Bjerrum equation

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. 

Biexponential kinetics, 72-76 Biphasic kinetics, 72-76 Bloch equations, 261 Branching reactions, 189 Brpnsted-Bjerrum equation, 204... 

This equation is known as the Br0nsted-Bjerrum equation. It may be-derived in several ways. It predicts that a plot of log k versus the square root of the ionic strength should be linear over the range of ionic strengths where... 

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. 

This is equivalent to the earlier Bronsted-Bjerrum equation X /b... 

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... 

At basic pH values the rate of 3-MPA formation is reduced, but continues at measurable rates even at a pH value as high as 10. These results indicate that acrylate ion possesses significant reactivity, although the undissodated form is much more reactive. In the addic pH ranee, the rate of 3-MPA formation in seawater is similar to that in Milli-Q water, but at basic pH values, the rates in seawater are higher than those in Milli-Q water (Figure 4). In an ionic medium such as seawater, for reactions involving ions, the Bronsted-Bjerrum equation predicts that ionic interactions cause deviations from ideal-solution behaviour (Equation 5) (451. 

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... 

If it is assumed that the Br0nsted-Bjerrum equation (Equation 1)... 

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 ... 

It should be pointed out that the influence of anion solvation on equilibrium (13) cannot be explained by use of the Born-Bjerrum equations [Eqs. (1) and (2)]. Use of Eq. (2) generally gives negative AG values for the overall free-energy contribution to equilibrium (13) due to anion solvation. This means that formation of [CoCl4] should be particularly favorable in solvents with high dielectric constants such as water in contrast to the experimental results. 

Figure 11. Empirical — aG° data for 1 1 metal sulfate complexes (1 = 0) plotted against z z./(ym + r o J, where z+ and z. are the valence of cation and sulfate ion, Ym is the crystallographic radius in Angstroms of the cation in sixfold coordination (3S), and ysoj, = 3.05 A (59). The locus of — aG° values computed for the complexes by the simple electrostatic model is shown as a dashed line, and computed by the Fuoss and Bjerrum equations as lines labeled (F) and (B), respectively.

The principal reducing species in the radiolysis of neutral water was shown to have unit negative charge from studies of the kinetic salt effect on its reactions [8, 9]. The dependence of the rate coefficient on ionic strength, /u, for a reaction in water at 298°K is given by the Bronsted— Bjerrum equation... 

A very interesting application of Eq. 1.7-12 is the Br nsted-Bjerrum equation for rate constants in solutions where the Debye-Huckel theory is applicable. The latter provides an equation for the activity coefficient, Rutgers [38] ... 

Ihe dependence on ion strength is called first salt effect. Its substance is the change in reaction rate due to addition to the solution of neutral outside salt, whose ions do not participate in reactions. This effect is only due to an increase in ion strength and may be expressed in the Bronsted-Bjerrum equation, which in logarithmic form looks as follows... 

The primary salt effect is described by die BrOnsted-Bjerrum Equation (2.13)... 

Effect of ionic strength on rates (Bronsted-Bjerrum equation)... 

The relevant equation for the dissection of solvent effects in terms of the Gibbs energy may be deduced from the Pronsted-Bjerrum equation for the reaction of Q and R through a transition state Tr(3-5,32,33). Here, k is the rate constant in a standard solvent and k is the rate constant in any other solvent. The terms and are primary medium activity coefficients. Equation can be recast as equation and the latter simplified by defining the... 

The concentration of solvated electrons was always much lower than the solute concentration to ensure that the biitolecular reaction follows pseudo first order kinetics. The rate constants were determined from the decay of the absorption of the solvated electron in solutions containing various concentrations of solutes after subtracting the decay arising from the solvent. Extrapolation to zero ionic strength was made according to the Bronsted Bjerrum equation (10). 

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