Elevated Temperatures in Liquid Chromatography, Part III: A Closer Look at the van 't Hoff Equation

Dec 01, 2012
Volume 30, Issue 12, pg 1052–1057

Part I of this article series discussed some of the advantages of and practical considerations for elevated temperature separations in liquid chromatography (LC) (1). Part II reviewed some of the basic thermodynamics of chromatography and elevated temperature separations, which included a brief derivation and discussion of the van 't Hoff equation (2). This third and final part continues the exploration of elevated temperatures in LC with a more detailed discussion of the van 't Hoff equation, exploring its usefulness and relevance using various examples from the literature.

Van 't Hoff plots can be a useful and interesting part of data analysis for high-temperature liquid chromatography (LC). Here, in part III of this series, we take a closer look at the van 't Hoff equation using various examples from the literature.

Review of the Advantages of Elevated-Temperature Separations

Elevated temperatures offer a number of benefits in LC. One such benefit is that they facilitate retention mapping in which the retention factor, k, is measured at different temperatures so that the values of k over a range of temperatures can be predicted (3,4). Retention mapping can also include the probing and predicting of k at different mobile-phase compositions and is widely used in method development (3,5,6). Another benefit is that selectivity (α) may change with temperature, which is important for retention mapping and is another parameter that can be considered in method development (3,5,6). Also, increasing temperatures can improve sample throughput because the van Deemter minima shifts to higher flow rates; that is, the optimal efficiency for a separation shifts to a higher mobile-phase velocity (7–9). Finally, a decrease in the organic modifier is possible due to the change in the polarity of water at increasing temperatures; water behaves more like an organic solvent at elevated temperatures. Furthermore, a more aqueous mobile phase is considered "greener" because of a reduction in the amount of organic modifier used (10–14). Clearly, there are good reasons for considering the use of elevated temperatures in LC. Now, let's discuss various aspects of high-temperature separations in the context of the van 't Hoff equation.

Review of the van 't Hoff Equation

The van 't Hoff equation is derived from the following two basic thermodynamic equations:

where ΔG 0 is the Gibbs free energy, ΔH 0 is the enthalpy of transfer, T is the absolute temperature in kelvins, ΔS 0 is the entropy of transfer, R is the gas constant, and K is the equilibrium constant. When we equate these two equations and solve for ln K we achieve the van 't Hoff equation:

As discussed in part II (2), ln K = ln kβ, where k is the retention factor and β is the phase ratio (V M/V S) — the ratio of the mobile-phase volume and stationary-phase volume. By substituting kβ for K in equation 3 we obtain the van 't Hoff equation as it is commonly encountered in LC:

Note that sometimes Φ is used instead of β, where Φ = 1/β = V S/V M. Thus, an equivalent form of equation 4 is:

Unfortunately, both β and Φ are referred to as the "phase ratio."

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