Box 23-2 Microscopic Description

A stochastic theory provides a simple model for chromatography.11 The term stochastic implies the presence of a random variable. The model supposes that, as a molecule travels through a column, it spends an average time Tm in the mobile phase between adsorption events. The time between desorption and the next adsorption is random, but the average time is Tm. The average time spent adsorbed to the stationary phase between one adsorption and one desorption is rs. While the molecule is adsorbed on the stationary phase, it does not move. When the molecule is in the mobile phase, it moves with the speed ux of the mobile phase. The probability that an adsorption or desorption occurs in a given time follows the Poisson distribution, which was described briefly in Problem 19-21. 

We assume that all molecules spend total time tm in the mobile phase. This is the retention time of unretained solute. Important results of the stochastic model are  

This is the average time that the solute is bound to the stationary phase during its transit through the column. 

Idealized liquid chromatographic separation of three components. 

A solute can be extracted from one phase into another in which it is more soluble. The ratio of solute concentrations in each phase at equilibrium is called the partition coefficient. If more than one form of the solute exists, we use a distribution coefficient instead of a partition coefficient. We derived equations relating the fraction of solute extracted to the partition or distribution coefficient, volumes, and pH. Many small extractions are more effective than a few large extractions. 

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