BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 211 



been unsuccessful, and we have been compelled in consequence to leave the examina- 

 tion of this reaction, and seek for a simpler case of chemical change. We may, how- 

 ever, in concluding this part of our work, show, first, from independent experiments, 

 that we have probably been dealing with more than one reaction ; and secondly, that 

 numbers agreeing with those of all the experimental series may be calculated from 

 equations expressing the hypothesis that three simultaneous changes take place. 



In determining the amount of free iodine at the end of each experiment, some diffi- 

 culty was experienced from the rapid return of the blue colour after its removal by the 

 last drop of hyposulphite, and it was found necessary to allow as short a time as possible 

 to elapse between the addition of potassic iodide and the determination. The con- 

 ditions of this gradual oxidation of hydriodic acid were afterwards examined, and it was 

 found that the action was due neither to the oxalic acid nor the manganous sulphate, 

 nor any other of the reagents employed, but occurred only in the fluid in which the 

 gradual oxidation of oxalic acid had taken place, and that moreover the rate of its 

 occurrence depended upon the quantity of oxalic acid thus oxidized. Some experi- 

 ments were made in which this secondary oxidation was allowed to reach its limit. The 

 action of the air, which in presence of manganous salt, when the solution is let stand 

 for many hours, is apt to be considerable, was rendered as small as possible by boiling 

 out the water used and keeping the liquid under carbonic acid ; a correction for it was 

 also obtained from a comparative experiment. It appeared that the secondary oxida- 

 tion did not exceed one-sixth of the primary, and bore to it often a still smaller pro- 

 portion, while at the same time its amount was always sufficient to leave no doubt as 

 to the reality of the phenomenon. The available oxygen of the permanganate is thus 

 finally distributed in two ways, part of it remaining in a form in which it acts gradually 

 on hydriodic acid, and another larger part having no such action. What oxidizing 

 substance the colourless solution still contains, whether a less reducible salt of manga- 

 nese, or some compound produced, as is most likely, by the gradual oxidation of oxalic 

 acid, we do not know ; but the fact that some substance is formed besides a manganous 

 salt, carbonic acid, and water, is certain. If, however, two products, or any number of 

 different products, are formed by the action, according to different equations, of one 

 oxidizing substance — binoxide of manganese, for example, — the quantities of this sub- 

 stance remaining after equal intervals of time should still be in geometric progression ; 

 for the amounts of each of the products which is formed at any given time is propor- 

 tional to the whole amount of binoxide present in solution at that time, and in conse- 

 quence the amount of binoxide which disappears owing to the formation of each of the 

 products is also proportional to the whole amount of binoxide present. 



Let (?,y, d^, . . . d^ be the amounts of binoxide which disappear during an infinitesimal 



d u d ^j d u 

 time dx, owing to the formation of n different products, then "^'X^'"^ ^^^ ^^e 



amounts of binoxide which disappear in a unit of time owing to their formation, and 

 each of these is proportional to the whole amount y of binoxide present at a time x ; 



2g2 



