Equilibrium constant of ionization

The equilibrium constants of ionization are relatively low in most polymerization systems, resulting in very small proportions of ionic species. The proportion of ionic species may be estimated from the overall polymerization rates by assuming that covalent species are inactive. In polymerization systems with a half-lifetime of monomer in the range of r 1=5 20 min to 3 hr, the concentration of propagating ionic species should... 

There are some measurements of the rates of polymerization in systems with reversible formation of covalent species. The equilibrium constants of ionization can be calculated from these kinetic data according to the procedure outlined subsequently in Section IV.D.2.a. The ionization constant depends on the strength of the Lewis acid. For example, the propagating species are almost completely ionized in polymerizations of vinyl ethers with SbCL-, BCLt-, and SnCl5- counteranions, but only partially ionized when the counteranions are I3- or Zn3-. 

Because the reactivities of ions and ion pairs are similar and only weakly affected by the structure of the counteranions, kp + or kp determined by either stopped-flow studies or y-radiated systems (cf., Section IV. 13) can be used in Eq. (75). The equilibrium constant of ionization can then be estimated from the apparent rate constant of propagation and the rate constant of propagation by carbenium ions [Eq. (77)]. For example, Kf 10-s mol-,L in styrene polymerizations initiated by R-Cl/SnCl4 [148]. Kt for vinyl ether polymerization catalyzed by Lewis acids can also be estimated by using the available rate constant of ionic propagation (kp- = 104 mol Lsec-1 at 0° C) [217], The kinetic data in Ref. 258 yields Kj == 10 3 mol - l L in IBVE polymerizations initiated by HI/I2 in toluene at 0° C and Kf 10-1 mol- -L initiated by HI/ZnI2/acetone can be calculated from Eq. (76). 

The dynamics of exchange is also very important. Figure 13 shows a system nearly identical to the ideal system shown in Fig. 12. The only difference is the dynamics of ionization the concentrations of monomer, initiator, Lewis acid, and anion are the same, and the equilibrium constants of ionization and dissociation are also the same. 

Equations (89)-(91) also may be applied to donor or acceptor levels in semiconductors so that the expressions for the equilibrium constants of ionization reactions such as Eqs. (49), (50), and (53)-(56)... 

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... 

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. 

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 ... 

Hence the experimental equilibrium constants of Table IV are proportional to the constants for ionization into ion pairs, and the ratios of the if exp reflect differences in the tendency of different molecules to form ion pairs. Since standard free energies are proportional to the logarithms of equilibrium constants, differences in the tabulated free energies represent differences in the standard free energy change for ionization, even though the individual values represent the standard free energy for the overall process of ionization plus dissociation. 

Proton transfer is one of the prominent representatives of an ion-molecule reaction in the gas phase. It is employed for the determination of GBs and PAs (Chap. 2.11.2) by either method the kinetic method makes use of the dissociation of proton-bound heterodimers, and the thermokinetic method determines the equilibrium constant of the acid-base reaction of gaseous ions. In general, proton transfer plays a crucial role in the formation of protonated molecules, e.g., in positive-ion chemical ionization mass spectrometry (Chap. 7). 

The first process produces doubly ionized positive oxygen vacancies and electrons (el) and the second produces doubly ionized positive cation interstitials and electrons. The equilibrium constants of the two processes are given by... 

Equilibrium constants for ionization reactions are usually called ionization or dissociation constants, often designated Ka. The dissociation constants of some acids are given in Figure 2-16. Stronger acids, such as phosphoric and carbonic acids, have larger dissociation constants weaker acids, such as monohydrogen phosphate (Ill Of ), have smaller dissociation constants. 

In acetic acid it is possible to measure separately the equilibrium constant of proton transfer to form an ion pair and the constant for dissociation of ion pairs to form free ions. [I. M. Kolthoff and S. Bruckenstein, J. Amer. Chem. Soc., 78, I (1956) S. Bruckenstein and I. M. Kolthoff, J. Amer. Chem. Soc., 78, 10 (1956)]. G. W. Geska and E. Grunwald, J. Amer. Chem. Soc., 89, 1371, 1377 (1967) applied this technique to a number of substituted anilines and concluded that the equilibrium constant of the ionization step, rather than the overall acid dissociation constant, is the quantity that should be considered in discussions of effects of structural changes on acidity. 

The underlying assumption in this concept is the absence of steric effects. Using the rate and equilibrium constants for ionization of benzoic acid as references, Hammett found that equilibrium constants for a variety of reactions showed a linear relationship with o and defined the LFER. Data for these equilibria are typically graphed as illustrated in Figure 5.4. 

The other application explained here is the ionic product of water, pKw [11], which is essentially the equilibrium constant of the auto-ionization process of water (Kw =... 

The dependence of the equilibrium constants of polyprotic weak acids and weak bases on ionic strength allows them to be treated in exactly the same manner as monoprotic weak acids and weak bases. The first, second, and third ionization constants for triprotic weak acids in terms of activity coefficient are given by ... 

Pyzhov Equation. Temkin is also known for the theory of complex steady-state reactions. His model of the surface electronic gas related to the nature of adlay-ers presents one of the earliest attempts to go from physical chemistry to chemical physics. A number of these findings were introduced to electrochemistry, often in close cooperation with -> Frumkin. In particular, Temkin clarified a problem of the -> activation energy of the electrode process, and introduced the notions of ideal and real activation energies. His studies of gas ionization reactions on partly submerged electrodes are important for the theory of -> fuel cell processes. Temkin is also known for his activities in chemical -> thermodynamics. He proposed the technique to calculate the -> activities of the perfect solution components and worked out the approach to computing the -> equilibrium constants of chemical reactions (named Temkin-Swartsman method). 

From the pKa values, the following sequence of 2-substituted 4-thiazolidinones with respect to the degree of acidity are 5 > 2 > 3.186 The opening of the thiazolidinone ring leads to an increase in acidity, but does not affect the activity sequence of the substituents.186 The acidity of a series of substituted 5-benzylidene-2,4-thiazoIidinediones has been investigated the entropy, enthalpy, and free energy of ionization have been calculated.187 Potentiometric determination of the tautomeric equilibrium constants of various 4-thiazolidinones has been reported.188... 

Figure 9 shows evolution of molecular weights with conversion for a hypothetical system, in which ions and ion pairs have the same reactivities (kp+ = kp = 10s mol L sec-1), covalent species are inactive, the ionization equilibrium constant is Ki = 10 5 mol-, L, and the dissociation constant is Kd = 10 7 mol/L. Kf is defined by the ratio of the rate constant of ionization to that of recombination of counterions within the ion pair (Kj = kj/kr). Kd is defined by the ratio of the rate constants of the dissociation of ion pair and that of the association of free ions (Kd... 

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