Page:Text-book of Electrochemistry.djvu/116

 CHAP. vii. INVERSION OF CANE SUGAR.

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��at this point of time there are in the solution {A — x) mols of sugar. The quantity dx which is inverted in time dt is, according to Wilhelmy, proportional to (-4 — x). We therefore have, if J^ is a constant —

and by integration we obtain —

The quantity of sugar present can be accurately determined by ascertaining the angle through which a definite length of the solution rotates the plane of polarised light. In the next table is given under t the time in minutes since the beginning of the reaction, under a° the angle of rotation produced by the solution on polarised light, and the third colimm contains the constant —

which is the specific velocity of the reaction. The original dextrorotation of the solution is due to the dextrorotatory cane sugar, and this passes into a laevorotation when the quantity of Isevorotatory invert sugar becomes su£5ciently great. When ^ = «>, i,e, after a very long time, the inversion is as good as complete. The results given were obtained at 25° with a 20 per cent, cane sugar solution, which was also 0*5-normal with respect to lactic acid —

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