368 Hole of Diffusion during Catalysis ty Colloidal Metals, etc. 



extremely great velocity. Such a behaviour is also, it seems, theoreti- 

 cally necessary, for, otherwise, finite differences of chemical potential 

 would occur on the boundary of two phases, i.e., at infinitely near 

 points, which would manifestly lead to infinitely great forces and 

 reaction velocities." 



As is well known, we owe Nernst the calculation of the diffusion 

 coefficient of an electrolyte, which probably forms the most brilliant 

 instance we possess for the deduction of the velocity of a natural 

 process from thermodynamical data. In this case, the force is calculated 

 which may be considered to act upon a g-ion of electrolyte (force due 

 to osmotic pressure) in a solution of uneven concentration, and by 

 assuming the mobility of the ions to be the same, whether under the 

 influence of forces due to difference of concentration, or under that of 

 electric forces, the diffusion coefficient of the electrolyte can be calcu- 

 lated. Here we have an instance to which the considerations quoted 

 above from Nernst apply beyond doubt. We may put the matter in 

 the following form : If a discontinuity of concentration were to occur 

 in a solution, we should have finite differences of thermodynamical 

 potential at infinitely near points, or, in other words, finite amounts of 

 work would become available in order to move a given quantity of 

 solute an infinitely small, or, at least, a very small way. Now, as the 

 work required to overcome internal resistance in moving a finite 

 quantity of solute through an infinitely small stretch of solution is 

 infinitely small, a condition such as the one considered would lead to 

 an infinite flow of solute. Similarly, if a solid be brought together with 

 its unsaturated solution, finite amounts of free energy are available to 

 dissolve a given quantity. Now, in this case, although it is not a priori 

 certain, yet it is exceedingly probable that the work is practically 

 infinitely small which is necessary to overcome internal resistance in 

 transferring substance an infinitely small distance from the solid to the 

 liquid phase. We may, therefore, conclude that a practically infinite 

 instantaneous flow would occur, and bring about equilibrium on the 

 boundary. Similar considerations probably apply to most physical 

 processes, or, at any rate, to such as are capable under any conditions 

 of occurring in a reversible manner. 



When, however, we turn to chemical processes, we meet with a 

 difference in principle. If we wish to consider a chemical reaction as a 

 transference of atoms over molecular distances, we can no longer say 

 that the work in overcoming internal friction during this transference 

 is a negligible quantity for a finite amount of substance. If it were, it 

 is evident that all chemical reactions in homogeneous systems during 

 which finite amounts of free energy are destroyed, should be instan- 

 taneous. This is, however, not the case. In fact, it is not clear why 

 a chemical reaction should proceed with greater velocity on the 

 boundary of two phases than in the interior of one of them. It is not 



