Heat of association

This high degree of association results in highly nonideal physical properties. For example, heat effects resulting from vapor association may be significantly larger than the latent heat of vaporization (Fig. 9). Vapor heats of association J for HF to (HF) per mole of (HF) are as follows. To... 

Measurements of binding curves without influencing the equilibria can be performed if the readout for complex formation is correlated with a change in a macroscopic signal. This can be either a change in fluorescence intensity, fluorescence polarization, optical absorption, or heat of association (see next chapter). Assume an equilibrium... 

The standard enthalpy of formation of monomeric HF is a hypothetical state that must be related to that of the real associated liquid, gas, or aqueous solution met in calorimetiy. Considerable difficulty has been encountered in allowing for the heat of association, which varies with temperature and pressure. For example, the presence of traces of water can affect the polymerization by entering into the hydrogen bonding (30) the treatment of results will depend on the association model adopted. The magnitude of corrections for gas imperfections has... 

The particular case of the solubilities of organic solutes in water can be dealt with by rather simple equations, based on a general equation for solvent-dependent properties, apphed to solubilities, distribution ratios, rate constants, chromatographic retention indices, spectroscopic quantities, or heats of association [4] [see Eq. (2.12) for an example of its application]. For the molar solubilities of (liquid) aliphatic solutes B in water at 25°C the equation... 

Fig. 22 Plot of log values (solid squares and circles) and modeled heat of association (open squares and circles) against oligomer length for ligands 40 (circles) and 44 (squares). Experimental values for 40 are taken from ref. [58] for direct comparison to 44...

J. S. Rowltnson (Manchester) I am very glad that Dr. Davies has stressed the importance of gas-phase measurements of the second virial coefficient as a measure of the strength of the bonds between dimers. The second virial coefficient is undoubtedly the simplest physical property which refers solely to the interaction of molecules in pairs. In particular, I would point out that the second virial coefficients of methanol give a heat of association of about 4-5 fecal/mole. The measurements would not, I think, be consistent with a heat as high as the 9 kcal reported by Dr. E. D. Becker for the formation of dimer in carbon tetrachloride. Moreover, the effect of the medium would be expected to bring a lowering of the gas-phase heat, as Dr. Davies has shown. 

The results were consistent only with a value n= 1. Hence apparently in this case a monoetherate only is formed. The heat of association of tetrahydrofuran with the ion-pair is found to be 18 kilocal/mole, a value about that expected from simple electrostatic calculations. At low THF concentrations where the dielectric constant is not appreciably different from that in pure hexane, kp for the etherate was evaluated as 0.14 litre/mole sec at 30°. The overall propagation rate increases steadily up to a tetrahydrofuran concentration of about 1 molar and then decreases... 

In summary, ions that exhibit a positive dependence of K on E/N can be understood to undergo clustering and declustering events as shown in Fig. 8. During a low-field portion of the waveform, ions are not electrically heated or are slightly over thermal energies, and associations with water and supporting atmosphere can occur with lifetimes proportional to the heats of association. These associations result in increases in flD and decreases... 

The bond strength or bond energy is usually defined as the heat of association of the neutral atoms rather than the ions however, the two heats differ only by the ionization potential and electron affinity of the reactants. We have chosen this form of the reaction since it is in the same form as that which has been used to discuss equilibria in aqueous solution, i. e. M( q) -f- nX (aq) = MXn(aqj. 

This is also the case for the heat of association of neutral atoms in the gas phase. 

Potentially interesting donors were first screened on the basis of the saturation pressure of the adduct. (The term saturation pressure refers to the total pressure of vapor in equilibrium with a sample of molecular addition compound. The vapor may consist of free acid, base, undissociated complex, or a combination of all of these constituents.) Measured quantities of BF3 and the donor were equilibrated at a given temperature in the apparatus shown in Reference 14. Manometric observations (corrected for the free volume of the equipment) were made over that part of the liquid range which lay between room temperature and the freezing point of the complex. Estimates of the heat of association of the complexes were obtained from the temperature dependence of the saturation... 

Huggins, Pimentel, and Shoolery measured NMR shifts of chloroform in acetone and in triethylamine (982). This study furnishes corroborative evidence that the chloroform-base interaction can be classified as a H bond. More important, however, it serves as a prototype of the use of NMR chemical shifts in the study of complex formation. Huggins et al, based their analysis on an expression analogous to equation (7). They show that two data—the experimental values of 5 in pure chloroform and at infinite dilution, combined with the equilibrium constant for association—permit csdculation of the entire concentration dependence of 5. This implies that the measurement of 5 over the range from pure liquid to infinite dilution gives an estimate of the equilibrium constant. Of course the temperature dependence of the constant gives the heat of association. The appropriate equations are given in reference 982 where they are used to obtain K and A// for the association of chloroform with the bases acetone and triethylamine. 

The heat of association needed to form the dimer (HCOOH)2, is rather low, viz., 14.11 kcal/mole of dimer calculation shows that at reaction... 

The heat of association, in aqueous solution, of fluoride ion with metal ions of the Mn(Il)-Zn(II) series has been measured by a direct calorimetric method at / = 0.5 M and... 

The constant 1.51 is the log of the association constant at 26.7 0 extrapolated back to Infinite dilution (K° = 32.). Using this equation, they calculated values for log K at temperatures from 20 to 50 C which were then plotted versus 1/T. From its slope, a value for the heat of association was determined. Values for G° and AS of the reaction were derived using the value of 30 for Kf at 25 C. The results presented are ... 

Isothermal titration calorimetry (ITC) measures heats of association for ligand complexation as one component is titrated into the other. ITC measurements provide direct determination of the number of binding sites, n, the enthalpy of binding, AH, and the association constant, K. The association constant can then be used to determine the free energy, AG, from which entropic contributions, AS, to binding can be calculated. This technique offers the benefit that titration can be done in solution and has been used extensively to characterize the thermodynamic contributions of multivalent ligand binding to proteins. ... 

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