The data has been curve fitted to a linear function and, thus, the enthalpy and entropy contributions are extracted as the slope and intercept of each curve. Thus

where (y₁₎ and (y₂₎ are the slopes of the curves for enantiomer (1) and enantiomer (2) respectively,

and (f₁) and (f₂) are the intercepts of the curves for enantiomer (1)

and enantiomer (2) respectively.

When k'₁ = k'₂ Then, or (18)

It is seen that if the enthalpies and entropies differ for two enantiomer pairs there will always be a temperature at which they elute coincidentally and cannot be separated.

From the curves and intercepts given in figure 28 the temperature for coincident retention of the two phenyl ethanol enantiomers is 432 K or 159 C and for the methylpiperidine enantiomers is 433 K or 160 C which is agrees excellently with the curves shown in figure 28. Now, suppose that in order to separate a pair of enantiomers, a separation ratio of (a) is required. Assuming, , it is now possible to calculate the temperatures at which a separation ratio of (a) can be realized.

(19)

Therefore, rearranging, (20)

Equation (20) allows the temperature to be calculated at which the separation ratio between the solutes would be a chosen value (a).

From equation (19) (21)

Thus, using equation (19) the separation ratio that will be obtained for any solute pair can be calculated at any temperature. In addition, from the column efficiency and the minimum separation ratio (a) of any two enantiomers that may be resolved can also be estimated. Thus, knowing (a), the optimum operating temperature for the column can also be determined As there is always an enthalpy difference between the enantiomers then there will always be a temperature of co-elution and that temperature may occur anywhere on the practical temperature scale.

In any given situation, it must be emphasized that the value for (a) will not necessarily be increased by reducing the temperature but may equally well be obtained by raising the temperature.

Retention measurements, taken at only two temperatures can provide enough data to identify the best operating temperature and the corresponding value of (a), and thus, the efficiency required from the column (i.e. its length and the particle size of the packing or the diameter of the open tube) (13).