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.[54] 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.[55]
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.[56] 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
| S = | a - b | . | |
| 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° |
| Then S = | 95 + 26 | = 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.[57]