Bjerrum effect

These large increases in rate might be attributed to the operation of a neutral salt effect, and, in fact, a plot of log k versus the square root of the ionic strength, fi, is linear. However, the reactants, in this case, are neutral molecules, not ions in the low dielectric constant solvent, chloroform, ionic species would be largely associated, and the Bronsted-Bjerrum theory of salt effects51 52, which is valid only for dilute-solution reactions between ions at small n (below 0.01 M for 1 1 electrolytes), does not properly apply. 

This equation is known as the Br0nsted-Bjerrum equation. Because y% appears in the denominator, it explicitly acknowledges the premise of TST that there is an equilibrium between the reactants and the transition state. Equation (9-27) provides the basis for understanding the direction and magnitude of rate effects arising from changes of reaction medium. This approach will be used to formulate effects of solvent and inert electrolytes in the sections that follow. 

Bjerrum and coworkers have assigned the three rate maxima shown in Figs. 10.7 and 10.8 to (starting from the negative potential) (a) destruction of vanadium polymeric chains (b) electric double layer effect at gold working electrode (c) stabilization of V (V) vs V (IV). These explanations are very plausible. 

The charge-state section highlighted the value of Bjerrum plots, with applications to 6- and a 30-pKa molecules. Water-miscible cosolvents were used to identify acids and bases by the slope in the apparent pKa/wt% cosolvent plots. It was suggested that extrapolation of the apparent constants to 100% methanol could indicate the pKa values of amphiphilic molecules embedded in phospholipid bilayers, a way to estimate pAi m using the dielectric effect. 

The book is organized into eight chapters. Chapter 1 describes the physicochemical needs of pharmaceutical research and development. Chapter 2 defines the flux model, based on Fick s laws of diffusion, in terms of solubility, permeability, and charge state (pH), and lays the foundation for the rest of the book. Chapter 3 covers the topic of ionization constants—how to measure pKa values accurately and quickly, and which methods to use. Bjerrum analysis is revealed as the secret weapon behind the most effective approaches. Chapter 4 discusses experimental... 

Bjerrum s theory includes approximations that are not fully justified the ions are considered to be spheres, the dielectric constant in the vicinity of the ion is considered to be equal to that in the pure solvent, the possibility of interactions between ions other than pair formation (e.g. the formation of hydrogen bonds) is neglected and the effect of ion solvation during formation of ion pairs is not considered (the effect of the solvation on ion-pair structure is illustrated in Fig. 1.7). 

It is generally observed that the rate of reaction can be altered by the presence of non-reacting or inert ionic species in the solution. This effect is especially great for reactions between ions, where rate of reaction is effected even at low concentrations. The influence of a charged species on the rate of reaction is known as salt effect. The effects are classified as primary and secondary salt effects. The primary salt effect is the influence of electrolyte concentration on the activity coefficient and rate of reaction, whereas the secondary salt effect is the actual change in the concentration of the reacting ions resulting from the addition of electrolytes. Both effects are important in the study of ionic reactions in solutions. The primary salt effect is involved in non-catalytic reactions and has been considered here. The deviation from ideal behaviour can be expressed in terms of Bronsted-Bjerrum equation. 

In order for a solvated ion to migrate under an electric field, it must be prevented from forming close ion pairs with its counterions by the solvating solvent. The effectiveness of the solvent molecule in shielding the interionic Coulombic attraction is closely related with its dielectric constant. The critical distance for the ion pair formation q is given by eq 4 according to Bjerrum s treatment, with the hypothesis that ion-pair formation occurs if the interionic distance is smaller than... 

Many factors play a role in establishing the value of the stability constants of a particular metal-ligand system. J. Bjerrum [4] considered such factors and their effect on the successive stability constants. The ratio of two stepwise constants is defined as ... 

Bjerrum divided this value into two terms S +i, which accounts for statistical effects and L +i, which accounts for all effects attributable to the nature of the hgand, including electrostatic effects. 

Effect of Electrostatic Interactions on the Bimolecular Rate Constant. The bimolecular rate equation presented above does not account for the effect of electrostatic interactions on reactivity of ionic molecules. Brpnsted and Bjerrum, among others, recognized that the behavior... 

A study19 of the effect of added lithium perchlorate on the second-order rate coefficients for reaction (12) (R = Et, Pr", Bu") showed that all three substitutions, in solvent 96 % methanol-4 % water, were subject to marked positive kinetic salt effects. The effects were analysed in terms of the Bronsted-Bjerrum equation... 

Electrostatic interactions involving permanent charges (salt bridges). Accord ing to the Bjerrum model the binding constant between two ions A+ and B can be described in terms of the product of the ionic charges zA-zB and the mean effective distance between the ions. These parameters along with the dielectric permittivity (e) determine the magnitude of the Bjerrum function Q(b). The... 

Solvent effects in electrochemistry are relevant to those solvents that permit at least some ionic dissociation of electrolytes, hence conductivities and electrode reactions. Certain electrolytes, such as tetraalkylammonium salts with large hydrophobic anions, can be dissolved in non-polar solvents, but they are hardly dissociated to ions in the solution. In solvents with relative permittivities (see Table 3.5) s < 10 little ionic dissociation takes place and ions tend to pair to neutral species, whereas in solvents with 8 > 30 little ion pairing occurs, and electrolytes, at least those with univalent cations and anions, are dissociated to a large or full extent. The Bjerrum theory of ion association, that considers the solvent surrounding an ion as a continuum characterized by its relative permittivity, can be invoked for this purpose. It considers ions to be paired and not contributing to conductivity and to effects of charges on thermodynamic properties even when separated by one or several solvent molecules, provided that the mutual electrostatic interaction energy is < 2 kBT. For ions with a diameter of a nm, the parameter b is of prime importance ... 

We also determined the effect of ionic strength on the formation of 3-MPA and 3-MPN in NaCl solutions at pH 8.0 and 40°C. Figure 6 shows plots of log k vs. I1/2, where k is the overall rate constant (units M day1), calculated as ki/fH ]. The rate of 3-MPA formation shows definite increase (slope from regression is 0.22) with ionic strength, which is in agreement with the Bronsted-Bjerrum equation. The formation of 3-MPN also shows an increase with ionic... 

Fig. 3 Effective potential between two counterions (left) and two monomers (right), respectively for various Bjerrum lengths /B. The chain length is N= 80 and the density 77= 1(T2...

Driven by a Boltzmann thermal-energy source kT and measured in kT units, coupled by a number of effective mobile ionic charges rs from Gibbs, the monopole-monopole correlation force is screened by Xnebye across the length 21, back and forth between point particles. At the same time its power-law dependence on length is measured in the natural thermal unit >.Bj. Boltzmann, Gibbs, Debye, Bjerrum—all at the same time. Can it get any prettier ... 

This is a generally accepted idea and recently it has been extended considerably in more accurate calculations of the absolute values of reaction rates. Bronsted and Bjerrum without any attempt to determine absolute values of X were able nevertheless to predict the effect of electroyltes and other factors on the reaction rate. 

The effect of added salts on the rate constant of a given ionic reaction has been studied for many years. The Br nsted-Bjerrum treatment of these salt effects has been particularly successful, the rate constant being related to the ionic strength of the solution. The observed trends can be quantitatively accounted for using the DHLL or a related expression for the activity coefficients of reactants and transition state. This subject has been reviewed in detail (Perlmutter-Hayman, 1971). The ionic-strength principle appears satisfactory when the reaction involves ions of opposite charge but less so when it involves ions of the same charge. 

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

Feb. 22,1879, Varde, Denmark - Dec. 17,1947, Copenhagen, Denmark) Ph.D. Copenhagen 1908, since 1908 Professor of Chemistry (the 3rd chair, i.e., the chair of Physical Chemistry at the Univ. of Copenhagen). 1926/27 visiting Professor at Yale Univ., New Haven, Connecticut, USA. Famous for his work on chemical reaction kinetics, chemical affinity, indicators, and thermodynamics of solutions. He could explain the effect of activity coefficients on reaction rates in solutions. In 1923 he developed independently of - Lowry, and - Bjerrum a new -> acid-base theory, the so-called Bronsted acid-base theory. 

Bronsted-Bjerrum equation — The rate constant k of a chemical reaction involving ionic species A and B may be influenced by other ionic species in solution not directly participating in this reaction (i.e., a dissolved salt, thus the associated observation is called primary salt effect). The change of the rate as a function of the ionic charge of the involved species and the - ionic strength of the solution is given by the Bronsted-Bjerrum equation... 

Bronsted s salt effect Bronsted-Bjerrum equation, -> charge transfer reaction... 

The increase of the -> ionic strength (I) will influence the electrostatic interactions (-> Bronsteds salt effect, -+ Bronsted-Bjerrum equation) which can be taken into account by using the Debye-Huckel theory ... 

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