Plate efficiency solutions

This equation, although originating from the plate theory, must again be considered as largely empirical when employed for TLC. This is because, in its derivation, the distribution coefficient of the solute between the two phases is considered constant throughout the development process. In practice, due to the nature of the development as already discussed for TLC, the distribution coefficient does not remain constant and, thus, the expression for column efficiency must be considered, at best, only approximate. The same errors would be involved if the equation was used to calculate the efficiency of a GC column when the solute was eluted by temperature programming or in LC where the solute was eluted by gradient elution. If the solute could be eluted by a pure solvent such as n-heptane on a plate that had been presaturated with the solvent vapor, then the distribution coefficient would remain sensibly constant over the development process. Under such circumstances the efficiency value would be more accurate and more likely to represent a true plate efficiency. 

HETP of a TLC plate is taken as the ratio of the distance traveled by the spot to the plate efficiency. The same three processes cause spot dispersion in TLC as do cause band dispersion in GC and LC. Namely, they are multipath dispersion, longitudinal diffusion and resistance to mass transfer between the two phases. Due to the aforementioned solvent frontal analysis, however, neither the capacity ratio, the solute diffusivity or the solvent velocity are constant throughout the elution of the solute along the plate and thus the conventional dispersion equations used in GC and LC have no pertinence to the thin layer plate. 

Electrolytic recovery systems work best on concentrated solutions. For optimal plating efficiency, recovery tanks should be agitated ensuring that good mass transfer occurs at the electrodes. Another important factor to consider is the anode/cathode ratio. The cathode area (plating surface area) and mass transfer rate to the cathode greatly influence the efficiency of metal deposition. 

Murphree plate efficiency is discussed in the solution to Problem 11.9. 

It is desired to separate 1 kg/s of an ammonia solution containing 30 per cent NH3 by mass into 99.5 per cent liquid NH3 and a residual weak solution containing 10 per cent NH3. Assuming the feed to be at its boiling point, a column pressure of 1013 kN/m2, a plate efficiency of 60 per cent and that an 8 per cent excess over the minimum reflux requirements is used, how many plates must be used in the column and how much heat is removed in the condenser and added in the boiler ... 

A thirty-plate bubble-cap column is to be used to remove n-pentane from a solvent oil by means of steam stripping. The inlet oil contains 6 kmol of n-pentane/100 kmol of pure oil and it is desired to reduce the solute content of 0.1 kmol/100 kmol of solvent. Assuming isothermal operation and an overall plate efficiency of 30 per cent, what is the specific steam consumption, that is kmol of steam required/kmol of solvent oil treated, and the ratio of the specific and minimum steam consumptions. How many plates would be required if this ratio is 2.0 ... 

To compensate for, what appeared to be very misleading efficiencies values, the effective plate number was introduced. The effective plate number uses the corrected retention distance, as opposed to the total retention distance to calculate the efficiency. Otherwise the calculation is the same as that used in the normal calculation of theoretical plates. In this way the effective plate number becomes significantly smaller than the true number of theoretical plates for solutes eluted at low k values At high k values, the the two measures of efficiency tends to converge. In this way the effective plate number appears to more nearly correspond to the column resolving power. In fact, it is an indirect way of trying to define resolution in terms of the number of effective plates in the column. 

In both models, a state of dynamic equilibrium is assumed to exist at the interface (/ = ff) and they have this one point (xy, y],) at the interface in common. In the model for the vaporization efficiency, the 7 found by Eq. (13-40) is the same throughout the vapor and liquid phases on plate j. Since equilibrium is assumed to exist at the interface, it follows that the vaporization efficiency must be equal to unity at the interface and, consequently, the Kj- s found by use of Eq. (13-40) must satisfy the equilibrium relationship y)i — yfiKjixfi (where it is supposed that the vapor phase forms an ideal solution). Since the liquid is assumed to be at its bubble-point temperature throughout the liquid phase in the Murphree model for the plate efficiency, it follows that y)i = yfi xjf = yjf Ky xjf or is equal to Kj. That is, the two models have the same interface temperatures and, furthermore, the temperature computed by use of vaporization efficiencies [Eq. (13-40)] is seen to be the bubble-point temperature of the interface [see Fig. 13-3]. 

The plate efficiency of fractionating columns and absorbers is affected by both the mechanical design of the column and the physical properties of the solution. 

Equilibrate the column with chloroform-acetic acid 99 + 1 v/v, monitoring the absorbance at 270 nm. Measure the dead time by repeated injections of 5 pL of a 50pg/mL solution of acetone in chloroform. The performance parameters of the packed column (number of theoretical plates, efficiency, selectivity) can be measured by repeated injections of 5 pL of a 50 pg/mL solution of theophylline and caffeine in chloroform. Calculate the imprinting factor, IF, as the ratio between the capacity factors for the theophylline eluted on the imprinted and nonimprinted columns (note 9)... 

Davies et al. (27) also extended their studies to distillation of formalin solutions, that is the analysis of a distillation coluOTi involving reactions of formaldehyde with water and methanol. The problem was complicated by the estimation of equilibrium data for a system of five-components of which one (hemiformal) does not exist in a pure state. Although good agreement is claimed between theory and experiment, some of the assumptions are rather doubtful, e.g. the use of the A.I.Ch.E. method for prediction of plate efficiencies. 

The usual correlations available for predicting column design parameters fail when applied to the hydrogen systems, since the bulk of the data for the correlations is obtained from higher boiling systems, such as aqueous solutions and hydrocarbons. For example, the optimum downcomer area was found to be much larger than predicted and one well known correlation [1] gives an overall plate efficiency of 130 /o. 

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