Van’t Hoff treatment

Instead, a wide variety of spectroscopic and electrochemical titration methods are often employed to determine the equilibrium constants for a molecular recognition process at several different temperatures, which are then analyzed by the van t Hoff equation to give the thermodynamic parameters for the process. However, there is a critical tradeoff between the accuracy of the value obtained and the convenience of the measurement since the thermodynamic parameters, evaluated through the van t Hoff treatment, do not take into account the possible temperature dependence of the enthalpy change, i.e. heat capacity, and are less accurate in principle. In fact, it has been demonstrated with some supramolecular systems that the van t Hoff treatment leads to a curved plot and therefore the thermodynamic parameters deviated considerably from those determined by calorimetry.3132 Hence one should be cautious in handling thermodynamic parameters determined by spectroscopic titration and particularly in comparing the values for distinct systems determined by different methods. 

Instead, a formula (6) must be used for calculation that honors a nonzero heat capacity AC° and allows the derivation of AH°(T ) from the affinity constant /Tassoc ( ) ) at the reference temperature and a series of binding constants Tassoc obtained at various temperatures T by a nonlinear fitting process. The substantial discrepancies found between association enthalpies AH° obtained by direct calorimetry or via the temperature dependence of the association constant using a van t Hoff treatment most likely arise from lack of precision in the original measurements eventually combined with inadequate data evaluation." Because calorimetry is the only method yielding enthalpies as direct experimental observables, the values derived on this basis appear more credible than from any other alternative method. 

The enthalpies of micellization, AH, , can be calculated indirectly by use of the van t Hoff treatment or directly by isothermal titration calorimetry (ITC). Except for few cases (e.g., some nonionic surfactants), the results of these methods do not agree [38]. The main reason is that there is no provision in van t Hoff equation for factors that are important for micelle formation of ionic surfactants, in particular, the dependence of micellar geometry, surface-charge density, and extent of hydration on temperature T) [38]. On the other hand, the effects of (T) on the aforementioned micellar parameters are included in the direct (i.e., calorimetric) determination of AH, . From Gibbs free energy relationship, any uncertainty introduced in the calculation of Ai7, j will be carried over to so that A5 rK > AS, Where available, therefore, we compare the thermodynamic quantities of micellization, based on experimental data of the same technique. 

Before showing data correlations, we discuss briefly the appropriateness of the techniques and data treatment employed. With regard to the former, the two most employed techniques to calculate AH are conductivity and ITC. Whereas use of the latter allows accurate determination of cmc and AH ,, conductivity is appropriate to determine cmc and The deficiency of the van t Hoff treatment for the determination of A// and the subsequent effect of the other micellar thermodynamic parameters have been discussed previously [36,38]. 

Id. Treatment of Data.—Typical osmotic data are shown in Figs. 38 and 39. Here the ratio ( n/c) of the osmotic pressure to the concentration is plotted against the concentration. If the solutions behaved ideally, van t Hoff s law Eq. (11) would apply and m/c should be independent of c. Owing to the large effective size of the polymer molecules in solution (Fig. 34) and the interactions between them which consequently set in at low concentrations, /c increases with c with a... 

All difficulties arising from an uncritical use of van t Hoff s concept are due to the treatment of the chirality of compounds with rigid polycentric skeletons on the basis of asymmetric C-atoms. For example, the chirality of the norbornane derivatives, i.e., 13, has been attributed to its asymmetric bridgehead C-atoms 20c>23). 

In essence the parity vectors are based upon van t Hoff s concept of decomposing polycentric configurations into asymmetric carbon subunits, both treatments correspond in scope and limitations. 

TRANSITION-STATE THEORY VAN T HOFF RELATIONSHIP Arrhenius treatment,... 

Historically, an understanding of the underlying causes of a thermal explosion was first demonstrated by van t Hoff (0.9) in 1884. A quantitative mathematical treatment... 

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-L 1), when all ions are independent, i = 2 for MX salts and i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i = 1. The i factor is so unreliable, however, that it is best to confine quantitative treatments of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. 

Wuhl E, Haffner D, Offner G, Broyer M, van t Hoff W, Mehls OEuropean Study Group on Growth Hormone Treatment in Children with Nephropathic Cystinosis. Long-term treatment with growth hormone in short children with nephropathic cystinosis. J Pediatr 2001 138(6) 880-7. 

In a different theoretical treatment, Chien (21.) used the Van t Hoff equation to derive the relationship (Eq. 13) between 1/T and... 

The calculation of Heitler and London (1927) of the energy of the hydrogen molecule must indeed be considered, together with the conception of the spatial model of the carbon atom by Van t Hoff and Le Bel, as the most important contribution to theoretical chemistry, since the advent of Dalton s atomic hypothesis. We shall, however, let the treatment of the hydrogen molecule itself be preceded by the discussion of the hydrogen molecule ion H2+, since this problem with only one electron is still simpler than that of the H2 molecule itself. 

In this chapter we will derive the Boyle-Van t Hoff relation using the chemical potential of water, and in Chapter 3 (Section 3.6B) we will extend the treatment to penetrating solutes by using irreversible thermodynamics. Although the Boyle-Van t Hoff expression will be used to interpret the osmotic responses only of chloroplasts, the equations that will be developed are general and can be applied equally well to mitochondria, whole cells, or other membrane-surrounded bodies. 

To appreciate the refinements that this thermodynamic treatment introduces into the customary expression describing the osmotic responses of cells and organelles, we compare Equation 2.18 with Equation 2.15, the conventional Boyle-Van t Hoff relation. The volume of water inside the chloroplast is VM,n because n v is the number of moles of internal water and Vw is the volume per mole of water. This factor in Equation 2.18 can be identified with V — b in Equation 2.15. Instead of being designated the nonosmotic volume, b is more appropriately called the nonwater volume, as it includes the volume of the internal solutes, colloids, and membranes. In other words, the total volume (V) minus the nonwater volume (b) equals the volume of internal water (Ew ). We also note that the possible hydrostatic and matric contributions included in Equation 2.18 are neglected in the usual Boyle-Van t Hoff relation. In summary, although certain approximations and assumptions are incorporated into Equation 2.18 (e.g., that solutes do not cross the limiting membranes and that the... 

Equation 3.48 indicates that not only does Js depend on An, as expected from classical thermodynamics, but also that the solute flux density can be affected by the overall volume flux density, Jv. In particular, the classical expression for Js for a neutral solute is P Ac (Eq. 1.8), which equals (Pj/RT)ATlj using the Van t Hoff relation (Eq. 2.10 II, = PT Cj). Thus to, is analogous to P/RT of the classical thermodynamic description (Fig. 3-19). The classical treatment indicates that Js is zero if An is zero. On the other hand, when An is zero, Equation 3.48 indicates that Js is then equal to c,(l - cr,)/y solute molecules are thus dragged across the membrane by the moving solvent, leading to a solute flux density proportional to the local solute concentration and to the deviation of the reflection coefficient from 1. Hence, Pj may not always be an adequate parameter by which to describe the flux of species , because the interdependence of forces and fluxes introduced by irreversible thermodynamics indicates that water and solute flow can interact with respect to solute movement across membranes. 

Figure 2-18. So-called van t Hoff plot for the retention of the same analyte at two different pH values of the mobile phase all other conditions are identical. This is to illustrate that any classical thermodynamic treatments are not applicable to the chromatographic system with multiple different processes involved.

A modern study of this system by Lord and Pritchard [1275] confirmed that the data of Bodenstein and Plaut [218] were of the highest accuracy when the data from Bodenstein and Plaut [218] and the modern study [1275] are combined (see Fig. 8.2(B)), a value of AH of +(112.5 1.5) kJ mol is obtained for reaction (8.2) from the van t Hoff plot [1275]. However, as the slight curvature of the plot betrays, AH varies slightly with temperature. The best data treatment yields AHjgg as +(108.6 i 0.4) kJ mol [1275]. The equilibrium constants for Equation (8.2) are given by [1275] ... 

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