60 VELOCITY OF REACTION, AND 



The second equation [2] of p. 59 may be written 



\ / 



or since dx= - d (a - x) 



~7 \f)~ = fC Cltm 



(a xy 



which on integrating yields 



= kt + const., 



a-x 



as before when t = Q, x = Q, hence - = const., and on subtracting the 

 two equations 





or 



or 7 \ 



a (a-x) 



and for the reaction constant (7r) 



x 



t . a . (a-x) 



These reactions, where two substances undergo change in con- 

 centration on the left-hand side of the equation of reaction when 

 the reaction is proceeding from left to right, are spoken of as bi- 

 molecular reactions. The best known examples are where an ester, 

 containing two monad radicles, such as ethyl-acetate, is saponified 

 by an alkali. The reaction is different from that with an acid, for 

 the alkali as w r ell as the ester is changing its concentration during 

 the reaction, while in the hydrolysis by the acid, the hydrogen ion 

 concentration which affects the change in the ester remains constant, 

 and the water produced being merely added to the water of the 

 solvent has no effect on the progress of the reaction. 



Tri-molecular reactions and higher are rare, from the tendency of 

 the reaction to break down into stages. For a tri-molecular reaction, 

 in which three molecules react together on the left-hand side of the 

 equation, the equation of velocity, supposing the three substances 

 present in equi-molecular proportions at the outset, would be 



~ = k(a-xY, 



