Modelling complex solution equilibria. II. Systems involving ligand substitutions and uncertainties in equilibrium constants derived from formation constants

1990 ◽  
Vol 68 (12) ◽  
pp. 2208-2211 ◽  
Author(s):  
Pierre G. Potvin
Keyword(s):  
Equilibrium Constants ◽  
Correlation Coefficients ◽  
Formation Constants ◽  
Ligand Substitution ◽  
Complex Solution ◽  
Unknown Parameters ◽  
Solution Equilibria

A general formalism is presented that expresses equilibrium constants K as combinations of pseudo-formation constants ψ. For equilibria involving complexes as reactants that undergo ligand substitutions, this formalism allows a reduction in the number of equations needed to model the system for faster calculation of species concentrations and refinement of unknown parameters. Gauss–Newton refinement of log ψ parameters is shown to be equivalent to that of log K parameters. Equations are developed for the calculation of uncertainties in log K and correlation coefficients between them from the corresponding values obtained for log ψ parameters. These equations can also be used to calculate the same quantities for constants (such as Ka's) derived from true formation constants. Keywords: Gauss–Newton, ligand substitution, equilibrium constants, formation constants.

Modelling complex solution equilibria. I. Fast, worry-free least-squares refinement of equilibrium constants

1990 ◽  
Vol 68 (12) ◽  
pp. 2198-2207 ◽  
Author(s):  
Pierre G. Potvin
Keyword(s):  
Least Squares ◽  
Taylor Series ◽  
Global Minimum ◽  
Infinite Order ◽  
Equilibrium Constants ◽  
Complex Solution ◽  
First Order ◽  
Solution Equilibria ◽  
Higher Derivatives ◽  
Series Expression

The methods of Steepest Descent, Gauss–Newton (first-order Taylor series) and Newton–Raphson (second-order Taylor series) least-squares iteration were examined in the context of the refinement of estimated equilibrium constants β in solution. Under certain conditions, all three can produce corrections to the parameters that overshoot the global minimum and diverge therefrom, owing to the shape of the parameter surface. The latter two methods are problematic when the β parameters are overestimated, or when their logarithms are underestimated, whence a useful approximation to the analytical second and higher derivatives was found for any data type. This reduces an exact, infinite-order Taylor series expression of any observable to a simple first-order expression. As illustrated with experimental pH data, faster, more reliable refinement results without overshoot or divergence problems, and without resort to computationally onerous algorithms, such as the Marquardt–Levenberg, Fletcher–Powell, or Hartley–Wentworth methods. Keywords: equilibrium constants, least-squares, Gauss–Newton, complex solution equilibria.

Substitution reactions of benzethonium chloride with ion associates of bromocresol green – quinine and bromophenol blue – quinine in dichloromethane

1991 ◽  
Vol 69 (6) ◽  
pp. 937-944 ◽  
Author(s):  
Alberto Hernandez Gainza ◽  
Roy Ikemefula Konyeaso
Keyword(s):  
Thermodynamic Parameters ◽  
Equilibrium Constants ◽  
Formation Constants ◽  
Bromocresol Green ◽  
Bromophenol Blue ◽  
Substitution Reactions ◽  
Dichloromethane Solution ◽  
Benzethonium Chloride ◽  
Quinine Hydrochloride ◽  
Ion Associate

An excess concentration of base quinine (Q) reacts with a sulphonphthalein diacidic dye XH2, (bromocresol green, BCGH2, or bromophenol blue, BPBH2) in dichloromethane solution to form an ion associate (X2−(QH+)2) of stoichiometry 1:2 (dye:amine). Benzethonium chloride (ClB) reacts with the 1:2 ion associate to form an ion associate (QH+,X2−,B+) and quinine hydrochloride ClQH+. This substitution reaction is a chemical equilibrium with formation constants of 1.50 ± 0.67, 1.61 ± 0.54, 1.07 ± 0.29, 1.04 ± 0.20, and 0.84 ± 0.26 for BCG and 1.86 ± 0.59, 1.47 ± 0.23, 1.40 ± 0.65, 1.13 ± 0.37, and 1.11 ± 0.27 for BPB at 283.16, 288.16, 293.16, 298.16, and 303.16 K respectively. The thermodynamic parameters determined by van't Hoff's equation are ΔH0 = −21.766 ± 7.482 kJ mol−1, ΔS0 = −73 ± 51 J mol−1 K−1, and ΔG0 = −1.134 ± 0.972 kJ mol−1for BCG and ΔH0 = −18.678 ± 7.482 kJ mol−1, ΔS0 = −61 ± 26 J mol−1 K−1, ΔG0 = −0.916 ± 0.401 kJ mol−1 for BPB (ΔG0 at 293.16 K; and ΔH0 and ΔS0 determined in the range 283–303 K). Key words: bromocresol green – quinine–benzethonium, ion associate mixture, bromophenol blue – quinine–benzethonium, equilibrium constants, thermodynamic parameters.

Nuclear magnetic resonance studies of the solution chemistry of metal complexes. XIV. The aqueous chemistry of trimethyllead(IV) and its carboxylic acid complexes

1977 ◽  
Vol 55 (18) ◽  
pp. 3255-3260 ◽  
Author(s):  
T. L. Sayer ◽  
S. Backs ◽  
C. A. Evans ◽  
E. K. Millar ◽  
D. L. Rabenstein
Keyword(s):  
Carboxylic Acid ◽  
Magnetic Resonance ◽  
Proton Magnetic Resonance ◽  
Ph Dependence ◽  
Equilibrium Constants ◽  
Formation Constants ◽  
Solution Chemistry ◽  
Resonance Spectroscopy ◽  
Coupling Constant ◽  
Proton Coupling

The aqueous solution chemistry of the trimethyllead(IV) species and the trimethyllead(IV) complexes of six carboxylic acids of pKa values ranging from 2.75 to 4.95 has been investigated by proton magnetic resonance spectroscopy. Equilibrium constants for the reaction of (CH3)3Pb+ with hydroxide ion to form (CH3)3PbOH and ((CH3)3Pb)2OH+, and the formation constants of the carboxylic acid complexes were determined from the pH dependence of the chemical shift of the methyl protons of trimethyllead. The formation constants of the complexes increase as the pKa of the ligand increases. The lead-207-proton coupling constant was found to be insensitive to complexation.

scholarly journals Thermodynamics of metal-ligand bond formation. VIII. Pyridine adducts of zinc(II) β-diketonates

1973 ◽  
Vol 26 (11) ◽  
pp. 2537 ◽  
Author(s):  
DR Dakternieks ◽  
DP Graddon
Keyword(s):  
Benzene Solution ◽  
Equilibrium Constants ◽  
Bond Formation ◽  
Formation Constants ◽  
Adduct Formation ◽  
Enthalpies Of Formation ◽  
Calorimetric Titration ◽  
Experimental Conditions ◽  
Metal Ligand ◽  
Ligand Bond

Equilibrium constants and enthalpies in benzene solution are reported for the formation of 1 : 1-adducts of pyridine with four zinc(II) complexes of β-diketones, determined by calorimetric titration. Adduct formation constants at 30�C fall in the range 300-2000 and enthalpies of formation lie between -15 and - 34 kJ mol-1. Though the enthalpies of formation differ little from those of corresponding copper(II) complexes, the adducts are about a hundred times more stable. The pyridine adduct of bis(2,2,6,6-tetramethylheptane-3,5-dionato)zinc(II) is entropy-stabilized relative to those of other complexes. No evidence was obtained for the addition of a second molecule of pyridine under the experimental conditions used.

scholarly journals Investigation of Charge Transfer Complexes Formed between Mirtazapine and Someπ-Acceptors

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hulya Demirhan ◽  
Mustafa Arslan ◽  
Mustafa Zengin ◽  
Mustafa Kucukislamoglu
Keyword(s):  
Charge Transfer ◽  
Dosage Form ◽  
Room Temperature ◽  
Equilibrium Constants ◽  
Formation Constants ◽  
Electron Acceptors ◽  
Spectral Studies ◽  
Charge Transfer Complexes ◽  
Ir And Nmr Spectroscopy ◽  
Ft Ir

Charge transfer complexes (CTC) of mirtazapine with tetracyanoethylene (TCNE), 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ), and tetracyanoquinodimethane (TCNQ) have been studied spectrophotometrically in dichloromethane at room temperature. The stoichiometries of the complexes were found to be 1 : 1 ratio by the Job Method between mirtazapine and the acceptors. The equilibrium constants and thermodynamic parameters of the complexes were determined by the Benesi-Hildebrand and Van't Hoff equations. Mirtazapine in pure and dosage form was applied in this study. The results indicate that the formation constants for the complexes depend on the nature of electron acceptors and donor. And also the spectral studies of the complexes were determined by FT-IR and NMR spectroscopy.

Conductance and Conductometric Titrations of Picric Acid in Sulfolane at 30°

1973 ◽  
Vol 51 (3) ◽  
pp. 448-450 ◽  
Author(s):  
P. M. P. Eller ◽  
Joseph A. Caruso
Keyword(s):  
Picric Acid ◽  
Weak Acid ◽  
Aprotic Solvents ◽  
Acid Solutions ◽  
Complex Solution ◽  
Solution Equilibria ◽  
Equivalent Conductance ◽  
Effect Of Water

Conductance of picric acid solutions in sulfolane resembles the behavior seen in several other aprotic solvents and is suggestive of complex solution equilibria. The effect of water on equivalent conductance of picric acid is large for concentrations greater than about 0.3 M. Picric acid behaves as a weak acid in conductometric titrations.

Vapor Pressures of Triethylamine + Chloroform and of Diethyl Ether + Chloroform at 298.15 K

1975 ◽  
Vol 53 (21) ◽  
pp. 3299-3304 ◽  
Author(s):  
Yash Paul Handa ◽  
David Edward Jones
Keyword(s):  
Diethyl Ether ◽  
Equilibrium Constants ◽  
Formation Constants ◽  
Enthalpies Of Formation ◽  
Vapor Pressures ◽  
Complex Formation Constants ◽  
Standard Enthalpies Of Formation ◽  
Vapor Pressure Measurements ◽  
Associated Solution Model ◽  
Associated Solution

Vapor pressures of triethylamine + chloroform and of diethyl ether + chloroform were measured at 298.15 K with a calibrated quartz spiral. The ideal associated solution model has been used to determine the equilibrium constants and standard enthalpies of formation of the complexes from the thermodynamic properties derived from the vapor pressure measurements and from earlier calorimetric measurements. These complex formation constants are compared with values obtained by calorimetric and spectroscopic methods.

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