The Thermodynamics of Distribution

Classical thermodynamics provides an expression that relates the change in standard energy of a solute when transferring from one phase to the other as a function of the equilibrium constant that, in the case of chromatographic retention, will be the distribution coefficient (K). The expression is as follows,

RT ln K = -DG_o (12)

Now, also from classical thermodynamics,

(13)

Thus, (14)

_or, (15)

It is seen that if the standard entropy change and standard enthalpy change for the distribution of any given solute between two phases can be calculated, then the distribution coefficient (K) and, consequently, its retention volume can also be predicted. Unfortunately, these properties of a distribution system are bulk properties, that include, in a single measurement, the effect of all the different types of molecular interactions that are taking place between the solute and the two phases. As a result, it is often difficult to isolate the individual interactive contributions in order to estimate the magnitude of the overall distribution coefficient or identify how it can be controlled. Nevertheless, there are a number of ways in which the thermodynamic approach can provide valuable information with regard to the nature of the distribution and the optimum conditions to effect a separation.

Rearranging equation (14)

Bearing in mind, V' = KV_s

(16)

In addition, if (V") is the retention volume per unit volume of stationary phase then, V_S=1 and lnV_S=0, and thus,

V_s=1 and as ln(V_s) = 0

then, (17)

It is seen that a curve relating ln(V') to 1/T should give a straight line, the slope of which will be proportional to the standard enthalpy change during solute transfer. In a similar way, the intercept will give the standard entropy change.