ELECTROLYSIS AND ELECTRO-CHEMISTRY. 235 



Diffusion of Electrolytes. — An application of the theory of ionic velocity 

 due to Nernst' and Planck - enables us to calculate the diffusion constant 

 of dissolved electrolytes. According to the molecular theory, diffusion is 

 due to the motion of the molecules of the dissolved substance through the 

 liquid. When the dissolved molecules are uniformly distributed, the 

 osmotic pressure will be the same everywhere throughout the solution, 

 but if the concentration varies from point to point, the pressure will vary 

 also. There must, then, be a relation between the rate of change of the 

 concentration and the osmotic pressure gradient, and thus we may consider 

 the osmotic pressure gradient to be analogous to a force driving a body 

 through a viscous medium. 



In the cases of non-electrolytes and of all non-ionised molecules this 

 analogy completely represents the facts, and the phenomena of diffusion 

 can be deduced from it alone. But the ions of an electrolytic solution can 

 move independently through the liquid, even when no current flows, as the 

 truth of Ohm's law for electrolytes indicates. They will therefore diffuse 

 independently, and the faster ion will travel quicker into pure water in 

 contact with a solution. The ions carry their charges with them, and, as a 

 matter of fact, it is found that, in general, water in contact with a solu- 

 tion takes with respect to it a positive or negative potential, according 

 as the positive or negative ion travels the faster. 



This process will go on until the simultaneous separation of electric 

 charges produces an electrostatic force strong enough to prevent further 

 separation of ions. We can therefore calculate the rate at which the 

 salt as a whole wiU diffuse by examining the conditions for a steady state, 

 in which the ions diffuse at an equal rate, the faster one being restrained 

 and the slower one urged forward by the electric forces. 



Let us imagine that we have an aqueous solution of some electrolyte 

 at the bottom of a tall glass cylinder with pure water lying above it. In a 

 layer of liquid at a height x let the concentration {i.e. the number of 

 gram-molecules per cubic centimetre) be c, and the osmotic pressure p. 

 At a height x + dx these become c—dc and p—dj) respectively. The 

 volume of the layer cut off by horizontal planes at these heights is qdx, 

 where q is the area of cross-section, and this volume contains cqdx 

 gram -molecules of electrolyte. The difference of osmotic pressure between 

 the planes is dp, so that, on our analogy, we must imagine that the 

 force acting on the layer is —qdp (the negative sign being taken 

 because the force is in the direction in which x> decreases) and the 



force on one gram-molecule is — 1-. Now from the velocities of the 



c dx 



two ions under unit potential gradient, as found by Kohlrausch's theory, 



it is easy to deduce the velocity with which they will travel when unit 



force acts on them. Let us call these velocities U and V for the kation 



and anion respectively. The actual velocities in our case will therefore 



be — — -^ and — — f, so that the amounts passing any cross-section 

 c dx c dx 



of the cylinder in a time dt are 



-Vq^ dt and-Vo ^ dt. 

 dx dx 



> Zeits. physikal. Cliem. vol. ii. p. 613. Account in Nemst's Tkeoretische Chemie, or 

 Whetham's Solution and Electrolysis. 

 2 Wied. Ann. 1890, vol. xl. p. 561. 



