Ratio capacity

R distillation column reflux ratio (-) or heat capacity ratio of 1-2 shell-and-tube heat exchanger (-)... 

Exponential Methods Rapid capital-cost estimates can be made by using capacity-ratio exponents based on existing cost data of a company or drawn from pubhshed correlations. 

Figure 1. Approximate heat-capacity ratios of hydrocarbon gases.

An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

The silica dispersion showed the smallest retention volume. It should be noted, however, that the authors reported that the silica dispersion required sonicating for 5 hours before the silica was sufficiently dispersed to be used as "pseudo-solute". The retention volume of the silica dispersion gave the value of the kinetic dead volume, /.e., the volume of the moving portion of the mobile phase. It is clear that the difference between the retention volume of sodium nitroprusside and that of the silica dispersion is very small, and so the sodium nitroprusside can be used to measure the kinetic dead volume of a packed column. From such data, the mean kinetic linear velocity and the kinetic capacity ratio can be calculated for use with the Van Deemter equation [12] or the Golay equation [13]. 

Equation (16) was first developed by Purnell [3] in 1959 and is extremely important. It can be used to calculate the efficiency required to separate a given pair of solutes from the capacity factor of the first eluted peak and their separation ratio. It is particularly important in the theory and practice of column design. In the particular derivation given here, the resolution is referenced to (Ra) the capacity ratio of the first... 

Equation (18) displays the relationship between the column efficiency defined in theoretical plates and the column efficiency given in effective plates. It is clear that the number of effective plates in a column is not aii arbitrary measure of the column performance, but is directly related to the column efficiency as derived from the plate theory. Equation (18) clearly demonstrates that, as the capacity ratio (k ) becomes large, (n) and (Ne) will converge to the same value. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

Figure 20. Graph of Peak Capacity against Capacity Ratio...

It has also been shown that the effect of sample volume on peak width will be most significant for the early peaks (the most narrow peaks). In addition, the degrading effect of sample volume will progressively decrease as the capacity ratio of the peak becomes larger. However, the resolution of both late and early peaks are equally important and, consequently, the limiting sample volume will be that which restrains the dispersion of the first peak to 5% or less. 

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

Table 1. Capacity Ratios and Peak Capacities for Detectors of...

The explicit form of those equations that satisfy the preliminary data criteria, must then be tested against a series of data sets that have been obtained from different chromatographic systems. As an example, such systems might involve columns packed with different size particles, employed mobile phases or solutes having different but known physical properties such as diffusivity or capacity ratios (k"). 

In order to relate the value of (H) to the solute diffusivity and, consequently, to the molecular weight according to equation (11), certain preliminary calculations are necessary. It has already been demonstrated in the previous chapter (page 303) that the dynamic dead volume and capacity ratio must be used in dispersion studies but, for equation (11) to be utilized, the value of the multipath term (2Xdp) must also be... 

If a series of solutes is chosen from the group determined and all have approximately the same capacity ratio (k") but significantly different values for the diffusivity (Dm) then equation (11) reduces to... 

Katz then tested the assumption that the dispersion of a high molecular weight solute such as a protein/peptide was largely independent of its capacity ratio, but strongly dependent on its relatively low diffusivity. That is. 

However, any given column operated at a specific flow rate will exhibit a range of efficiencies depending on the nature and capacity ratio of the solute that is chosen for efficiency measurement. Consequently, under exceptional circumstances, the predicted conditions for the separation of the critical pair may not be suitable for another pair, and the complete resolution of all solutes may still not be obtained. 

The capacity ratio of the first solute of the critical pair. 

Column design involves the application of a number of specific equations (most of which have been previously derived and/or discussed) to determine the column parameters and operating conditions that will provide the analytical specifications necessary to achieve a specific separation. The characteristics of the separation will be defined by the reduced chromatogram of the particular sample of interest. First, it is necessary to calculate the efficiency required to separate the critical pair of the reduced chromatogram of the sample. This requires a knowledge of the capacity ratio of the first eluted peak of the critical pair and their separation ratio. Employing the Purnell equation (chapter 6, equation (16)). 

It should be noted that Purnell s equation utilizes the thermodynamic capacity ratio calculated using the thermodynamic dead volume. 

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