568 Dr. George Senter. The Role of Diffusion in the [Mar. 7 



particles, we find, from Sand's Equation (19), p. 367, that the amount 

 removed by each particle in the time dt is 



Ydt = 4dbry (D - C r ) (ft (3), 



where k is the diffusion coefficient of hydrogen peroxide, r is the 

 radius of the particle, and y = R/R - r, where R is at such a distance 

 from the [particle that the concentration there is D, which does not 

 differ appreciably from the average concentration in the solution.* The 

 amount removed from unit volume containing N particles (where 

 4/3?rr 3 N = v) is N times as great, or 



L 2 



where L = 2r the diameter of a particle. 

 Hence K 



Further, since KD = K Cr, we have 



_ y 

 "D 



(5). 



(6). 



If K is infinite (Nernst's hypothesis) C r = 0, and from Equation (5) 

 we obtain for K, which in this case is KD, the value 



K D = 12%/L2 (7), 



which Sand shows is at least 16 times as large as the velocity-constant 

 determined by Bredig. Hence, if Sand's value for K^ be accepted, we 

 must conclude that C r is not zero, and that experiment therefore does 

 not justify Nernst's hypothesis. 



From Equations (5) and (7) we can readily find the relation between 

 C r and D. If we deal with the case where K D is 16 times as large as 

 the observed velocity-constant K, it is obvious that 



or C r = 



In general, if K D is n times as large as K, we have 



(8). 



The way in which the observed velocity of a heterogeneous chemical reaction 

 depends upon the relative values of the " diffusion " constant and the " chemical " 

 velocity constant. From Equation (8) we find that if K D is great in 

 comparison with K, the concentration at the surface of the particles, 

 with a minimum of stirring, is practically equal to the average concen- 

 tration in the solution. Since K C r = KD, it follows that in this case 

 * Sand, loc. cit., p. 362. 



