Intermolecular constants

Under the given conditions, there are only four possible states for the receptor free BB, the partially bound 1 1 open complex o-AA-BB, the fuUy bound 1 1 cyclic complex c-AA-BB and the 1 2 complex BB-(AA)2. The macroscopic equffibrium constants in Scheme 24 have been factored as the product of statistical factors and microscopic equffibrium constants specifically, K is the microscopic intermolecular constant that expresses the strength of the binding interaction between A and B, and EM is the microscopic effective molarity, defined as the microscopic equffibrium constant of the reaction in Eq. [6] (see Section 5.1). It is useful to recall that positive allosteric cooperativity is characterized by a low concentration of partially bound species. In the most extreme cases only the unbound and... 

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

Transalkylation is also catalyzed by acids, but requires more severe conditions than isomerization. As shown below, the methyl migration is intermolecular and ultimately produces a mixture of aromatic compounds ranging from benzene to hexamethylbenzene. The overall equiHbrium constants for all possible methylbenzenes have been deterrnined experimentally and calculated theoretically (Fig. 2 and Table 3). 

With a three-parameter model of the intermolecular potential, the theoretical spall strength is not simply a constant times the bulk modulus. Although the slightly greater accuracy obtained is not critical to the present investigation, an energy balance is revealed in the analysis which is not immediately transparent in the Orowan approach. 

Fig. 18. Rate constant calculated with the use of (2.80a) plotted against (m/mH). The hydrogen transfer rate is assumed to be 10 s the effective symmetric vibration mass 125mH. The ratio of force constants corresponding to the intra (Kq) and intermolecular (K,) vibrations is (Ki/Ko) = 2.5 x 10 , 5 x 10 and l.Ox 10 for curves 1-3, respectively.

Such calculations have been performed by Takayanagi et al. [1987] and Hancock et al. [1989]. The minimum energy of the linear H3 complex is only 0.055 kcal/mol lower than that of the isolated H and H2. The intermolecular vibration frequency is smaller than 50cm L The height of the vibrational-adiabatic barrier is 9.4 kcal/mol, the H-H distance 0.82 A. The barrier was approximated by an Eckart potential with width 1.5-1.8 A. The rate constant has been calculated from eq. (2.1), using the barrier height as an adjustable parameter. This led to a value of Vq similar to that of the gas-phase reaction H -I- H2. 

Fig. 60. Configuration and relevant coordinates of the planar HF dimer in stable and transition configurations. The angles and intermolecular distance are = 9°, 6 = 116°, R = 2.673 A in the stable configuration 0, = 02 = 54.9°, R = 2.S61 k in the transition configuration. The HF bond lengths are constant within an accuracy of 0.003 A.

Derive the general expression for the observed rate constant for hydrolysis of A as a function of pH. Assume, as is the case experimentally, that intramolecular general acid catalysis completely outweighs intermolecular catalysis by hydronium ion in the pH range of interest. Does the form of your expression agree with the pH rate profile given for this reaction in Fig. 8.6 (p. 489) ... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

In a force-displacement curve, the tip and sample surfaces are brought close to one another, and interact via an attractive potential. This potential is governed by intermolecular and surface forces [18] and contains both attractive and repulsive terms. How well the shape of the measured force-displacement curve reproduces the true potential depends largely on the cantilever spring constant and tip radius. If the spring constant is very low (typical), the tip will experience a mechanical instability when the interaction force gradient (dF/dD) exceeds the... 

This treatment obviously is oversimplified. At the next level of development, it is necessary to incorporate the intermolecular forces between A and B. ° If A and B are ions of opposite charge, it is found that the diffusion-limited rate constant is about 10 M s . ... 

First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu-... 

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