# The Thermodynamics of Chromatography - Other Thermodynamic Methods that are Used for Studying Chromatographic Systems > Optimum Operating Conditions for Chiral Separations in Liquid Chromatography > The Effect of Temperature and Solvent Composition on the Minimum Variance/Unit&nbsp; Column Len

### The Effect of Temperature and Solvent Composition on the Minimum Variance/Unit  Column Length (Hmin)

Taking the values for the capacity ratios and separation ratios derived from equations (47), (48) and (49) in equation (40) the manner in which (Hmin) changes with temperature and solvent composition can be identified. The minimum variance per unit length of the column is solely a function of the capacity factor of the solute, the particle diameter and the packing factors (see Book 9). Thus, the influence of temperature and solvent composition on (Hmin) can only result from the effect of these variables on the magnitude of (k'). Curves relating (Hmin) to temperature for different solvent compositions are shown in figure 23. The magnitude of (Hmin) is seen to be strongly dependent on the solvent composition. At 50˚C by decreasing ethanol concentration form 50% v/v to 5% v/v the magnitude of (Hmin) is reduced by about 25% (the column efficiency increased by 25%).

The influence of temperature is more complicated. At an ethanol content of 5%v/v the magnitude of (Hmin) is virtually independent of temperature. This is because the magnitude of (k') is large, and the function of (k') in the equation for (Hmin) tends to a constant value of 2.46dp at high values of (k'). At high ethanol concentrations, (k') values are small, and the magnitude of (Hmin) becomes more dependent on the magnitude of (k') and, thus, more dependent on the temperature.  It is seen that,, at an ethanol concentration of 50%v/v, the value of (Hmin) is only reduced by about 5% for a temperature change from 5˚C to 50˚C. Figure 23. Curves Relating (Hmin) to Temperature for Different Solvent Compositions