360 Dr. H. J. S. Sand. The Eole of Diffusion during [Nov. 22, 



and the product of the diffusion coefficient and the time, the average 

 concentration being a function only of the product of the diffusion 

 coefficient and the time.* 



By the application of this theorem to Equation 1, we find that 

 if this equation were the result solely of diffusion in a stationary 

 liquid, then in order that it may conform with Nernst's hypothesis, 

 the constant K must increase by about 2J per cent, per degree. 

 This is a far smaller increase than that actually observed. If, however, 

 convection takes place with increasing efficiency as the temperature 

 rises, there is so far no contradiction with Nernst's hypothesis. 



If the Distribution of the Particles is Fine Enough, the Concentration 

 Throughout the Liquid will be Practically Uniform. It should be pointed 

 out here that if only the disintegration of the particles is great enough 

 and their distribution consequently fine enough, changes of concentra- 

 tion occurring on their surfaces will be transmitted practically 

 instantaneously throughout the liquid by diffusion. In this case, 

 if Nernst's hypothesis is correct, the concentration of the whole 

 solution would be instantaneously reduced to zero, but even if this 

 hypothesis does not hold, the idea of a heterogeneous reaction would 

 demand that the velocity of reaction at a given concentration of the 

 solute should be proportional to the concentration of the catalysing 

 particles. 



If Nernst's Hypothesis Holds, the Reaction Velocities Found by Bredig 

 must be Greater than those Calculated for a, Stationary Liquid. We have 

 thus seen that convection currents play an important part in the 

 processes under discussion, and always tend to accelerate them. 

 The last-named fact opens up a way by means of which to apply a 

 direct test to Nernst's hypothesis. If, on this hypothesis, an ex- 

 pression could be calculated which is equal to or smaller than the 

 reaction velocity under the smallest conceivable amount of convection, 

 this expression should always be smaller than the experimentally 

 found values, and if it is equal to or greater than the latter, this 

 would prove that Nernst's hypothesis must be discarded in the cases 

 under investigation, i.e., that the concentration of hydrogen peroxide 

 on the surfaces of the particles is not permanently maintained at 

 zero. 



As has already been stated, we possess an upper limit for the 

 diameter of the particles, and we shall assume them all to be spheres 

 of this diameter, thus being certain to obtain a minimum value for 



* There is no difficulty whatever in proving this theorem in a purely mathe- 

 matical way, but it becomes immediately obvious, when we remember that we can 

 give the diffusion coefficient any desired value OK by increasing the unit of time 

 to its o-fold value. In the new units any interval of time which before was 

 expressed by t is now given by tja, and in order that concentrations after any real 

 interval of time may remain unaltered, the above tbeorem must hold. 



