# liquid chromatography column - Scott R.P.W.

**Download**(direct link)

**:**

**14**> 15 16 17 18 19 20 .. 80 >> Next

Thus, Vr = Vm + KVs ...................................... (ID

In practice,for an unretained peak eluted at the dead volume,(V0),

Vo = Vr(o) + Ve = Vm + Ve

(12)

24

Where, (Ve), 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,

vr = vm ¦ KVs ¦ vE .......................................(13)

The exact nature of the dead volume Is complex, and, at the same time, is extremely important particularly when it is employed in LC to determine the thermodynamic properties of a distribution system and to identify the nature of solute/phase interactions. It is also important in the development and use of equations for the prediction of the optimum phase systems for particular separations. As a consequence, the subject of the dead volume and its measurement in LC systems will be extensively discussed in the next chapter.

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),

Vr = Vr - Vo

Thus, from equations (12) and (13),

V'r= Vm + KVs + VE-(Vm + VE)

and, VY = KVs ...................................................... (14)

To avoid any confusion, it should be reiterated that although the stationary phase is assumed to have a volume and thus implies a liquid/liquid system, by replacing the vofumeot stationary phase with massoi stationary phase, then the equations can be exactly applicable to liquid solid systems. However, as already stated, the units of concentration must also be redefined in the measurement of (K).

Referring back to figure (4) The retention volume of solutes (A) and (B) will be,

Vr(A) = Vm * K(a)Vs ¦ Ve ........................... (15)

and

Vr(B) = Vm ¦ K(B)VS * VE

(16)

25

Furthermore, the corrected retention volumes will be,

Vr(A) = K(A)Vs

(17)

and

V’r(B) = K(B)Vs

(18)

The Capacity Ratio or a Solute

The capacity ratio of a solute (Þ was introduced early in the development of chromatography theory and was defined as the ratio of the distribution coefficient of the solute to the phase ratio (a) of the column. In turn the phase ratio of the column was defined as the ratio of the volume of mobile phase in the column to the volume of stationary phase in the column.

Note that (Vm) is the volume of mobile phase in the column and not Vo the total dead volume of the column.

Furthermore, it will be shown later that both (Vm) and (Vs) will not only vary between different columns, but also between different solutes, due to the exclusion properties of silica gel. Thus, some caution must be shown in comparing (Þ values for the same solute from different columns and for different solutes on the same column. This will be discussed in detail in the next chapter.

Nevertheless it must be pointed out that, in calculating (k'), the value taken in practice is often the ratio of the corrected retention distance (the distance in centimeters on the chart, between the dead point and the peak maximum) to the dead volume distance (the distance in centimeters on the chart, between the injection point to the dead point on the chromatogram). This calculation assumes the extra column dead volume is not significant and, unfortunately, in almost all cases this is not true, (k') values calculated in this way will be in error and should not be used for solute identification. Where computer data processing is used and no chart is available the distances defined above would be replaced by the corresponding times

Thus, k'= — a

and, as a = Vm/Vs,

Consequently, in practice

(19)

The Separation Ratio

The capacity ratio of a solute, (Þ, was introduced to develop a chromatographic measurement, simple to calculate, independent of flow-rate and one that could be used in solute identification. Although helpful, the capacity ratio is so dependent on the accurate measurement of extra column volume and on very limited solute exclusion by the support and stationary phase, that it is less than ideal for solute identification. An alternative measurement, the separation ratio (ct) was suggested where, for two solutes (A) and (B),

r(B)

_K(A)Vs

K(B,VS

_K(A)

K(B)

It is seen that the separation ratio is independent of all column parameters and depends only on the nature of the two phases and the temperature. Thus providing the same phase system is used on two columns, and the solutes are chromatographed at the same temperature, then the two solutes will have the same separation ratio on both columns. The separation ratio will be independents the phase ratios of the two columns and the f/ow-rates. It follows, that the separation ratio of a solute can be used reliably as a means of solute identification .

A standard substance is often added to a mixture and the separation ratio of the substance of interest to the standard is used for identification. In practice the separation ratio is taken as the ratio of the distances in centimeters between the dead point and the maximum of each peak. If computer data processing is being employed replace distances by corresponding times.

**14**> 15 16 17 18 19 20 .. 80 >> Next