Van’t Hoff model

When he suggested that the liaison between atoms that constitute a molecule could be formulated in terms of directed bonds, van t Hoff encountered serious opposition. It is all the more remarkable how his ideas later became so firmly embedded in chemical thinking that even the mighty quantum theory has so far failed to have a visible impact on this classical model. In fact, van t Hoffs model, although largely incompatible with quantum theory, managed to entrench itself in a guise that resembles that theory. 

By comparison, numerical solution of the one-electron Schrodinger equation for clamped nuclei, predicts the correct dissociation energy and interatomic distance for HJ. These calculations show that the electrostatic interaction which stabilizes the molecule arises from quantum-mechanical charge distributions. Classical models, such as the Lewis or van t Hoff models, can therefore be rejected at the outset. Semi-classical models such as LCAO, are of the same kind, in view of the demonstrated classical nature of hybridization. 

Raudino et al. [136] proposed a DSC method based on the van t Hoff model of the depression of the freezing temperature to investigate slow kinetics involving lipid vesicles or liposomes and drug complexes. The melting temperature of vesicles is affected by drug solubilization according to... 

The molecular weight analysis presented above is a purely thermodynamic result and is independent of any model. The procedure requires dilute solutions, but is not based on the assumption of ideality, even though Eq. (8.88) is a variation of the van t Hoff equation. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

Within this historical setting, the actual birth of stereochemistry can be dated to independent publications by J. H. van t Hoff and J. A. Le Bel within a few months of each other in 1874. Both scientists suggested a three-dimensional orientation of atoms based on two central assumptions. They assumed that the four bonds attached to a carbon atom were oriented tetrahedrally and that there was a correlation between the spatial arrangement of the four bonds and the properties of molecules, van t Hoff and Le Bell proposed that the tetrahedral model for carbon was the cause of molecular dissymmetry and optical rotation. By arguing that optical activity in a substance was an indication of molecular chirality, they laid the foundation for the study of intramolecular and intermolecular chirality. 

But what was the meaning of the pictorial formulas What did they explain Were they theoretical models What was the aim of Hofmann s croquet balls, Dewar s brass-and-rod models, Kekule s wooden sausages, and van t Hoffs cardboard tetrahedrons 86... 

But what about the three-dimensional images or formulations of molecules What about "la chimie en l espace" introduced by Joseph Achille Le Bel, van t Hoff, and Wislicenus toward the end of the nineteenth century Were these carbon tetrahedra realistic "models" of real molecules in space Van t Hoff argued in favor of the carbon tetrahedron that if atoms were arranged in a plane, there would be more isomers of the type CR1R2R3R4 predicted in principle than are actually observed. With the tetrahedral structure, only two isomers are possible, related to each other as mirror images. 102... 

The second period, from 1890 to around 1920, was characterized by the idea of ionic dissociation and the equilibrium between neutral and ionic species. This model was used by Arrhenius to account for the concentration dependence of electrical conductivity and certain other properties of aqueous electrolytes. It was reinforced by the research of Van t Hoff on the colligative properties of solutions. However, the inability of ionic dissociation to explain quantitatively the properties of electrolyte solutions was soon recognized. 

The impact of van t Hoff s concept of asymmetric C-atoms upon the thought of stereochemists was so strong that many configurational problems were treated on the basis of the model without questioning its pertinence for the given case. 

The dissection of a molecular model into those components that are deemed to be essential for the understanding of the stereochemistry of the whole may be termed factorization (9). The first and most important step toward this goal was taken by van t Hoff and Le Bel when they introduced the concept of the asymmetric carbon atom (10a, 1 la) and discussed the achiral stereoisomerism of the olefins (10b,lib). We need such factorization not only for the enumeration and description of possible stereoisomers, important as these objectives are, but also, as we have seen, for the understanding of stereoselective reactions. More subtle differences also giving rise to differences in reactivity with chiral reagents, but referable to products of a different factorization, will be taken up in Sect. IX. 

The Mills-Nixon hypothesis that small ring annelation on benzene would induce bond fixation (bond alternation) by trapping out one Kekul6 tautomer is a casualty of early twentieth century structural chemistry. Due to a lack of direct methods for analyzing molecular structure, structural postulates of that time were often supported by an analysis of product distributions. An experimental observable such as product selectivity or isomer count was correlated to an unobservable structural feature derived on the basis of a chemical model. Classical successes of this method are van t Hoff s proof of the tetrahedral carbon atom and Fischer s proof for the configuration of sugars. In the case of Mills and Nixon, however, the paradigm broke down. 

Alternative mechanistic schemes can also be devised to account for nonlinear van t Hoff plots. A particularly sinq>le case occurs when more than one binding site on the stationary phase surfoce is involved in the retention of eluite. The retention process can formally be modeled for the... 

The majority of solutes will show decreased values of In k as the temperature is increased. The slopes of the van t Hoff plots are often similar for compounds of the same functional group as shown by the three solid lines. The dashed lines show the irregular results often seen for solutes of different compound classes which can vary widely and have either a positive or a negative slope. All of these systems can be easily modeled with optimization software and require only two temperature points to define the system [4],... 

Problems arise for solutes that exhibit behavior shown in the dotted line. For these systems, simple models will not work. Reasons for non-linear van t Hoff plots will be discussed in Sections 9.3.2 and 9.3.3. 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, using software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Rtf. To facilitate these calculations, the following data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sh, is defined as Sh = 0.04 Re0 75 Sc0-33, where Sc is the Schmidt number (2) osmotic pressure follows van t Hoff s equation, ie, 7r = iCRgTy where i is the number of ions (3)... 

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