5. The retention factor, kA, for solute A is related to the rate at which A migrates through a column.
It is the amount of time a solute spends in the stationary phase relative to the time it spends in mobile phase.

6. As shown in Figure 31-9, tR and tM are easily obtained from a chromatogram.
A retention factor much less than unity means that the solute emerges from the column at a time near that of the void time.
When retention factors are larger than perhaps 20 to 30, elution times become inordinately long.

7. Ideally, separations are performed under conditions in which the retention factors for the solutes of interest in a mixture lie in the range between 1 and 5.
Ideally, the retention factors for analytes in a sample are between 1 and 5.

8. In gas chromatography, retention factors can be varied by changing the temperature and the column packing.
In liquid chromatography, retention factors can often be manipulated to give better separations by varying the composition of the mobile phase and the stationary phase.

9. The selectivity factor, a, for solutes A and B is defined as the ratio of the distribution constant of the more strongly retained solute (B) to the distribution constant for the less strongly held solute (A).
The selectivity factor for two analytes in a column provides a measure of how well the column will separate the two.

11. 31E-5 Band Broadening and Column Efficiency
The amount of band broadening that occurs as a solute passes through a chromatographic column strongly affects the column efficiency.
Before defining column efficiency in more quantitative terms, let us examine the reasons that bands become broader as they move down a column.

12. Rate Theory of Chromatography
The rate theory of chromatography describes the shapes and breadths of elution bands in quantitative terms based on a random-walk mechanism for the migration of molecules through a column.
Why bands broaden and what variables improve column efficiency?

13. Examineing chromatograms, the elution peaks look very much like the Gaussian or normal error curves.
The typical Gaussian shape of a chromatographic band can be attributed to the additive combination of the random motions of the various molecules as they move through the column.

14. In the narrow zone, the injection width (no column) is not the limiting factor determining the overall width of the band that elutes.
It is important to realize that the widths of eluting bands can never be narrower than the width of the injection zone.
Consider a single solute molecule as it undergoes many thousands of transfers between the stationary and the mobile phases during elution.
Residence time in either phase is highly irregular as transfer from one phase to the other is different for different molecules.

15. Therefore, the residence time in a given phase may be very short after some transfers and relatively long after others.
Recall that movement through the column can occur only while the molecule is in the mobile phase.
As a result, certain particles travel rapidly by virtue of their accidental inclusion in the mobile phase for a majority of the time while others lag because they happen to be incorporated in the stationary phase for a greater-than-average length of time.
The result of these random individual processes is a symmetric spread of velocities around the mean value, which represents the behavior of the average analyte molecule.

16. As shown in Figure 31-10, some chromatographic peaks are nonideal and exhibit tailing or fronting.
In the former case, the tail of the peak, appearing to the right on the chromatogram, is drawn out while the front is steepened.
With fronting, the reverse is the case. A common cause of tailing and fronting is a distribution constant that varies with concentration.

17. Fig. 31-10 Illustration of fronting and tailing in chromatographic peaks.

18. Fronting also arises when the amount of sample introduced onto a column is too large or called overloading.
Distortions of this kind are undesirable because they lead to poorer separations and less reproducible elution times.
Usually tailing and fronting are assumed to be minimal in good systems.

19. A Quantitative Description of Column Efficiency
Two related terms are widely used as quantitative measures of chromatographic column efficiency:
plate height, H, and
(2) plate count or number of theoretical plates, N.
The two are related by the equation

20. where L is the length (usually in centimeters) of the column packing.
The efficiency of chromatographic columns increases as the plate count N becomes greater and as the plate height H becomes smaller.

21. Enormous differences in efficiencies are encountered in columns as a result of differences in column type and in mobile and stationary phases.
Efficiencies in terms of plate numbers can vary from a few hundred to several hundred thousand, while plate heights ranging from a few tenths to one thousandth of a centimeter or smaller are not uncommon.

22. The breadth of a Gaussian curve is described by the standard deviation s and the variance s2.
Because chromatographic bands are often Gaussian and because the efficiency of a column is reflected in the breadth of chromatographic peaks, the variance per unit length of column is used by chromatographers as a measure of column efficiency.
That is, the column efficiency H is defined as

23. This definition of column efficiency is illustrated in Figure 31-11, which shows a column having a packing L cm in length (Figure 31-11a) and a plot (Figure 31-11b) showing the distribution of molecules along the length of the column at the moment the analyte peak reaches the end of the packing (that is, at the retention time).
In fact, the plate height can be thought of as the length of column that contains a fraction of the analyte that lies between L and L±s.

24. Fig. 31-11 Definition of plate height H = s2/L
Fig Definition of plate height H = s2/L. In (a), the column length is shown as the distance from the sample entrance point to the detector. In (b), the Gaussian distribution of sample molecules is shown.

25. What is the Source of the Terms Plate and Plate Height?

26. The 1952 Nobel Prize was awarded to two Englishmen, A. J. P
The 1952 Nobel Prize was awarded to two Englishmen, A.J.P. Martin and R.L.M. Synge, for their work in the development of modern chromatography.
In their theoretical studies, they adapted a model that was first developed in the early 1920s to describe separations on fractional distillation columns.
Fractionating columns, which were first used in the petroleum industry for separating closely related hydrocarbons, consist of numerous interconnected bubble-cap plates at which vapor-liquid equilibria is established when the column is operated under reflux conditions.

27. Martin and Synge treated a chromatographic column as if it were made up of a series of contiguous bubble-cap-like plates within which equilibrium conditions always prevail.
This plate model successfully accounts for the Gaussian shape of chromatographic peaks as well as for factors that influence differences in solute-migration rates.

28. The plate model does not adequately account for zone broadening, however, because of its basic assumption that equilibrium conditions prevail throughout a column during elution.
This assumption can never be valid in the dynamic state of a chromatographic column, where phases are moving past one another fast enough that there is not adequate time for equilibration.

29. Because the plate model is not a very good representation of a chromatographic column, it is strongly advised
to avoid attaching any special significance to the terms plate width and plate height and
(2) to view these terms as designators of column efficiency that are retained for historic reasons only and not because they have physical significance.
Unfortunately, these terms are so well entrenched in the chromatographic literature that their replacement by more appropriate designations seems unlikely.

30. Determining the Number of Plates in a Column
The number of theoretical plates, N, and the plate height, H, are widely used in the literature and by instrument manufacturers as measures of column performance.
Fig shows how N can be determined from a chromatogram.
In the figure, the retention time of a peak tR and the width of the peak at its base W (in units of time) are measured.
It can be shown that the number of plates can then be computed by the relationship

32. 31E-6 Variables Affecting column Efficiency
Band broadening reflects a loss of column efficiency.
The slower the rate of masstransfer processes occurring while a solute migrates through a column, the broader the band at the column exit.
Some of the variables that affect mass-transfer rates are controllable and can be exploited to improve separations.
Table 31-5 lists the most important of these variables.

34. Effect of Mobile-Phase Flow Rate
The extent of band broadening depends on the length of time the mobile phase is in contact with the stationary phase, which in turn depends on the flow rate of the mobile phase.
For this reason, efficiency studies generally have been carried out by determining H (Eq ) as a function of mobile phase velocity.
The plots for liquid chromatography and for gas chromatography shown in Fig are typical of the data obtained from such studies.

35. Figure 31-13 Effect of mobile-phase flow rate on plate height for
(a) liquid chromatography and (b) gas chromatography.

36. While both show a minimum in H (or a maximum in efficiency) at low linear flow rates, the minimum for liquid chromatography usually occurs at flow rates that are well below those for gas chromatography.
Often these flow rates are so low that the minimum H is not observed for liquid chromatography under normal operating conditions.

37. Linear flow rate and volumetric flow rate are two different but related quantities.
Recall that the linear flow rate is related to the volumetric flow rate by the cross-sectional area and porosity (packed column) of the column (Equations and 31-13).

38. Generally, liquid chromatograms are obtained at lower linear flow rates than gas chromatograms.
Also, as shown in Figure 31-13, plate heights for liquid chromatographic columns are an order of magnitude or more smaller than those encountered with gas chromatographic columns.

39. Offsetting this advantage is the fact that it is impractical to use liquid chromatographic columns that are longer than about 25 to 50 cm because of high pressure drops.
n contrast, gas chromatographic columns may be 50 m or more in length.
As a result, the total number of plates, and thus overall column efficiency, are usually superior with gas chromatographic columns.