A three-parameter cubic equation of state for asymmetric mixture density calculations

A new three-parameter cubic equation of state of the van der Waals type with one parameter temperature dependent, P = RT/(V − b) − a(T)/[V(V + c) + b(3V + c)], has been developed for representation of liquid volumes (or densities) for asymmetric mixtures such as CO₂C₁₉ and C₁C₁₀. The calculated results are better than those obtained from the two-parameter Peng—Robinson equation, the three parameter Schmidt—Wenzel equation, the volume-translated Soave—Redlich—Kwong equation proposed by Peneloux et al., and the volume-translated Peng—Robinson equation developed in this work. The parameters of the new equation have been generalized in terms of the acentric factor ω and reduced temperature T_r.     

The crystal and molecular structure of 5,5-diphenyloctafluorogermanthrene, (C6H5)2GeC12F8

F---F steric interaction between the two 6,6′-fluorines of the C₆F₄ rings in C₁₂F₈Ge(C₆H₅)₂ cause quite distortions in the molecule as these two fluorine atoms are forced to within 2.419 Å of each other (Van der Waals distance ⋍ 2.7 Å). Crystal data: C₁₂F₈Ge(C₆H₅)₂, M_r 522.89, C2/c, a 29.065(2), b 8.066(2), c 23.000(3) Å, β 129.85°, U 4139.63 ų, Z = 8, D_x 1.678 Mg m⁻³, Mo-K_α, λ 0.7107 Å, μ 15.58 cm⁻¹, F(000) = 2064, T 293 K, R = 0.044 for 2264 reflections with I > 3σ(I); Δϱ ± 0.5 e⁻     

Koordinationsverhältnisse in basenfreien tricyclopentadienyl-lanthanoid(III)-komplexen: IV. Die röntgenstrukturen von tricyclopentadienyl-erbium(III) und -thulium(III)

The single crystal X-ray analyses of sublimated (C₅H₅)₃Er (6) and (C₅H₅)₃Tm (7) confirm, for the first time, the existence of coordinatively well-saturated molecules containing just three η⁵-C₅H₅ ligands per metal ion (formal coordination number: 9, space group: Pna2₁, lattice parameters: a 1972.1(3), b 1389.4(1), c 862.4(3) pm for 6, and a 1999.1(3), b 1379.8(4), c 1379.8(4), c 857.8(3) pm for 7; R = 0.076 and 0.047, respectively). Individual molecules align themselves into chains by Van der Waals interactions. The structures of 6 and 7 show a marked contrast to those of their La und Pr homologues on the one hand, and with the structure of (C₅H₅)₃Lu on the other.     

Influence of the molecular weight of polystyrene on its thermodynamic properties

The thermodynamic properties of a series of polystyrene samples with different molecular weights (M _w was varied from 2.5·10³ to 6.57·10⁴) were studied by precision adiabatic vacuum, high-accuracy dynamic, and combustion calorimetry: temperature dependences of the heat capacity in a wide temperature range, thermodynamic characteristics of glass transition and glassy state under standard pressure, and energy of combustion. The thermodynamic functions C ^○ _p (T), H ^○(T) - H ^○(0), S ^○(T) - S ^○(0), and G ^○(T) - H ^○(0) of polystyrene with different molecular weights, enthalpies of combustion Δ_c H ^○, thermodynamic parameters of formation from simple substances Δ_f H ^○, Δ_f S ^○, and Δ_f G ^○ at T = 298.15 K, and parameters of their synthesis from monomers were calculated from the experimental data. The temperature dependences of the heat capacity for a region of 0–380 K, glass transition temperatures, and thermodynamic characteristics of formation and synthesis of polystyrene depending on its molecular weight were examined.     

Thermolabile kohlenwasserstoffe. XXVI. Bildungsenthalpie von 1,1,2,2-tetra-tert-butylethan

The title compound (1) was prepared in high purity by reducing 3,3-dibromo-2,2,4,4-tetra-methylpentane (2) with magnesium in the last step. The heat of combustion, ΔH⁰_c(c), of 1 was measured using an aneroid isoperibol microcalorimeter and the heat of sublimation, ΔH_sub, was obtained from the vapour pressure (35–93°C) measured in a flow system. The results: ΔH⁰_c(c) = ?2913.3(±0.9), ΔH⁰_f(c) = ?77.6(±0.9) and ΔH⁰_f(g) = ?59.9(±0.9) kcal mol^?1 lead to an outstandingly high value for the excess strain enthalpy (H_s = 66.3 kcal mol^?1) revealing strong van der Waals repulsions in this highly crowded alkane.     

Crystal structure and luminescence of europium(III) acrylate

The atomic structure of europium acrylate crystals [Eu₂(Acr)₅OH·3H₂O]·2(0.5H₂O) was studied by X-ray analysis (a = 24.360(3) Å, b = 18.466(2) Å, c = 8.5818(9) Å, β = 96.087(2)°, space group C2/c, Z = 6, ρ_calc = 2.036 g/cm³). The crystal structure involves chains of binuclear [Eu₂(C₃H₃O₂)₅OH·3H₂O] molecules, running infinitely in the [101] direction and having pairs of C₉H₉EuO₇H₂O molecules alternating with C₆H₆EuO₄OH·2H₂O molecules that link the pairs. The infinite chains are linked by hydrogen bonds and van der Waals interactions. The thermal behavior of luminescence of the europium(III) complex is discussed.     

The low-temperature (5 to 310 K) heat capacity and thermodynamic functions of cesium fluoroxysulfate (CsSO4F) and the standard potential at 298.15 K for the half-reaction: SO4F−(aq) + 2H+(aq) + 2e− = HSO4−(aq) + HF(aq)

The low-temperature (5 to 310 K) heat capacity of cesium fluoroxysulfate, CsSO₄F, has been measured by adiabatic calorimetry. At T = 298.15 K, the heat capacity C_p^o(T) and standard entropy S^o(T) are (163.46±0.82) and (201.89±1.01) J · K^?1 · mol^?1, respectively. Based on an earlier measurement of the standard enthalpy of formation ΔH_f^o the Gibbs energy of formation ΔG_f^o(CsSO₄F, c, 298.15 K) is calculated to be ?(877.6±1.6) kJ · mol^?1. For the half-reaction: SO₄F^?(aq)+2H⁺(aq)+2e^? = HSO₄^?(aq)+HF(aq), the standard electrode potential E at 298.15 K, is (2.47±0.01) V.     

Accurate ab initio determination of the van der Waals interaction in the X 2Σ+ ground state of LiHe

Accurate quantum-chemical ab initio calculations have been performed at the SCF and CEPA (coupled electron pair approximation) levels for the van der Waals interaction in the X ² Σ ⁺ ground state of LiHe. An extended basis set has been used and the counterpoise correction for the basis set superposition error (BSSE) has been applied. The calculated potential energy curve has a very shallow minimum at 11.56 a ₀ with a well depth of only 1.49 cm^?1. This is too small to allow for a bound vibrational level. The analysis of the results shows that the interaction mainly consists of the Pauli repulsion between Li(1s ²2s) and He (1s ²), which is decaying exponentially, and the attractive London dispersion energy. Van der Waals coefficients C₆, C₈, and C₁₀ have been determined by a least squares fit to the long-range part of the calculated potential curve.     

Extraction of certain actinide and lanthanide elements from different acidic media by polyurethane foams loaded with di-(2-ethylhexyl)phosphoric acid (HDEHP)

The extraction of cerium(III) from weakly acidic chloride solutions by HDEHP-nitrobenzene-loaded polyurethane foams could be analyzed quantitatively in terms of the equation: log(9.056 D_c)=log K_c+2.14 log (C_d?6C_c)+3 pH+log f_c where D_c is the distribution ratio of cerium(III) between the foam and aqueous phases, C_d and C_c are the total HDEHP and Ce(III) concentrations on the foam, respectively, log f_c=[Ce³⁺]_(sq)/[ΣCe(III)]_(aq), and K_c is the equilibrium constant of the equation: Ce _(aq) ³⁺ +2.14(HX)_2.8(o) ? ? CeX₆·H_3(o)+3H _(aq) ⁺ . Values of K_c under the different extraction conditions tested are given.     

CEPA calculations of potential energy surfaces for open-shell systems.: III. Van der Waals interaction between O(3P) and He(1S)

Quantum-chemical ab initio calculations have been performed for the van der Waals interaction between helium and oxygen atoms in their respective ground states: He(¹S)+ O(³P). As long as fine-structure effects are neglected, there are two low-lying electronic states, ³Σ^? and ³Π resulting from the degeneracy of the O(³P) ground state. Both states are purely repulsive at the SCF level, after inclusion of electronic correlation by the CEPA method they exhibit shallow van der Waals (dispersion) minima at large interatomic separation: R_? = 3.61 Å, ? = 1.0 meV (³Σ^?) and R_? = 3.05 Å, ? = 2.3 meV (³Π). The analysis of the results shows the very slow convergence of the dispersion interaction with increasing basis size, while SCF repulsion and the repulsion due to the change of the intra-atomic correlation are obtained reasonably accurately with moderate basis stes. Van der Waals coefficients C₆, C₈, C₁₀, potential curves of the type HFD (i.e. Hartree-Fock plus damped dispersion) and the influence of fine-structure effects (mainly spin-orbit coupling) on the shape of the adiabatic potential curves are discussed as well.     

Synthesis and structure of [UO2(SeO4)(C2H4N4)2] · 0.5H2O

The single-crystal X-ray diffraction analysis of [UO₂(SeO₄)(C₂H₄N₄)₂] · 0.5H₂O (I) is performed. The crystals are monoclinic: space group C2/c, Z = 8, a = 19.035(2), b = 7.1326(8), c = 21.477(2) Å, β = 109.683(4)°. The main structural units of the crystal are chains of [UO₂(SeO₄)(C₂H₄N₄)₂]. Compound I belongs to the crystal-chemical group AT³M ₂ ¹ (A = UO ₂ ²⁺ , T³ = SeO ₄ ^2? , M¹ is a cyanoguanidine molecule) of the uranyl complexes. The chains are united into three-dimensional framework through hydrogen bonds involving the oxygen atoms of the selenate and uranyl groups, the nitrogen atoms of cyanoguanidine, and the hydrogen atoms of the cyanoguanidine or water molecules.     

Neutron diffraction study of uranyl oxalate [UO2(C2O4)(D2O)] · 2D2O

A powdered sample of uranyl oxalate [UO₂(C₂O₄)(D₂O)] · 2D₂O (compound I) is studied using neutron diffraction. The crystals are monoclinic, space group P2₁/c, with a = 5.608(1) Å, b = 17.016(3) Å, c = 9.410(2) Å, β = 98.9369(2)°, Z = 4, R _f = 0.042, R _I = 0.054, x ² = 1.5. The main structural units of the crystals are [UO₂(C₂O₄)(D₂O)] chains. These chains, which belong to the AK⁰²M¹ (A = UO ₂ ²⁺ ) crystal-chemical group of the uranyl complexes, lie parallel to [101]. The water molecules in the crystals of I are hydrogen-bonded into zigzag chains running along [100]. Since each third oxygen atom of the chain formed of water molecules is coordinated to the uranium atom, the uranyl oxalate chains are linked into {[UO₂(C₂O₄)(D₂O)] · 2D₂O} layers that lie normal to [010]. The layers are linked into the framework through interlayer hydrogen bonds (D₂O)O-D···O (oxalate).     

Formation and Stability of Gaseous WS2Cl2, WS2Br2 and WS2I2 – A Combined Experimental and Theoretical Study

Gaseous WS₂Cl₂ and WS₂Br₂ are formed by the reaction of solid WS₂ with chlorine resp. bromine at temperatures of about 1000 K. This could be shown by mass spectrometric measurements. The heats of formation and entropies of WS₂Cl₂ and WS₂Br₂ have been determined by means of mass spectrometry (MS) and quantum chemical calculations (QC). WS₂I₂ could not be detected by experimental methods. This is in line with the quantum chemically determined equilibrium constant of the formation reaction. The following values are given:, Δ_fH⁰₂₉₈(WS₂Cl₂) = –230.8 kJ · mol^–1 (MS), Δ_fH⁰₂₉₈(WS₂Cl₂) = –235.0 kJ · mol^–1 (QC),, S⁰₂₉₈(WS₂Cl₂) = 370.7 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂Cl₂) = 103.78 + 7.07 × 10^–3 T – 0.93 × 10⁵ T^–2 – 3.25 × 10^–6 T² (298.15 K < T < 1000 K) (QC). Δ_fH⁰₂₉₈(WS₂Br₂) = –141.9 kJ · mol^–1 (MS), Δ_fH⁰₂₉₈(WS₂Br₂) = –131.5 kJ · mol^–1 (QC),, S⁰₂₉₈(WS₂Br₂) = 393.9 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂Br₂) = 104.84 + 5.32 × 10^–3 T – 0.75 × 10⁵ T^–2 – 2.45 × 10^–6 T² (298.15 K < T < 1000 K) (QC). Δ_fH⁰₂₉₈(WS₂I₂) = –18.0 kJ · mol^–1 (QC), S⁰₂₉₈(WS₂I₂) = 409.9 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂I₂) = 105.17 + 4.77 × 10^–3 T – 0.67 × 10⁵ T^–2 – 2.19 × 10^–6 T² (298.15 K < T < 1000 K) (QC). These molecules have the expected C_2v‐symmetry.     

Syntheses and structures of nine-coordinate K3[DyIII(nta)2(H2O)]·5H2O and eight-coordinate (NH4)3[DyIII(nta)2] complexes

K₃[Dy^III(nta)₂(H₂O)]·5H₂O and (NH₄)₃[Dy^III(nta)₂] have been synthesized in aqueous solution and characterized by IR, elemental analysis and single-crystal X-ray diffraction techniques. In K₃[Dy^III(nta)₂(H₂O)]·5H₂O the Dy^III ion is nine coordinated yielding a tricapped trigonal prismatic conformation, and its crystal belongs to monoclinic system and C2/c space group. The crystal data are as follows: a = 15.373(5) Å, b = 12.896(4) Å, c = 26.202(9) Å; β = 96.122(5)°, V = 5165(3) ų, Z = 8, D _c = 1.965 g·cm^?3, μ = 3.458 mm^?1, F(000) = 3016, R ₁ = 0.0452 and wR ₂ = 0.1025 for 4550 observed reflections with I ≥ 2σ(I). In (NH₄)₃[Dy^III(nta)₂] the Dy^III ion is eight coordinated yielding a usual dicapped trigonal anti-prismatic conformation, and its crystal belongs to monoclinic system and C2/c space group. The crystal data are as follows: a = 13.736(3) Å, b = 7.9389(16) Å, c = 18.781(4) Å; β = 104.099(3)°, V = 1986.3(7) ų, Z = 2, D _c = 1.983 g·cm^?3, μ = 3.834 mm^?1, F(000) = 1172, R ₁ = 0.0208 and wR ₂ = 0.0500 for 2022 observed reflections with I ≥ 2σ(I). The results indicate that the difference in counter ion also influences coordination numbers and structures of rare earth metal complexes with aminopolycarboxylic acid ligands.     

RBaCuCoO<Subscript>5 + δ</Subscript> (R = Nd,Sm, Gd) layered cuprocobaltites: Synthesis,structure, and properties

Cuprocobaltites RBaCuCoO_{5 + gd}(R = Nd, Sm, Gd) were prepared. Their unit cell parameters were determined, and thermal expansion, electrical conductivity (σ), and Seebeck coefficient (S) were studied in air in the range 300–1100 K. The compounds have tetragonal structures (space group P4/mmm, Z = 1). Their unit cell parameters are a = 0.3906(2) nm, c= 0.7648(7) nm for NdBaCuCoO_5.21; a = 0.3904(2) nm, c = 0.7609(6) nm for SmBaCuCoO_5.06; and a = 0.3891(2), c = 0.7592(6) nm for GdBaCuCoO_5.02. The RBaCuCoO_{5 + δ} cuprocobaltites at room temperature are p-type semiconductors, whose electrical conductivity and linear thermal expansion coefficient (LTEC) increase with increasing R³⁺ ionic radius, whereas the Seebeck coefficient decreases. The LTECs of RBaCuCoO_{5 + δ} phases in the range 500–575 K increase by a factor of 1.2–1.5 because of the elimination of weakly bound oxygen. S = f(T) curves for RBaCuCoO_{5 + δ} (R = Nd, Sm, Gd) feature maxima at 510 K for R = Sm and 365 K for R = Gd, probably, due to the change in the spin state of cobalt cations in these phases.     

High-temperature heat capacity and thermodynamic properties of pyrovanadate Pb<Subscript>2</Subscript>V<Subscript>2</Subscript>O<Subscript>7</Subscript> and orthovanadate Pb<Subscript>3</Subscript>(VO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The heat capacities of Pb₂V₂O₇ and Pb₃(VO₄)₂ as a function of temperature in the range 350–965 K have been studied by the differential scanning calorimetry method. The C_P = f(T) curve for Pb₂V₂O₇ is described by the equation C_p = (230.76 ± 0.51) + (73.60 ± 0.50)×10^-3T ? (18.38 ± 0.54)×10⁵T^-2 in the entire temperature range. For Pb₃(VO₄)₂, there is a well-pronounced extreme point in the C_P = f(T) curve at T = 371.5 K, which is caused by the existence of a structural phase transition. The thermodynamic properties of the oxide compounds have been calculated.     

Architecture of framework copper(I) halide π-complexes with N-allyl-N,N,N′,N′-tetramethyl-ethylenediaminium and N,N′-diallyl-N,N,N′,N′-tetramethylethylenediaminium: Synthesis and crystal structure of [{C2H4N2(H+)×(CH3)4(C3H5)} Cu4Cl6] and [{C2H4N2(CH3)4(C3H5)2}0.5Cu2Cl1.67Br1.33]

N,N,N??,N??-tetramethylethylenediamine is obtained by the reaction of ethylenediamine with formaldehyde and formic acid (the Eschweiler-Clarke reaction) and then alkylated with allyl chloride (or bromide) in a ratio of 1:1 or 1:2 to obtain N-allyl-N,N,N??,N??-tetramethylethylenediaminium and N,N??-diallyl-N,N,N??,N??-tetramethylethylenediaminium bromide respectively. [{C₂H₄N₂(H⁺)(CH₃)₄(C₃H₅)}Cu₄Cl₆] (1) and [{C₂H₄N₂(CH₃)₄(C₃H₅)2}_0.5Cu₂Cl_1.67Br_1.33] (2) ??-complexes are obtained from alcohol solutions containing an ethylenediamine derivative and copper(II) chloride by ac-electrochemical synthesis on copper wire electrodes. An XRD study of the complexes is carried out. The crystals are monoclinic; 1: P2₁/n space group, a = 9.0081(6) ?, b = 12.5608(7) ?, c = 16.8610(10) ?, ?? = 102.061(3)°, V = 1865.7(2) ?³, Z = 4; 2: C2/c space group, a = 14.462(2) ?, b = 12.519(1) ?, c = 12.762(2) ?, ?? = 107.861(5)°, V = 2199.1(4) ?³, Z = 8. The structure of 1 consists of infinite copper halide networks with four crystallographically independent copper atoms, one of which coordinates the double bond of the allyl group of the ligand. The [C₂H₄N₂(H)(CH₃)₄(C₃H₅)]²⁺ cations are attached above and below the plane of the network. The individual fragments are bonded via an extensive system of (N)H??Cl and (C)H??Cl hydrogen bonds. The structure of 2 contains a three-dimensional copper halide framework whose cavities contain the [C₂H₄N₂(CH₃)₄(C₃H₅)₂]²⁺ cations that are ??-coordinated with copper(I) atoms. In both structures, the Cu(I) atom that coordinates the C=C bond has a trigonal-pyramidal coordination environment consisting of the double C=C bond of the corresponding ligand and three halogen atoms. The other Cu(I) atoms have a tetrahedral environment consisting solely of halogen atoms. The Cu-(C=C) distance is 1.958(1) ?, (1) and 1.974(1) ? (2).     

Thermally induced incomplete high-spin (5T2) ⇌ low-spin (1A1) transition in solid bis[2-(2-pyridylamino)-4-(2-pyridyl) thiazolato]iron (II)

The ⁵⁷Fe Mössbauer effect in two samples (A and B) of [Fe(papt)₂] and in its solvates with CHCl₃ and C₆H₆ has been studied between 4.2 and 343 K and clearly indicates a temperature induced high-spin (⁵T₂) ? low-spin (¹A₁) transition in these compounds [paptH = 2-(2-pyridylamino)-4-(2-pyridyl) thiazole]. At 343 K, sample B shows a doublet with ΔE_Q = 2.03 mm s^?1 and δIS = +0.87 mm s^?1, characteristic of a ⁵T₂ ground state. At 257 K, a second doublet, typical for a ¹A₁ ground state, is observed and its intensity increases as the transition progresses but levels off below ～ 100 K. At 4.2 K, 83% of the intensity is due to the ¹A₁ state, and ΔE_Q(¹A₁) = 1.56 mm s^?1 and δ^IS(¹A₁ = +0.32 mm s^?1. In an applied magnetic field, V_zz(¹A₁) < 0 and η ≈ 0.7 have been determined, whereas for the ^sT₂ ground state, V_zz(^sT₂) > 0, η ≈ 0.75, and an internal hyperfine field H_n ≈ ?13 kG have been observed. Similar results have been obtained with the other samples.Debye-Waller factors f5_T2 and f1_A1 were determined from the saturation corrected areas in the Mössbauer spectra, assuming Curie-Weiss dependence of the magnetic susceptibility for the ⁵T₂ and constant υ_cff for the ¹A₁ ground state. The temperature dependence of ?In f1_A1 closely follows the Debye model with Θ1_A1 = 165 K, whereas the same applies to ?ln f5_T2 only above ～ 210 K and Θ5_T2 = 134 K. The nature of the observed transition is discussed and the data presented are shown to be incompatible with a model based on a Boltzmann distribution between the two states.     

La(Li1/3Ti2/3)O3: a new 1:2 ordered perovskite

A new 1:2 ordered perovskite La(Li_1/3Ti_2/3)O₃ has been synthesized via solid-state techniques. At temperature >1185°C, Li and Ti are randomly distributed on the B-sites and the X-ray powder patterns can be indexed in a tilted (b⁻b⁻c⁺) Pbnm orthorhombic cell (a=a_c√2=5.545 Å, b=a_c√2=5.561 Å, c=2a_c=7.835 Å). However, for T?1175°C, a 1:2 layered ordering of Li and Ti along 〈111〉_c yields a structure with a P2₁/c monoclinic cell with a=a_c√6=9.604 Å, b=a_c√2=5.552 Å, c=a_c3√2=16.661 Å, β=125.12°. While this type of order is well known in the A²⁺(B²⁺_1/3B⁵⁺_2/3)O₃ family of niobates and tantalates, La(Li_1/3Ti_2/3)O₃ is the first example of a titanate perovskite with a 1:2 ordering of cations on the B-sites.