THE CLAKIFICATION OR DEFECATION OF THE JUICE. 



Inversion. Cane sugar, under the influence of acids, is quantitatively 

 converted into dextrose and levulose under the equation 



CxaH^O^+H^CeH^Oe + CeH^Qe 

 Cane Sugar Water Dextrose Levulose 



Under the ionic hypothesis an acid in solution is conceived as being in 

 part dissociated into hydrogen ions and into acid-radical ions ; thus hydrochloric 

 acid in solution is taken as consisting of undissociated HC1, and of H ions, and 

 of Cl ions, the former carrying a -j- and the latter a charge of electricity. 

 The inversion of cane sugar under the same hypothesis, and, indeed, all the 

 particular properties of an acid, are held to he due to the hydrogen ions. A 

 strong acid is one which is largely, and a weak acid is one which is slightly, 

 dissociated. The chief laws under which the inversion of cane sugar proceeds 

 are summarized below. 



1. Rate of Inversion. "When all other conditions are unchanged, the 

 rate of inversion is proportional to the active mass, i.e., when the temperature 

 and the concentration of the acid are unchanged, a 20 per cent, solution of 

 cane sugar inverts twice as fast as a 10 per cent, solution. Developed 

 mathematically, this statement becomes reduced to the following form : 



In a sugar solution let there be a parts of sugar present ; in a small interval 

 of time, t, let x parts be inverted. There are now present a x parts of cane 

 sugar. Since the rate of change is proportional to the active mass, 



d x 



= k (a x) where 1c is a constant. 



d t 



"Whence, by integration log. = k t 



d x 



I a 



-J lo s- j-n = k 



The constant k gives a means of comparing the strength of different 

 acids, or, under the ionic hypothesis, the degree of dissociation. This law was 

 found experimentally by "Wilhelmy in 1350, and developed on a priori reasoning 

 by Guldberg and Waage in 1867. It forms a typical instance of the 

 universal law that rate of chemical change is proportional to the active mass. 



As definitely applied to a sugar solution in acid medium, let the total 

 change in polarization due to inversion be- a; then a is proportional to the 

 amount of sugar originally present. Let the fall in polarization, i.e., the 

 algebraical difference between the initial reading and the reading after any 

 time interval, t, be x ; then x is proportional to the amount of sugar inverted. 

 The calculation of the constant will then appear as in the following example. 



Initial reading, 40; reading after complete inversion, 12; total 

 change = # = 52; reading after 60 minutes, 30; proportionate amount of 

 sugar inverted = # = 40 30 = 10. Then 



| " Constant = ^-log. ^- Q = -001546. . 



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