Dissociation equilibrium constant measurement

These results show that if the relationship between the concentration of an agonist and the proportion of receptors that it occupies is measured directly (e.g., using a radioligand binding method), the outcome should be a simple hyperbolic curve. Although the curve is describable by the Hill-Langmuir equation, the dissociation equilibrium constant for the binding will be not KA but Ke, which is determined by both E and KA. 

Measurement of dissociation equilibrium constants, which is of particular value in receptor classification and in the study of structure/activity relationships, where the effects of changes in chemical structure on affinity (and efficacy) are explored. 

Simpler expressions for the line shape are available for both the fast and slow exchange regimes (see Ref. [9]). The possibility of measuring the dissociation equilibrium constant in each of these three regimes will now be considered. 

Acidity has been most widely studied in aqueous solution and is easily defined in this medium by the acid dissociation equilibrium constant, (Eq. 3) where S represents the solvent employed in the measurement. Given the magnitudes of values, they are often expressed as pKa values for convenience (Eq. 4). 

Acids are often divided into categories such as strong and weak. One measure of the strength of an acid is the acid-dissociation equilibrium constant, K, for that acid. 

Table 1.7 Calculation of the dissociation equilibrium constant of acetic acid from measured values of molar conductivity...

As Eq. 13 shows, this feature can be used to derive the dissociation equilibrium constant ICD directly from the frequency difference at the end of measurement A f The main drawback of this method is that long-term experiments and large quantities of analyte are required. 

The measured values of the formation constant for Cu-NTA at intermediate pH will then be 10 which is significantly less than the value of 10 measured at high pH. The same is true for the humic substance-metal ion complex equilibrium constants measured at low pH values. Morgan estimates that at pH 2 to 3 the —COO groups, which are important in forming fulvic acid-metal ion complexes, are virtually all in the —COOH or protonated form. Thus to obtain the value of the formation constant at intermediate pH for metal ion fulvic acid complexes, when the carboxyl groups are ionized, we should divide the equilibrium constant values presented in Table 5-13 by the dissociation constant of the —COOH group, that is,... 

Bell and co-workers (1949, 1952) reported extensive studies on the base-catalyzed halogenation of a series of ketones and esters and related the reactivity as measured by k(, with the parameter / . We know that ko has to be defined for a standard substrate. In this particular case, it is defined as the rate constant for the halogenation of a hypothetical catalyzing base with a dissociation equilibrium constant ATb of 10 . Specifically, let us demonstrate the procedure for the reagent acetone. Equation (E2.4.2) can be written as... 

The polymerization rate depends very much on the proportion of free macroanions present. In the anionic polymerization of styrene with sodium as gegenion in THF, kinetic measurements (see below) gave the rate constants for polymerization via free macroanions as /C(-> = 65000 dm mol s" and fc(+) = 80 dm mol s for the polymerization via ion pairs (Table 18-2). According to the relation Vp = kp[P ] [M], the rate of the propagation reaction depends on the active species concentration [P ] as well as on the rate constant kp. But in this system, the dissociation equilibrium constant Kjy for ion pairs into free ions is only 10" mol/dm. If the polymerization is carried out in a solution with 10 mol/dm, then the proportion of free ions is consequently only (10 10 ) = 0.01, that is, 1 %, with 99% of the active species being ion pairs. Thus, despite a much lower rate constant, the polymerization rate is also determined to a considerable extent by the ion pairs. 

In order to determine the energies of dissociation of the metal-ligand bond, the following methods are commonly utilized calorimetric combustion, solution calorimetry, ion cyclotron resonance, mass spectrometry, ion beam technique, equilibrium constant measurements, kinetic methods, and photochemical determination of the threshold wavelength of the photolytic dissociation of the metal-ligand bond. ... 

In order to obtain more information about the importance of the transfer according the nature of the ionic species, we have calculated the final equilibrium concentrations under typical initial conditions, computing them from electroneutrality and measured partition coefficients and dissociation equilibrium constant of HPi in nitrobenzene. The results are summarized and schematized in figure 4a. They show a full dissociation of HPi and... 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

The strength of a weak acid is measured by its acid dissociation constant, which IS the equilibrium constant for its ionization m aqueous solution... 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

D2O and the tritium analogue T2O (p. 41). The high bp is notable (cf. H2S, etc.) as is the temperature of maximum density and its marked dependence on the isotopic composition of water. The high dielectric constant and measurable ionic dissociation equilibrium are also unusual and important properties. The ionic mobilities of [H30] and [OH] in water are abnormally high (350 X 10 " and 192 x 10 cms per V cm... 

The value for the equilibrium constant at 25°C given in the last column of Table 10 is 4.52 X 10 7. Multiplying logoff by RT, we find for AF° the value 8683 cal/mole. The heat of dissociation has been measured calorimetrically1 and found to be 1843 cal/mole. By subtraction we find... 

In the dilute aqueous solution normally used for measuring acidity, the concentration of water, H20], remains nearly constant at approximately 55.4 M at 25 °C. We can therefore rewrite the equilibrium expression using a new quantity called the acidity constant, Ka. The acidity constant for any acid HA is simply the equilibrium constant for the acid dissociation multiplied by the molar concentration of pure water. 

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

The very slow dissociation rates for tight binding inhibitors offer some potential clinical advantages for such compounds, as described in detail in Chapter 6. Experimental determination of the value of k, can be quite challenging for these inhibitors. We have detailed in Chapters 5 and 6 several kinetic methods for estimating the value of the dissociation rate constant. When the value of kofS is extremely low, however, alternative methods may be required to estimate this kinetic constant. For example, equilibrium dialysis over the course of hours, or even days, may be required to achieve sufficient inhibitor release from the El complex for measurement. A significant issue with approaches like this is that the enzyme may not remain stable over the extended time course of such experiments. In some cases of extremely slow inhibitor dissociation, the limits of enzyme stability will preclude accurate determination of koff the best that one can do in these cases is to provide an upper limit on the value of this rate constant. 

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