Structure of water (H2O) 6 − and ammonium (NH3) 13 − clusters with an excess electron: Quantum chemical studies

The B3LYP method within DFT and the ab initio MP2 method with an extended 6-311++G(3df,3pd) basis set are employed to calculate the adiabatic bound state of an excess electron in (H₂O) ₆ ^? water and (NH₃) ₁₃ ^? . ammonium clusters. Adiabatic electron affinity of (H₂O)₆ and (NH₃)₁₃ clusters is 0.03–0.18 eV and 0.18 eV respectively. The calculated vertical binding energies of the excess electron in anionic clusters ((H₂O) ₆ ^? 0.37÷0.66 eV and (NH₃) ₁₃ ^? 0.26 eV) agree well with the experimental values of 0.50 eV and 0.22 eV obtained from photoelectron spectra. A cavity model of solvated electrons in water and ammonium is considered.     

Photoemission from tin and lead cluster anions

Photoelectrons from mass-identified jet-cooled tin and lead cluster anions (Sn _n ^? , Pb _n ^? ) are detached by ultraviolet laser light (hν=3.68 eV). The photoelectron energy spectra give the detachment energies of ground state cluster anions (electron affinities) as well as excitation energies of neutral clusters in the geometry of the anions. The energy spectra for Sn _n ^? are dominated by flat thresholds with ann-dependence similar to that of other group IV clusters. In contrast, for Pb _n ^? we find pronounced narrow lines close to threshold, generally followed by a 0.3–1.4 eV gap which indicates closed-shell behaviour of Pb _n ^? for nearly alln.     

Calculated vibrational structure of the first band of the photoelectron spectrum of HO 2 − and the electron affinity of HO2

The vibrational structure of the first band of the photoelectron (PE) spectrum of HO ₂ ^? and DO ₂ ^? has been calculated on the basis of (slightly modified) ab initio potentials. The best agreement with the experimental spectrum of HO ₂ ^? is obtained for a vibrational temperature of ca. 600 K. “Peak D”, which has been under debate in earlier work, is composed of two transitions, with the “hot” transition 3 ₁ ¹ being more intense than the adiabatic transition. Since thev ₂ bending mode of DO₂ has significant OO stretching character, the vibrational structure of the PE spectrum of DO ₂ ^? is more complex than that of HO ₂ ^? . Large-scale RCCSD(T) calculations of the equilibrium electron affinity of HO₂ yield 1.058 eV which agrees with the experimental value of 1.044 ± 0.020 eV.     

Fragmentation of clusters induced by collision with a solid surface: comparison of antimony and bismuth cluster ions

Mass-selected antimony cluster ions Sb _n ⁺ (n = 3-12) and bismuth cluster ions Bi _{ntn} ⁺ (n = 3-8) are allowed to collide with the surface of highly oriented pyrolytic graphite at energies up to 350 eV. The resulting fragment ions are analysed in a time-of-flight mass spectrometer. Two main fragmentation channels can be identified. At low impact energies both Sb _n ⁺ and Bi _n ⁺ cluster ions lose neutral tetramer and dimer units upon collision. Above about 150 eV impact energy Sb ₃ ⁺ becomes the predominant fragment ion of all investigated antimony clusters. The enhanced stability of these fragment clusters can be explained in the framework of the polyhedral skeletal electron pair theory. In contrast, Bi _n ⁺ cluster scattering leads to the formation of Bi ₃ ⁺ , Bi ₂ ⁺ and Bi+ with nearly equal abundances, if the collision energy exceeds 75 eV. The integral scattering yield is substantially higher in this case as compared to Sb _n ⁺ clusters.     

Analytical photoion spectroscopy applied to dissociative single and double photoionization of diatomic molecules (H2, N2, O2, CO,and NO)

This work reports the principle, advantage, and limitations of analytical photoion spectroscopy which has been applied to dissociative photoionization processes for diatomic molecules such as H₂, N₂, CO, and NO. Characteristic features observed in the differential photoion spectra are summarized with a focus on (pre)dissociation of(i) multielectron excitation states commonly observed in the inner valence regions,(ii) shape resonances, and(iii) doubly charged parent ions. Possible origins for negative peaks in the differential spectra are discussed. This spectroscopy is applied to the reported photoion branching ratios for D₂ (and H₂ at high energies). The main findings are as follows: (1) The direct dissociation of theX ²Σ _g ⁺ (1sσ _g ) state of D ₂ ⁺ , the two-electron excited state¹Σ _u ⁺ (2pσ _u 2sσ _g ) of D₂, and the²Σ _u ⁺ (2pσ _u ) state of D ₂ ⁺ appear clearly in the differential spectrum, as previously observed for H₂. (2) Decay of H ₂ ⁺ (D ₂ ⁺ ) to H⁺ (D⁺) above 38 eV is due to the direct dissociation of highly excited states of H ₂ ⁺ (D ₂ ⁺ ) such as the²Σ _g ⁺ (2sσ _g ) and high-lying Rydberg states converging on H ₂ ²⁺ (D ₂ ²⁺ ). (3) In the ionization continuum of H ₂ ²⁺ (D ₂ ²⁺ ) peculiar dissociation pathways are observed. The differential photoion spectra for O₂ derived from the reported photoion branching ratios are also presented. The (pre)dissociation of theb ⁴Σ _g ^? ,B ²Σ _g ^? , III²Π _u ,²Σ _u ^? , and^2,4Σ _g ^? states of O ₂ ⁺ appears as the corresponding positive values in the spectra in accord with previous observations. Some other dissociation pathways possibly contributing to the spectra are discussed including dissociative double ionization.     

Sampling of aryldiazonium, anilino, and aryl radicals by membrane introduction mass spectrometry: Thermolysis of aromatic diazoamino compounds

Membrane introduction mass spectrometry (MIMS) is used to sample free radicals generated by thermolysis at atmospheric pressure. This is done by heating the solid sample in a custom-made probe that is fitted with a silicone membrane to allow selective and rapid introduction of the pyrolysates into the ion source of a triple quadrupole mass spectrometer. Phenyldiazonium radical (C₆H₅N ₂ ^· ) and some of its ring-substituted analogs, the methoxy anilino radical CH₃OC₆H₄NH^·, and aryl radicals are generated by gas phase thermolysis of symmetrical aryl diazoamino compounds (ArNH-N₂Ar). The radicals are identified by measurement of their ionization energies (IE) using threshold ionization efficiency data. A linear correlation between the ionization energy of the phenyldiazonium radicals and their Brown σ⁺ values is observed, and this confirms the formation of these species and validates the applicability of MIMS in sampling these radicals. The ionization energies of the aryldiazonium radicals are estimated as IE (p-CH₃O-C₆H₄N ₂ ^· ), 6.74 ± 0.2 eV; IE (p-CH₃-C₆H₄N ₂ ^· ), 7.72 ± 0.2 eV; IE (C₆H₅N ₂ ^· ), 7.89 ± 0.2 eV; IE (m-Cl-C₆H₄N ₂ ^· ), 7.91 ± 0.2 eV; IE (p-F-C₆H ₄ ^· N ₂ ^· ), 8.03 ± 0.2 eV; and IE (m-NO₂-C₆H₄N ₂ ^· ), 8.90 = 0.2 eV. The ionization energies of the aryl radicals are estimated as IE (p-CH₃O-C₆H ₄ ^· ), 7.33 ± 0.2 eV; IE (p-CH₃-C₆H ₄ ^· ), 8.31 ± 0.2 eV; IE (C₆H ₅ ^· ), 8.44 ± 0.2 eV; IE (m-Cl-C₆H ₄ ^· ), 8.50 ± 0.2 eV and IE (p-F-C₆H ₄ ^· ), 8.54 ± 0.2 eV. Also, the ionization energy of the p-methoxyanilino radical (p-CH₃O-C₆H₄NH^·) is estimated as 7.63 ± 0.2 eV.     

Photoelectron spectroscopy of (CO2)n(H2O) m − clusters

Photoelectron spectra of (CO₂)_nH₂O^? (2≤n≤8) and (CO₂)_n(H₂O) ₂ ^? (1≤n≤2) were measured at the photon energy of 3.49 eV. The spectra show unresolved broad features, which are approximated by Gaussians. The vertical detachment energies (VDEs) were determined as a function of the cluster size. For (CO₂)_nH₂O^?, the VDE-n plots exhibit a sharp discontinuity between n=3 and 4; the VDE value is ≈3.5 eV at n=3, while it drops down abruptly to 2.59 eV at n=4. This discontinuity in VDE is ascribed to "core switching" at n=4; a C₂O ₄ ^? dimer anion forms the core of (CO₂)_nH₂O^? for n≤3, while a monomer CO ₂ ^? is the core for n≥4. The (CO₂)₂(H₂O) ₂ ^? ion has a VDE of 2.33 eV, indicating the presence of a CO ₂ ^? monomer core in the binary clusters containing two H₂O molecules.     

Fragmentation of doubly charged ammonia cations NH 3 ++ studied by the photoion-photoion coincidence (PIPICO) method

Doubly charged NH ₃ ⁺⁺ cations were produced by double photoionization of neutral ammonia molecules by using the synchrotron radiation from ACO as a photon source of variable energy in the 35–49 eV energy range. The fragmentation of NH ₃ ⁺⁺ was studied by the photoion-photoion coincidence (PIPICO) method. NH ₃ ⁺⁺ cations were produced in the \(\tilde X^1 \) A ₁ and \(\tilde B^1 \) electronic states of which the onset energies were measured at, respectively, 35.4±0.5 eV and 44.5±0.5 eV. It was shown that the NH ₃ ⁺⁺ ions, initially produced in their \(\tilde X^1 \) A ₁ state, rapidly dissociate (in less than 50 ns), into NH ₂ ⁺ + H⁺. Furthermore, the comparison with results obtained by other methods indicates that NH ₃ ⁺⁺ ions can either be long-lived (τ>10 µs) or slowly dissociating (1 µs<τ<10 µs) or rapidly dissociating (τ<50 ns), depending on their geometry and/or internal energy in their \(\tilde X^1 \) E A ₁ electronic state.     

Pressure and isotope effects on the proton jump of the hydroxide ion at 25°C

The limiting molar conductances Λ⁰ of potassium deuteroxide KOD in D₂O and potassium hydroxide KOH in H₂O were determined at 25°C as a function of pressure to disclose the difference in the proton-jump mechanism between an OH^? (OD^?) and a H₃O⁺ (D₃O⁺) ion. The excess conductance of the OD^? ion in D₂O λ _E ^O (OD ^-), as estimated by the equation $$\lambda _E^O (OD^ - ) = \Lambda ^O (KOD/D_2 O) - \Lambda ^O (KCl/D_2 O)$$ increases a little with pressure as well as the excess conductance of the OH^? ion in H₂O $$\lambda _E^O (OH^ - ) = \Lambda ^O (KOH/H_2 O) - \Lambda ^O (KCl/H_2 O)$$ However, their rates of increase with pressure are much smaller than those of the excess deuteron and proton conductances, λ _E ^O (D ⁺) and λ _E ^O (H ⁺). With respect to the isotope effect on the excess conductance, λ _E ^O (OH ^-)/λ _E ^O (D ⁺) decreases with presure as in the case of λ _E ^O (H ⁺)/λ _E ^O (D ⁺), but the value of λ _E ^O (OH ^-)/λ _E ^O (OD ^-) itself is much larger than that of λ _E ^O (H ⁺)/λ _E ^O (D ⁺) at each pressure. These results are ascribed to the difference in the pre-rotation of water molecules, which is brought about by the difference in the intial orientation of the rotating water molecule adjacent to the OH^? (OD^?) or the H₃O⁺ (D₃O⁺) ion.     

Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.     

The Standard Chemical-Thermodynamic Properties of Phosphorus and Some of its Key Compounds and Aqueous Species: An Evaluation of Differences between the Previous Recommendations of NBS/NIST and CODATA

The aqueous chemistry of phosphorus is dominated by P(V), which under typical environmental conditions (and depending on pH and concentration) can be present as the orthophosphate species H₃PO ₄ ⁰ (aq),H₂PO ₄ ^? (aq),HPO ₄ ^2? (aq) or PO ₄ ^3? (aq). Many divalent, trivalent and tetravalent metal ions form sparingly soluble orthophosphate phases that, depending on the solution pH and concentrations of phosphate and metal ions, can be solubility limiting phases. Geochemical and chemical engineering modeling of solubilities and speciation require comprehensive thermodynamic databases that include the standard thermodynamic properties for the aqueous species and solid compounds. The most widely used sources for standard thermodynamic properties are the NBS (now NIST) Tables (from 1982 and earlier, with a 1989 erratum) and the final CODATA evaluation (1989). However, a comparison of the reported enthalpies of formation and Gibbs energies of formation for key phosphate compounds and aqueous species, especially H₂PO ₄ ^? (aq) and HPO ₄ ^2? (aq), shows a systematic and nearly constant difference of 6.3 to 6.9 kJ?mol^?1 per phosphorus atom between these two evaluations. The existing literature contains numerous studies (including major data summaries) that are based on one or the other of these evaluations. In this report we examine and identify the origin of this difference and conclude that the CODATA evaluation is more reliable. Values of the standard entropies of the H₂PO ₄ ^? (aq) and HPO ₄ ^2? (aq) ions at 298.15 K and p?° =1 bar were re-examined in the light of more recent information and data not considered in the CODATA review, and a slightly different value of S _m ^o (H₂PO ₄ ^? , aq, 298.15 K) = (90.6±1.5) J?K^?1?mol^?1 was obtained.     

Electron attachment to oxygen and oxygen/ozone clusters studied in a high-resolution crossed beams experiment

Highly monochromatized electrons (with 30 meV FWHM) are used in a crossed beams experiment to investigate electron attachment to oxygen clusters (O₂)_n at electron energies from approximately zero eV up to 2 eV. At energies close to zero the attachment cross section for the reaction (O₂)_n +e → O ₂ ^? varies inversely with the electron energy, indicative of s-wave electron capture to (O₂)_n. Peaks in the attachment cross section present at higher energies can be ascribed to vibrational levels of the oxygen anion. The vibrational spacings observed can be quantitatively accounted for. In addition electron attachment to mixed oxygen/ozone clusters has been studied in the energy range up to 4 eV. Despite the initially large excess of oxygen molecules in the neutral clusters the dominant attachment products are undissociated cluster ions (O₃) _m ^? including the O ₃ ^? monomer while oxygen cluster ions (O₂) _n ^? appear with comparatively low intensity.     

Production and stability of oxygen cluster cations and anions,revisited

Stoichiometric and non-stoichiometric, positive and negative oxygen cluster ions (n up to 70) have been produced in a crossed neutral beam/electron beam ion source. The abundance and stability of the ions formed have been analyzed with a double focussing sector field mass spectrometer in a series of experiments. Positive and negative ion mass spectra observed exhibit distinct abundance anomalies, however, at different cluster sizes. Abundance maxima and minima correlate with correspondingly small and large metastable fractions of (O₂) _n ⁺ and (O₂) _n ^? ions, respectively. (O₂) _n ⁺ ions may also lose up top=(n?1) monomers by collision induced dissociation with monotonously decreasing probability with increasingp. Metastable fractions determined for (O₂) _n ^? ions produced with appr. zero eV electrons are in general larger than those for ions produced with appr. 7 eV electrons. (O₂) _n ^? ions are also observed to decay via autodetachment, with lifetimes increasing with increasing cluster size. Finally, here we were able to prove that an apparent loss of the monomer fragment O (and higher homologues) observed in the metastable time regime is due to ordinary metastable monomer evaporation in the acceleration region. Moreover, we will also present here some new data and interpretation concerning the electron attachment cross section function for O₂ clusters.     

Equilibria of aqueous solutions of isopolyniobotungstates-6 with c Nb : c W = 1 : 5

Complex formation in the Nb₆O ₁₉ ^8? -WO ₄ ^2? -H⁺-H₂O system with c _Nb : c _W = 1 : 5 and varied c _{Nb + W} ⁰ = 10^?2, 5 × 10^?3, 2.5 × 10^?3, and 10^?3 mol/L) has been studied. Distribution diagrams were simulated for individual niobium(V) and tungsten(VI) isopolyanions and mixed isopolyniobotungstates for $Z = \frac{{c_{H^ + }^0 }}{{c_{Nb + W}^0 }} = 0 - 3.0$ in an NaCl background electrolyte. We have shown that isopolyniobotungstates-6 of composition H _x NbW₅O ₁₉ ^{(3 ? x)?} are formed via H _x Nb _n W_6?n O ₁₉ ^{(2 + n ? x)?} (n=2, 3, 5) ions. The concentration formation constants and thermodynamic formation constants of isopolyniobotungstate anions (IPNTAs) in aqueous solution have been calculated. Salt Tl₃NbW₅O₁₉·9H₂O has been synthesized and identified by chemical analysis and IR spectroscopy.     

On the stability of Pb n m+ -clusters

The stability of multiply charged Pb _n ^m+ -clusters (n ≤ 3;m=0, 1, 2) was studied by solving exactly for the valencep-electrons a many body Hubbard-like Hamiltonian with intra- and interatomic Coulomb interactions. Particularly we obtain that Pb ₃ ²⁺ has a metastable ground state, in which Pb ₃ ²⁺ has isosceles shape (bond lengthR=3.2 Å, bond angle θ=124°) and a positive binding energyE _B =3.4 eV. The activation barrier against dissociation into Pb ₂ ⁺ + Pb⁺ is 0.13 eV, yielding a very long lifetime. This is in agreement with recent experiments [1] in which the lifetime of Pb ₃ ²⁺ was determined to be at least 10^?6 s. Comparison with self consistent Hartree-Fock calculations shows that the metastability of Pb ₃ ²⁺ is due to electronic correlations within the paramagnetic ground state.     

Ab initio calculation of the vertical excitation energies of small helium cluster ions

Quantum chemical ab initio calculations have been performed for the vertical excitation energies and oscillator strengths of all low-lying electronically excited states of small helium cluster ions, He _n ⁺ ,n=2, ..., 7. The geometrical structures of the ions were fixed at the equilibrium geometries of the respective ground states, for He ₄ ⁺ and He ₅ ⁺ also one alternative structure was considered. The low-lying excited states can be classified into two categories: the electronic transition can occur either within the central He ₂ ⁺ or He ₃ ⁺ unit or from the peripheral weakly bound He atoms to this unit. The latter transitions are very weak (f≈0.001), closely spaced, with vertical excitation energies of about 5.7 eV. The He ₂ ⁺ and He ₃ ⁺ units have strong transitions at 9.93 and 5.55 eV, respectively; these transitions are only slightly blue-shifted if He ₂ ⁺ or He ₃ ⁺ are placed as “chromophores” into the centre of a larger He _n ⁺ cluster. The large difference in the vertical excitation energy of the strong transition should enable an experimental decision of the question whether the cluster ions have He ₂ ⁺ or He ₃ ⁺ cores.     

Production of negatively charged fragments in collisions of swift positive hydrogen ions with molecules

A first detection and analysis of negatively charged fragments produced in collisions of fast (20–150 keV) positive hydrogen ions (H⁺, H ₂ ⁺ and H ₃ ⁺ ) with gas-phase molecules is presented. The fragments and their abundances were determined by means of a time-of-flight mass spectrometer. Negative ions did emerge from every investigated target molecule species, such as halomethanes, sulfur hexafluoride, propane and propene, but in all cases with distinctly lower probability (cross sections in the range 10^?20?10^?18 cm²) than positively charged fragments (approximately on the scale 10^?3 or even less). Another essential result is that stable collisionally induced negative fragments are mostly monatomic ions, whereas positive fragments are in their majority more complex polyatomic ions. Furthermore, we observed a direct electron capture from a positively charged but not totally stripped projectile (here: H ₂ ⁺ and H ₃ ⁺ ) into stable or very longlived states of the molecular ions SF ₆ ^? and O ₂ ^? , the latter with the largest cross section (10^?18?10^?17 cm²) found up to now.     

Gas-phase reactions between O−. and C6H5F: On the acidity of fluorobenzene and 1,4-difluorobenzene

The gas-phase reactions of negative ions (O^-., NH ₂ ^? , C₂H₅NH^?, (CH₃)₂N^?, C₆H ₅ ^t- , and CH₃SCH ₂ ^? ) with fluorobenzene and 1,4-difluorobenzene have been studied with Fourier transform ion cyclotron resonance mass spectrometry. The O^?. ion reacts predominantly by (1) proton abstraction, (2) formal H ₂ ^+. abstraction, and (3) attack on an unsubstituted carbon atom. In addition to these processes, attack on a fluorine bearing carbon atom yielding F^? and C₆H₄FO^? ions occurs with 1,4-difluorobenzene. Site-specific deuterium labeling reveals the occurrence of competing 1,2-, 1,3-, and 1,4-H ₂ ^+. abstractions in the reaction of O^?. with fluorobenzene. Attack of the O^?. ion on the 3- and 4-positions in fluorobenzene with formation of the 3- and 4-fluorophenoxide ions, respectively, is preferred to reaction at the 2-position, as indicated by the relative extent of loss of a hydrogen and a deuterium atom in the reactions with labeled fluorobenzenes. The NH ₂ ^? , C₂H₅NH^?, (CH₃)₂N^?, C₆H ₅ ^? , and CH₃SCH ₂ ^? anions react with fluoroberuene and 1,4-difluorobenzene only by proton abstraction. The relative importance of H⁺ and D⁺ abstraction in the reaction of these anions with labeled fluorobenzenes indicates that the 2-position in fluorobenzene is more acidic than the 3- and 4-positions, suggesting that the literature value of the gas-phase acidity of this compound (ΔH _acid ^o = 1620 ± 8 kJ mol^?1) refers to the former site. Based on the occurrence of reversible proton transfer between the CH₃O^? ion and 1,4-difluorobenzene, the ΔH _acid ^o of this compound is redetermined to be 1592 ± 8 kJ mol^?1.     

Features of the Diels-Alder reaction between 9,10-diphenylanthracene and 4-phenyl-1,2,4-triazoline-3,5-dione

The Diels-Alder reaction between substituted anthracenes 1a?1j and 4-phenyl-1,2,4-triazoline-3,5 (2) is studied. In all cases except one, the reaction proceeds on the most active 9,10-atoms of substituted anthracenes. The orthogonality of the two phenyl groups at the 9,10-position of diene 1a is found to shield 9,10-reactive centers. No dienophiles with C=C bonds are shown to participate in the Diels-Alder reaction with 1a; however, the reaction 1a + 2 proceeds with the very active dienophile 2,4-phenyl-1,2,4-triazoline-3,5-dione. It is shown that attachment occurs on the less active but sterically accessible 1,4-reactive center of diene 1a. The structure of adduct 3a is proved by ¹H and ¹³C NMR spectroscopy and X-ray diffraction analysis. The following parameters are obtained for reaction 1a + 2 ? 3a in toluene at 25°C: K _eq = 2120 M^?1, ΔH _f ^≠ = 58.6 kJ/mol, ΔS _f ^≠ = ?97 J/(mol K), ΔV _f ^≠ = ?17.2 cm³/mol, ΔH _b ^≠ = 108.8 kJ/mol, ΔS _b ^≠ = 7.3 J/(mol K), ΔV _b ^≠ = ?0.8 cm³/mol, ΔH _r-n = ?50.2 kJ/mol, ΔS _r-n = ?104.3 J/(mol K), ΔV _r-n = ?15.6 cm³/mol. It is concluded that the values of equilibrium constants of the reactions 1a?1j + 2 ? 3a?3j vary within 4 × 10¹?10¹¹ M^?1.