Instability constant determination

Spectrophotometric characteristics of gallate complexes in methanol and aqueous methanol have been investigated, and successive instability constants determined. 

The more stable a complex, the larger is its formation constant. The reciprocal of the formation constant is the instability constant. Determination of these formation constants is relevant to understanding the chemistry of such systems. Like many other equilibrium constants, such stability constants may be determined by gas chromatography. 

Stability constant — is the - equilibrium constant of formation of a - complex. The reciprocal quantity is called instability constant. Extensive compilations of various kinds of stability constants are available [i—iv]. Stability constants are reported for a given ionic strength (or extrapolated to zero ionic strength), and pH. In many cases, stability constants can be determined with the help of electrochemical techniques, e.g., -> chronopotentiometry, -> potentiometry, -> polarogra-phy, and - voltammetry, provided that the systems exhibit -> electrochemical reversibility, and some other prerequisites are fulfilled [v]. See also -> conditional equilibrium constants. 

Moskvin, A. I., and Gel man, A. D. Determination of the composition and instability constants of oxalate and carbonate complexes of plutonium(IV), Russ. J. Inorg. Chem., 2>... 

Determination of Instability Constant.—Two methods have been mainly used for determining the instability constants of complex ions one involves the measurement of the e.m.f. s of suitable cells, which will be described in Chap. VII, and the other depends on solubility studies. The latter may be illustrated by reference to the silver-ammonia (argent-ammine) complex ion. If the formula of the complex is Agm(NH8)n , the... 

With [Co(phen)3] + as oxidant for PCu(I), rate constants determined by the stopped-flow method approach zero at low pH, consistent with zero reactivity of the trigonally coordinated Cu(I) form. However, with [FelCNlel as oxidant there is sometimes difficulty in fitting rate constants to the relevant [H ] dependence, which leaves open the question as to whether the rates actually become zero (57). Whereas [Co(phen)3l + is believed to react with PCu(I) at both the remote (acidic) and the adjacent (hydrophobic) patches, [FefCNleP reacts predominantly at the latter. The instability of PCu(I) in solution at pH < 4.5 makes it difficult to settle this issue conclusively. The range of studies has been extended using the pH-jump method in which protein, at high pH (with relatively small concentration of buffer), is stopped-flow mixed with the redox reagent at low pH (with excess buffer), and this approach has been used more extensively in recent studies. 

TURyRUV] Tur yan, Y. 1., Ruvinskii, 0. E., Sulphate anion effect on kinetic and catalytic polarographic currents of nickel(ll) aquo ion and nickel(Il) complexes. Determination of the instability constant of nickel-sulphate complex, J. Electroanal. Chem. Interfacial Electrochem., 28, (1970), 381-390. Cited on pages 181, 182, 183, 187, 344. 

There are many approaches to experimentation in a laboratory. One type that physical chemists engage in is the measurement of a known system to obtain new fundamental information about the system. These experiments are usually well planned and most of the equipment is in place before the first experiment is undertaken. High precision and attention to minute detail is essential if these works are to be worthy of completion. The kinetics of the hydrolytic degradation is such a study. The electrical conduction of solutions of condensed phosphates as a function of complexing cations and the determination of instability constants is another. The list could be almost endless and this science is usually conducted by highly trained personnel. 

Moskvin AI, Khalturin GV, Gel man AD (1962) Determination of the composition and instability constants of citrate and tartrate complexes of americium(III) by the ion-exchange method. Radiokhim 4 162-166... 

It is noteworthy that eq. (4.15a) is nothing but the linearized classical upside-down barrier equation of motion (8S/8x = 0) for the new coordinate x. Therefore, while x = 0 corresponds to the instanton, the nonzero solution to (4.15a) describes how the trajectory escapes from the instanton solution, when it deviates from it. The parameter X, referred to as the stability angle [Gutzwil-ler 1967 Rajaraman 1975], generalizes the harmonic-oscillator phase co, which would appear in (4.15), if CO, were a constant. The fact that X is real indicates the aforementioned instability of the instanton in two dimensions. Guessing that the determinant det( — -I- co, ) is a function of X only,... 

The optimum value of c is determined by the variational principle. If c = 1, the UHF wave function is identical to RHF. This will normally be the case near the equilibrium distance. As the bond is stretched, the UHF wave function allows each of the electrons to localize on a nucleus c goes towards 0. The point where the RHF and UHF descriptions start to differ is often referred to as the RHF/UHF instability point. This is an example of symmetry breaking, as discussed in Section 3.8.3. The UHF wave function correctly dissociates into two hydrogen atoms, however, the symmetry breaking of the MOs has two other, closely connected, consequences introduction of electron correlation and spin contamination. To illustrate these concepts, we need to look at the 4 o UHF determinant, and the six RHF determinants in eqs. (4.15) and (4.16) in more detail. We will again ignore all normalization constants. 

We have seen in Chapter 2 that the frequency of an EPR spectrum is not a choice for the operator (once the spectrometer has been built or bought) as it is determined by the combined fixed dimensions of the resonator, the dewar cooling system, and the sample. Even if standardized sample tubes are used and all the samples have the same dielectric constant (e.g., frozen dilute aqueous solutions of metalloproteins), the frequency will still slightly vary over time over a series of consecutive measurements, due to thermal instabilities of the setup. By consequence, two spectra generally do not have the same frequency value, which means that we have to renormalize before we can compare them. This also applies to difference spectra and to spectra... 

A value of kjkp = 17 000 has been determined for partitioning of the acetophenone oxocarbenium ion [12+] in water.15,16 It is not possible to estimate an equilibrium constant for the addition of water to [12+], because of the instability of the hemiketal product of this reaction. However, kinetic and thermodynamic parameters have been determined for the reaction of [12+] with methanol to form protonated acetophenone dimethyl ketal [12]-OMeH+ and for loss of a proton to form a-methoxystyrene [13] in water (Scheme 10).15,16 Substitution of these rate and equilibrium constants into equation (3) gives values of AMeoH = 6.5 kcal mol-1 and Ap = 13.8 kcal mol-1 for the intrinsic... 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

Novozhilov (Ref 9) noted other instances where the instability criterion of Zel dovich is not satisfied. He also noted ZeTdovich s assertion that the form of the stability criterion may change if the variation in the surface temperature and the inertia of the reaction layer of the condensed phase are taken into account, and stability criteria obtained under the assumption that the chemical reaction zone in the condensed phase and all of the processes in the gas phase are without inertia. Novozhilov used a more general consideration of the problem to show that the stability region is determined by only two parameters Zel dovich s k and the partial derivative r of the surface temperature with respect to the initial temperature at constant pressure t=(dTi/(fro)p. Combustion is always stable if k 1, combustion is stable only when r >(k — l) /(k +1)... 

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