Length of column

Under constant pattern conditions the LUB is independent of column length although, of course, it depends on other process variables. The procedure is therefore to determine the LUB in a small laboratory or pilot-scale column packed with the same adsorbent and operated under the same flow conditions. The length of column needed can then be found simply by adding the LUB to the length calculated from equiUbrium considerations, assuming a shock concentration front. 

Figure 3. Graph of Length of Column Traversed by the Solute Before Radial Equilibrium Is Achieved against Particle Diameter...

In an experimental wetted wall column, pure carbon dioxide, is absorbed in water. The mass transfer rate is calculated using the penetration theory, application of which is limited by the fact that the concentration should not teach more than 1 per cent of the saturation value at a depth below the surface at which the velocity is 95 per cent of the surface velocity. What is the maximum length of column to which the theory can be applied if the flowrate of water is 3 cm3/s per cm of perimeter ... 

A is the multiple path term which accounts for different portions of the mobile phase, and consequently the solute, travelling different total distances because of the various routes taken around the particles of stationary phase. The effect is minimized by reducing particle size but increases with length of column... 

Ctl is the mass transfer term and arises because of the finite time taken for solute molecules to move between the two phases. Consequently, a true equilibrium situation is never established as the solute moves through the system, and spreading of the concentration profiles results. The effect is minimal for small particle size and thin coatings of stationary phase but increases with flow rate and length of column or surface. 

The steady-state mass balances for countercurrent flow can be formulated by considering changes in the component mass rates over a differential length of column. In this case, the length is measured from the top of the column (Z = 0) to the bottom, as shown in Fig. 1. The column is assumed to consist of a moist solid or liquid phase with volume Vs, and a gas phase of volume VG. The actual support volume is included in Vs. 

Based on the following information, we can relate ux to retention time tR, the time, a component, is retained in the column, and column length L The retention time tR is the time required for band X to travel the length of column and is generally given as seconds or minutes the distance is the column length L (in centimeters), and the velocity is that of band X, ux (cm/sec). 

The height equivalent to a theoretical plate, H, is that length of column that represents one theoretical plate, or one equilibration step. Obviously, the smaller the value of this parameter, the more efficient the column. The more theoretical plates packed into a length of column, the better the resolution. It is calculated by dividing the column length by N ... 

As the Plate Theory has two serious limitation, viz., first it does not speak of the separating power of a definite length of column, and second it does not suggest means of improving the performance of the column the Rate Theory has been introduced which endeavours to include the vital fact that- the mobile-phase flows continuously, besides the solute molecules are constantly being transported and partitioned in a gas chromatographic column . It is usually expressed by the following expression ... 

More rigorous treatments of retention theory start from conservation of mass over a differential length of column 5,6). They require the same assumptions as the simpler analysis presented here and lead to the same result, equation 19.8. 

Number of moles of solute in equilibrated mobile and stationary phases in elemental length of column kmol N... 

To develop an HETP equation it is necessary to first identify the dispersion processes that occur in a column and then determine the variance that will result from each process per unit length of column. The sum of all these variances will be (H), the Height of the Theoretical Plate or the total variance per unit column length. There are a number of methods used to arrive at an expression for the variance resulting from each dispersion process and these can be obtained from the various references provided. However, as an example, the Random-Walk Model introduced by Giddings (5) will be employed here to illustrate the procedure.The theory of the Random-Walk processes itself can be found in any appropriate textbook on probability (6) and will not be given here but the consequential equation will be used. 

H height of theoretical plate or variance/unit length of column... 

In Fig 3 is shown the dependence of critical length (lcr) of detonators (diam d=24.5 mm charged with Tetryl of p0=1.6) from the length of column. As can be seen, 50 mm is the optimal length... 

Length of column = 280 cm Inside diameter = 4.0 cm Volume = 3.5 liters Foam capacity = 420 g (typical)... 

Calculate tM from the following experiment, employing the method above A mixture of linear alkanes, possessing six, seven and eight atoms of carbon, is injected into the chromatograph. The total retention times for these compounds were respectively, 271 s, 311 s, and 399 s, under a constant temperature of 80 °C. (Length of column 25 m, ID = 0.2 mm, <7f — 0.2 pm and the stationary phase is made up of polysiloxanes). 

Plate height is the constant of proportionality between the variance, cr2, of the band and the distance it has traveled, x. The name came from the theory of distillation in which separation could be performed in discrete stages called plates. Plate height is also called the height equivalent to a theoretical plate. Plate height is approximately the length of column required for one equilibration of solute between mobile and stationary phases. We explore this concept further in Box 23-2. The smaller the plate height, the narrower the bandwidth. 

Plate height CT2 L // = — = — x N o = standard deviation of band x = distance traveled by center of band L = length of column N = number of plates on column... 

Particles in a packed column resist flow of the mobile phase, so the linear flow rate cannot be very fast. For the same length of column and applied pressure, the linear flow rate in an open tubular column is much higher than that of a packed column. Therefore, the open tubular column can be made 100 times longer than the packed column, to give a similar pressure drop and linear flow rate. If plate height is the same, the longer column provides 100 times more theoretical plates, yielding VTOO = 10 times more resolution. 

The relationship in Equation 2.109 also can be used to determine the length of column necessary for a separation L. We know that... 

The relative "goodness" of a column is expressed in terms of efficiency, n/L, as plates per foot. A 6-foot column having 2000 plates would only be half as efficient as a 3-foot column with the same number of plates. Although the total number of plates, n, influences the degree to which peaks will be resolved, column efficiency is a measure of how well the column has been prepared and operated. A performance of 1000 plates per foot can be obtained but 500 is reasonable anything less is indicative of a problem. Column efficiency is also expressed as h, which is the length of column (expressed in millimeters) equivalent to one theoretical plate. This efficiency is related to column variables by the van Deemter equation ... 

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