Equilibria slowly established

The hallmark of slow binding inhibition is that the degree of inhibition at a fixed concentration of compound will vary over time, as equilibrium is slowly established between the free and enzyme-bound forms of the compound. Often the establishment of enzyme-inhibitor equilibrium is manifested over the time course of the enzyme activity assay, and this leads to a curvature of the reaction progress curve over a time scale where the uninhibited reaction progress curve is linear. We saw... 

Although from the thermodynamic point of view one can speak only about the reversibility of a process (cf. Section 3.1.4), in electrochemistry the term reversible electrode has come to stay. By this term we understand an electrode at which the equilibrium of a given reversible process is established with a rate satisfying the requirements of a given application. If equilibrium is established slowly between the metal and the solution, or is not established at all in the given time period, the electrode will in practice not attain a defined potential and cannot be used to measure individual thermodynamic quantities such as the reaction affinity, ion activity in solution, etc. A special case that is encountered most often is that of electrodes exhibiting a mixed potential, where the measured potential depends on the kinetics of several electrode reactions (see Section 5.8.4). 

In the absence of polarization effects, if the material can flow, as in a drop, and if the stress is applied slowly enough, an equilibrium is established with surface tension. When any perturbation is applied to this system, vibrations are set up with frequencies given by... 

The keto/enol equilibrium (15) has been a spur to much research. In the absence of catalysts the equilibrium is established slowly and is very sensitive to a variety of influences, both internal, such as the nature of a- and P-substituents, and external, such as temperature and solvent. The discovery that the equilibrium was established sufficiently slowly to permit both keto and enol tautomers to be observed by H-nmr spectroscopy allowed these several influences to be easily investigated (see Kol tsov and Kheifets, 1971, for a review of the early work, and Emsley, 1984, for later work). 

Because of the dosing technique associated with the vacuum volumetric method there exists a potential source of error which in principle cannot be avoided on samples that are slow to equilibrate. Figure 14.2 represents a plot of the pressure in the sample cell versus time. The pressure up to time tj represents the equilibrium pressure in the sample cell before a new quantity of adsorbate is admitted. At time adsorbate is admitted into the sample cell and is accompanied by a rapid pressure rise. The pressure then gradually decreases to a new equilibrium value at time t2- If the decay to the new equilibrium pressure is slow, it is possible for open or accessible parts of the surface, such as the interior of wide pores, to contain more adsorbate before equilibrium is attained than after equilibrium is established. Less accessible regions, such as the interior of long narrow pores, will adsorb slowly and as the pressure falls because of adsorption in these pores, desorption must occur from the more accessible pores which tend to equilibrate more rapidly. If a porous sample is subjected to... 

Demougin and Bonnet reported that both these reactions occurred at the same rate in cone, acids, equilibrium being established after about fourteen days. With nitrating acids containing an exceptionally high percentage of water, i.e. 21.7% water in experiments of Miles and Milbourn [20], or 24.6% in the experiments of Berl and Hefter [27], the balance tends to establish itself very slowly, and considerably altered products are formed due to side reactions. Efforts to achieve an absolute equilibrium fail in such instances. 

Titration curves of PAA rise only slowly with increasing neutralization. Because of this, partial salts of PAA are good buffers in the pH range of 4 to 6.4. PAA is difficult to titrate because equilibrium is only slowly established (4). 

Empirical equations of the form T = aF + bD + c, expressing the relation between total solids (T), fat (F), and density (D), have been used for years. Such derivations assume constant values for the density of the fat and of the mixture of solids-not-fat which enter into the calculation of the coefficients (a, b, and c). Since milk fat has a high coefficient of expansion and contracts as it solidifies (note that the solid-liquid equilibrium is established slowly), the temperature of measurement and the previous history of the product must be controlled carefully (see Sharp and Hart 1936). Variations in the composition of... 

The time required to reach equilibrium very much depends on the pKd value of the acid. An acid with a pKa value of 4, for example, deprotonates with a rate of 106 s Thus, the equilibrium is established within a few microseconds. On the other hand, an acid with a pKa value of 7 dissociates with a rate of ca. 103 s"1, and the equilibrium becomes established only on the millisecond time range. In a pulse radiolytic experiment, a large part of the radicals will thus have disappeared in bimolecular termination reactions, before an equilibrium is reached. Buffers speed-up the protonation/deprotonation reactions, and their addition can overcome this problem. Yet, they deprotonate acids and protonate their corresponding anions typically two to three orders of magnitude more slowly than OH and H+ (for a DNA-related example, see Chap. 10.4 for potential artifacts in the determination of pKa values using too low buffer concentrations, see, e.g., von Sonntag et al. 2002). 

Since the S02/S03 equilibrium is established relatively slowly, the rate- determining step is likely to involve the expulsion of an S03 molecule from the crystal lattice. All of the reported activation energies are much less than AH = 526 kJ, but AH per mole of S03 is 526/3 = 176 kJ which is at least in the right range. 

The number of components is the minimum number of independent species required to define the composition of all of the phases in the system. The simplest example usually cited to demonstrate the concept of components is that of water, which can exist in various equilibria involving the solid, liquid, and gas. In such a system there is one component. Likewise for acetic acid, even though it associates into dimers in the solid, liquid, and gaseous state, the composition of each phase can be expressed in terms of the acetic acid molecule and this is the only component. The important point for such a system is that the monomer-dimer equilibrium is established very rapidly, that is, faster than the time required to determine, say, the vapour pressure. In the cases in which the equilbrium between molecular species is established more slowly than the time required for a physical measurement, the vapour pressure, for example, will no longer be a function only of temperature, but also of the composition of the mixture, and the definition of a component acquires a kinetic aspect. 

For the determination of the differential values of r and / the PVT cell containing mercury and a known volume of reservoir fluid is immersed in the constant temperature bath at reservoir temperature and the pressure is reduced 200 psi below the saturation pressure by withdrawing mercury from the cell through the mercury pump. The cell and its contents are thoroughly agitated until equilibrium is established and the volume of the gas-oil system is recorded. The gas is bled off through the metering device and at the same time the piston of the mercury pump is slowly advanced to keep the pressure in the cell constant. When the gas has been bled off, the volume of the residual oil in the cell is measured and recorded. The volume of the... 

CoHMD + homogeneously catalyzes both electroreduction of CO2 and water reduction in water, water-acetonitrile or DMF solutions [8, 9], The CO-to-Fl2 ratio produced is typically less than 1 and strongly depends on the experimental conditions used (i.e., applied potential, amount of water, electrolysis time, etc). The chiral N-H centers of the HMD macrocycle give rise to two isomers, N-rac and N-meso, as shown in Figure 2. The N-rac isomers of both Co HMD + and Co HMD+ predominate in MeCN (>90 %) and water at room temperature. The equilibrium between the N-rac and N-meso cobalt(II) isomers is very slowly established in acidic aqueous and organic media (<2 x 10 s ) by contrast, equilibration of the cobalt(I) isomers is relatively rapid (>2 x 10 s ) [13, 14]. 

The equilibrium perturbed by the electrolytic process el) tries to be re-established. The compound C is replenished in the vicinity of the electrode by a chemical conversion of A with rate constant k[. In this way the amount of C that can undergo reduction at the surface of the electrode is increased and the wave becomes higher when compared with the conditions for a slowly established equilibrium (Fig. 18). The magnitude of this increase depends, for given experimental conditions, on the value of the formal rate constant k[, i.e. on the magnitude of ki and the concentration of the component B present in excess. 

Such a solution is said to be saturated. Saturation occurs at very low concentrations of dissolved species for slightly soluble substances and at high concentrations for very soluble substances. When imperfect crystals are placed in saturated solutions of their ions, surface defects on the crystals are slowly patched with no net increase in mass of the solid. Often, after some time has passed, we see fewer but larger crystals. These observations provide evidence of the dynamic nature of the solubility equilibrium. After equilibrium is established, no more solid dissolves without the simultaneous crystallization of an equal mass of dissolved ions. 

To conclude, the movement of potassium across the cell membrane sets up an electric potential across the cell membrane which opposes this same flow. Charged protein structures are unable to move across the membrane, while sodium ions cross very slowly, and so an equilibrium is established. The cell is polarized and the electric potential at equilibrium is known as the resting potential. 

That the time dependence of the H2 chemisorption was anyway caused by a slow attainment of equilibrium, was established by performing the H2 chemisorption measurement in a modified way. Hydrogen was admitted to the evacuated catalyst at ca. 200 C and subsequently the reactor was slowly cooled down to room temperature and H2 chemisorption was measured. In this case equilibrium was quickly established and the chemisorption value was substantially higher (about 20%) than that reached during room temperature measurements for 18 h. Furthermore, since there was no difference between the H2 chemisorption measured after admission of H2 at 190 C during 10 min and that measured after admission at 205 C during 30 min, a temperature of about 200 C during 10 min seems sufficient to quickly reach equilibrium. 

The observation was made that the pressure developed in the closed apparatus could be made to serve as a fair measure of the decomposition of the substance. By increasing the temperature slowly and studying the effect of temperature upon pressure by means of a series of experiments in which the substance was subjected to the action of heat at various temperatures and during different periods of time the further important observation was made that certain zones of temperature exist within the limits of which a condition of equilibrium seems to prevail between the substance and those of its decomposition products which tend to form at such temperatures. In other words, it may be said that pressure tends to decrease the complete decomposition of the alcohol and to establish regions of temperature and pressure within which a condition of equilibrium is established between it and its decomposition products. 

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