The kinetics of the reaction of iodine with hydrazine as studied by pulse radiolysis

Pulse radiolysis was utilized to study the iodine — hydrazine reaction in aqueous solutions of pH3 to 7, at I^– concentrations of 0.02 to 0.34M, and a constant ionic strength of 0.35M. The reaction rate was found to be proportional to [H⁺]^–1 and [I^–]^–1. Experimental results support the assumption that the rate-determining step is the reaction of I₂ with N₂H₄ with a rate constant K1.2×10⁷ M^–1s^–1.     

Photometrische Bestimmung von Anionen mit Chloranils?ure I

Zusammenfassung Es wird eine übersicht über die Anwendbarkeit der ChloranilsÄure für photometrische Bestimmungen von Kationen und Anionen gegeben. ChloranilsÄurelösungen sind nur begrenzt haltbar; im allgemeinen sind die Extinktionen solcher Lösungen über mindestens 5 Std konstant. Es werden die Dissoziationskonstanten der ChloranilsÄure bestimmt und zwar in wÄ\rigen Lösungen und in wÄ\rig-alkoholischen Lösungen, die 41,6 Gew.-% Äthanol enthalten. In rein wÄ\rigen Lösungen wird für T=25 C und I=1,0 gefunden: K ₁=1 · 10^–1 und K ₂=2,3 · 10^–3. In wÄ\rig-alkoholischen Lösungen wird für T=25 C und I=0,1 gefunden K ₁=4 · 10^–2 und K ₂=1,56 · 10^–4.

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Summary A report is given on the applicability of chloranilic acid for photometric determinations of cations and anions. Solutions of chloranilic acid are of limited stability only; the extinctions of these solutions remain constant for at least 5 hours. The dissociation constants of chloranilic acid have been determined in aqueous and in aqueous-alcoholic solutions containing 41.6% (w/w) ethanol. The following results have been obtained: K ₁=1 · 10^–1 and K ₂=2,3 · 10^–3 for purely aqueous solutions (T=25 C; I=1.0); K ₁=4 · 10^–2 and K ₂=1.56 · 10^–4 for aqueous-alcoholic solutions (T=25 C; I=0.1).

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Herrn Prof. Dr., Dr. h. c. W. Klemm zum 70. Geburtstag gewidmet.

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Die Arbeit wurde durch die Deutsche Forschungsgemeinschaft und den Fonds der Chemie durch Sachbeihilfen gefördert.     

Solid-state electrode with a Cu(I)-based membrane hydrophobised by PTFE for the measurement of Cu2+ and I?

The preparation of CuI + Ag₂S and Cu₂[HgI₄] + Ag₂S membranes hydrophobised by PTFE is described. The pressed membranes mounted in a multi-purpose all-solid-state electrode body have been examined as electrochemical sensors for Cu²⁺ and I^– ions. For the electrode with (CuI + Ag₂S + PTFE)-membrane experimental slopes of 29 mV(pCu)^–1 and 62 mV(pI)^–1 were obtained, in good agreement with the theoretical values. For practical measurement in solutions where both Cu²⁺ and I^– can be present, the investigated electrode offers certain advantages in comparison with a commercial Cu-ISE.     

Thermodynamics of the dissociation of ammonium ion in seawater from 5 to 40°C

The dissociation constant of NH ₄ ⁺ and the associated thermodynamic functions H° and S° in synthetic seawaters of salinity 20.31, 35.00, and 44.55 have been determined by emf measurements of cells without liquid junction over the temperature range 5 to 40°C. Cells with hydrogen electrodes and silver-silver chloride electrodes, whose standard potentials in seawater media were determined in an earlier investigation, were used. At a given temperaturet (in °C), pK _a varies linearly with the formal ionic strengthI _f (uncorrected for ion pairing) according to pK _a=pK _a ^w +(0.1552–0.0003142t)I _f where pK _a ^w is the pK in pure water. The medium effect of seawater on H° amounts to less than 200 cal-mole^–1 for a change inI _f from 0 to 0.72 mole-kg^–1, and S° is less than 1 cal-°K^–1-mole^–1 in all of the media studied, as it is in water. The observed salt effect on pK _a is in close agreement with values predicted from theories of ion-ion interactions.     

Disordered Crystal Structure of Bis[(2.2.2-Cryptand)Sodium] Bis[Aqua(Isothiocyanato)(μ-Isothiocyanato)Sodium] 2[Na(2.2.2-Crypt)]+ · [Na2(NCS)2(μ-NCS)2(H2O)2]2–

Crystals of bis[(2.2.2-cryptand)sodium] bis[aqua(isothiocyanato)(-isothiocyanato)sodium]: 2[Na(C₁₈H₃₆N₂O₆)]⁺ · [Na₂(NCS)₂(-NCS)₂(H₂O)₂]^2– (I) were synthesized and studied by X-ray diffraction analysis. The disordered structure of I (a = 12.715 Å, b = 10.458 Å, c = 21.767 Å, = 102.56°, space group P2₁/n) was solved by the direct method and refined by the full-matrix least-squares method in anisotropic approximation to R = 0.058 from 3896 independent reflections (CAD4 automated diffractometer, MoK ). The crystal consists of two complex ions [I¹]⁺ and [I²]^2– (molar ratio 2 : 1). The Na⁺ cation of the host–guest cation I¹ is coordinated by all eight heteroatoms (6O + 2N) of the cryptand ligand. The coordination polyhedron of this Na⁺ cation is a distorted cube. The atoms of two groups (CH₂–CH₂ and CH₂–O–CH₂–CH₂) in the cryptand ligand are disordered over two positions. The independent cation Na⁺ of the centrosymmetric binuclear complex anion I² is coordinated by one bifurcated O atom of the disordered water molecule and by three N atoms of the SCN^– ligands (including two bridging ligands). The coordination polyhedron of this Na⁺ caiotn is a distorted tetrahedron. The complex ions in the crystal structure of I are united by hydrogen bonds.     

Crystal and Molecular Structure of Bis(O,O"-diisopropyldithiophosphato-S,S")(dimethylglyoximato-N,N")rhodium(III)

The crystal and molecular structure of bis(O,O"-diisopropyldithiophosphato-S,S")(dimethylglyoximato-N,N")rhodium(III) (I) was studied using X-ray diffraction analysis: space group P2₁/c, a = 13.644 Å, b = 10.350 Å, c = 20.906 Å, = 109.02°, Z = 4. The structure was solved by the direct method and anisotropically refined by the full-matrix least-squares method to R = 0.029 using 5447 independent reflections (CAD-4 autodiffractometer, MoK ). Compound I is a mononuclear tris-chelate complex whose three ligands are singly charge anions. The individual molecule of the complex has a noncrystallographic two-fold axis; its Rh atom is coordinated by four S atoms and two N atoms, forming a distorted octahedron. The average coordination bond lengths are Rh–S 2.402 and Rh–N 2.023 Å. The molecules in structureI are joined into infinite chains via weak intramolecular C–H···S hydrogen bonds and intermolecular N–O–H···O–N hydrogen bonds.     

Determination of toxic and non-toxic arsenic species in urine by microwave assisted mineralization and hydride generation atomic absorption spectrometry

Flow injection — microwave oven — hydride generation — atomic absorption spectroscopy (FI-MO-HG-AAS) has been optimized for the determination of the total and toxic arsenic in urine with and without persulfate, respectively. With microwave oven assisted digestion of urine with 5% (w/v) K₂S₂O₈ and 5% (w/v) NaOH all arsenicals completely can be converted to arsenate, which is determined by HG-AAS to give the total concentration of the six species present in urine. The detection limits of 4–6 g l^–1, the relative standard deviation of 3–7% and the high sample throughput make the methods suitable for rapid routine on-line determination. Application of the proposed procedures to the analysis of urine from people on a diet rich in seafood revealed a significant increase in total urinary arsenic due to the rapid excretion of organoarsenicals. Efficient decomposition and quantitative recovery of all arsenic species in spiked urine is achieved by using 5% K₂S₂O₈ in 5% NaOH at 4.6 ml min^–1, microwave power of 700 W and a 1.5 m coil.     

Triterpene glycosides of Thalictrum squarrosum. III. Structures of squarrogenins 1 and 2

Two genins — squarrogenin 1 and squarrogenin 2 — have been isolated from nodding meadow rue by the hydrolysis of squarrosides A1 and A2. The compounds are epimeric at C-21 and have the following structures: 1 — (21R, 22S, 23R)-21-methoxy-21,23-epoxycycloart-24-ene-3,22-30-triol, C₃₁H₅₀O₅, mp 169–171°C (hexane-acetone), [] ₅₄₆ ²⁰ –11.06° (c 4.52; pyridine); and 2 — (21S, 22S, 23R)-21-methoxy-21,23-epoxycycloart-24-ene-3,22,30-triol, C₃₁H₅₀O₅, mp 190–193°C (hexane-acetone), [] ₅₄₆ ²⁰ +106.6° (c 0.3; pyridine). The results of¹H and¹³C NMR spectroscopy and of mass spectrometry for the new compounds are given.Irkutsk Institute of Organic Chemistry, Siberian Division of the USSR Academy of Sciences. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 510–516, July–August, 1989.     

Synthesis and Crystal Structure of Diaqua(2.2.2-Cryptand)strontium Dichloride Trihydrate

Absract—Diaqua(2.2.2-Cryptand)strontium dichloride trihydrate [Sr(2.2.2-Crypt)(H₂O)₂]²⁺ · 2Cl^– · 3H₂O (I) was prepared and studied by X-ray diffraction. The triclinic structure of I (space group P , a = 9.152 Å, b = 10.140 Å, c = 15.219 Å, = 88.84°, = 88.19°, = 87.62°, Z = 2) was solved by the direct method and refined by full-matrix least-squares calculations in the anisotropic approximation to R = 0.050 for 4188 independent reflections (CAD4 automated diffractometer, CuK radiation). The structure contains the [Sr(2.2.2-Crypt)(H₂O)₂]²⁺ host–guest cation. The Sr²⁺ cation resides in the 2.2.2-cryptand cavity and is coordinated by all eight heteroatoms (6O + 2N) of the cryptand ligand and by two O atoms of water molecules. The Sr²⁺ coordination polyhedron (C.N. 10) is a highly distorted dibase-centered two-cap trigonal prism. The crystal structure of I contains a branched system of ion–ion (intermolecular) hydrogen bonds O(w)–H···Cl^–, which connect the complex cations, the Cl^– anions, and the crystal water molecules to form infinite thick layers parallel to the yz plane.     

Polypeptides possessing catalytic properties

The catalytic properties of synthetic polypeptides containing L-amino acids with the sequences H-(His-Glu)_n-OH, H-(Ser-Glu)_n-OH, H-(His-Tyr)_n-OH, and H-(Trp-Glu)_n-OH in the hydrolysis of p-NPA (para-nitrophenyl acetate) are considered. The dependences of the rates of the polypeptide-catalyzed hydrolysis of p-NPA on the pH of the medium, the temperature, and the concentration of p-NPA are discussed. V_max, K_m, and K — the effective rate constants of the hydrolysis of p-NPA — and K₂ — the constant for the splitting out of p-nitrophenol from the substrate — have been found and calculated.V. I. Lenin Tadzhik State University, Dushanbe. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 503–506, July–August, 1984.     

Gold(I) complexes with tertiary phosphine sulfide ligands

Phosphine sulfides and their gold(I) complexes with general formula R₃P=S—Au—X (X = Cl^–, Br^– or CN^–) were prepared and characterized by elemental analyses, i.r. and ³¹P-n.m.r. spectroscopy. A decrease in the i.r. frequency of the P=S bond in the ligands upon complexation, is indicative of S coordination to gold (I). The ³¹P-n.m.r. spectra revealed that electronegativity of the substituents and angles between them were the two most important factors influencing the ³¹P-n.m.r. chemical shifts. The phosphorus resonance was observed to be more downfield in alkyl substituted phosphine sulfides as compared to the aryl substituted phosphine sulfides. Ligand scrambling in the Cy₃P=S—Au—CN complex in solution, to form [(Cy₃P=S)₂Au]⁺ and [Au(CN)₂]^–, was investigated by ¹³C and ¹⁵N-n.m.r. spectroscopy. Equilibrium constants (K _eq) for scrambling of the Cy₃P=S—Au—CN complex and for its analogue, Cy₃P=Se—Au—CN were measured by integrating the ¹³C-n.m.r. at 297 K and were found to be 0.147 and 1.81 respectively.     

Bis[(1,2-bis(2-(o-hydroxyphenoxy)ethyloxy)ethane)-(isothiocyanato)potassium] [K2(NCS)2(C18H22O6)2]: Crystal and Molecular Structure

Complex of podand 1,2-bis(2-(o-hydroxyphenoxy)ethyloxy)ethane (L) with potassium thiocyanate, [K₂(NCS)₂L₂] (I) was synthesized and studied using X-ray diffraction analysis: space group P , a = 7.771 Å, b = 11.711 Å, c = 11.965 Å, = 72.22°, = 79.21°, = 89.07°, Z = 1. Structure I was solved by direct method and anisotropically refined by the full-matrix least-squares method to R = 0.040 for all 4370 independent reflections (CAD4 autodiffractometer, MoK ). Structure I contains [K(NCS)L] monomers of the host–guest type united into centrosymmetrical [K₂(NCS)₂L₂] dimers via two bridging OH groups (one group from two L podands). In the monomer, the L podand appears as though to envelope the octacoordinated K⁺ cation, whose the coordination polyhedron is a strongly distorted hexagonal bipyramid with all six oxygen atoms of the L podand in its base and the N atom of the SCN^– ligand and the O atom of one of OH group of the neighboring (in dimer) L podand at its axial vertices. Molecules of I in crystal are joined through the O–H···N hydrogen bonds to form broad infinite chains along the x-axis.     

Kinetics and mechanisms of the oxidation of the octacyanoniobate(III)ion by oxyanions in alkaline aqueous media

Summary The kinetics and mechanisms of the oxidation of Nb(CN) _inf8 ^sup5– by the oxyanions S₂O _inf8 ^sup2– , BrO _inf3 ^sup– , and IO _inf4 ^sup– have been investigated in alkaline aqueous media (pH 12). The second-order rate constant for the electron transfer reaction between Nb(CN) _inf8 ^sup5– and S₂O _inf8 ^sup2– at 25.0 °C, I = 0.36m (K⁺), is 11.1± 0.3 m ^–1 s ^–1 with H = 30 ± 2kJmol^–1 and S = - 125 + 7JK^–1 mol^–1. The rate constant for the oxidation of Nb(CN) _inf8 ^sup5– by BrO _inf3 ^sup– at 25.0 °C, I = 0.20m (Na⁺), is 2.39 ± 0.08m ^–1 s ^–1 with H = 28 ± 2kJmol^–1 and S = -139 ± 7JK^–1mol^–1. The oxidation of Nb(CN) _inf8 ^sup5– by IO _inf4 ^sup– proceeds by two parallel pathways involving the monomeric IO _inf4 ^sup– ion and the hydrated dimer H₂I₂O _inf10 ^sup4– . The second-order rate constant for the oxidation of Nb(CN) _inf8 ^sup5– by monomeric IO _inf4 ^sup– at 5.0 °C, I = 0.050m (Na⁺), is (3.3 ± 0.6) × 10³ m ^–1 s ^–1 with H = 75 ± 6 kJ mol^–1 and S = 94 ± 15 J K^–1 mol^–1, while the rate constant for the oxidation by H₂I₂O _inf10 ^sup4– is (1.8 ± 0.1) × 10³ m ^–1 s ^–1 with H = 97 ± 5 kJ mol^–1 and S = 166 ± 16 J K^–1 mol^–1 under the same reaction conditions. The rate constants for each of the oxidants employed display specific cation catalysis with the order of increasing rate constants: Li⁺ < Na+ < NH _inf4 ^sup+ < K⁺ < Rb⁺ < Cs⁺, in the same direction as the electronic polarizability of the cations. The results are discussed in terms of the outer-sphere electron-transfer processes and compared with the corresponding data and mechanisms reported for other metal-cyano reductants.     

Dissociation quotients of succinic acid in aqueous sodium chloride media to 225°C

The first and second molal dissociation quotients of succinic acid were measured potentiometrically with a hydrogen-electrode, concentration cell. These measurements were carried out from 0 to 225°C over 25° intervals at five ionic strengths ranging from 0.1 to 5.0 molal (NaCl). The dissociation quotients from this and two other studies were combined and treated with empirical equations to yield the following thermodynamic quantities for the first acid dissociation equilibrium at 25°C: log K_1a=–4.210±0.003; H _1a ⁰ =2.9±0.2 kJ-mol^–1; S _1a ⁰ =–71±1 J-mol^–1-K^–1; and C _p1a ⁰ =–98±3 J-mol^–1-K^–1; and for the second acid dissociation equilibrium at 25°C: log K_2a=–5.638±0.001; H _2a ⁰ = –0.5±0.1 kJ-mol^–1; S _2a ⁰ =–109.7±0.4 J-mol^–1-K^–1; and C _p2a ⁰ = –215±8 J-mol^–1-K^–1.     

Some remarks on the periodical change of the stability constants of the lanthanide complexes

The correlations between the values of the lgK (K = stability constant of the lanthanide complex) and the reciprocal of the ionic radius 1/r or the sum of the ionization potentials ₁ ³ I for the lanthanide ions were reviewed for different ligands. A straight-line relationship (lgK – lgK)/lgK vs. (1/r – 1/r)/(1/r) or vs. ( ₁ ³ I – ₁ ³ I)/ ₁ ³ I was found within the tetrads La-Nd, Gd-Ho, and Er-Lu.

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Bemerkungen zum periodischen Wechsel der Stabilitätskonstanten von Lanthaniden-Komplexen

Zusammenfassung Es wurde eine Übersicht der Korrelationen zwischen den Werten von logK (K = Stabilitätskonstante der Lanthanidenkomplexe) und den reziproken Ionenradien 1/r oder der Summe der Ionisierungspotentiale ₁ ³ I für die Lanthanidenionen für verschiedene Liganden gegeben. Dabei wurde eine lineare Korrelation für (lgK – lgK)/lgK gegen (1/r – 1/r)/(1/r) oder gegen ( ₁ ³ I – ₁ ³ I)/_1/3 I innerhalb der Tetraden La-Nd, Gd-Ho und Er-Lu aufgefunden.

     

Determination of Aqueous Nickel-Carbonate and Nickel-Oxalate Complexation Constants

An ion-exchange method was used to determine complexation constants for the Ni-oxalate and Ni-carbonate systems in a NaClO₄ background electrolyte. The Ni-oxalate data were interpreted in terms of a single Niox(aq) complex having log K ₁ values for Ni²⁺ + ox^2– Niox(aq) of 3.9 ± 0.1 (I.S. = 0.5 mol-L^–1 p[H] = 7.1) and 4.4 ± 0.1 (I.S. = 0.1 mol-L^–1 p[H] = 8.6) at 22 ± 1C. Specific ion-interaction theory (SIT) was used to obtain log K ₁ = 5.17 ± 0.05 (95% confidence level and = –0.23 ± 0.15) at I.S. = 0. The Ni-carbonate studies were carried out at p[H] values of 7.5, 8.5, and 9.6 in 0.5 mol-L^–1 NaClO₄/NaHCO₃ solutions. The NiCO₃(aq) species was the dominant complex in the [CO₃ ^2–] concentration ranges studied at all three p[H] values. A log K ₁ value for Ni²⁺ + CO₃ ^2– NiCO₃(aq) of 2.9 ± 0.3 was deduced at I.S. = 0.5 mol-L^–1. Extrapolating this value to zero ionic strength using the SIT approach yielded log K ₁ = 4.2 ± 0.3 (95% confidence level and = –0.26 ± 0.04). The data allowed upper bound values for the complexation constants for NiHCO₃ ⁺ and Ni(CO₃)₂ ^2– to be estimated, i.e., log K < 1.4 for Ni²⁺ + HCO₃ ^– NiHCO₃ ⁺, and log K ₂ < 2 for NiCO₃(aq) + CO₃ ^2– Ni(CO₃)₂ ^2–, respectively.     

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.     

Preparation and properties of [PtII(SS)(NN)]-type complexes and their iodine-doped analogues

Summary Complexes of the general formula [Pt(SS) (NN)], where SS is dddt (5,6-dihydro-1,4-dithiin-2,3-dithiolate) or pddt (6,7-dihydro-5H-1,4-dithiepin-2,3-dithiolate) and NN is bipy (2,2-bipyridine) or phen (1,10-phenanthroline), were prepared by the reaction of [PtCl₂(NN)] with dithiolate ligands. The¹H-n.m.r. spectra shows upfield shifts in the bipy or phen signals upon substitution of the chlorides in [PtCl₂(bipy)] or [PtCl₂(phen)] by dddt or pddt. The u.v.-vis. spectra exhibits intense intramolecular ligand-to-ligand charge transfer bands ca. 600 nm. Cyclic voltammograms show a reversible oxidation step, assigned to [Pt(SS) (NN)]⁰/[Pt(SS)(NN)]⁺. When the complexes were partially oxidized by I₂, two broad e.s.r. signals atg = 1.91,g = 2.02 appeared. Raman spectra show the presence of I ₃ ^– and I^5/– in the iodine-doped complexes. The electrical conductivities of the neutral mixed ligand complexes (10^–9-10^–10S cm^–1) are raised to 10^–7–10^–8S cm^–1 by I₂ doping.     

Iodination of B12H11OC(O)CH2–3, B12H11OH2–, and B12H11SCN2–

Reactions of iodination of monosubstituted derivatives of B₁₂H₁₁X^2–anion (X = OC(O)CH₃, OH, SCN) were studied. The reactions were shown to proceed smoothly to give B₁₂H₁₀(OC(O)CH₃)I^2–((carboxy)(iodo)[decahydro[I _h1551-²⁰-closo]dodecaborate(2–)] anion), B₁₂H₁₀(OH)I^2–((hydroxo)(iodo)[decahydro[I _h1551-²⁰-closo]dodecaborate(2–)] anion), and B₁₂H₁₀(SCN)I^2–((thiocyanato)(iodo)[decahydro[I _h1551-²⁰-closo]dodecaborate(2–)] anion) in high yields, irrespective of the solvent used (benzene, H₂O–ROH, where R = C₂H₅, CH₂CH₂CH₃).¹     

Electroconductivity of Potassium Orthophosphate Modified by Four-Charged Cations

Solid solutions based on K₃PO₄ in systems K_{3 – 4x} E" _x PO₄ (E" = Si, Ti, Ge, Zr, Sn, Hf, Ce) are synthesized. The crystal structure, thermal behavior, and electroconduction of the synthesized solutions is studied. The narrowest single-phase regions take place in the systems where E" = Si, Ge (x 0.025), and the widest, in the system with Zr (x 0.125, at 700°C). Introducing Ti or Sn additives (x 0.05) and minimum quantities of Zr, Hf, or Ce (x = 0.025) into potassium orthophosphate leads to stabilization of highly-conductive -modification of K₃PO₄ at room temperature. Maximum values of potassium-cation conduction in all the systems studied correspond to regions of single-phase solid solutions based on K₃PO₄. The maximum electroconductivity (0.005 S cm^–1 at 300°C, 0.1 S cm^–1 at 700°C) and the smallest activation energies (32–35 kJ mol^–1) take place in the systems with Zr and Hf.