BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 213 



instantaneous reaction between permanganic acid and manganous salt ; for when the two 

 solutions are mixed, the deep-red colour of the former is at once destroyed and the liquid 

 becomes dark brown. The action of these two substances under constant conditions takes 

 place presumably according to but one equation, and gives rise to but one oxidized 

 product. From the results of our experiments on the "Variation of Manganous 

 Sulphate," p. 195, and the reaction of the two substances when oxalic acid is not present, 

 this product appears to be manganic binoxide. But in the experiment just related with 

 the three equivalent solutions, the liquid produced by acting on permanganate with a 

 great excess of manganous sulphate nearly identified itself by its rate of decomposition 

 with that containing the salt of the proto-sesquioxide, while it differed in this respect 

 from that into which binoxide had been introduced. 



The account of the changes occurring under the circumstances of the two sets of expe- 

 riments, Tables IX. and X., to which these observations appear to lead, is the following. 



By the reaction of permanganic acid on a great excess of manganous sulphate there 

 is formed at once manganic binoxide ; we may therefore consider this oxide to be con- 

 tained in the liquid at the moment of starting the reaction. It finds itself in presence 

 of two substances, both of which act gradually^ upon it, oxalic acid and manganous 

 sulphate, the latter producing an intermediate oxide, probably the proto-sesquioxide, 

 which is also reducible by oxalic acid. It is possible that other oxides besides these 

 may be formed, but it is almost certain from our experimental results that the action is 

 not more simple than this. At the end of each experiment both these oxides are alike 

 instantaneously reduced by hydriodic acid, and thus measured conjointly. 



A mathematical discussion of various theoretical points that have been raised in the 

 course of our experiments is appended to this account of them. It is there shown that 

 the equation embodying the above hypothesis is 



where a is the amount of binoxide present in the solution at the commencement of the 

 action, a the fraction of it which disappears in a unit of time by the action of the 

 oxalic acid, /3 the fraction of it converted into the other oxide, and y the fraction of this 

 lower oxide which disappears in a unit of time. 



In the following Tables some of the numbers obtained in the preceding experiments 

 (pp. 206 & 210) are compared with those calculated from equations of this form. It will 

 be seen that in general the three fractions upon which the whole rate of action depends 

 increase as the sulphuric acid is increased, and that a increases more rapidly than y ; 

 a being first less than y, then equal to it, and finally greater. 



The number and exactness of our experimental results are not, however, sufficient to 

 make the calculation of the three constants in these equations more than approximate, 

 and thus no such comparison can be made of the rates of change with different amounts 

 of sulphuric acid as might serve to reveal how these quantities are related. In the first 

 of the following Tables the residues of the two oxidizing substances at the time of each 



