# 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 Column Len

### The Effect of Temperature and Solvent Composition on the Minimum Variance/Unit Column Length (H_{min})

Taking the
values for the capacity ratios and separation ratios derived from equations
(47), (48) and (49) in equation (40) the manner in which (H_{min}) 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 (H_{min})
can only result from the effect of these variables on the magnitude of (k').
Curves relating (H_{min}) to
temperature for different solvent compositions are shown in figure 23. The
magnitude of (H_{min}) 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 (H_{min}) 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 (H_{min}) is
virtually independent of temperature. This is because the magnitude of (k') is
large, and the function of (k') in the equation for (H_{min}) tends to a constant value of 2.46d_{p} at high values of (k'). At high ethanol
concentrations, (k') values are small, and the magnitude of (H_{min}) 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 (H_{min}) is only reduced by about 5% for a
temperature change from 5˚C to 50˚C.

**Figure 23.
Curves Relating (H**_{min})
to Temperature for Different Solvent Compositions