440 PRINCIPLES OF CHEMISTRY 



not added to the mixture but proceed from it, then if k represent the 

 coefficient of the rate of the action of MX on NY and if k' represent 

 the same coefficient for the pair MY and NX, then we shall have at 

 the moment when the decomposition equals x a measure of action for 

 the first pair : k (1 x) (1 - x) and for the second pair k'xx, and a 

 state of equilibrium or limit will be reached when k (I #j 2 = k'x*, 

 whence the ratio k/k* = [#/(! x )]*' Therefore in the case of the 

 action of alcohol on an acid, when x = |, the magnitude k/k' = 4, 

 that is, the reaction of the alcohol on the acid is four times as fast as 

 that of .the ethereal salt on water. If the ratio k/k' be known, then 

 the influence of mass may be easily determined from it. Thus if instead 

 of one molecule of alcohol two be taken, then the equation will be 

 k(2 #)(! x) = k'xx, whence x = 0'85 or 85 per cent., which is close 

 to the result of experiment. Jf 300 molecules of alcohol be taken, then 

 x proves to be approximately 100 per cent., which is also found to be the 

 case by experiment. 26 



But it is impossible to subject the formation of salts to any process 

 directly analogous to that which is so conveniently effected in etherifi- 

 cation. Many efforts have, however, been made to solve the problem 

 of the measure of reaction in this case also. Thus, for example, 

 Khichinsky (1866), Petrieff (1885), and many others investigated the 

 distribution of metals and haloid groups in the case of one metal and 

 several haloids taken in excess, as acids ; or conversely with an excess 

 of bases, the distribution of these bases with relation to an acid ; in 

 cases where a portion of the substances forms a precipitate and a 

 portion remains in solution. But such complex cases, although they in 

 general confirm Berthollet's teaching (for instance, a solution of silver 

 nitrate gives some silver oxide with lead oxide, and a solution of 

 nitrate of lead precipitates some lead oxide under the action of 

 silver oxide, as Petrieff demonstrated), still, owing to the complexity 

 of the phenomena (for instance, the formation of basic and double salts), 

 they cannot give simple results. But much more instructive and 

 complete are researches like those made by Pattison Muir (1876), 

 who took the simple case of the precipitation of calcium carbonate, 

 CaCO 3 , from the mixture of solutions of calcium chloride and sodium or 

 potassium carbonate, and found in this case that not only was the 



2C From the above it follows that an excess of acid should influence (he reaction like 

 an excess of alcohol. It is in fact shown by experiment that if two molecules ot 

 acetic acid be taken to one molecule of alcohol, 84 p.c. of alcohol is etherified. If with 4 

 large preponderance of acid or of alcohol certain discrepancies are observed, their cause 

 must be looked for in the incomplete correspondence of the 'Conditions and external 

 Influences. 



