## Thermodynamic Considerations

In order to understand the thermodynamic considerations of the separation process, we need to look at the basic equations which describe the retention of a solute and relate the parameters of retention time, retention volume, and capacity factor to the thermodynamic solute distribution coefficient.

Figure 1 shows a model chromatogram for the separation of two compounds. The time required for the elution of a retained compound is given by tr, the retention time, and is equal to the time the solute spends in the moving mobile phase plus the time spent in the stationary phase, not moving. If a solute is unre-tained and has no interaction with the stationary phase, it will elute at to, the hold-up time or dead time, which is the same time required for the mobile-phase solvent molecules to traverse the column.

Another fundamental measure of retention is retention volume, Vr. It is sometimes preferable to record values of Vr rather than tr, since tr varies with the flow rate F, while Vr is independent of F. If we wish to describe the volume of mobile phase required to elute a retained compound, then the retention volume is the product of the retention time and the mobile-phase flow rate.

Vo is a measure of the total volume of space available to the mobile phase in the system and correlates to to as the volume necessary to elute an unretained compound.

The most commonly used retention parameter in high-performance liquid chromatography (HPLC) is the capacity factor, k'. While the distribution coefficient, K, describes the concentration ratios, the capacity factor, k', is the ratio of amounts of solute in each phase.

' _ moles of X in stationary phase _ [X]sVs _ KVs k — — — (4)

moles of X in mobile phase [X]mVm Vm

Equation (4) shows that the capacity factor is directly proportional to Vs, and so k' for each solute changes with the stationary-phase loading on the silica support.

The capacity factor is conveniently measured from retention parameters, since k' also describes the amount of time the solute spends in each phase.

to Vo

Rearrangement of Eq. (5) gives

The retention volume can then be related to the capacity factor by substituting Eq. (4) for k' in Eq. (6), where Vm — Vo.

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