Secondary equilibria effects

Equation (1-7) shows that in an ideal case the selectivity of the system is only dependent on the difference in the analytes interaction with the stationary phase. It is important to note that the energetic term responsible for the eluent interactions was canceled out, and this means that the eluent type and the eluent composition in an ideal case does not have any influence on the separation selectivity. In a real situation, eluent type and composition may influence the analyte ionization, solvation, and other secondary equilibria effects that will have effect on the selectivity, but this is only secondary effect. 

The process of analyte retention in high-performance liquid chromatography (HPLC) involves many different aspects of molecular behavior and interactions in condensed media in a dynamic interfacial system. Molecular diffusion in the eluent flow with complex flow dynamics in a bimodal porous space is only one of many complex processes responsible for broadening of the chromatographic zone. Dynamic transfer of the analyte molecules between mobile phase and adsorbent surface in the presence of secondary equilibria effects is also only part of the processes responsible for the analyte retention on the column. These processes just outline a complex picture that chromatographic theory should be able to describe. 

Most chromatographic systems with absence of the secondary equilibria effects (such as analyte ionization, specific interactions with active adsorption sites, etc.) show linear dependencies of the logarithm of the retention factors on the inverse temperature, as shown in Figure 2-11. 

Application of the partitioning mechanism for the description of the retention process leads to another theoretical consequence applicable to ideal chromatographic systems that is, only one retention mechanism is present and no secondary equilibria effects are observed. Liquid chromatography is a competitive process, where analyte molecules compete with the eluent molecules for the retention on the stationary phase based on that, the standard state of... 

Expression (2-58) contains only the Gibbs free energies of the analyte interactions in the column and no eluent-related terms. This means that in ideal systems (in the absence of secondary equilibria effects) the eluent type or the eluent composition should not significantly influence the chromatographic selectivity. This effect could be illustrated from the retention dependencies of alkylbenzenes on a Phenoemenex Luna-C18 column analyzed at various ace-tonitrile/water eluent compositions (Figure 2-13, Table 2-2). 

Analyte ionization, tautomerization, or solvation equilibrium in the chromatographic column has a profound effect on the retention and efficiency. These effects are known as secondary equilibria effects [34,35]. The effect of the analyte ionization on the retention has been extensively studied [36, 37]. Fundamental work by C. Horvath and co-workers created a solid foundation in this held [30, 38] for ionic equilibria of... 

Assumption of the presence of single partitioning mechanism of analyte chromatographic retention has been the basis for the development of various methods for the evaluation of specific analyte interaction energies from retention data [44-46]. All these methods are only applicable in ideal chromatographic systems with proven absence of secondary equilibria effects, and all require specific assumptions regarding the volume of the stationary phase. Equation (2-43) is the main basis for these theories. 

In this chapter we discussed the influence of most known secondary equilibria effects as well as the utilization of the organic eluent component absorption on the surface to describe the analyte retention in reversed-phase HPLC. 

The advantage of using a combination of low pH and a higher perchlorate concentration is that at these low pHs interactions with the silanols or secondary equilibria effects will be non-existent. 

If we consider Fig. 1 in more detail, it is clear that the largest changes in retention time occur when the pH of the mobile phase is close to the pfQ of the analyte. In addition, the secondary equilibria that result in peak broadening can also be emphasized at this pH. There is a fairly simple solution to this problem where analyte pfCj values are known, the chromatographer can simply retrieve these values and be sure to work at least 2 pH imits above or below the pK, . Chromatographic mechanisms should be relatively free from secondary equilibria effects in this area i.e., the analytes will exist in either fully ionized or fully unionized form. This should result in better peak shape and more reproducible chromatography. 

When ideal retention dependencies prevail in the RPC separations of peptides, i.e. no secondary equilibrium effects occur, these empirical dependencies reduce to the familiar form given by equations 9 and 10. 

In order to avoid any secondary equilibrium effects on the retention of iono-genic analytes, it is preferable to use a mobile-phase pH either two units greater or less than the analyte pA. Therefore knowledge of the analyte pA is very important. A basic understanding of how functional group substitution on a molecule affects the pA of the ionizable group on the substrate is given. An exhaustive description of all the nuances of analyte substitution on analyte pAa is not included in this section. However, further details can be found in the references 29-31. 

The magnitude of D enables one to understand the extent to which all chemical forms of the analyte of interest are partitioned between two immiscible phases. D accounts for all secondary equilibrium effects that occur. Let us go back to the concept of acetic acid partitioning between diethyl ether and water while considering the influence of the secondary equilibrium, that of weak acid dissociation due to an adjustment of the pH of the aqueous phase. This discussion will help us enlarge the scope of LLE and set the stage for further insights into the role of secondary equilibrium. 

Hence, the concentration of solute present in the organic phase can be directly related to the concentration of solute initially present in the aqueous groundwater sample, Cjnitai, provided the partition coefficient and phase ratio, are known. The reader should see some similarity between Eqs. (3.20) and (3.16). Equation (3.20) was derived with the assumption that secondary equilibrium effects were absent. This assumption is valid only for nonionizable organic solutes. 

Both equations describe what we have been calling secondary equilibrium effects to the primary distribution equilibria, which, in this case, is the distribution of neutral SO2 molecules between the aqueous phase and the HS described as follows ... 

Secondary equilibrium effects are handled by defining the degree of ionization by a as done previously, refer to Eqs (3.17) and (3.18), and expressing the activity of neutral SO2 in terms of a and the total activity, Uj-, according to... 

It should become clear that pH is a powerful secondary equilibrium effect that can be used to selectively extract a particular metal from a sample that may contain more than one metal. 

If the rate equation contains the concentration of a species involved in a preequilibrium step (often an acid-base species), then this concentration may be a function of ionic strength via the ionic strength dependence of the equilibrium constant controlling the concentration. Therefore, the rate constant may vary with ionic strength through this dependence this is called a secondary salt effect. This effect is an artifact in a sense, because its source is independent of the rate process, and it can be completely accounted for by evaluating the rate constant on the basis of the actual species concentration, calculated by means of the equilibrium constant appropriate to the ionic strength in the rate study. 

T-secondary isotope effect can be determined. As recounted in the last item of Chart 3, such effects are expected to be measures of transition-state structure. If the transition state closely resembled reactants, then no change in the force field at the isotopic center would occur as the reactant state is converted to the transition state and the -secondary kinetic isotope effect should be 1.00. If the transition state closely resembled products, then the transition-state force field at the isotopic center would be very similar to that in the product state, and the a-secondary kinetic isotope effect should be equal to the equilibrium isotope effect, shown by Cook, Blanchard, and Cleland to be 1.13. Between these limits, the kinetic isotope effect should change monotonically from 1.00 to 1.13. 

If secondary isotope effects arise strictly from changes in force constants at the position of substitution, with none of the vibrations of the isotopic atom being coupled into the reaction coordinate, then a secondary isotope effect will vary from 1.00 when the transition state exactly resembles the reactant state (thus no change in force constants when reactant state is converted to transition state) to the value of the equilibrium isotope effect when the transition state exactly resembles the product state (so that conversion of reactant state to transition state produces the same change in force constants as conversion of reactant state to product state). For example in the hydride-transfer reaction shown under point 1 above, the equilibrium secondary isotope effect on conversion of NADH to NAD is 1.13. The kinetic secondary isotope effect is expected to vary from 1.00 (reactant-like transition state), through (1.13)° when the stmctural changes from reactant state to transition state are 50% advanced toward the product state, to 1.13 (product-like transition state). That this naive expectation... 

Without enzyme catalysis, the secondary KIE is 1.15-1.16. The equilibrium secondary isotope effect was estimated as 1.01-1.03 (but see entry below). 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

These studies had therefore found the tunneling phenomenon, with coupled motion, as the explanation for failures of these systems to conform to the expectations that the kinetic secondary isotope effects would be bounded by unity and the equilibrium effect and that the primary and secondary effects would obey the Rule of the Geometric Mean (Chart 3), as well as being consistent with the unusual temperature dependences for isotope effects that were predicted by Bell for cases involving tunneling. 

Ah/At = 7.4 and A /Ax = 1.8 and isotopic activation energy differences that are within the experimental error of zero. The values of the two A-ratios correspond to a Swain-Schaad exponent of 3.4, not much different from the semiclassical expectation of 3.3. The a-secondary isotope effects are 1.19 (H/T), 1.13 (H/D), and 1.05 (D/T), which are exactly at the limiting semiclassical value of the equilibrium isotope effect. The secondary isotope effects generate a Swain-Schaad exponent of 3.5, again close to the semiclassical expectation. At the same time that the isotope effects are temperature-independent, the kinetic parameter shows... 

The observation of exalted secondary isotope effects, i.e., those that are substantially beyond the semiclassical limits of unity and the equilibrium isotope effect. These observations require coupling between the motion at the primary center and motion at the secondary center in the transition-state reaction coordinate, and in addition that tunneling is occurring along the reaction coordinate. 

Kurz, L.C. and Erieden, C. (1980). Anomalous equilibrium and kinetic alpha-deuterium secondary isotope effects accompanying hydride transfer from reduced nicotinamide adenine dinucleotide. J. Am. Chem. Soc. 102, 4198-4203... 

A nonunity ratio (sometimes called a thermodynamic isotope effect) of the equilibrium constants ( ught/ heavy) for two reactions differing only in the isotopic composition at one or more positions of their otherwise chemically identical substances . If the equilibrium isotope effect is attributable to a covalent bond making/breaking, then the effect is often referred to as a primary equilibrium isotope effect. If isotopic substitution at a position other than the scissile bond results in an equilibrium isotope effect, the term secondary equilibrium istope effect is used. 

Although these effects are often collectively referred to as salt effects, lUPAC regards that term as too restrictive. If the effect observed is due solely to the influence of ionic strength on the activity coefficients of reactants and transition states, then the effect is referred to as a primary kinetic electrolyte effect or a primary salt effect. If the observed effect arises from the influence of ionic strength on pre-equilibrium concentrations of ionic species prior to any rate-determining step, then the effect is termed a secondary kinetic electrolyte effect or a secondary salt effect. An example of such a phenomenon would be the influence of ionic strength on the dissociation of weak acids and bases. See Ionic Strength... 

For many reactions the type of intermediate that is involved may be deduced from a study of a family of reactants. For example, by noting that in allylic oxidation the order of reactivity is isobutene > trans-2-butene > cis-2-butene > 1-butene one may deduce that an allyl radical or cation is an intermediate. For other oxidations, if the reaction rate order is primary > secondary > tertiary, then an anionic intermediate is implicated. However, care must be taken that the formation of the intermediate is involved in the ratedetermining step and that there are no adsorption equilibrium effects. To rule out the latter, the reaction should be carried out at conditions of low coverage. 

Verify that a decrease in H—C (D—C) vibrational frequency on dissociation will cause the observed secondary equilibrium isotope effect KH/KD > 1 for dissociation of HCOOH (DCOOH). 

This chapter is a review of secondary equilibrium isotope effects (IEs) on acidity, primarily on the comparison of protium with deuterium (and also tritium), but also addressing the IEs of 13C, 14C, 15N, and lsO. Secondary IEs are those where the bond to the isotope remains intact, whereas primary IEs are those where the bond is broken. Primary isotope effects are generally... 

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