Comparison of Ab Initio MP2/6-311+G(d,p) Predicted Carbon–Hydrogen Bond Distances with Experimentally Determined r 0 (C–H) Distances

Fifty different carbon–hydrogen distances have been predicted from ab initio MP2/6-311+G(d,p) calculations, which range from a short value of 1.0611 Å for HCNO to a long value of 1.1044 Å for H₂CO. The values include those predicted for a series of methyl (CH₃) moieties where the two different C–H distances vary by as much as 0.005 Å. These predicted values are compared to r ₀(C–H) distances obtained from the isolated carbon–hydrogen stretching frequencies, as well as to r ₀ or r _s parameters obtained from microwave data. Except for the very short C–H bonds, the ab initio values from the MP2/6–311+G(d,p) calculations can be used for the carbon–hydrogen distances with error limits of ± 0.003 Å. By utilizing the spectral data from CD₃CClO, it is shown that combination bands in the C–H stretching region could cause problems in the identification of the isolated C–H stretching frequency from the CD₂HCClO isotopomer. The value of the ab initio predicted C–H distances for checking unusually long or short r _s (C–H) or r ₀ values is demonstrated.     

Theoretical Study of Chemical Binding of Noble Gas Atom and Transition Metal Complexes: Ng–NiCO, Ng–NiN2, Ng–CoCO (Ng = He–Xe)

Ab initio multireference and coupled cluster methods (MR-SDCI(+Q), CASPT2, CCSD(T)) and density functional theory methods (B3LYP, MPWPW91) have been applied to examine geometrical structures and vibrational frequencies of noble gas (Ng) – transition metal compounds, Ng–NiCO, Ng–NiN₂, and Ng–CoCO (Ng = He, Ne, Ar, Kr, Xe). It is shown that the respective compounds can have a larger binding energy than a typical van der Waals interaction energy. The binding mechanism is explained by a partial electron transfer from a noble gas atom to the low-lying 4s and 3d vacant orbitals of the transition metal atom. Theoretical calculations show that the binding of noble gas atom results in a large shift of the bending frequency: 361.1cm^–1 (NiCO) to 403.5cm^–1 (Ar–NiCO); 308.5cm^–1 (NiN₂) to 354.8cm^–1 (Ar–NiN₂); 373.0cm^–1 (CoCO) to 422.6cm^–1 (Ar–CoCO). The corresponding experimental frequencies determined in solid argon are 409.1cm^–1 (NiCO), 357.0cm^–1 (NiN₂), and 424.9cm^–1 (CoCO), which are much closer to the corresponding frequency of Ar–NiCO, Ar–NiN₂, and Ar–CoCO, respectively.     

Tin(IV) complexes ofSchiff bases derived from salicylaldehyde and aminoalcohols

11 and 12 molar reactions of tin(IV) chloride with theSchiff bases, HO–C₆H₄CHNROH [where R=–(CH₂)₂–, –CH₂–, –CH(CH₃)–, –(CH₂)₃–, and –CH(C₂H₅)CH₂–] have been studied in different stoichiometric ratios and derivatives of the type SnCl₄(SBH₂) and SnCl₄(SBH₂)₂ (whereSBH₂ represents theSchiff base molecule) have been isolated. These have been characterised by elemental analysis, conductivity measurements and I.R. spectral studies.     

Kinetics and mechanism of the acid-catalyzed hydrolysis of [carbonatoethylenediamine(L)2cobalt(III)]+ ions

The kinetics of acid-catalyzed hydrolysis of the [Co(en)(L)₂(O₂CO)]⁺ ion (L = imidazole, 1-methylimidazole, 2-methylimidazole) follows the rate law –d[complex]/dt = {k ₁ K[H⁺]/(1 + K[H⁺])}[complex] (15–30 or 25–40 °C, [H⁺] = 0.1–1.0 M and I = 1.0 M (NaClO₄)). The reaction course consists of a rapid pre-equilibrium protonation, followed by a rate determining chelate ring opening process and subsequent fast release of the one-end bound carbonato ligand. Kinetic parameters, k ₁ and K, at 25 °C are 5.5 × 10^–2 s^–1, 0.44 M^–1 (ImH), 5.1 × 10^–2 s^–1, 0.54 M^–1 (1-Meim) and 3.8 × 10^–3 s^–1, 0.74 M^–1 (2-MeimH) respectively, and activation parameters for k ₁ are H₁ = 43.7 ± 8.9 kJ mol^–1, S₁ = –123 ± 30 J mol^–1 deg^–1 (ImH), H₁ = 43.1 ± 0.3 kJ mol^–1, S₁ = –125 ± 1 J mol^–1 deg^–1 (1-Meim) and H₁ = 64.2 ± 4.3 kJ mol^–1, S₁ = –77 ± 14 J mol^–1 deg^–1 (2-MeimH). The results are compared with those for similar cobalt(III) complexes.     

Dissociation constants of the ampholyte glycine in 50 mass % methanol-water from 5 to 55°C,with related thermodynamic quantities

The two thermodynamic dissociation constants of glycine at 11 temperatures from 5 to 55°C in 50 mass % methanol-water mixed solvent have been determined from precise emf measurements with hydrogen-silver bromide electrodes in cells without liquid junction. The first acidic dissociation constant (K ₁)for the process HG⁺H⁺+G^± is expressed as a function ofT(^oK) by the equation pK ₁ = 2043.5/T – 9.6504 + 0.019308T. At 25°C, pK ₁is 2.961 in the mixed solvent, as compared with 2.350 in water, with H°=1497 cal-mole^–1, G°=4038 cal-mole^–1, S°=–8.52 cal-°K^–1-mole^–1, and C _p ^o =–53 cal-°K^–1-mole^–1. The second acidic dissociation constant (K ₂)for the process G^±H⁺+G^– over the temperature range studied is given by the equation pK ₂ = 3627.1/T – 7.2371 + 0.015587T. At 25°C, pK ₂is 9.578 in MeOH–H₂O as compared with 9.780 in water, whereas H° is 10,257 cal-mole^–1, G° is 13,063 cal-mole^–1, S° is –9.41 cal-°K^–1-mole^–1, and C _p ^o is –43 cal-°K^–1-mole^–1. The protonated glycine becomes weaker in 50 mass % methanol-water, whereas the second dissociation process becomes stronger despite the lower dielectric constant of the mixed solvent (=56.3 at 25°C).     

Physicochemical properties of electrode materials based on substituted yttrium manganite

Electrode materials Y_0.5Ca_0.5Mn_1–x (Co,Ni)_xO₃(x = 0–0.1) have an o-orthorhombic perovskite structure. Doping with transition metals raises the content of ions Mn⁴⁺ from 49% at x = 0 to 62% at x = 0.05 Ni. At 500–650 K there takes place an o-o-orthorhombic transition, with the thermal expansion coefficient rising from (7.1–8.1) × 10^–6 to (10.5–11) × 10^–6 K^–1. Composition Y_0.5Ca_0.5Mn_1–x (Co, Ni)_xO₃ is n-type semiconductor with a considerable oxygen constituent at >1000 K. Effect of the electrode material composition on the resistance parameter (/d) of an intermediate layer E/SE and on the polarization resistance (R ) of the triple-phase boundary E/SE/GP is similar. At 300–1100 K and 10²–10⁵ Pa, minimum values of these quantities are exhibited by samples with the Y_0.5Ca_0.5Mn_0.95Ni_0.05O₃ electrode layer 50 mg cm^–2 thick.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 291–297.Original Russian Text Copyright © 2005 by Tikhonova, Poluyan, Glushko, Vecher, Znosok.     

Theoretical Study of Chemical Binding of Noble Gas Atom and Transition Metal Complexes: Ng–NiCO, Ng–NiN2, Ng–CoCO (Ng = He–Xe)

Summary. Ab initio multireference and coupled cluster methods (MR-SDCI(+Q), CASPT2, CCSD(T)) and density functional theory methods (B3LYP, MPWPW91) have been applied to examine geometrical structures and vibrational frequencies of noble gas (Ng) – transition metal compounds, Ng–NiCO, Ng–NiN₂, and Ng–CoCO (Ng = He, Ne, Ar, Kr, Xe). It is shown that the respective compounds can have a larger binding energy than a typical van der Waals interaction energy. The binding mechanism is explained by a partial electron transfer from a noble gas atom to the low-lying 4s and 3d vacant orbitals of the transition metal atom. Theoretical calculations show that the binding of noble gas atom results in a large shift of the bending frequency: 361.1cm^–1 (NiCO) to 403.5cm^–1 (Ar–NiCO); 308.5cm^–1 (NiN₂) to 354.8cm^–1 (Ar–NiN₂); 373.0cm^–1 (CoCO) to 422.6cm^–1 (Ar–CoCO). The corresponding experimental frequencies determined in solid argon are 409.1cm^–1 (NiCO), 357.0cm^–1 (NiN₂), and 424.9cm^–1 (CoCO), which are much closer to the corresponding frequency of Ar–NiCO, Ar–NiN₂, and Ar–CoCO, respectively.     

Thermodynamics of tri- and pentabromide anions in aqueous solution

Formation constants for the tribromide and pentabromide anions were measured by a vapor partitioning method from 5 to 80°C. The molal thermodynamic parameters for these respective species at 25°C are: K ₃ –16.73, H ^o =–5.90 kJ-mol ^–1 , Cp ^o =–29 J-K ^–1 -mol ^–1 , and S ^o =3.6 J-K ^–1 -mol ^–1 ; K ₅ =37.7, H ^o =–13.0 kJ-mol ^–1 , S ^o =–13.6 J-K ^–1 -mol ^–1 , with Cp ^o assumed zero. These results are used to reevaluate published emf results for the bromine/bromide couple.     

Structure,vibrational spectra,and energetic stability of LnX<Stack><Subscript>4</Subscript><Superscript>−</Superscript></Stack> ions (Ln=La,Lu; X=F,Cl, Br,I)

Molecular structure and properties of La and Lu tetrahalide ions LnX ₄ ^– ) are studied by the configuration interaction singles-and-doubles method augmented with quadruple excitation correction (CISD+Q) and by the fourth-order Möller-Plesset perturbation theory with account for single, double, triple, and quadruple excitations (SDTQ-MP4). The atomic inner shells are described by Stevens relativistic effective core potentials. Valence basis sets are augmented with diffuse s-, p-, and polarization d-, f-, and g-functions. The equilibrium configuration of nuclei in LnX ₄ ^– ions was found to be tetrahedral. The equilibrium internuclear distances, quadratic force constants, vibrational frequencies, and IR intensities of LnX ₄ ^– ions are compared with the corresponding parameters of La and Lu trihalide molecules (LnX₃), calculated within the same approximations. Regularities in the behavior of molecular parameters on going along the LnF ₄ ^– LnCl ₄ ^– LnBr ₄ ^– LnI ₄ ^– series and from La compounds to Lu compounds are revealed. Heights of the energy barriers to the LnX ₄ ^– inversion through the square planar structures (T _d D _4h T _d ) are evaluated: 100–110 and 130–150 kJ/mol for LaX ₄ ^– and LuX ₄ ^– , respectively. Enthalpies of dissociation reactions LnX ₄ ^– LnX₃+X^– are calculated and the results obtained are compared with the available experimental data.Translated from Koordinatsionnaya Khimiya, Vol. 31, No. 3, 2005, pp. 218–228.Original Russian Text Copyright © 2005 by Solomonik, Smirnov, Mileyev.This revised version was published online in April 2005 with a corrected cover date.This revised version was published online in April 2005 with a corrected cover date.     

Determination of ratios of sulfate to bisulfate ions in aqueous solutions by Raman spectroscopy

Raman spectra are presented for aqueous ammonium bisulfate and zinc sulfate-sulfuric acid solutions over a wide range of concentration and from 20 to 85°C. The heights of the 980 cm ^–1 (primarily SO ₄ ^–2 ) and 1053 cm ^–1 (primarily HSO ₄ ^– ) bands are correlated with the pH of the solutions. The ratio of the species SO ₄ ^–2 and HSO ₄ ^– can be obtained from the ratio of scattering intensities at 980 and 1053 cm ^–1 . The H obtained from plots of the log of the concentration products versus 1/T is –37±5 kJ-mol ^–1 for ammonium bisulfate solutions and –48±4kJ-mol ^–1 for the ZnSO ₄ -H ₂ SO ₄ solutions. This compares to –22 kJ-mol ^–1 for the H of bisulfate ion dissociation as obtained from thermodynamic equilibrium constants.     

Mechanism of the oxidation of L-ascorbic acid by the bis(pyridine-2,6-dicarboxylate)cobaltate(III) ion in aqueous solution

A detailed investigation of the oxidation of L-ascorbic acid (H₂A) by the title complex has been carried out using conventional spectrophotometry at 510 nm, over the ranges: 0.010 [ascorbate] _T 0.045 mol dm^–3, 3.62 pH 5.34, and 12.0 30.0 °C, 0.50 I 1.00 mol dm^–3, and at ionic strength 0.60 mol dm^–3 (NaClO₄). The main reaction products are the bis(pyridine-2,6-dicarboxylate)cobaltate(II) ion and l-dehydroascorbic acid. The reaction rate is dependent on pH and the total ascorbate concentration in a complex manner, i.e., k _obs = (k ₁ K ₁)[ascorbate] _T /(K ₁ + [H⁺]). The second order rate constant, k ₁ [rate constant for the reaction of the cobalt(III) complex and HA^–] at 25.0 °C is 2.31 ± 0.13 mol^–1 dm³ s^–1. H = 30 ± 4 kJ mol^–1 and S = –138 ± 13 J mol^–1 K^–1. K ₁, the dissociation constant for H₂A, was determined as 1.58 × 10^–4 mol dm^–3 at an ionic strength of 0.60 mol dm^–3, while the self exchange rate constant, k ₁₁ for the title complex, was determined as 1.28 × 10^–5 dm³ mol^–1 s^–1. An outer-sphere electron transfer mechanism has been proposed.     

Formation Enthalpy and Entropy of Exciplexes with Variable Extent of Charge Transfer in Solvents of Different Polarity

Temperature dependence was studied for relative quantum yields of emission from some exciplexes of pyrene, 1,12-benzoperylene, and 9-cyanoanthracene with methoxybenzenes or methylnaphthalenes in solvents of different polarity (ranging from toluene to acetonitrile). The enthalpy H _Ex ^*, the entropy S _Ex ^*, and the Gibbs free energy G _Ex ^*of formation of the exciplexes were determined. Depending of the Gibbs free energy of excited-state electron transfer (G _et ^*) and solvent polarity, the values of H _Ex ^*, S _Ex ^*, and G _Ex ^*vary over the ranges from –5 to –40 kJ mol^–1, from +3 to –90 J mol^–1K^–1, and from +3 to –21 kJ mol^–1, respectively. The possibility is discussed that the effect of solvent polarity G _et ^*on the exciplex formation enthalpies can be rationalized in terms of the model of correlated polarization of an exciplex and the medium.     

Spectrochemistry of solutions,part 23. Changes of enthalpy and entropy in the formation of contact ion pairs: A vibrational spectroscopic appraisal using thiocyanate and azide solutions

Summary The vibrational spectra of solutions have been analyzed to assess both qualitatively and quantitatively the changes in enthalpy and entropy for ion pair formation in solutions of LiNCS, Mg(NCS)₂, and LiN₃ in liquid ammonia, dimethylformamide, dimethylsulphoxide and acetonitrile. Contrary to predictions both the H _ass and S _ass terms are all positive in the cases examined, indicating that the driving force in the ion association process derives from solvent-solute restructuring, and not the energy of the interaction between the cation and anion. This characteristic of contact ion pair formation is likely to be found to be applicable over a wide range of solvents. The following specific values of the thermodynamic parameters at 298 K have been obtained: LiNCS/DMF, G=–1.3 (1) kJ mol^–1, H _ass =+1.8 (5) kJ mol^–, S _ass =+10 (2) J mol^–1 K^–1; LiNCS/DMSO, G=+0.9 (2) kJ mol^–1, H _ass =+0.3 (3) kJ mol^–1; Mg(NCS)₂/DMF, G _ass =–4.0 (3) kJ mol^–1, H _ass =+15 (4) kJ mol^–1, S=+64 (17) kJ mol^–1; LiN₃/DMSO, G _ass =–2.5 (3) kJ mol^–1, H _ass =+4.9 (9) kJ mol^–1, S _ass =+25 (10) J K^–1 mol^–1.Submitted to celebrate the 70th Birthday of Professor Viktor Gutmann, and in recognition of his considerable contributions towards the better understanding of Chemistry in the Solution Phase     

Electrostriction of polymethylmethacrylates

Electrostriction of tactic polymethylmethacrylates in response to step-on and step-offdc-fields was investigated in the field strength range from 1 to 5 MV m^–1 at room temperature; one example of electrostriction under sinusoidal field is given.Three principal retardation time regions were found: ₁=1.5 s, ₂=30 s, and ₃=140 s, each field strength independent. The retardation strengths belonging to these electrostrictive processes depend on tacticity.The low frequency limit of the electrostrictive volume compliance for the investigated PMMA is _a =–1.2×10^–15 m² V ^–2 for atactic, _S =–2.3×10^–14 m² V ^–2 for syndiotactic, and _i=–4.5 × 10^–14 m² V ^–2 for isotactic PMMA.Herrn Prof. Dr. F. H. Müller gewidmet.     

Novel Immobilized Hydrosilylation Catalysts Based on Rhodium 1,3-Bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidenes

Summary. The reactivity of a well defined Rh (I) complex, i.e. Rh(CF₃COO)(NHC)(COD) (1, NHC=1,3-bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidene, COD=⁴-cycloocta-1,5-diene) in the hydrosilylation of 1-alkenes, alkynes, and ,-unsaturated carbonyl compounds, respectively, is described. With this complex, excellent reactivity was observed and turn-over numbers (TONs) up to 1000 were reached. A supported version of 1 was realized by reaction of RhCl(NHC)(COD) with PS-DVB–CH₂–O–CO–CF₂–CF₂–CF₂–COOAg (PS-DVB=poly(styrene-co-divinylbenzene) to yield PS-DVB–CH₂–O–CO–CF₂–CF₂–CF₂–COORh(NHC)(COD). This supported version of 1 exhibited at least comparable, in some cases increased reactivity compared to 1 and allowed the rapid removal of the catalyst from the reaction mixture. Due to reduced catalyst bleeding, the synthesis of target compounds with a Rh-content of less than 130ppm was accomplished.This revised version was published online in February 2005. In the previous version the issue was not marked as a special issue, and the issue title and the editor was missing     

Novel Immobilized Hydrosilylation Catalysts Based on Rhodium 1,3-Bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidenes

The reactivity of a well defined Rh (I) complex, i.e. Rh(CF₃COO)(NHC)(COD) (1, NHC=1,3-bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidene, COD=⁴-cycloocta-1,5-diene) in the hydrosilylation of 1-alkenes, alkynes, and ,-unsaturated carbonyl compounds, respectively, is described. With this complex, excellent reactivity was observed and turn-over numbers (TONs) up to 1000 were reached. A supported version of 1 was realized by reaction of RhCl(NHC)(COD) with PS-DVB–CH₂–O–CO–CF₂–CF₂–CF₂–COOAg (PS-DVB=poly(styrene-co-divinylbenzene) to yield PS-DVB–CH₂–O–CO–CF₂–CF₂–CF₂–COORh(NHC)(COD). This supported version of 1 exhibited at least comparable, in some cases increased reactivity compared to 1 and allowed the rapid removal of the catalyst from the reaction mixture. Due to reduced catalyst bleeding, the synthesis of target compounds with a Rh-content of less than 130ppm was accomplished.     

First and second dissociation constants of deuterio-o-phthalic acid in D2O from 5 to 50°C

The first and second dissociation constants of deuterio-o-phthalic acid in deuterium oxide have been determined by the emf method over the temperature range of 5 to 50°C. The pD values for potassium deuterium phthalate have been calculated from these two constants and experimentally verified. The thermodynamic properties for the dissociation of deuterio-o-phthalic acid have been evaluated. At 25°C, these values in the molality scale are: pK _1A =3.505, pK _2A =5.890, and pD=4.518. From K _1A and K _2A , respectively: G ^o =20.003, 33.582 kJ-mol^–1; H ^o =2.851, 2.208 kJ-mol^–1; S ^o =–76.7, –105.2 J-mol^–1-K^–1; and C _p ^o =–52.7, –315.6 J-mol^–1-K^–1. The isotope effect is discussed.     

Complexes of dioxouranium(VI) with zwitter-ionic forms of Bi- and tetra-dentateSchiff bases

Potentially bi- and tetra-dentateSchiff bases derived from salicylaldehyde react with hydrated uranyl salts to give complexes: UO₂H₂ LX ₂, UO₂H₂ LX ₂ and UO₂(HL)₂ X ₂ [H₂ L=N,N-propane-1,3-diylbis(salicylideneimine), H₂ L=N,N-ethylenebis(salicylideneimine) and HL=N-phenylsalicylideneimine;X ^–=Cl^–, Br^–, I^–, NO₃ ^–, ClO₄ ^–, and NCS^–]. Because of marked spectral similrities with the structurally known Ca(H₂ L) (NO₃)₂, theSchiff bases are coordinated through the negatively charged phenolic oxygen atoms and not the nitrogen atoms of the azomethine groups which carry the protons transferred from phenolic groups on coordination. Halide, nitrate, perchlorate and thiocyanate groups are covalently bonded to the uranyl ion, resulting a 6-coordinated uranium ion in the halo and thiocyanato complexes and 8-coordinated in nitrato and perchlorato complexes.

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Komplexe von Dioxouranyl(VI) mit zwitterionischen Formen von zwei- und vierzähnigen Schiff-Basen

Zusammenfassung Von Salizylaldehyd abgeleitete zwei- und vierzähnigeSchiff-Basen reagieren mit hydratisierten Uranylsalzen zu Komplexen folgenden Typs: UO₂H₂ LX ₂, UO₂H₂ LX ₂ und UO₂(HL)₂ X ₂ [H₂ L=N,N-Propan-1,3-diylbis(salicylidenimin), H₂ L=N,N-Ethylen-bis(salicylidenimin) und HL=N-Phenylsalicylidenimin;X ^–=Cl^–, Br^–, I^–, NO₃ ^–, ClO₄ ^– und NCS^–]. Auf Grund eindeutiger spektraler Ähnlichkeiten mit dem bekannten Ca(H₂ L) (NO₃)₂ wird auf Koordination über die negativ geladenen phenolischen Sauerstoffatome (und nicht über die Azomethin-Stickstoffe) geschlossen. Die AnionenX ^– sind kovalent an das Uranyl-Ion gebunden; damit ergibt sich ein hexakoordiniertes Uranyl-Ion für die Halogen- und Thiocyanat-Komplexe und Oktakoordination für die Nitrat- und Perchlorat-Komplexe.

     

Force constant calculations of the LAM-1 modes ofn-alkanes and their substituted α-Monohalo- and α,ω-dihalo- species in their extended zig-zag planar configurations as found in urea inclusion compounds

Force constants were determined for the C₈, C₁₀, C₁₂ and C₁₄ series ofn-alkanes C _n H_{2n + 2} using an approximate SVFF calculation and observed LAM = 1 wave numbers. In this calculation the hydrogen atoms were neglected and only the carbon backbone chain and terminal atoms were considered; this was valid since only low-frequency vibrations were under consideration. Using force constant transfer, the wavenumbers of the LAM = 1 accordion modes for the analogous -C_n H_2n + 1 X and ,-C_n H_2nX₂ species, where X = C1, Br or I were calculated. For -chloroalkanes and ,-dichloroalkanes, them = 1 accordion modes are calculated to be in the 220–130 cm^–1 and 200–120 cm^–1 regions, respectively. For the bromo- and iodo-analogues them = 1 accordion modes are calculated to be in the 200–100 cm^–1, 150–90 cm^–1 and in the 170–100, 135–80 cm^–1 regions, respectively.     

Conductimetric determination of ion-association constants for calcium,cobalt, zinc,and cadmium sulfates in aqueous solutions at various temperatures between 0°C and 45°C

Thermodynamic ion-association constants for calcium, cobalt, zinc, and cadmium sulfates in aqueous solutions were determined by means of conductivity measurements at various temperatures between 0°C and 45°C. The standard Gibbs energy, enthalpy, and entropy for the reaction M ²⁺ +SO ₄ ^2– M ²⁺ ·SO ₄ ^2– (M=Ca, Co, Zn, and Cd) were calculated from the temperature dependence of the ion-association constants. The values obtained are as follows: G ₂₉₈ ^o =–12.42 kJ-mole ^–1 , H ^o =6.11 kJ-mole ^–1 , and S ₂₉₈ ^o =62.1 J- ^o K ^–1 -mole ^–1 for Ca ²⁺ ·SO ₄ ^2– ; G ₂₉₈ ^o =–12.84 kJ-mole ^–1 , H ^o =5.00 kJ-mole ^–1 , and S ₂₉₈ ^o =59.8 J- ^o K ^–1 -mole^–1 for Co ²⁺ ·SO ₄ ^2– ; G ₂₉₈ ^o =–12.65 kJ-mole ^–1 , H ^o =8.65 kJ-mole ^–1 , and S ₂₉₈ ^o =71.4 J- ^o K ^–1 -mole ^–1 for Zn ²⁺ ·SO ₄ ^2– ; G ₂₉₈ ^o =–13.28 kJ-mole ^–1 , H ^o =8.39 kJ-mole ^–1 , and S ₂₉₈ ^o =72.7 J- ^o K ^–1 -mole ^–1 for Cd ²⁺ ·SO ₄ ^2– .