Cumulative Formation Constants Research Articles

Determination of the Distribution of Ferric Chloro Complexes in Hydrochloric Acid Solutions at 298 K

Abstract Understanding the intrinsic nature of materials requires ultrahigh-purity materials because impurities affect various properties. Ion-exchange separation is one of the most promising purification technologies; however, the thermodynamic details of the ion-exchange reaction have not been made clear. The condition of metal species in the solution phase is fundamental to investigating the ion-exchange reaction. In this paper, the distribution of ferric chloro complexes in hydrochloric acid solutions was investigated by factor analysis of UV-Vis absorption spectra, followed by fitting analysis of a theoretical model to individual molar attenuation coefficients obtained by mathematical decomposition of UV-Vis absorption spectra. Five ferric species were detected by principal component analysis using a novel index proposed in this paper. In the results of factor analysis followed by fitting analysis, [FeIII]3+, [FeIIICl]2+, [FeIIICl2]+, [FeIIICl3]0, and [FeIIICl4]− were identified. The activity coefficients of charged species in concentrated aqueous solutions were estimated by using a modified Debye-Hückel equation. The thermodynamic parameters of the four cumulative formation constants and a Setchénow coefficient for neutral species of [FeIIICl3]0 were determined. The adsorbability of ferric, cupric, and cobalt species to an anion exchanger from hydrochloric acid solutions was qualitatively discussed using the results obtained in this paper.

Investigation of Uranyl Sulfate Complexation under Hydrothermal Conditions by Quantitative Raman Spectroscopy and Density Functional Theory

Quantitative first and second formation constants of aqueous uranyl sulfate complexes were obtained from Raman spectra of solutions in fused silica capillary cells at 25 MPa, at temperatures ranging from 25 to 375 °C. Temperature-dependent values of the symmetric O-U-O vibrational frequencies of UO22+(aq), UO2SO40(aq), and UO2(SO4)22-(aq) were determined from the high-temperature spectra. Temperature-independent Raman scattering coefficients of UO22+(aq) were calculated directly from uranyl triflate spectra from 25 to 300 °C, while those of UO2SO40(aq) and UO2(SO4)22-(aq) were derived from spectroscopic data at 25 °C and concentrations calculated using the formation constants of Tian and Rao ( J. Chem. Thermodyn. 2009 , 41 , 569 - 574 ), together with the Specific Ion Interaction Theory (SIT) activity coefficient model. Chemical structures and vibrational frequencies predicted from Density Functional Theory (Gaussian 09) were employed to interpret the Raman spectra. Values of the cumulative formation constants ranged from log β1 = 3.23 ± 0.08 and log β2 = 4.22 ± 0.15 at 25 °C, to log β1 = 12.35 ± 0.22 and log β2 = 14.97 ± 0.02 at 350 °C. This is the first reported use of high-pressure fused silica capillary cells to determine formation constants of metal ligand complexes from their reduced isotropic Raman spectra under hydrothermal conditions.

Determination of structures of cupric-chloro complexes in hydrochloric acid solutions by UV-Vis and X-ray absorption spectroscopy

Ultrahigh-purity metals are indispensable to understanding the nature of materials, but the purity of contemporary metals is insufficient for determining their intrinsic properties. The fundamentals of the anion-exchange reaction must be clear in order to increase the refining efficiency of anion-exchange separation for purification of metals. The thermodynamic analysis of the anion-exchange reaction needs to take account of the distributions of metal-chloro complexes in the solution phase in addition to those between the resin and the solution phase. The structures of metal-chloro complexes in the solution phase must be determined as the first step in determining what species is adsorbed on the resin. Copper is one of the base metals most commonly used in modern society, and the anion-exchange behavior of cupric species is representative. The distribution and the molar attenuation coefficients of cupric-chloro complexes in hydrochloric acid solutions were obtained employing factor analysis followed by fitting a thermodynamic model to ultraviolet-visible absorption spectra. The cumulative formation constants were determined as follows: $\log _{10}\beta _{1} = 0.599$ , $\log _{10}\beta _{2} = 0.343$ , $\log _{10}\beta _{3} = -1.88$ , and $\log _{10}\beta _{4} = -5.25$ , and the Setchenow coefficient for the neutral species of [CuIICl2]0 is 0.188. Using the distribution assessed by the above thermodynamic parameters, the X-ray absorption spectra (XAS), consisting of X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) of individual species, were assessed by factor analysis. EXAFS theoretical models were fitted to experimental spectra of individual species to determine their structures and coordination geometries for the first time, although it is generally very difficult to obtain the spectrum of the individual species in a matrix containing other species simultaneously. The structures of five cupric-chloro complexes were determined to be distorted octahedrons of $\left [\mathrm {Cu^{II}(H_{2}O)_{4}^{eq}(H_{2}O)_{2}^{ax}}\right ]^{2+}, \left [\mathrm {Cu^{II}(H_{2}O)_{4}^{eq}(H_{2}O)^{ax}Cl^{ax}}\right ]^{+}$ , and $\left [\mathrm {Cu^{II}Cl_{2}^{ax}(H_{2}O)_{4}^{eq}}\right ]^{0}$ , a planar triangle of $\left [\mathrm {Cu^{II}Cl_{3}}\right ]^{-}$ , and a tetrahedron of [CuIICl4]2−. The obtained spectra can be used as standards. The XANES spectra of cupric-chloro complexes were interpreted qualitatively. The Cl− ligand in $\left [\mathrm {Cu^{II}(H_{2}O)_{4}^{eq}(H_{2}O)^{ax}Cl^{ax}}\right ]^{+}$ is attracted to the center atom of CuII by electrostatic force, as the H2O ligands are. Contrastingly, the bonding system of the Cl− ligands in the latter three species involves covalency.

Determination of the Distribution of Cupric Chloro-Complexes in Hydrochloric Acid Solutions at 298 K

Knowledge of the distribution of metal-chloro complexes in hydrochloric acid solutions is fundamental for understanding the anion-exchange reaction. Anion-exchange separation allows ultrahigh purification during hydrometallurgical processes. However, at present the exchange reactions are not understood in detail. A more sophisticated purification needs improvement of the anion-exchange separation process. The process is based upon anion-exchange reactions and the distribution of metal-chloro complexes. The present work deals with cobalt-chloro complexes which exhibit a beautiful deep blue color in a concentrated hydrochloric acid solution. The intensity of the absorption attributed to the deep blue color is so strong that it is hard to obtain meaningful results by factor analysis. Another absorption band was chosen to be used in factor analysis and the attempt was successful. The number of cobalt-chloro complexes in hydrochloric acid solutions was determined to be three, and the cumulative formation constants were fitted to absorption spectra decomposed by factor analysis. During the optimization of the cumulative formation constants, a modified Debye–Huckel model for estimation of the activity coefficients of $$\hbox {Cl}^{-}$$ was used. It was found that there are three cobalt complexes $$[\hbox {Co}^{\mathrm{II}}(\hbox {H}_{2}\hbox {O})_{6}]^{2+}$$ , $$[\hbox {Co}^{\mathrm{II}}\hbox {Cl}(\hbox {H}_{2}\hbox {O})_{5}]^{+}$$ , and $$[\hbox {Co}^{\mathrm{II}}\hbox {Cl}_{4}]^{2-}$$ , and the two cumulative formation constants were optimized such that $$\log _{10}\beta _{1} = -\,0.861$$ and $$\log _{10}\beta _{4} = -\,7.40$$ . The geometries of the complexes are proposed by assignment of absorption bands using ligand field theory. A qualitative assessment of the relationship between the acquired distribution of cobalt-chloro complexes and the adsorption function of cobalt species from hydrochloric acid solutions to anion-exchange resin was made.

Ion-selective electrodes with unusual response functions: simultaneous formation of ionophore-primary ion complexes with different stoichiometries.

It is well known that the selectivity of an ion-selective electrode (ISE) depends on the stoichiometry of the complexes between its ionophore and the target and interfering ions. It is all the more surprising that the possibility for the simultaneous occurrence of multiple target ion complexes with different complex stoichiometries was mostly ignored in the past. Here, we report on the simultaneous formation of 1:1 and 1:2 complexes of a fluorophilic crown ether in fluorous ISE membranes and how this results in what looks like super-Nernstian responses. These increased response slopes are not caused by mass transfer limitations and can be readily explained with a phase boundary model, a finding that is supported by experimentally determined complex formation constants and excellent fits of response curves. Not only Cs(+) but also the smaller ions Li(+), Na(+), K(+), and NH(4)(+) form 1:1 and 1:2 complexes with the fluorophilic crown ether, with cumulative formation constants of up to 10(15.0) and 10(21.0) for of the 1:1 and 1:2 complexes, respectively. Super-Nernstian responses of the type observed with these electrodes are probably not particularly rare but have lacked in the past an adequate discussion in the literature, remaining ignored or misinterpreted. Preliminary calculations also predict sub-Nernstian responses and potential dips of a similar origin. The proper understanding of such phenomena will facilitate the development of new ISEs based on ionophores that form complexes of higher stoichiometries.

Complexation in the Cu(II)–LiCl–H 2O system at temperatures to 423 K by UV-Visible spectroscopy

Thermodynamic data for the solubility and formation of copper(I)and copper(II) species are required to model innovative designs of the electrolysis cells used in the thermochemical copper-chloride hydrogen production process. Cumulative formation constants of Cu 2+(aq) complexes with Cl −(aq) were determined by Principal Component Analysis of UV-spectra, obtained over a very wide range of solution compositions and temperature, coupled with an appropriate model for activity coefficients of the solution species. Shortcomings in the existing database and future work to extend these studies to higher temperatures and much higher copper concentrations are discussed.

Phenyl boronic acid complexes of diols and hydroxyacids

Cumulative formation constants for the interaction of phenyl boronic acids with 1,2-diols and structurally related α-hydroxy carboxylic acids were determined by potentiometric titration in aqueous solution. Although there is a significant electronic effect on the acidity of phenyl boronic acid (ρ = 2.1), there is no marked electronic effect on the stability of the complexes. Rather, the complexes are significantly destabilised by adjacent anionic groups, by steric interactions across the face of the cyclic boronate ester and by angle strain within the boronate ester ring. Binding that is nearly independent of pH is observed for some favourably constituted α-hydroxy acid complexes as a result of the relatively high acidity of the acids, which in turn allows tetrahedral boronate complexes to persist in acidic solution (pH < 3). Boronate complex stability is remarkably sensitive to steric and electrostatic factors.

Solution interactions between the uranyl cation [formula omitted] and histidine, N-acetyl-histidine, tyrosine, and N-acetyl-tyrosine

Complexes of the uranyl cation [ UO 2 2 + ] with histidine (His), N-acetyl-histidine (NAH), tyrosine (Tyr), and N-acetyl-tyrosine (NAT) were studied by UV–visible and NMR spectroscopy, and by potentiometric titration. Protonation constants for each ligand are reported, as are cumulative formation constants for uranyl–amino acid complexes. Coupling constant data ( J CH) for uranyl–histidine complexes indicate that inner-sphere solution interactions between histidine and uranyl cation are solely at the carboxylate site. At 25 °C the major uranyl–histidine complex has a cumulative formation constant of log β 110 = 8.53, and a proposed formula of [UO 2HisH 2(OH) 2] +; the stepwise formation constant, log K UL, is estimated to be ⩽5.6 (≈8.53 − (−6.1) − (−6.1) − 15.15). Outer-sphere interactions, H-bonding or electrostatic interactions, are proposed as contributing a significant portion of the stability to the ternary uranyl–hydroxo-amino acid complexes. The temperature dependent protonation constants of histidine and formation constants between uranyl cation and histidine are reported from 10 to 35 °C; at 25 °C, Δ G = −43.3 kJ/mol.

Effects of low-molecular-weight organic acids on Cu(II) adsorption onto hydroxyapatite nanoparticles

Adsorption kinetics and adsorption isotherms of Cu(II) onto a nanosized hydroxyapatite (HAP) in the absence and presence of different low-molecular-weight organic acids are studied in batch experiments. The results show that the adsorption kinetics of Cu(II) onto the HAP are best described by pseudo-second-order model, and the adsorption isotherms of Cu(II) onto the HAP fit Dubinin–Radushkevich model very well with high correlation coefficient ( R 2 = 0.97–0.99). The amount adsorbed of Cu(II) onto the HAP at pH 5.5 was much higher than that at pH 4.5. The presence of organic acids significantly decreased the adsorption quantity of Cu(II), clarifying the lower sorption affinities of Cu(II)–organic acid complexes onto the HAP rather than Cu(II) ion. The decreased maximal adsorption quantity of Cu(II) onto the HAP increased with the increasing logarithm of cumulative formation constants of Cu(II) and organic acids. The stronger coordination of organic acid with Cu(II), the more decreased Cu(II) adsorption quantity onto the HAP.

A spectrophotometric study of samarium (III) speciation in chloride solutions at elevated temperatures

The speciation of samarium (III) in chloride-bearing solutions was investigated spectrophotometrically at temperatures of 100–250 °C and a pressure of 100 bars. The simple hydrated ion, Sm 3+, is predominant at ambient temperature, but chloride complexes are the dominant species at elevated temperatures. Cumulative formation constants for samarium chloride species were calculated for the following reactions: Sm 3 + + Cl - = SmCl 2 + β 1 Sm 3 + + 2 Cl - = SmCl 2 + β 2 Within experimental error, the values for the first formation constant ( β 1), are identical to the values predicted by Haas et al. [Haas J. R., Shock E. L. and Sassani D. C. (1995) Rare earth elements in hydrothermal systems: estimates of standard partial molal thermodynamic properties of aqueous complexes of the rare earth elements at high pressures and temperatures. Geochim. Cosmochim. Acta, 59, 4329–4350]. The values for the second formation constant ( β 2) at 200 and 250 °C are in fair agreement with those of Haas et al. (1995) and Gammons et al. [Gammons C. H., Wood S. A. and Li Y. (2002) Complexation of the rare earth elements with aqueous chloride at 200 ° C and 300 ° C and saturated water vapor pressure. Special Publication—The Geochemical Society, (Water–Rock Interactions, Ore Deposits, and Environmental Geochemistry), pp. 191–207]. Calculations of monazite solubility indicate that Sm is less mobile in chloride-bearing solutions than Nd, which may indicate that the HREE are less mobile than the LREE.

Predicting speciation in the multi-component equilibrium self-assembly of a metallosupramolecular complex

A practical method to predict the speciation in a multi-component equilibrium self-assembly process has been developed and applied to the formation of the square macrocyclic complex formed from (ethylenediamine)Pd(II) and 4,4′-bipyridyl. The method is based on an additive free energy approach that derives the cumulative formation constants of all 56 species at equilibrium from a set of five pair-wise interactions. Estimates for the required values of the pair-wise interactions were derived from potentiometric titration of (ethylenediamine)Pd(II) and 3-phenylpyridine, and from (diethylenetriamine)Pd(II) and 4,4′-bipyridyl systems. The method calculates the equilibrium speciation as a function of reactant concentrations and pH and produces a map of the range of compositions in which the square complex and competing species are dominant. The predictions of the method closely correlate with available experimental data.

Gold(I) complexing in aqueous sulphide solutions to 500°C at 500 bar

The solubility of gold has been measured in aqueous sulphide solutions from 100 to 500°C at 500 bar in order to determine the stability and stoichiometry of sulphide complexes of gold(I) in hydrothermal solutions. The experiments were carried out in a flow-through system. The solubilities, measured as total dissolved gold, were in the range 3.6 × 10 −8 to 6.65 × 10 −4 mol kg −1 (0.007–131 mg kg −1), in solutions of total reduced sulphur between 0.0164 and 0.133 mol kg −1, total chloride between 0.000 and 0.240 mol kg −1, total sodium between 0.000 and 0.200 mol kg −1, total dissolved hydrogen between 1.63 × 10 −5 and 5.43 × 10 −4 mol kg −1 and a corresponding pH T, p of 1.5 to 9.8. A non-linear least squares treatment of the data demonstrates that the solubility of gold in aqueous sulphide solutions is accurately described by the reactions Au ( s ) + H 2 S ( aq ) = AuHS ( aq ) + 0 .5H 2 ( g ) K s,100 Au ( s ) + H 2 S ( aq ) + HS – = Au ( HS ) 2 – + 0 .5H 2 ( g ) K s,110 where AuHS(aq) is the dominant species in acidic solutions and Au(HS) 2 − under neutral pH conditions. With increasing temperature, the stability field of Au(HS) 2 − shifts to more alkaline pH in accordance with the shift of the first ionisation constant of H 2S(aq). In addition, AuOH(aq) was found to be an important species in acidic solutions at t > 400°C. The equilibrium solubility constant to form AuHS(aq) was found to increase from log K s,100 = −6.20 ± 0.11 at 200°C to maximum of −5.63 ± 0.07 to 0.11 at 350°C and then decrease to −6.25 ± 0.19 at 500°C. The solubility constant to form Au(HS) 2 − increases with increasing temperature from log K s,110 = −2.33 ± 0.14 at 100°C to −1.27 ± 0.07 at 250°C and then decrease to −1.73 ± 0.25 at 500°C. From these measurements, the equilibrium stepwise and cumulative formation constants were calculated. The complex formation at 25°C is characterised by an exothermic enthalpy and small positive entropy, both of which are consistent with the predominantly covalent interaction between Au + and HS −. With increasing temperature, the cumulative formation reactions become endothermic and are accompanied with large positive entropy of reaction, indicating greater electrostatic interaction. The aqueous speciation of gold(I) is very sensitive to fluid composition and temperature. In low-temperature geothermal fluids, gold(I) sulphide complexes predominate whereas at higher temperatures, gold(I) hydroxide and chloride complexes may also play a role in hydrothermal gold transport in the Earth’s crust.

Binary and ternary phenylboronic acid complexes with saccharides and Lewis bases

Cumulative formation constants for the association of three boronic acids (phenylboronic acid and its ortho-anilinomethyl and ortho-benzylaminomethyl derivatives) with four saccharides (fructose, glucose, mannitol, and sorbitol) were determined by potentiometric titration. Similarly, the constants for the formation binary complexes of the three boronic acids with (hydrogen) phosphate, (hydrogen) citrate, or imidazole were determined. Finally, the formation of ternary complexes of the boronic acids, phosphate, citrate or imidazole, and the saccharides were determined based on the determined values of the binary complexes. The previously unrecognized ternary complexes are significant in all systems investigated, and under some solution compositions, they can be the dominant species in solution over a wide pH range. A value of 15–25 kJ mol −1 was determined for the energy of the B–N interaction in the benzylmethyl derivative based on the relative stabilities of the ternary phosphate complexes of the three boronic acids. The data are used to rationalize the medium dependence of stepwise formation constants and the apparent acidity constants of previous literature reports.

Dismutation of divalent americium induced by the addition of fluoride anion to a LiCl–KCl eutectic at 743 K

The three oxidation states of americium (III), (II) and (0) are stable in a molten LiCl–KCl eutectic at 743 K. Addition of fluoride anion to the melt led to the disproportionation of Am 2+ into Am 3+ and Am. The effect of fluoride additions was monitored with potentiometric and cyclic voltammetry methods and the relative cumulative formation constants of the Am(III) fluoro-complexes determined.

THE SIGNIFICANCE AND RELATIONSHIP OF CORRELATION COEFFICIENTS FOR STEPWISE FORMATION CONSTANTS (K) AND CUMULATIVE FORMATION CONSTANTS (β)

The relationship between the correlation coefficients for stepwise formation constants (K) and cumulative formation constants (β) is derived and discussed. The correlation between paris of cumulative formation constants in a non-linear least-squares fit does not generally reflect the correlation between the underlying stepwise formation constants. The consequences of these results are discussed.

The stability of aqueous silver bromide and iodide complexes at 25–300°C: Experiments, theory and geologic applications

The solubilities of AgBr (s) in NaBr solutions and AgI (s) in NaI solutions were measured at elevated temperature. Referring to the following general reactions (where X = Cl, Br, or I): AgX (s) ⇋ Ag + + X − (1) AgX (s) ⇋ AgX (aq) (2) AgX (s) + X − ⇋ AgX 2 − (3) AgX (s) + 2X − ⇋ AgX 3 2− (4) the following equilibrium constants were obtained: log K 2,Br = −4.01 ± 0.20 (200°C) and −3.12 ± 0.20 (300°C); log K 3,Br = −1.81 ± 0.10 (200°C) and −1.01 ± 0.10 (300°C); log K 3,I = −2.46 ± 0.20 (150°C), −1.92 ± 0.20 (200°C) and −1.47 ± 0.10 (250°C); and log K 4,I = −1.9 ± 0.4 (150°C) and −2.2 ± 0.4 (200°C). These results were combined with previously published data and our own extrapolations to obtain smoothed equilibrium constants at 25–300°C for reactions (1)–(4) at 25–300°C. Values of log K 1 and log K 2 at any given temperature decrease in the order X = Cl > Br > I, whereas the opposite trend is shown for log K 4 at 18°C. Values of log K 3 are similar for X = Cl, Br, I at all temperature, with Δ r H° = +40.7 to + 45.9 kJ mol −1. The enthalpies of reactions 2 Br and 2 Cl are also similar ( Δ r H° = +56.0 and +54.1 kJ mol −1, respectively). Conversion of the above data to cumulative formation constants ( β i , i = 1, 2, 3) indicates that the bromide and iodide complexes of silver are much stronger than their chloride counterparts. However, chloride complexes will dominate silver transport in most cases, due to the low Br Cl and I Cl ligand ratios of natural waters. Exceptions include certain oil field brines with I Cl > 10 −3 , in which case iodide or mixed chloride-iodide complexes become the dominant silver species. Our calculations indicate that AgI (s) is many orders of magnitude less soluble than AgCl (s) in connate brines, and may be an important solubility-limiting phase in sedimentary basins. AgI (s) may also form in the weathering environment, especially in the supergene zones of silver-rich hydrothermal mineral deposits, although AgCl (s) is more stable at Eh conditions above the aqueous I − IO 3 − boundary. Except in very unusual circumstances, silver halide minerals with be too soluble to precipitate directly from high-temperature hydrothermal fluids.

Thermodynamic Study of Ce4+ /Ce3+ Redox Reaction in Aqueous Solutions at Elevated Temperatures: 1. Reduction Potential and Hydrolysis Equilibria of Ce4+ in HCIO4 Solutions

Abstract The redox potential (E) of the couple Ce4+/Ce3+ has been determined up to 368 K by means of cyclic voltammetric measurement in aqueous HClO4 solutions with cHClO4 decreasing from 7.45 to 0.023 mol kg-1 . A constant potential of (1.741 V)298 K, resp. (1.836 V)368K, indicating the existence of pure unhydrolysed Ce4+ was obtained at cHClO4 ≥ 6.05 m. At lower HClO4 concentration, the potential as a function of the HClO4 molality, as well as of the pH shows 4 further distinct steps. At 298 K, for instance, the potential became nearly constant at pH values of 0.103, 0.735,1.115, after which it drastically decreased, respectively at 1.679, just before the precipitation of Ce(OH)4 occurred. The curves indicate obviously the stepwise formation of the Ce(IV) mono-, di-, tri- and tetrahydroxo complexes. The slope of the curves E vs. pH increased gradually with increasing temperature. ΔS and ΔH of the redox reaction were determined as functions of T at the different HClO4 concentrations. ΔSis positive at cHClO4 &gt; 1.85 m and turns to be negative at lower concentrations. ΔHis negative at all HClO4 concentrations studied. The cumulative formation constants ßi, of the Ce(IV) hydroxo complexes and the corresponding hydrolysis constants (Kh)i were calculated. An unusual decrease of ßi with increasing temperature has been discussed

Calculation of site enthalpy for binding of ligands and protons to macromolecules

The analysis of equilibria in solution by the partition function method has shown how the total chemical amounts [T[ M], [T A], and [T H] of the components M, A, and H respectively can be expressed and determined as functions of different powers of site affinity constants k j and cooperativity functions γ( i j,b j ), whereas the cumulative formation constants β PQR cannot be used as statistically independent parameters to be refined in least-squares processes. The same drawback holds for molar enthalpies, Δ H PQR . A special algorithm has been developed by which the heat evolved can be expressed as a function of specific site enthalpies Δ j and specific cooperativity enthalpies Δ h γj for each class j of sites. The algorithm represents the mathematical analog of the interconnections between components in the types of complex macrospecies M PA QH R, M PA Q, A QH R, M P H R , M P (A Q H R ), etc., of the chemical model assumed and their deconvolution into microspecies M P A Q H R . Each class j of sites with site constant k j and cooperativity coefficient b j is described by a polynomial ▪ where Y j is any ligand M, A, or H and i t is the number of sites in the class j. The concentrations of the microspecies are calculated as single terms of the polynomials J j or by products of more terms, each of which belongs to a different J j . Each term of the polynomial is labeled by its own index ( p j , or q j , or r j , or in general i j ), which is the exponent of the term and contains the statistical factor m ij . calculated as the coefficient of the term of the polynomial. The product of more terms is labeled by the indices of the component terms. The relations are therefore represented by combinations of indices ▪. In order to perform the calculation of concentrations of the microspecies and macrospecies by a procedure suitable for computer programming, each polynomial J j is associated with a vector J j whose elements [ i j ] are the terms of J j . The cooperativity factors are set in a diagonal matrix Γ j , whose elements are ▪ and then introduced into the non-cooperative polynomials J j by vector products ▪. The product of terms giving for each microspecies the contribution to the total concentrations [T M], [T A], and [t H] is calculated as the element of a matrix ▪ obtained as tensor product: (1,2= j 1J 2 or ▪ etc. Depending on the chemical model, there are additional different matrices L l. The combination of indices of each element of L l is ▪. The indices are said to define an index space {i.s.}, parallel to the affinity cooperativity space. The elements of the matrices L l are also used to set a matrix ΔC, whose elements Δ c pqr are the changes of concentration of the microspecies during the thermochemical reaction. The i.s. is parallel to the concentration space also. The enthalpy change at the nth experimental point for each microspecies M p,A qH r is calculated from the quantities ▪ ▪ which are then summed for all the indices p,q,r. This relation can also be put in a matrix form: ▪. All these matrices define spaces which are parallel to {i.s.}. The observed heat at the nth experimental point is the scalar product ▪ where the elements of the vector X j, with 1 ⩽ j' ⩽2j max are the whole set of j couples of variables Δ h j , Δ h yj , and the elements of the vector a j' are weighted experimental thermochemical values. By repeating the calculations and summing successively the values for all the n experimental points, the system of normal equations Ax j' = ΔQ is set up, where the elements of ΔQ are sums of n weighted experimental heats. By solution of the system, the values of Δ h j and Δ h yj for all the j classes are obtained.

Vibrational spectral studies of solutions at elevated temperatures and pressures. 12. Magnesium acetate

Raman spectra of aqueous solutions of magnesium acetate at temperatures from 25 to 250°C and at a pressure of 9 MPa have been studied to determine the cumulative formation constants for magnesium acetate complexes. The spectra obtained were analysed using bandfitting techniques, the Gauss-Z least squares method, and Factor Analysis with Equilibrium Constraints (FAEC). The results of this study suggest the presence of two complexes, [Mg(H 2O) 5OAc] + and [Mg(H 2O) 4(OAc) 2](where OAc − refers to CH 3COO −), at 25, 50, 100, and 150°C. The existence of a third complex [Mg(H 2O) 3(OAc) 3] − is also suggested at 150°C. Average enthalpies of formation were estimated as 9.0 ± 1.2 kJ mol −1 for the 1:1 complex and 17.0 ± 1.2 kJ mol −1 for the 1:2 complex.

The stability of calcium chloride ion pairs in aqueous solutions at temperatures between 100 and 360°C

The speciation of calcium in chloride solutions has been investigated between 100 and 360°C by measuring the solubility of AgCl in HCl-CaCl 2 solutions in which chloride varies from 0.3 to 3.0 m and calcium is maintained constant at 0.1 m. Cumulative equilibrium formation constants of calcium chloride ion pairs were evaluated using a non-linear least squares procedure. Association constants could not be evaluated for calcium chloride ion pairs from the data at 100°C. However, at 150°C the cumulative formation constants for CaCl + and CaCl 2 0 are 0.85 and 1.73, respectively. The stability field for CaCl + decreases with increasing temperature, whereas that for CaCl 2 0 increases sharply and at 360°C K 2 is 4.95 · 10 4. Higher order calcium chloride ion pairs either do not form or have stability fields too small to be detected by the methods used in this study. The neutral aqueous calcium chloride ion pair CaCl 2 0 contributes significantly to calcium speciation in intermediate to high salinity hydrothermal solutions: at 250°C, 50 mol percent of the calcium in a 1 m HCl solution occurs as CaCl 2 0. The effect of this ion pairing is to increase the pH stability limits and solubilities of calcium-bearing minerals in such solutions.