Van t Hoff curves

It is clear that a graph of ln(V j-) or In(k ) against 1/T will give straight line. This line will provide actual values for the standard enthalpy (AH ), which can be calculated from the slope of the graph and the standard entropy (AS ), which can be calculated from the intercept of the graph. These types of curves are called van t Hoff curves and their important characteristic is that they will always give a linear relationship between In(V r) and (1/T). However, it is crucial to understand that the distribution... 

Returning to the nature of van t Hoff curves, there are some cases in the literature that purport to show nonlinear van t Hoff curves. This, in fact, is a contradiction in... 

Plateau pressures or temperatures desired depend on the application intended. The plateau pressure at a given temperature is a strong function of the metal composition. The state of the art has expanded greatly in the last few years, so that we now have a wide variety of hydrides available and can, in many cases, tailor-design plateau pressures or dissociation temperatures. We will survey the main classes of hydrides later. As a preview to that survey, desorption Van t Hoff curves of just a few representative materials are presented in Figure 4 to show the wide range of materials that are available in the 300°C to -20°C range. 

Yanson et al. [41] using field-ionization mass spectrometry studied the formation of gas-phase GC, CC, AT and TT pairs. From measurements of temperature dependence of equilibrium constants, an interaction enthalpy for the base pair formation was derived. This technique was sometimes questioned because the determination of enthalpy from the slopes of appropriate van t Hoff curves might not be unambiguous. From Table 6 it is evident that the agreement with the present theoretical values is good, and concerns not only the relative interaction enthalpies but even the absolute values the average absolute error is less than 1.5 kcal/mol. 

For system A, it is characteristic to have a relatively very large enthalpy contribution (the slope of the van t Hoff curve is steep) with, conversely, a very low entropy contribution (the intercept is relatively small). The large value of the slope means that molecular forces dominate the distribution in favor of the stationary phase. It can be said that molecules are retained in the stationary phase as a result of molecular interactions. Thus, the change in enthalpy is the major contribution to the change in free energy and it can be said, in thermodynamic terms, the distribution is energy driven. 

It is seen that a curve relating log(V ) to l/T should give a straight Une, the slope of which will be proportional to the enthalpy change during solute transfer. In a similar way, the intercept will be related to the entropy change and, thus, the dominant effects in any distribution system can be identified from such curves. Curves relating to l/T are called van t Hoff curves, which can be used to identify the mechanism of retention and elucidate the role played by temperature in a separation (see van t Hoff Curves, p. 2406 and Chiral Separations by GC, p. 425). 

The van t Hoff curve fitting methods presented above for hairpin transitions are general, but for higher molecularity the equilibrium expressions are different equations 6, 9 and 11) (9, 10, 18). For selfcomplementaiy duplexes the relevant equilibrium equations are ... 

The second type of van t Hoff curve, also grossly exaggerated, is depicted in Figure 2. 

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