1904.] Catalysis ~by Colloidal Metals and similar Substances. 361 



reaction velocity. It is evident that if a given volume were dis- 

 tributed in pieces of larger surface and more especially in flat pieces 

 or in pieces of smaller diameter, a much larger reaction velocity would 

 arise. 



We again assume each particle to be surrounded by an adhering 

 film of liquid, in which no convection occurs, in such a manner that 

 the greater the amount of stirring or motion in the solution, the 

 smaller the thickness of this layer. On the outside of the film the 

 concentration may be considered to have a definite value which is 

 not exceeded in any part of the solution. If the film is exceedingly 

 thin, then the flow of solute to the particle will continually be very 

 great and roughly inversely proportional to the thickness of the film. 

 If the latter, however, be thick, then, as will be seen in the sequel, 

 the flow of solute to the particle rapidly decreases to a value corre- 

 sponding to a permanent distribution of concentration in such a 

 manner that this flow becomes practically independent of the thickness 

 of the layer and only depends on the concentration outside. 



It should be pointed out here that a limit is set to the thickness 

 of the films by the fact that their total volume must be smaller than 

 that of the liquid. If each layer with its enclosed particle forms a 

 sphere of radius R, and N is the number of particles per unit volume, 

 we, therefore, have the inequality 



|7rR 3 N<l (3). 



The concentration outside the films, as will be seen in the sequel, 

 is practically the average concentration of the liquid. If, therefore, 

 the particles are far apart, we shall by always assuming the 

 permanent flow to take place, corresponding to a very (infinitely) 

 thick layer, on the outside of which the average concentration of the 

 liquid is maintained, obtain values for reaction velocity, which may 

 be taken to be those belonging to the minimum conceivable amount 

 of convection. 



Deduction of a Formula for the Reaction Velocity Corresponding to a 

 Minimum Amount of Convection. We have to deal with the following 

 case : A sphere of given radius r is immersed in a solution of the 

 concentration Co. On its surface the concentration is kept continually 

 at zero, and at a distance R from its centre the concentration D is 

 always to be found, which is not exceeded in any part of the liquid. 

 The smallest conceivable amount of solute, Fdt, that could under 

 these conditions flow to the sphere in the time dt, is the value which 

 Vdt would have if the conditions we have assumed had already been 

 in operation for an infinite period of time. This would mean that 

 a permanent state had been established, and as it is our object to 

 find a minimum value for the substance removed, the first part of 

 our problem consists in determining J?dt corresponding to the 

 permanent state. 



