The Thermodynamic Explanation of Retention

Classical thermodynamics provides an expression that describes the change in free energy of a solute when transferring from one phase to the other as a function of the equilibrium constant (distribution coefficient). The expression is as follows,

RT ln K = -DGo

where (R) is the gas constant,

(T) is the absolute temperature,

and (DGo) is the Standard Free Energy Change.

In addition, classical thermodynamics provides an expression for (DGo),

i.e.,

where (DHo) is the Standard Enthalpy Change,

and (DSo) is the Standard Entropy Change.

Thus,

(2)

or,

(3)

It is seen that if the standard entropy change and standard enthalpy change for the distribution could be calculated, then the distribution coefficient (K) and, consequently, the retention volume could also be predicted. Unfortunately, these properties are difficult, if not impossible, to isolate and estimate and so the magnitude of the overall distribution coefficient cannot be estimated in this way. Nevertheless, once the phase system has been identified, with sufficient experimental data being available, empirical equations can be developed to optimize a given distribution system for a specific separation. Computer programs, based on this rationale, are available for LC to carry out such optimization procedures for solvent mixtures having three or more components. Nevertheless, the appropriate stationary phase is still usually identified from the types of interactions that need to be exploited to effect the required separation. By measuring the retention volume of a solute over a range of temperatures equation (2) can also be used to identify the type of retention mechanism that is operative in a particular separation.

Rearranging equation (2)

Noting, V' = KVs