Macroscopic Dissociation Equilibria

From this we see that the relation between the concentration of A and the amount of it that is bound should follow the Hill-Langmuir equation. Ke, the macroscopic dissociation equilibrium constant, is given by ... 

In Appendix 1.6B we obtained an expression for the macroscopic dissociation equilibrium constant, Ke, for the binding of a ligand on the same scheme as in Figure 1.14. Allowing for the difference in terms, KeS and EC50 are seen to be identical. 

Potentiometric titration of phenylephrine vs NaOH (Figure 4-8) yields the macroscopic dissociation constants while the microscopic dissociation constants are accessible from simultaneous observation of potentiometric and C H -NMR-controlled titrations (Figure 4-9 and Figure 4-10). TTie microscopic dissociation species defined in Table 4-1 are involved in the microscopic dissociation equilibrium shown in Figure 4-6. 

Figure 7.1 shows the pK s of some dicarboxylic acids along with the pK s of some related monocarboxylic acids. As noted earlier, complications can arise when a compound contains groups that have dissociations with close pK values [93,173,434]. In such a case one must consider the equilibria shown in Figure 7.2 for dissociation of an original acid RH Ht [173], In this scheme K, Kg, Kc, and are so-called microscopic equilibrium constants and is the equilibrium constant for tautomerization between RH and RH. . The experimentally measured (macroscopic) dissociation constants Kj and K2 pertain to the following equilibria ... 

The perturbation of energy distribution by the chemical reaction can be caused in two ways. The first is by a decrease in the concentration of energy-rich molecules in the course of the reaction. This is mostly encountered in endothermal reactions (specifically in dissociation) that result in lower molecular population of high vibrational levels. When the microscopic dissociation rate of energy-rich molecules is higher than the rate of restoring equilibrium concentration, the vibrational energy distribution will be different from equilibrium and the macroscopic dissociation rate will become lower than the equilibrium rate. 

The equilibrium constants Ka, which are determined experimentally, are the macroscopic ones. They quantify together the two ionization ways. They are overall acid-dissociation equilibrium constants. They are defined as follows ... 

This review is structured as follows. In the next section we present the theory for adsorbates that remain in quasi-equilibrium throughout the desorption process, in which case a few macroscopic variables, namely the partial coverages 0, and their rate equations are needed. We introduce the lattice gas model and discuss results ranging from non-interacting adsorbates to systems with multiple interactions, treated essentially exactly with the transfer matrix method, in Sec. II. Examples of the accuracy possible in the modehng of experimental data using this theory, from our own work, are presented for such diverse systems as multilayers of alkali metals on metals, competitive desorption of tellurium from tungsten, and dissociative... 

By direct visual observation we can watch the contents of these two bulbs approach the constancy of macroscopic properties (in this case,, color) that indicates equilibrium. In bulb A equilibrium was approached by the dissociation of > N2Qi, reaction (4) in bulb B it was approached by the opposite reaction, reaction (5). Here it is clear why the color of each bulb stopped changing at the particular hue characteristic of the equilibrium state at 25°C. The reaction between N02 and N204 can proceed in both directions ... 

A principal theme of this text is the direct relation of macroscopic properties to molecular structure. In concluding the discussion on the si and sll cavity size ratios, two examples are given of how macroscopic engineering properties (equilibrium pressure and temperature, and heat of dissociation) are determined by the size ratios in Table 2.4. 

Taylor et al. conducted DFT simulations using a periodic model of the interface between water and various metal surfaces with an index of (1 1 l).102 The chemistry of water at these charged interfaces was investigated and the parameters relevant to the macroscopic behavior of the interface, such as the capacitance and the potential of zero charge (PZC), were evaluated. They also examined the influence of co-adsorbed CO upon the equilibrium potential for the activation of water on Pt(l 1 1). They found that for copper and platinum there was a potential window over which water is inert. However, on Ni(l 1 1) surface water was always found in some dissociated form (i.e., adsorbed OH or H ). The relaxation of water... 

The same approach can be applied not only to the bulk equilibrium constants (K) but also to the microscopic connection processes (given the symbol k). Recall that the macroscopic equilibrium constant is simply the sum of all the microscopic equilibrium constants. For example, if an acid (H2A) has two non-equivalent ionisable protons there are two distinct but equivalent ways to remove a proton to produce HA- and hence there are two microscopic equilibrium constants kx and k2) for this deprotonation process. Thus the macroscopic acid dissociation constant, K = k1+k2. Don t get confused between microscopic equilibrium constants and rate constants, both of which have the symbol k. So, in terms of... 

As with the continuum model, the particle based threshold line probability must at the macroscopic level recover a specified Arrhenius rate coefficient under equilibrium conditions. Unlike the continuum model, however, the Arrhenius constants a and rj do not appear in the model. Instead, the constant of proportionality, Ai, must be obtained through calibration of the model against rate data by performing test simulations under equilibrium conditions. Hence, with this approach, it is not possible to guarantee that the model will produce a specific temperature dependence for the dissociation rate. This could perhaps be achieved through inclusion of further dependencies of the dissociation probability on the various energies involved in the collision. 

According to these expressions, the intensity of the OH emission will decay as a biexponent, the rapid initial phase 72 represents the reaction as it proceeds until the velocity of dissociation and recombination become equal. The slower phase 71 represents the decay when the two populations (< >OH and 0 ) are in equilibrium with each other. The relative amplitudes of the two phases Ar = (a2i — 7i)/(72 7i) and the macroscopic rate constants (71,72) allow one to calculate the rate of all partial reactions. The agreement between rate constants calculated by time-resolved measurements and steady-state kinetics is usually good. In a limiting case, where the rate of recombination is much slower than dissociation pKo > pH >> pK, the amplitude of the slow phase representing recombination will diminish to zero and the emission of the < >OH state will decay in a single exponent curve with a macroscopic rate constant 72 = k + %,nr) k. ... 

A reversible gel based upon dissociable cross-links is characterized by the finite size of the network that is chemically linked into a unit at any instant. In a reversible gel, some of the network connections will always open, close, and interchange. A reversible gel, too, can thus be divided into structural subentities, but the bonds that link these substructures into a macroscopic whole do not possess infinite lifetimes. The coherence of the system depends upon it being contained in a chemically closed, semipermanent, mechanically rigid confinement. A reversible gel cannot, for example, be brought into true (open) swelling equilibrium with an excess of... 

The classical example is that of a symmetrical dicarboxylic acid. Since the two ends are chemically identical, the microscopic energy and therefore the microscopic equilibrium constant for the acid dissociation of each of the two groups is identical to, say, K. If we now look at the macroscopic level, we are not able to distinguish between the two ends of the molecules, and the observed, or macroscopic, first acid dissociation constant, is related to the probability that either site is deprotonated, thus Kai — 2. On the... 

The relationships between the various equilibrium constants in this scheme and macroscopic acid dissociation constants, and Ka are as follows ... 

The equilibrium dissociation constants, both macroscopic or global Kn) and microscopic or intrinsic (kn), for the various ES complexes are... 

Based on equilibrium arguments, a general expression for the velocity of a cooperative enzyme-catalyzed reaction can be derived. The equilibrium macroscopic (Kj, Kr) and microscopic ( x, r) dissociation constants for the different enzyme-substrate species present in a two-protomer enzyme are... 

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