Determination of protonation constants by coulometric titration

Application of coulometric titration to the determination of the protonation constants of acids and bases offers several advantages because of its simplicity, precision and accuracy. This procedure is rapid and requires only one calibration solution of strong acid in the same solvent and at the same ionic strength as the solution of acid (or base) being investigated. The procedure seems to be especially advantageous in the case of non-aqueous or mixed solvents having amphiprotic character. The validity of the method has been checked with several substances in water, 95% ethanol and ethylene glycol.     

Determination of borate ion-pair stability constants by potentiometry and non-approximative linearization of titration data

Borate anions, B(OH)(-)(4), are known to associate with alkali and alkaline-earth metal cations in sea-water. The borate cation ion-pairs are of the general form MB(OH)((n-1)+)(4), where M(n+) is the cation. In this work, the cation borate stability constants (K*(MB)) have been evaluated for Na(+), Li(+), Mg(2+), Ca(2+) and Sr(2+) where K*(MB) = [MB(OH(4))((n-1)+)]/[M(n+)][B(OH)(-)(4)]. The K*(MB) values were obtained from values found for the stability constant of boric acid (K*(B)) in various electrolyte media at 25 degrees and an ionic strength of 0.7. Acid-base potentiometric titrations were performed in the electrolyte media with a standard Pt/H(2) electrode and a junctionless Ag/AgCl reference electrode to monitor the emf. A non-approximative equation was used to linearize the titration data. The values obtained were: K*(Lib) = 0.89 +/- 0.02, K*(NaB) = 0.44 +/- 0.01, K*(MgB) = 13.6 +/- 0.7, K*(CaB) = 11.4 +/- 0.15, K*(SrB) = 3.47 +/- 0.06. The values for K*(MB) correlate with the charge-density parameter z(2)/(r + 0.85), where r is the radius of the cation. The speciation of boron in sea-water was predicted from the K*(MB), data for the major cations present.     

Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by traditional three-way chemometrics methods such as TLD and PARAFAC. In this work, the effects of these violations are studied using simulated and experimental data used in conjunction with the well-established TLD and PARAFAC. The results obtained by both methods are compared with the results obtained by MLPARAFAC, which is a method designed to optimally accomodate a variety of measurement error structures. The impact on the estimates of different parameters linked to the data sets and the DECRA method is investigated using simulated data. The results indicate that PARAFAC produces estimates of much poorer quality than TLD and MLPARAFAC. Also, it was found that the quality TLD estimates was comparable or only marginally poorer than the MLPARAFAC estimates. A number of commonly used algorithms were also compared to MLPARAFAC using two sets of published experimental data from kinetic studies. The MLPARAFAC estimates of rate constants were more precise than the other methods examined.     

Determination of individual stability constants of coexisting molecular complexes formed by unresolvable isomers

Some biogenic substances undergo steric isomerism or tautomerism in which the isomers are unresolvable. Naturally, the isomers are expected to form molecular complexes with distinct stabilities. This paper proposes the method of determining individually the stability constants of complexes formed under isomerisation and complexation equilibria: the NMR titration curves are modelled and formulated for fast and slow isomeric equilibria, the process of least-squares fittings is explained, and the application to supramolecular complexation of unresolvable isomers is discussed as compared with NMR titration data reported for α- and β-D-glucosamine anomers.     

Multiparametric curve fitting-IX Simultaneous regression estimation of stoichiometry and stability constants of complexes

A chemical model (i.e., the number of complexes, their stoichiometry and stability constants with molar absorptivities) in solution equilibria may be established by (i) the trial-and-error method in which stability constants are estimated for an assumed set of complexes in the mixture and a fitness test is used to resolve a choice of plausible models to find the true one; (ii) the simultaneous estimation of the stoichiometry and stability constants for species divided into "certain" species for which the parameters beta(pqr), (p, q, r) are known and held constant, and "uncertain" species with unknown parameters which are determined by regression analysis. The interdependence of stability constants and particular sets of stoichiometric indices requires that the computational strategy should be chosen carefully for each particular case. The benefits and limitations of both approaches are compared by means of examples of potentiometric titration data analysis by the POLET(84) program and of spectrophotometric data analysis by the SQUAD(84) program. A strategy for efficient computation is suggested.     

Determination of the stability constants of lanthanide complexes with oxyacids using capillary electrophoresis

Different algorithms for calculating the stability constants of lanthanide complexes with hydroxycarbonic acids on the basis of experimental data obtained by capillary electrophoresis are compared. It is shown that the optimal approach is based on the consideration of the electrophoretic mobilities of all complex forms present in the solution, taking into account their fractions. The most satisfactory approximation of the experimental data by the calculated ones is achieved on the assumption that the electrophoretic mobilities of the complex species depend on their charge only, regardless of the particle size. The obtained stability constants of lanthanide complexes with lactic and 2-hydroxy-2-methylpropanoic acids agree with the literature data. The stability constants of lanthanide complexes with tartaric and citric acids were significantly corrected, while the constants for complexes with mandelic, 2-hydroxy-2-methylbutanoic, 2-hydroxy-2-propy-lpentanoic, and malic acid were determined for the first time.     

Determination of the stability constants of macrocyclic ligand-alkali cation complexes by fast atom bombardment mass spectrometry

Quantitative studies of the complexation of the macrocylic ligands, 18 crown 6 (18C6,1) and cyclogentiotetraose peracetate (CGD4Ac,2), with alkali cations, have been investigated by fast atom bombardment mass spectrometry (f.a.b.m.s.). Complexation curves of 18C6 with Na⁺, K⁺, Rb⁺ and Cs⁺ in glycerol, and of CGD4Ac with Cs⁺ in PEG 200, were obtained by plotting the complex peak intensity against the alkali cation concentration. From these curves we describe a method to calculate the stability constant for an alkali cation-macroyclic ligand complex. There is a good agreement between stability constants obtained either by f.a.b.m.s. or calorimetric techniques for 18C6-alkali cation complexes. These results suggest that the f.a.b. technique can be used to study complex formation and determine the stability constant.     

Multiparametric curve fitting-XIII Reliability of formation constants determined by analysis of potentiometric titration data

The formation (protonation) constants log K_i, of the acid H_jL are determined by regression analysis of potentiometric titration data when common parameters (log K_i, i = 1,…, j) and group parameters (E⁰′, L₀, H_T) are refined. The influence of three kinds of error on the protonation constants has been investigated: error from the strategy of minimization, random error, and error from uncertain estimates of group parameters. An analysis of variance of the log K_i, matrix was made for 7 identical titrations and 8 computational strategies, or of 7 identical titrations and 8 different options of group parameters to be refined. The influence of the standard potential E⁰ of the glass-electrode cell on the systematic error in log K is greater than that of the acid concentration (L₀) or the concentration of titrant used (H_T). The ill-conditioned group parameters should be refined together with the common parameters (K_i), otherwise the estimates of log K_i, are not accurate enough. Two ways of calibrating the glass electrode cell were compared. Internal calibration (performed during titration) was more accurate than external calibration done separately. Of the programs tested ESAB and ACBA are the most powerful because they permit refinement of group parameters and internal calibration. Citric acid was chosen as model substance.     

Determination of stability constants for alkaline-earth and alkali metal ion complexes of glycine by spectrophotometry

The complex equilibria between alkaline-earth and alkali metal ions with glycine were studied by a spectrophotometric method. The following stability constant (concentration) values valid at 25 degrees and ionic strength 1.0M were found: K(HL) = 10(9.57), K(LiL) = 10(-1.2), K(BaL) = 10(-0.40), K(SrL) = 10(0.14), K(CaL) = 10(0.55), K(MgL) = 10(1.17).     

Determination of the stability constants for the complexes of rare earth elements and tetracycline

Stability constants for the lanthanide elements complexes with tetracycline were determined by the methods of average number of ligands, the two parameters and by weighted least squares. The technique of solvent extraction was applied to obtain the values of the parameters required for the determination of the constants.     

Autoprotolysis constants by coulometric titration

A procedure is described for the evaluation of autoprotolysis constants in which a strong acid is titrated with coulometrically generated strong base. A two-compartment cell is used, and the acid may be added as such to the solvent under study, or generated in situ in the cell. When a silver auxiliary electrode can be used, as with solutions containing bromide ion, a single-compartment cell may be used, which seems to give more accurate results because it avoids the errors caused by diffusion of solution through the diaphragm. The results for the constants obtained for ethylene glycol, for methanol and for water are in reasonable agreement with values in the literature.     

Determination of stability constants of complexes of neutral analytes with charged cyclodextrins by affinity capillary electrophoresis

A novel procedure for the determination of stability constants in systems with neutral analytes and charged complexation agents by affinity capillary electrophoresis was established. This procedure involves all necessary corrections to achieve precise and reliable data. Temperature, ionic strength, and viscosity corrections were applied. Based on the conductivity measurements, the average temperature of the background electrolyte in the capillary was kept at the constant value of 25°C by decreasing the temperature of the cooling medium. The viscosity correction was performed using the viscosity ratio determined by an external viscosimeter. The electrophoretical measurements were performed, at first, at constant ionic strength. In this case, the increase of ionic strength caused by increasing complexation agent concentration was compensated by changing of the running buffer concentration. Subsequently the dependence of the analyte effective mobility on the complexation agent concentration was measured without the ionic strength compensation (at variable ionic strength). The new procedure for determination of the stability constants even from such data was established. These stability constants are in a very good agreement with those obtained at the constant ionic strength. The established procedure was applied for determination of the thermodynamic stability constants of (R, R)-(+)- and (S, S)-(-)-hydrobenzoin and R- and S-(3-bromo-2-methylpropan-1-ol) complexing with 6-monodeoxy-6-mono(3-hydroxy)propylamino-β-cyclodextrin hydrochloride.     

Determination of the composition and stability constants of the complexes of AgI with sulphur-containing aminopyridines

The stability of the complexes of Ag^I with sulphur-containing aminopyridines of general formula Py? (CH₂)_n?1? S? (CH₂)_m? NH₂ (where: n ? 1, m = 1,2; 1,3; 2,2; 2,3) have been determined at 25°C and for an ionic strength of 0.5 M (K)NO₃ by a combined pH–pM metric method. The study of complex formation and the determination of the approximative values for the constants proceeded by graphical means. The constants were refined by a least squares computer method. In acid medium (pH < 3) the protonated species AgLH₂³⁺ and AgL₂H₄⁵⁺ are formed and coordination occurs through the thioether group. At higher pH values (pH > 3) additional chelation occurs through the pyridine-nitrogen donor in the complexes AgLH²⁺, AgL₂H₃⁴⁺, and AgL₂H₂³⁺. The former complex extensively transforms into a dimer Ag₂L₂H₂⁴⁺, which may also arise on the addition of a protonated ligand to the dinuclear Ag₂LH³⁺ species. At still higher PH values (pH > 6) also the aminogroup participates in chelation in the species Ag₂L₂H³⁺, Ag₂L₂²⁺ and Ag₂L²⁺. With an excess of ligand however a white precipitate is formed.     

Application of maximum likelihood multivariate curve resolution to noisy data sets

In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR‐ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time‐course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA‐MCR‐ALS are practically identical to those obtained by MCR‐WALS and that they can differ from those resolved by ordinary MCR‐ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA‐ALS and MCR‐WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR‐ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA‐MCR‐ALS over MCR‐WALS is then that the former does not require changing the traditional MCR‐ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Prediction of chromatographic retention of metal complexes from stability constants measured by ion chromatography

Chromatographia - A theoretical model is used to predict retention times of divalent metal cations in single-column ion chromatography using one or more ligands in the eluent. Stability constants...     

Determination of dissociation constants for some pyrogallol azo derivatives and stability constants of their complexes with rare-earth metals

The dissociation constants of some haloazo derivatives of pyrogallol and the stability constants of their complexes with rare-earth metals (La, Ce, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) are determined by potentiometric titration in aqueous ethanol (3: 7). A correlation between the dissociation constants of the reagents and the stability constants of their complexes is found.     

Determination of acid dissociation constants based on continuous titration by feedback-based flow ratiometry

We propose a method for the determination of acid dissociation constants based on the rapid detection of the equivalence point (EP) by feedback-based flow ratiometry and the subsequent estimation of the half equivalence point (EP_1/2). The titrant (e.g., NaOH) flow rate F_B was varied in response to a control voltage V_c from a controller, while the titrand (e.g., CH₃COOH) flow rate F_A was held constant. The pH of the mixed solution was monitored downstream from the confluence point of the solutions following a knotted tubular mixer. Initially, V_c was increased linearly. At the instance the detector sensed EP, the ramp direction of V_c changed downward. The pH increased further because of the lag time between the mixing of solutions and the sensing of pH. Following the pH maximum, the pH decreased. The EP was sensed again in this downward scan. The V_c that gives EP_1/2 was computed from the V_c just at the time of the EP detection. The V_c was held constant at this level for 18 s, and the plateau pH value thus obtained was taken to be the pK_a of the analyte subject to activity corrections. Studies on the dependence of the pK_a on the ionic strength or dielectric constant of the solution were conducted in an automated fashion by delivering NaCl solution or acetonitrile through an additional channel. Satisfactory results were obtained with good throughput (53 s per determination) and precision (R.S.D.≈0.3%) for various acids.     

Determination of stability constants of valinomycin complexes with ammonium and alkali metal ions by capillary affinity electrophoresis

Capillary affinity electrophoresis (CAE) has been employed to investigate quantitatively the interactions of valinomycin, macrocyclic depsipeptide antibiotic ionophore, with univalent cations, ammonium and alkali metal ions, K(+), Cs(+), Na(+), and Li(+), in methanol. The study involved measuring the change in effective electrophoretic mobility of valinomycin while the cation concentrations in the BGE were increased. The corresponding apparent stability (binding) constants of the valinomycin-univalent cation complexes were obtained from the dependence of valinomycin effective mobility on the cation concentration in BGE using a nonlinear regression analysis. The calculated apparent stability constants of the above-mentioned complexes show the substantially higher selectivity of valinomycin for K(+) and Cs(+) ions over Li(+), Na(+), and NH(4)(+) ions. CAE proved to be a suitable method for the investigation of both weak and strong interactions of valinomycin with small ions.     

Determination of stability constants of some bivalent metal complexes with thiovioluric and diphenylthiovioluric acids

Stability constants of complexes of some bivalent metal ions, viz, Cu(II), Ni(II), Zn(II), Pb(II) and Mg(II) with thiovioluric and diphenylthiovioluric acid have been determined potentiometrically in 50 and 75% dioxan media, respectively. The order of stability constants for the complexes investigated has been found to be: Mn < Ni < Cu > Zn. The stability of lead complexes has been found to be intermediate between Mn(II) and Ni(II) while magnesium forms the least stable complexes.