Equilibrium constant for bases

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

The acid-base equilibrium constant for the Me residue can be determined by spectroscopic pH titration. An example for the titration is shown in Fig. 2. The electrostatic potential

difference between the apparent pK on the charged surface (pKobs) and that on an intrinsic neutral surface (pK1) by... 

For HA a weak acid the products of the dissociation are hydrogen ion (H" ) and an anion (A ), which is the conjugate base. Equilibrium constants for acids can be written in the following form ... 

For TIOA with hydrochloric acid the concentration-based equilibrium constant for salt formation" according to reaction (8.2-6) is 1.51 x 10 and the equilibrium constant for amine-hydrochloride salt dimerization" is 8.0 M Combination of these parameters and the ion-complex stability constants with experimental metal-distribution data allows determination of the equilibrium constants for reactions (8.2-5) or (8.2-7). This completes the description of the amine-metal extraction-phase equilibria. For cobalt(II) in acidic sodium chloride solutions the equilibrium constant" for reaction (8.2-7) with TIOA is 2.0 X 10 and that for coppeifll) is 370 The corresponding value for zinc" is 7.5 x 10 Af -In spile of these relative values, the order of selectivity of TIOA for extraction of the metals is Zn > Cu > Co because of the relative extent of chloride complex formation. For the same reason, zinc stripping is difficult in this system, and copper has a tendency to be reduced to cuprous, which also complexes and extracts extensively. 

K. mole fraction based equilibrium constant for reaction involving reactants and transition state... 

The logarithmic form of the acid-base equilibrium constant for water will then be... 

In equation (2) c, is the liquid mole fraction, the vapor pressure, Y,- the liquid activity coefficient, F, a correction factor for pure components, 2, the true vapor mole fraction, and p is the system pressure. F. and the relation between 2 and y., the vapor mole fraction without dimerization, are calculated according to Marek, Standart, 1954. The temperature and pressure dependent mole fraction based equilibrium constant for the dimerization can be found in Fredenslund et al. 1977. With a heat of reaction of about -6lkJ I mole, the vapor phase dimerization affects the enthalpy calculations as well. 

Dissociation of oxygen, O2 -> 20. Compute Kp, the pressure-based equilibrium constant for this dissociation reaction at T = 3000 K. The electronic ground-state degeneracy for 0 is o(O) = 9. 

This equilibrium constant is based on activity, not concentration. It now must be converted to a concentration-based equilibrium constant. For a gas,... 

According to the Arrhenius definitions an acid ionizes m water to pro duce protons (H" ) and a base produces hydroxide ions (HO ) The strength of an acid is given by its equilibrium constant for ionization m aqueous solution... 

The carbon-metal bonds of organolithium and organomagnesium compounds have appreciable carbamomc character Carbanions rank among the strongest bases that we 11 see m this text Their conjugate acids are hydrocarbons—very weak acids indeed The equilibrium constants for ionization of hydrocarbons are much smaller than the s for water and alcohols thus hydrocarbons have much larger pA s... 

The equilibrium constant for a reaction in which a base accepts a proton from the solvent (i b)-... 

A species that can serve as both a proton donor and a proton acceptor is called amphiprotic. Whether an amphiprotic species behaves as an acid or as a base depends on the equilibrium constants for the two competing reactions. For bicarbonate, the acid dissociation constant for reaction 6.8... 

The equilibrium constant for equation 6.13 is K. Since equation 6.13 is obtained by adding together reactions 6.11 and 6.12, may also be expressed as the product of Ka for CH3COOH and Kb for CH3COO-. Thus, for a weak acid, HA, and its conjugate weak base, A-,... 

In a simple liquid-liquid extraction the solute is partitioned between two immiscible phases. In most cases one of the phases is aqueous, and the other phase is an organic solvent such as diethyl ether or chloroform. Because the phases are immiscible, they form two layers, with the denser phase on the bottom. The solute is initially present in one phase, but after extraction it is present in both phases. The efficiency of a liquid-liquid extraction is determined by the equilibrium constant for the solute s partitioning between the two phases. Extraction efficiency is also influenced by any secondary reactions involving the solute. Examples of secondary reactions include acid-base and complexation equilibria. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

Although this experiment is written as a dry-lab, it can be adapted to the laboratory. Details are given for the determination of the equilibrium constant for the binding of the Lewis base 1-methylimidazole to the Lewis acid cobalt(II)4-trifluoromethyl-o-phenylene-4,6-methoxysalicylideniminate in toluene. The equilibrium constant is found by a linear regression analysis of the absorbance data to a theoretical equilibrium model. 

The equilibrium constant for an acid-base indicator is determined by preparing three solutions, each of which has a total indicator concentration of 1.35 X lQ-5 M. The pH of the first solution is adjusted until it is acidic enough to ensure that only the acid form of the indicator is present, yielding an absorbance of 0.673. The absorbance of the second solution, whose pH was adjusted to give only the base form of the indicator, was measured at 0.118. The pH of the third solution was adjusted to 4.17 and had an absorbance of 0.439. What is the acidity constant for the acid-base indicator ... 

Since in most practical circumstances at temperatures where vapour transport is used and at around one atmosphere pressure, die atomic species play a minor role in the distribution of atoms, it is simpler to cast the distribution equations in terms of the elemental molecular species, H2, O2 and S2, tire base molecules, and the derived molecules H2O, H2S, SO2 and SO3, and eliminate any consideration of the atomic species. In this case, let X, be tire initial mole fraction of each atomic species in the original total of atoms, aird the variables Xi represent the equilibrium number of each molecular species in the final number of molecules, N/. Introducing tire equilibrium constants for the formation of each molecule from tire elemental atomic species, with a total pressure of one aurros, we can write... 

In the case of tire direct oxidation, the oxygen partial pressure must be greater than that at the Pb/PbO equilibrium, while in the process involving sodium-based salts, the oxygen pressure is less than this. The two equilibrium constants for the refining reactions... 

PK. — the negative logarithm of the equilibrium constant for acids or bases. This parameter is an indicator of the strength of an acid or base. Strong acids, such as H2SO4, and HCl, have low pK s (i.e., -1.0) while strong bases such as KOH and NaOH, have pK s close to 14.0. Weak acids and weak bases fall in the intermediate range. 

Pyridine bases are well known as ligands in complexes of transition metals, and it might well be anticipated that the equilibrium constants for the formation of such complexes, which are likely to be closely related to the base strength, would follow the Hammett equation. Surprisingly, only very few quantitative studies of such equilibria seem to have been reported, and these only for very short series of compounds. Thus, Murmann and Basolo have reported the formation constants, in aqueous solution at 25°, of the silver(I) complexes... 

Equilibrium Constants for Weak Acids and Their Conjugate Bases... 

The general approach illustrated by Example 18.7 is widely used to determine equilibrium constants for solution reactions. The pH meter in particular can be used to determine acid or base equilibrium constants by measuring the pH of solutions containing known concentrations of weak acids or bases. Specific ion electrodes are readily adapted to the determination of solubility product constants. For example, a chloride ion electrode can be used to find [Cl-] in equilibrium with AgCl(s) and a known [Ag+]. From that information, Ksp of AgCl can be calculated. 

Calculate equilibrium constants for the two acid-base reactions just cited. 

This reaction shows that the hydrated oxide SiCV-xHjO is acidic, since it reacts with a base-As we mentioned earlier, phosphorus can be found in four different oxidation states. The hydroxides of the +1, +3, and +5 states of phosphorus are hypophosphorous acid, H3P02, phosphorous acid, H3P03, and phosphoric acid, H3P04. Their structures are shown in Figure 20-4. As suggested by their names, these compounds are distinctly acidic, and are of moderate strength. The equilibrium constant for the first ionization of each acid is approximately 10-2 hypophosphorous acid ... 

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