Equilibrium constant ionization

Equilibrium constant Ionization constant of H2CO3 Ionization constant of the bicarbonate ion Equilibrium constant of CaCOj Equilibrium constant of CaHCOj Equilibrium constant of CaOH ... 

Equilibrium constants (ionization, complexation, and solubility) can be calculated from the data contained in the NBS Technical... 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

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

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 the overall reaction is related to an apparent equilibrium constant Ki for carbonic acid ionization by the expression... 

In a series of organic acids of similar type, not much tendency exists for one acid to be more reactive than another. For example, in the replacement of stearic acid in methyl stearate by acetic acid, the equilibrium constant is 1.0. However, acidolysis in formic acid is usually much faster than in acetic acid, due to higher acidity and better ionizing properties of the former (115). Branched-chain acids, and some aromatic acids, especially stericaHy hindered acids such as ortho-substituted benzoic acids, would be expected to be less active in replacing other acids. Mixtures of esters are obtained when acidolysis is carried out without forcing the replacement to completion by removing one of the products. The acidolysis equilibrium and mechanism are discussed in detail in Reference 115. 

The use of UV spectroscopy as an identification method is continuously decreasing in relative importance compared to the use of NMR or mass spectrometry. However, due to the general validity of Beer s law, it continues to be an appropriate method for quantitative studies such as the measurement of ionization constants (Section 4.04.2.1.3(iv) and (v)) and the determination of tautomeric equilibrium constants (Section 4.04.4.1.5). 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

It is possible to measure equilibrium constants and heats of reaction in the gas phase by using mass spectrometers of special configuration. With proton-transfer reactions, for example, the equilibrium constant can be determined by measuring the ratio of two reactant species competing for protons. Table 4.13 compares of phenol ionizations. 

Free energies of ionization are calculated from equilibrium constants according to the relationship... 

An expression for the ionization of H2CO3 under such conditions (that is, in the presence of dissolved CO2) can be obtained from Kh, the equilibrium constant for the hydration of CO2, and from the first acid dissociation constant for H2CO3 ... 

Therefore, the overall equilibrium constant for the ionization of H2CO3 in equilibrium with C02(d) is given by... 

Equilibrium constants and activation parameters have been determined [76ACS(B)101] [for a review see 82AHC(30)127]. Ionization potentials for tautomeric 2-hydroxyselenophenes have been analyzed by comparison with IP data for compounds derived from either tautomeric form. The enol form could not be detected [75ACS(B)647]. 

Hence for the ionization of water, the equilibrium constant expression can be written ... 

Certain weak acids are polyprotic they contain more than one ionizable hydrogen atom. Such acids ionize in steps, with a separate equilibrium constant for each step. Oxalic acid, a weak organic acid sometimes used to remove bloodstains, is diprotic ... 

Equilibrium constants of weak bases can be measured in the laboratory by procedures very much like those used for weak acids. In practice, though, it is simpler to take advantage of a simple mathematical relationship between Kb for a weak base and Ka for its conjugate acid. This relationship can be derived by adding together the equations for the ionization of the weak acid HB and the reaction of the weak base B- with water ... 

The equation just written is the reverse of that for the ionization of water, so the equilibrium constant can be calculated by using the reciprocal rule (Chapter 12). 

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 ... 

Unionized mercuric acetate is also a mercurating species, for the second-order rate coefficient for mercuration of benzene by mercuric acetate in acetic acid at 25 °C is 0.41 x 10"7. If mercuration took place via ionized acetate ion pairs HgOAc+OAc" for which AT, the equilibrium constant can be estimated at 2 x 10"8, then since the rate of mercuration by this ion pair will be approximately the same as by the acetoxymercury perchlorate ion pair for which k2 the second-order rate coefficient has been determined (above) as 0.37x10"3 at 25 °C, the observed second-order rate should be 2 x 10"8 x0.37 x 10"3 = 0.74xl0-11. This is so different from the rate actually observed that mercuration by the ion pair can be eliminated which leaves ionized mercurcy acetate as the only possible mercurating species439. 

One of the most important types of aqueous equilibrium involves proton transfer from an acid to a base. In aqueous soiutions, water can act as an acid or a base. In the presence of an acid, symbolized HA, water acts as a base by accepting a proton. The equilibrium constant for transfer of a proton from an acid to a water molecule is caiied the acid ionization constant (Zg) ... 

All equilibrium constants in the present discussion are based on the concentration (not activity) scale. This is a perfectly acceptable thermodynamic scale, provided the ionic strength of the solvent medium is kept fked at a reference level (therefore, sufficiently higher than the concentration of the species assayed). This is known as the constant ionic medium thermodynamic state. Most modern results are determined at 25 °C in a 0.15 M KCl solution. If the ionic strength is changed, the ionization constant may be affected. For example, at 25 °C and 0.0 M ionic strength, the pXj of acetic acid is 4.76, but at ionic strength 0.15 M, the value is 4.55 [24]. 

It is important to note that each hydrogen ion is accompanied by a hydroxy ion, so that in neutral solution the concentrations of these two ions are equal to each other, and therefore from the equation, 11 l+][OI I = Kw, each of these concentrations is equal to (Kv)"5. It is worthwhile adding additional fundamentals pertaining to the ionization of water. The equilibrium constant (Kr) of the ionization reaction of water as shown above is ... 

The ionization of water is so important in the study of aqueous equilibria that the equilibrium constant is given the special symbol, Kw. It can be seen that, Kw, like all equilibrium constants, depends on temperature. Since Kw is larger (the forward reaction is encouraged) at higher temperatures, the forward reaction must consume heat, so the ionization of water must be endothermic. 

Equilibrium constants can be written for the ionization of weak acids and weak bases, just as for any other equilibria. For the equation... 

Ionization constant the equilibrium constant for the reaction of a weak acid or base with water. 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

Since the days of Bronsted13 the strengths of acids in aqueous solution have been defined in terms of the equilibrium constant K.d for the ionization of HA, equation (1) ... 

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