Isosbestic point method

When two compounds in a solution are in chemical equilibrium, and both contribute to the absorbance in a particular wavelength region, there will be at least one wavelength where absorbance is a funtion of the total concentration of both species, but does not depend on the relative concentrations. This wavelength is known as the isosbestic point. 

Derivative spectra sometimes also have isosbestic points. When another signal overlaps these points, an alteration only occurs because of the second substance, and its concentration can easily be estimated. 

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In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

Exploitation of analytical selectivity. We have seen, in our discussion of the A —> B C series reaction (Scheme IX), that access to the concentration of A as a function of time is valuable because it permits to be easily evaluated. Modern analytical methods, particularly chromatography, constitute a powerful adjunct to kinetic investigations, and they render nearly obsolete some very difficult kinetic problems. For example, the freedom to make use of the pseudoorder technique is largely dependent upon the high sensitivity of analytical methods, which allows us to set one reactant concentration much lower than another. An interesting example of analytical control in the study of the Scheme IX system is the spectrophotometric observation of the reaction solution at an isosbestic point of species B and C, thus permitting the A to B step to be observed. 

Several studies have been carried out to investigate the effect of pH on azo dye decolorization. In these assays, the decrease of absorbance at the wavelength corresponding to the maximum absorption for each dye is used as the method to evaluate the effectiveness of decolorization. Unfortunately, in most cases it is not clear if the isosbestic point of each dye was taken into account, and so it cannot be well understood if the different decolorization rate at different pH is due to a physical factor or to a differently influenced metabolic activity. 

Fig. 9.4.25 Optical absorption spectra of copper colloid prepared by the gas flow-solution trap method as a function of lime development. The numbers in the figure are the time after the preparation of Lhe sample. The spectrum of sodium eihoxidc in ethanol (authentic sample) is also shown in the same figure, marked by b. The insertion is the expansion of the region of the isosbestic point. The deviation from the isosbestic point at 10 h after the preparation of colloids is shown by a in the insert. (From Ref. 26.)...

The basis of the method is akin to the Pfeiffer effect [8] except that, in this instance, the roles of the ligands are reversed and reorganization of the inner sphere and not the outer sphere of the metal is intimately involved. The racemate originates in the solution environment and the enantiomer is part of the coordination compound (vide infra). Calculation of the enantioexcess is most easily done using spectral differences. Figure 5 shows the CD spectrum for the parent complex (lowest curve) where M is Cu(II) and L is L-tartrate in strong base together with a series of curves in which the L-pseudoephedrine concentration has been systematically increased. An isosbestic point at 538 nm is obvious [51]. 

Redox titrations involve determination of equilibrium between the enzyme and a redox agent of known redox potential. The method requires a redox agent with redox potential close to the protein of interest, to ensure reversibility. The protein is exposed to different concentrations of the redox agent, and once equilibrium is attained, the half cell potential is measured with electrodes and the oxidation-reduction state of the proteins is measured by some physical technique, usually UV-Vis spectrophotometry. The concentration of the oxidized and reduced forms is determined at isosbestic points, and thus spectral characterization of redox species (ferric enzyme,... 

When kinetics have been complicated by partial decomposition of the reaction product (e.g., 3,5-dimethoxy-2,6-dinitropyridine), the rate coefficients for the second nitration could be obtained by taking measurements at the isosbestic point of the mono- and dinitro-compounds, and also at another wavelength if there is a large extinction coefficient difference between the two compounds [67JCS(B)12U]. This method assumes that the decomposition product does not absorb at the wavelength concerned. The concentration x, of product formed after time t was calculated from Eq. (3.8), where the subscript i refers to optical densities at the isosbestic point. 

A good example of application is given by the protein structural changes of bovine ribonuclease A in the course of its denaturation by pressure. The UV spectrum of RNase is dominated by the absorbance of tyrosine - this RNase does not contain tryptophan. As shown in Figure 6, an increase of pressure from 1 to 500 MPa results in a blue-shift of the 4th derivative maximum from 285.7 0.05 to 283.5 0.05 nm. This shift of 2.2 nm corresponds to an increase of the mean dielectric constant from 25 to 59. It is characteristic of the exposure to the aqueous solvent of part of the 6 tyrosines, as it is expected for a partly denaturation. The transition is fully reversible with clear isosbestic points. The pressure effect can therefore be described by a simple two-state model between the native (e,. = 25) and the partially denatured (e,. = 59) state. A simulation on the basis of this model permitted us to determine the thermodynamic parameters of this transition AG° = 10.3 kJ/mol and AV = - 52 ml/mol. A comparison with results obtained by other methods indicates that the (e,. = 59) state corresponds to an intermediate in the defolding process which has molten globule like characteristics [12]. It thus appears that fourth derivative... 

In the spectrophotometric method, the molar absorptivity of the complex is an additional variable to be determined. As well, it is necessary to determine the stoichiometry of the complex before calculations can be performed. The mole-ratio and continuous variations methods are useful in determining the stoichiometry. The observation (or lack) of isosbestic points is also a useful guide to the complexity of the system. 

The UV-visible absorptivities of humic substances do vary as a function of pH (Salfield, 1965 MacCarthy and O Cinneide, 1974) and one can speculate that these changes are due to the ionization of carboxylic and phenolic functional groups. The UV-visible spectra of humic substances do not exhibit an isosbestic point when plotted at various pH values, which is consistent with their multicomponent nature. As with other spectroscopic methods it is not known what proportion of the molecules contribute to the absorbance at a particular wavelength. 

The development of a new spectrophotometric method is usually preceded by studies of the colour system (complex composition and stability), which is the basis of the method. Fundamental physicochemical studies of the colour complexes existing in the solution enable one to establish the optimum parameters of the method [74-76]. The composition of the complex (molar ratio of metal to ligand) in the solution is determined by Job s continuous variation method, the Bent and French method of equilibrium shift, the method of mole ratio proposed by Yoe and Jones, and the method based on the ratio of slopes and isosbestic points. Studies of complex compounds in solutions are described in many works, especially [77-80]. 

Sensitive tests for the uniformity of a reaction can be done by global analysis of the complete set of spectra recorded during photolysis. These methods, described in Section 3.7.5, provide the best evaluation of the minimum number of spectral components required to reproduce a sequence of spectra within experimental accuracy and the time-dependent species concentrations thus obtained accurately define the reaction progress. Simpler versions use absorbance differences observed at a few selected wavelengths where the changes are largest. Uniform reactions give linear plots of Aversus AA(/,2, ). For two sequential photoreactions, absorbance difference plots are curved, but plots of absorbance difference quotients, AA(21,7)/AA(/l24) versus AA(21,7)/AA(/l3,7), are linear. Isosbestic points provide the simplest criterion... 

The simplest method to study a spectra set evolution is to display the spectra on Fig. 10. Several examples can be further shown for degradation tests. More than the general evolution, leading in this case to the decrease of spectra shape and thus of absorbance values, isosbestic points can appears with time. 

This can be made the basis of a method for determining concentrations of the compounds in a mixture of the two. The absorption is measured at the isosbestic point, and this gives the total molar concentration of the mixture. A measurement can also be made at another wavelength, such as 500 nm. The ratio of the two absorptions at 500 nm and 431 nm, varies linearly with the proportion... 

These results provided the first experimental evidence for the existence of bathorhodopsin at physiological temperatures and also permitted conclusions to be drawn and models of the intermediate to be postulated that would be consistent with this time scale for formation. When later the complete difference spectra for bathorhodopsin at room temperature were obtained in the time range of 6-300 ps (Fig. 5), it was possible to measure (Fig. 6) the formation kinetics of a band located between 530 and 680 nm that corresponds to bathorhodopsin having its maximum absorption at 580 nm and its isosbestic point at approximately 525 nm. These values correspond quite well with previously published data. Picosecond experiments performed by the same method revealed that rhodopsin also bleached with the same time constant as bathorhodopsin was formed, namely, < 6 ps. 

If a reaction spectrum exhibits isosbestic points, the reaction is assumed to be a single step process. During complex reactions, time intervals can be found during which quasi-isosbestic points are recorded. In both cases the assumption of a simple reaction can be erroneous because of similar absorption spectra of reactants or lack of spectral resolution of the spectrometer. Therefore the simplicity of any reaction has to be proven by other methods. In any case an irradiation wavelength close to an isosbestic point or exactly at the wavelength of the isosbestic point reduces the expenditure in evaluation as discussed in Section 3.3.1 (Example 3.31). 

A prerequisite to apply equation (8) besides c > c, (see above) is the formation of 1 1 complexes. In contrast, 2 1 and nonstoichiometric and other associates can be excluded through a nonlinear arrangement of the values measured according to equation (8). An additional indication for 1 1 inclusion stoichiometry is the appear-ence of two isosbestic points in the fluorescence spectra By an extension of this method the complex constants Kq of other non-fluorescing guests G can be calculated... 

The rate of anion diffusion can be measured in various ways. The conventional way is to use classical electrochemical methods, e.g., chronoamperometry or chronocoulome-try. The measurement of electrochemical impedance is also sometimes used. However, the electronically conducting polymers have a special property, potential-dependent absorption spectrum, which can be advantageously used to monitor the oxidation state of the polymer. In addition to the neglect of capacitive current, monitoring of the spectral change gives additional information. For instance, the presence of an isosbestic point shows that most likely... 

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