Dispersion in Chromatography Columns - Resistance to Mass Transfer Dispersion > Page 27

On average, a molecule will remain in the mobile phase a time (ta) before it is adsorbed. During this time, it will be moving at the mean velocity of the mobile phase (u) and will, thus, move a distance (uta). Thus, in moving a distance , the total number of adsorptions will be  and the total number of steps including the adsorption and desorption steps will be . It also follows, from the Random Walk Model  that,

                               where   

It is now necessary to determine the average step length (s) to obtain an expression for (H).

The step length is that length moved by the molecule relative to that of the zone center and, while the molecule has move (vta) during time (ta), the zone center has also moved. Now, it was shown in the Plate theory that the zone velocity is where (k") is the dynamic capacity ratio of the solute.

 Consequently, .

  and,     ,

      i.e.,