Van’t Hoff relationship

The binding enthalpy change (AH) could be determined either from the plots of the temperature dependence of the binding constant according to the van t Hoff relationship ... 

Techniques are available for estimating binary and multi-component solubility behaviour. One example is the van t Hoff relationship which, as stated by Moyers and Rousseau(25), takes the following form for an ideal solution ... 

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

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

Free energy diagrams for enzymes REACTION COORDINATE DIAGRAM ENZYME ENERGETICS POTENTIAL-ENERGY SURFACES TRANSITION-STATE THEORY ARRHENIUS EQUATION VAN T HOFF RELATIONSHIP... 

TEMPERATURE CONTROL TEMPERATURE DEPENDENCE ARRHENIUS LAW VAN T HOFF RELATIONSHIP TRANSITION-STATE THEORY TEMPERATURE DEPENDENCE OF KINETIC ISOTOPE EFFECTS... 

The entropy and enthalpy changes associated with the reversible binding of the eluite by the stationary phase are defined by applying (he van t Hoff relationship to the chromatographic process as follows... 

MeCN/H,0 mixtures of volume fractions from ip = 0.41 to ip = 0.45 containing 0.1% TFA and butylsilica at temperatures T= 278-338 K. The plots show the experimental data and the lines of best fit according to the quadratic form of the relationship given in eq 7 and the polynomial form of the van t Hoff relationship. b Adapted from Jong, Boysen, and Hearn)24 with permission. 

Reactions 15 and 16 depend on experimental conditions such as heating rate, helium flow rate, etc., and both reactions occur simultaneously to some extent. Therefore, it was not possible to determine the enthalpies of these reactions individually. However, by using a differential scanning calorimeter, we determined the combined enthalpy of Reactions 15 and 16 which is, of course, the enthalpy of Reaction 8 with the sign reversed. The value obtained was 100 10 kj/mol H2, which is in fair agreement with the value obtained from the van t Hoff relationship. 

Using equation (4), Torocheshnikov et al. (50) have calculated the values of <5C and K for Me3SnCl and Et3SnCl in acetone, acetonitrile, and dioxan. The molar enthalpy of complex formation, AH, can be obtained from a In K vs. l/T plot (Fig. 5) using the Van t Hoff relationship ... 

If one accepts the above small modification of the Flory model for equilibrium swelling, and also assumes that the turgid end-state is described by the van t Hoff relationship ... 

Examples of linear van t Hoff relationships can be found in the literature. Almost linear relationships between InA versus 1/T were reported for alkaloids under IPC conditions at a temperature range of 10 to 50°C with a linear decrease of retention with the increase of temperature [10]. A linear van t Hoff plot was also obtained in IPC of impurities in 2,4-disulfonic acid benzaldehyde di-sodium salt [21], even if nonlinear dependencies were also reported [22],... 

Once the probabilities are known, other physical quantities, which are function of the occupation probabilities, can be calculated from (A) — J2yPy y- or order parameters for order-disorder phase transitions. Different examples will appear in the following. For instance, the orientational contribution to the absolute polarization of the ferroelectric compound pyridinium tetrafluoroborate was estimated from 2H NMR temperature-dependent measurements on the perdeuterated pyridinium cations.116 The pyridinium cation evolves around a pseudo C6 axis, and the occupation probabilities of the different potential wells were deduced from the study of 2H NMR powder spectra at different temperatures. The same orientational probabilities can be used to estimate the thermodynamical properties, which depend on the orientational order of the cation. Using a generalized van t Hoff relationship, the orientational enthalpy changes were calculated and compared with differential scanning calorimetry (DSC) measurements.116... 

The transition between a normal and an inverse EIE reflects the fact that these systems are not characterized by the typical monotonic variation predicted by the van t Hoff relationship. Instead, as discussed in an edifying review by Parkin,194 the EIEs in these systems are zero at OK, increase to a value >1, and then decrease to unity at infinite temperature. This unusual behavior is, nevertheless, rationalized by consideration of the individual factors that contribute to the EIE. As discussed above, the EIE may be expressed in the form EIE = SYM x MMI x EXC x ZPE (where SYM is the symmetry factor, MMI is the mass moment of inertia term, EXC is the excitation term, and... 

An additional requirement for the liquid-liquid system in Fig, 7,8-5 is that the solute distribution cneflicieni must increase with temperature. Since, from the van t Hoff relationship. 

Equation (11.2-6) is often referred to as the van t Hoff relationship. To use this equation to compute solute solubility for an ideal solution only the beat of fusion A A/, and tbe pure-component melting temperature Tm are required. The interesting feature of this equation is that the solubility depends only on the jMOperties of the solute and is independent of the nature of tbe solvent. 

A key thermodynamic equation for the characterisation of binding events is the Van t Hoff relationship, which is a partial derivative equation as shown ... 

Figure 7.24 Van t Hoff Relationship Plots, (a) Classical linear plots obtained in the event that AW bind is temperature independent over the temperature range studied, (b) Curved plots that characterise the situation when AH md is temperature dependent. Negative curvature is characteristic of the involvement of hydrophobic effect in receptor-ligand binding interactions.

The experimental data are interpreted through the average number of fluorides per thorium atom. The concentration-dependent stability constants thus calculated were converted to constants at zero ionic strength through the modified Debye-Hiickel relationship for the experimental temperatures. These constants were then used to calculate other thermodynamic parameters through the use of van t Hoff relationship assuming that Aj/f ° (A.60) is independent of temperature. The log, (A.60) values for ... 

The pC-pH diagrams can be used for systems having temperatures other than 25°C and ionic strengths other than zero. The modification of a 25°C-based pC-pH diagram for temperatures other than 25 C merely entails the use of equilibrium constants for the appropriate temperature in the equilibrium expressions used to construct the diagram. The Van t Hoff relationship (Eq. 3-27) can be used to convert 25°C equilibrium constants to the values at the desired temperature. 

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