The Retention Volume of a Solute

The retention volume of a solute is that volume of mobile phase that passes through the column between the injection point and the peak maximum. Consequently, by differentiating equation (10), equating to zero and solving for (v), an expression for the retention volume (Vr) can be obtained. 

Equating to zero and solving for (v), then at the peak maximum, 

It is seen that the peak maximum is reached after (n) plate volumes of mobile phase have passed through the column. Thus, the retention volume in ml of mobile phase will be obtained by multiplying by the plate volume, (vm + Kvg). 

The volume of mobile phase per plate (vm), multiplied by the number of plates (n), will give the total volume of mobile phase in the column (Vm)- Similarly, the volume of stationary phase per plate (vs), multiplied by the number of plates (n), will give the total volume of stationary phase in the column (Vs). 

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In practice,for an unretained peak eluted at the dead volume,(Vo), 

Is the extra column volume contained In the injection system, connecting tubes and detector cell. In some cases, (Ve), may be sufficiently small to be ignored, but for accurate measurements of retention volume the actual volume measured should always be corrected for the extra column volume of the system and equation (12) should be put in the form, 

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By measuring the retention volume of a solute, the distribution coefficient can be obtained. The distribution coefficient, determined over a range of temperatures, is often used to determine the thermodynamic properties of the system this will be discussed later. From a chromatography point of view, thermodynamic studies are also employed as a diagnostic tool to examine the actual nature of the distribution. The use of thermodynamics for this purpose will be a subject of discussion in the next chapter. It follows that the accurate measurement of (VV) can be extremely... 

In general, (Q) and ( ) will be equal, but the general case is assumed, where they are not. Equation (37) gives an explicit and accurate expression for the retention volume of a solute. The importance of each function in the expression will depend on the physical properties of the chromatographic system. At one extreme, using an open tubular column in GC, then... 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

The equation for the retention volume of a solute, that was derived by differentiating the elution curve equation, can be used to obtain an equation for the retention time of a solute (tr) by dividing by the flowrate (Q), thus,... 

Now, it has already been shown that the retention volume of a solute is given by n(vm + Kvs), and twice the standard deviation of the peak at the inflexion points is given by 2 /11 (v + Kvg)... 

One of the difficulties with any form of chromatography is that a band of solute is dispersed, becoming less concentrated as it travels through the system. The efficiency of the column is a measure of the amount of spreading that occurs. In the chromatogram in Fig. 2.3b, Vr = the retention volume of a solute and wg = the volume occupied by the solute. This is called the peak width, but remember it means a volume, not a length. 

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

Returning to equation (13) which gives the retention volume of a solute, it is now possible to derive and equation for the adjusted retention volume, (VV),... 

It can be clearly seen from equation (9) that the expression for the retention volume of a solute, although generally correct, is grossly over simplified if accurate measurements of retention volumes are required Some of the stationary phase may not be chromatographically available and not all the pore contents have the same composition as the mobile phase and, therefore, being static, can act as a second stationary phase. This situation is akin to the original reverse phase system of Martin and Synge where a dispersive solvent was absorbed Into the pores of support to provide a liquid/liquid system. As a consequence a more accurate form of the retention equation would be,... 

So far the Plate Theory has been used to determine the equation for the retention volume of a solute, calculate the capacity factor of a solute and identify the dead volume of the column and how it should be calculated. However, the equation for the elution curve of a solute that arises directly from the Plate Theory can do far more than that to explain the characteristics of a chromatogram. The equation will now be used in a variety of ways to expand our knowledge of the chromatographic process. 

Once the retention volume of a solute is calculated for a particular gradient profile, corresponding bandwidth and resolution can be determined by introducing the appropriate instantaneous retention factor A, at the elution of the peak maximum calculated from the gradient function tpf = /(Tr) and from the retention equation A, = f chromatographic mode and gradient function used [851 ... 

The retention volume of a solute is that volume of mobile phase that passes through the column between the injection point and the peak... 

The simple, linear relationship between volume fraction of one component of a binary mixture and the retention volume of a solute, where there is only weak interaction between the individual components, again, is to be expected. The volume fraction of each phase will determine the probability that a given solute molecule will interact with a molecule of that phase, in much the same way as the partial pressure of a solute in a gas, determines the probability that a solute molecule will collide with a gas molecule. For those phase systems that give a linear relationship between retention volume and volume fraction of stationary phase, it is clear that the linear functions of the distribution coefficients could be summed directly, but their logarithms could not. The results of Purnell indicate that when there is little, or only weak, interaction between the components of a binary mixture used as a stationary phase, the solute retention or distribution coefficient is linearly, not exponentially, related to the stationary phase composition. 

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