Capacity factor,

The capacity factor, k, is the product of the phase ratio 0 between stationary and mobile phases in the separator column and the Nernst distribution coefficient, K, 

A more practical quantity for the distribution of the analyte between the two phases is the capacity factor, k, which is defined by the total number of moles of X in the stationary phase over the total number of moles of x in the mobile phase 

By substituting for Vj. and Vjjj in equation (1), a simpler expression for the capacity factor is obtained  

For effective liquid chromatographic separations, a column must have the capacity to retain samples and the ability to separate sample components, efficiently. The capacity factor, k R, of a column is a direct measure of the strength of the interaction of the sample with the packing material and is defined by the expression 

The retention time fg depends on the interaction of the analyte with the stationary phase, but also on the flowrate of the mobile phase and the length of the column. If the mobile phase moves slowly or the column is long, tg is large and so is fg. Thus, fg is not suitable for the comparative characterization of a substance, for example, between two laboratories. It is better to use the capacity factor, also known as the Id value, which relates the net retention time to the dead time  

the k value is independent of the column length and the flow rate of the mobile phase and represents the molar ratio of a particular component in the stationary and mobile phases. Large k values mean long analysis times. 

The capacity factor is, therefore, directly proportional to the volume of the stationary phase (or for adsorbents, their specific surface area in m /g). 

W Peak width of a peak. W = A r with (7 = standard deviation of the Gaussian peak. 

A substance which is not retarded, that is, a substance which does not interfere with 

The distribution of a solute, S, between the mobile phase and stationary phase can be represented by an equilibrium reaction 

Conservation of mass requires that the total moles of solute remain constant throughout the separation, thus 

Solving equation 12.3 for the moles of solute in the stationary phase and substituting into equation 12.2 gives 

Note that this equation is identical to that describing the extraction of a solute in a liquid-liquid extraction (equation 7.25 in Chapter 7). Since the volumes of the stationary and mobile phase may not be known, equation 12.4 is simplified by dividing both the numerator and denominator by V thus 

A measure of how strongly a solute is retained by the stationary phase k ). 

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Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

A solute s capacity factor can be determined from a chromatogram by measuring the column s void time, f, and the solute s retention time, (see Figure 12.7). The mobile phase s average linear velocity, m, is equal to the length of the column, L, divided by the time required to elute a nonretained solute. 

In a chromatographic analysis of low-molecular-weight acids, butyric acid elutes with a retention time of 7.63 min. The column s void time is 0.31 min. Calculate the capacity factor for butyric acid. 

The ratio of capacity factors for two solutes showing the column s selectivity for one of the solutes (a). 

First we must calculate the capacity factor for isobutyric acid. Using the void time from Example 12.2, this is... 

Now that we have defined capacity factor, selectivity, and column efficiency we consider their relationship to chromatographic resolution. Since we are only interested in the resolution between solutes eluting with similar retention times, it is safe to assume that the peak widths for the two solutes are approximately the same. Equation 12.1, therefore, is written as... 

The retention times for solutes A and B are replaced with their respective capacity factors by rearranging equation 12.10... 

Finally, solute A s capacity factor is eliminated using equation 12.11. After rearranging, the equation for the resolution between the chromatographic peaks for solutes A and B is... 

Equations 12.21 and 12.22 contain terms corresponding to column efficiency, column selectivity, and capacity factor. These terms can be varied, more or less independently, to obtain the desired resolution and analysis time for a pair of solutes. The first term, which is a function of the number of theoretical plates or the height of a theoretical plate, accounts for the effect of column efficiency. The second term is a function of a and accounts for the influence of column selectivity. Finally, the third term in both equations is a function of b, and accounts for the effect of solute B s capacity factor. Manipulating these parameters to improve resolution is the subject of the remainder of this section. 

One of the simplest ways to improve resolution is to adjust the capacity factor for solute B. If all other terms in equation 12.21 remain constant, increasing k improves resolution. As shown in Figure 12.11, however, the effect is greatest when the... 

Any improvement in resolution obtained by increasing ki generally comes at the expense of a longer analysis time. This is also indicated in Figure 12.11, which shows the relative change in retention time as a function of the new capacity factor. Note that a minimum in the retention time curve occurs when b is equal to 2, and that retention time increases in either direction. Increasing b from 2 to 10, for example, approximately doubles solute B s retention time. 

The relationship between capacity factor and analysis time can be advantageous when a separation produces an acceptable resolution with a large b. In this case it may be possible to decrease b with little loss in resolution while significantly shortening the analysis time. 

Adjusting the capacity factor to improve resolution between one pair of solutes may lead to an unacceptably long retention time for other solutes. For example, improving resolution for solutes with short retention times by increasing... 

If the capacity factor and a are known, then equation 12.21 can be used to calculate the number of theoretical plates needed to achieve a desired resolution (Table 12.1). For example, given a = 1.05 and kg = 2.0, a resolution of 1.25 requires approximately 24,800 theoretical plates. If the column only provides 12,400 plates, half of what is needed, then the separation is not possible. How can the number of theoretical plates be doubled The easiest way is to double the length of the column however, this also requires a doubling of the analysis time. A more desirable approach is to cut the height of a theoretical plate in half, providing the desired resolution without changing the analysis time. Even better, if H can be decreased by more than... 

A useful guide when using the polarity index is that a change in its value of 2 units corresponds to an approximate tenfold change in a solute s capacity factor. Thus, if k is 22 for the reverse-phase separation of a solute when using a mobile phase of water (P = 10.2), then switching to a 60 40 water-methanol mobile phase (P = 8.2) will decrease k to approximately 2.2. Note that the capacity factor decreases because we are switching from a more polar to a less polar mobile phase in a reverse-phase separation. 

Changing the mobile phase s polarity index, by changing the relative amounts of two solvents, provides a means of changing a solute s capacity factor. Such... 

Selectivity In chromatography, selectivity is defined as the ratio of the capacity factors for two solutes (equation 12.11). In capillary electrophoresis, the analogous expression for selectivity is... 

Haddad and associates report the following capacity factors for the reverse-phase separation of salicylamide (k i) and caffeine... 

Explain the changes in capacity factor. What is the advantage... 

Salt Effects. The definition of a capacity factor k in hydrophobic interaction chromatography is analogous to the distribution coefficient, in gel permeation chromatography ... 

In equation 6, characterizes the settling behavior of the soHd particles or Hquid drops in the suspension, whereas the second part of the right-hand side refers to speed and size of the centrifuge and is expressed by the capacity factor Z g. For a bottle centrifuge, it takes the following form ... 

The capacity factor, Zg, defined by equation 7, is derived from a set of assumptions. An additional assumption is specific to the botde centrifuge. Namely, a particle is considered sedimented when it reaches the surface of the cake without contacting the tube wall. 

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