Movements A Case of the Random Walk

Long before the movements of ions in solution were analyzed, the kinetic theory of gases was developed and it involved the movements of gas molecules. The overall 

It would be of interest to have an idea of the path of such a gas molecule in the course of time. One might think that the detailed paths of all the particles could be predicted by applying Newton s laws to the motions of molecules. The problem, however, is obviously too complex for a practical solution. To use the laws ofmotion requires a knowledge of the position and velocity of each particle and even in 1 mole there are 6.023 x 10 (the Avogadro number) particles. 

Instead of mirrors, one could equally consider pistons of a microscopic size, large enough to be seen with the aid of a microscope but small enough to display motions due to collisions with molecules. Such small pistons are present in nature. A colloidal particle in a liquid medium behaves as such a piston if it is observed in a microscope. It shows a haphazard, zigzag motion as shown in Fig. 4.12. The irregular path of the particle must be a slow-motion version of the random-walk motion of the molecules in the liquid. 

One has therefore a picture of the solvated ions (in an electrolytic solution) in ceaseless motion, perpetually colliding, changing direction, staggering hither and thither from site to site. This is the qualitative picture of ionic movements. 

The Mean Square Distance Traveled in a Time fby a Random-Walking Particle 

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