614 REPORT — 1897. 



A = A', it is found tliat if tlie reaction proceeds entirely to an end, the velocity is 

 directly proportional to c, the concentration of A, But since all reactions of thia 

 nature do not go on at the same rate when their concentrations are the same, 

 another factor must be introduced which is distinctive for each reaction. The 

 velocity is therefore V = k.c, where A; is a constant for each separate reaction. It is 

 called the velocity constant. The concentration of c of course diminishes as the 

 reaction proceeds, and therefore the velocity V also diminishes ; but if we start 

 with a known concentration a, and determine the amount x, which has been 

 changed after a definite interval of time t, the concentration will now be a — x, 

 and the amount changed in the next very small interval of time dt is called dx, 

 and is proportional to the concentration at that point, so that the velocity is 



— = Z;(a-.r) ; x of course varies between the values and a, so that the above 

 equation gives on integration h =— log 



t a—x 



This is the equation for a mono-molecular reaction, and it can be employed to 

 discover whether a particular reaction is mono-molecular or not. For this purpose 

 experiments are made with several different values of the initial concentration a, 

 and from each of these a large number of observations of x and its corresponding 

 time t are obtained. When these experimental values for a, x and t are substituted 

 in the equation 



7 T , a 



t 



■> 



If the reaction be really mono-molecular they will all give the same value for k. 

 If they do not it is not a mono-molecular reaction. 

 When the reaction is bi-molecular — for example, 



A + B = A' + B' 



it is found that the velocity is proportional to the product of the concentrations cf 

 A and B, i.e., 



V = kc^c.;^ or - ' = k{a - x) {h- x) ; 



and if it ia poly-molecular, e.g., 



A + B + C + . . . . = A' + B' + C + ." . . . 



the velocity is proportional to the product of the concentrations of A, B, 0, &c., 

 i.e., 



dv 

 Y = kc^c.c^ . . . ox ^ = k (a- .r) (6 - .i) (c - x) . , , 



If, in this last case, A and B are the same, the expression for the velocity becomes 



-^ = k {a — x)" (c — .i) . . , 



which shows that when two, or generally n, molecules of a substance take part in 

 the reaction, the concentration of that substance must be raised to the n"* power 

 in the expression for the velocity of the reaction, e.g., in the reaction 



7nA + «B = J? A' + jB' 

 V - A-Cj" c/ or p' = k(a - a;)"' (« - a-)", 



on substituting the observed values of «, b, x, and t in the integrated form of this 

 equation it can be found by trial and error what the correct values of m and n are 

 which always give a constant value for k. 



A mono-molecular reaction ought to give a constant with the equation of the first 



