Dissociation constants, calculation

According to modem views, the basic points of the theory of electrolytic dissociation are correct and were of exceptional importance for the development of solution theory. However, there are a number of defects. The quantitative relations of the theory are applicable only to dilute solutions of weak electrolytes (up to 10 to 10 M). Deviations are observed at higher concentrations the values of a calculated with Eqs. (7.5) and (7.6) do not coincide the dissociation constant calculated with Eq. (7.9) varies with concentration and so on. For strong electrolytes the quantitative relations of the theory are altogether inapplicable, even in extremely dilute solutions. 

This yielded a fe+i of 0.0091 + 0.002 nM mm for NO 711 binding to mGATl. Hence, the equilibrium dissociation constant calculated from kinetic MS binding experiments resulted in = 11.7 2.5 nM. This is in good accord with Kj determined in MS saturation binding experiments and confirms the validity of the new setup. 

Porcine anterior pituitary membranes were incubated as described in Figure 1 with [3HJspiro-peridol (10-1100 pM). Nonspecific binding was determined in the presence of 1 mM (- -)buta-clamol. Data were analyzed by curve fitting with a model for the binding of the radioligand to one or two classes of sites (14). Data are presented in the Scatchard plot coordinates. The experiment was performed in duplicate and is similar to several other experiments with the same results but it represents an extreme case of the ability of the [3H] antagonist to discriminate between the two forms of the receptor. The two dissociation constants calculated for the control curve are different by about 10-fold. (Reproduced with permission from Ref. 25. 

These KD values are much smaller than those of trityl and benz-hydryl salts (lO-MO-4 mol/L) (cf Tables 7 and 16). The KD values of trityl salts correspond to interionic distances of approximately 5 A. The smaller (Kd 107-10-6 mol/L) dissociation constants calculated from the common ion effect in styrene polymerizations with triflate and perchlorate anions correspond to interionic distances =4 A. However, perchlorate and triflate anions may not be spherical, and their dipole moments should therefore also be considered in calculating their interionic distances and dissociation constants. As discussed in Section II.D, specific interactions of counteranions with the ar-H atoms of the secondary carbenium ions may result in lower dissociation constants [39],... 

The second group of values came from studies where it was assumed that polymerization reactions occurred, such as the formation of H5As206 (aq>, in addition to the deprotonation reaction. For chemical and mathematical reasons, the dissociation constant calculated from a set of measurements becomes smaller as one introduces polymeric anions into the model. The differences of the models chosen, at first appearance, could serve to explain the differences of the equilibrium constants given in the previous table. Unfortunately, the situation, from the perspective of data evaluation, is more complex. In principle, there should be a sufficient dilution of arsenious acid for which one would not expect the formation of a significant proportion of species like HsAsaOe caq) upon addition of base. For such a condition, the equilibrium constant determined assuming that only the monomer exists, should approach that determined for the multi-species model. Britton and Jackson (1934) performed potentiometric titration at two concentrations of arsenious acid (0.0170 and 0.0914 molar) and obtained essentially the same... 

To determine Ki and K2 for H3PO4 from titration data, careful pH measurements ar e made after 0.5 and 1.5 mol of base are added for each mole of acid. It is then assumed that the hydrogen ion activities computed from these data are identical to the desired dissociation constants. Calculate the relative error incurred by the assumption if the ionic strength is 0.1 at the time of each measurement. 

By way of illustration we present the two following tables which include the thermodynamic dissociation constants of acetic acid and o-nitrobenzoic acid calculated from conductivity measurements by J. Kendall. The first column contains the acid concentration, the second contains the classical degree of dissociation a multiplied by 100, in the third is found the dissociation constant calculated by the classical method, the fourth gives ac (classical ion concentration), the fifth column shows the true ion concentration ac//x, the sixth contains the concentration of undissociated acid [cHA] = c — (aclf ), and in the last column is found Ka calculated by equation (15). 

M. Sramko, M. Smiesko, and M. Remko, Accurate aqueous proton dissociation constants calculations for selected angiotensin-converting enzyme inhibitors, J. Biomol. Struct. Dyn. 25 (2008), pp. 599-608. 

As seen in Fig. 6, the Henderson-Hasselbalch reversible binding isotherm adequately describes the relationship between pH and electrical resistance of the hydrogel-coated electrode anays. The apparent dissociation constant calculated for the tertiary amine of the DMA monomer, is slightly higher than, but similar... 

A sample contains a weak acid analyte, HA, and a weak acid interferent, HB. The acid dissociation constants and partition coefficients for the weak acids are as follows Ra.HA = 1.0 X 10 Ra HB = 1.0 X f0 , RpjHA D,HB 500. (a) Calculate the extraction efficiency for HA and HB when 50.0 mF of sampk buffered to a pH of 7.0, is extracted with 50.0 mF of the organic solvent, (b) Which phase is enriched in the analyte (c) What are the recoveries for the analyte and interferent in this phase (d) What is the separation factor (e) A quantitative analysis is conducted on the contents of the phase enriched in analyte. What is the expected relative erroi if the selectivity coefficient, Rha.hb> is 0.500 and the initial ratio ofHB/HA was lO.O ... 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

The initial goal of the kinetic analysis is to express k as a function of [H ], pH-independent rate constants, and appropriate acid-base dissociation constants. Then numerical estimates of these constants are obtained. The theoretical pH-rate profile can now be calculated and compared with the experimental curve. A quantitative agreement indicates that the proposed rate equation is consistent with experiment. It is advisable to use other information (such as independently measured dissociation constants) to support the kinetic analysis. 

Figure 6-14 shows FhjS. Fhs, and Fs plotted against pH for an acid with pF, = 5.0 and pA"2 = 10.0. Evidently with such widely spaced dissociation constants the solution contains, at any one pH, significant fractions of only two species. The fraction of monoanion rises essentially to unity at one point. The pH at which the monoanion fraction achieves its maximum value is calculated by differentiating Eq. (6-74) and setting the result equal to zero this gives... 

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. 

Apparent partition coefficient (logZ)) at an ionic strength of / = 0.02M, log P value of the neutral microspecies and the acidic dissociation constant of 5 was calculated (97ANC4143). The distribution coefficient of 5 was determined between 1-octanol and universal buffer in the pH range 3-10 at a... 

Using these acid dissociation constants for glycine, calculate the ratios [Z]/[C+] and [Z]/[A-] at pH... 

Aspartic acid acts as a triprotic acid with successive dissociation constants of 8.0 x 10-3, 1.4 X 10-4, and 1.5 X 10-10. Depending upon pH, aspartic acid can exist in four different forms in water solution. Draw these forms and calculate the pH range over which each form is the principal species. 

Therefore, a double reciprocal plot of equiactive agonist concentrations in the presence (1/[A ] as abscissae) and absence (1 /[A] as ordinates) of antagonist should yield a straight line. The equilibrium dissociation constant of the antagonist is calculated by... 

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