 13.024 grams of the sample are conveniently used in the examination, half the normal weight for the ventzke sugar scale. The error, however, due to difference in concentration is quite compensated for by the ease of clarification and manipulation. Alumina cream alone is used in the clarification, thus avoiding the danger of heating the solution to a high temperature in the presence of an excess of lead acetate.

An interesting fact is observed in cooling solutions of honey to 0°. The maximum left hand rotation is not reached as soon as the temperature reaches 0° but only after it has been kept at that temperature for two or three hours. The line representing the change in rotatory power in solutions of honey between 10° and 88° is practically straight but from 10° to 0°, if measured by the readings taken without delay, it is decidedly curved; the reading being less at first than it is afterwards. After three hours the 0° becomes sensibly constant and then the whole line is nearly straight, but still with a slight deficiency in the reading at the 0°. For this reason the computations should be based on readings between 10° and 88° rather than on a number covering the whole range of temperature. Nevertheless, if the solution be kept at 10° for three hours before the final reading is taken, no error of any practical magnitude is introduced.

The calculations given above, for the cane sugar scale, can also be made in an exactly similar manner for angular rotation. The angular variation produced by one gram of levulose for 1° of temperature is 0°.01256. For 88° this would become 1°.10528. Suppose the total observed angular deviation in a given case between 0° and 88° to be 10°.404, then the weight of levulose present is 10.404 ÷ 1.10528 = 9.413 grams.

In the case mentioned 26.048 grams of honey were taken for the examination. The percentage of levulose present, therefore, was 9.413 × 100 ÷ 26.048 = 36.13.

=241. General Formula for the Calculation of Percentage of Levulose.=—Let K = deviation in divisions of the cane sugar scale or in angular rotation produced by one gram of levulose for 1° temperature.

Let T and tʹ = temperatures at which observations are made.

Let R = observed deviation in rotation.

Let W = weight of levulose obtained.

Let L = per cent of levulose required.

R Then L = --------------- ÷ W. K(T - tʹ)

In most genuine honeys the value of R between 0° and 88° is approximately thirty divisions of the cane sugar scale or 10° angular measure for 26.048 grams in 100 cubic centimeters, read in a 200 millimeter tube, or, for 13.024 grams in 100 cubic centimeters read in a 400 millimeter tube.

The method of analysis outlined above has been applied in the examination of a large number of honeys with most satisfactory results. It can also be applied with equal facility to other substances containing levulose.

=242. Sucrose and Dextrose.=—In mixtures these two sugars are easily determined by optical processes, provided no other bodies sensibly affecting the plane of polarized light be present. The total deviation due to both sugars is determined in the usual way. The percentage of sucrose is afterwards found by the inversion method (=92=). The rotation, in the first instance due to the sucrose, is calculated from the amount of this body found by inversion, and the residual rotation is caused by the dextrose. The percentage of dextrose is easily calculated by a simple proportion into which the numbers expressing the gyrodynats of sucrose and dextrose enter. When the readings are made on a ventzke scale the calculations are made as follows: