NaBO2-NaCl-Na2CO3, NaBO2- Na2CO3-NaMoO4, NaBO2- Na2CO3-NaWO4, and NaBO2-NaCl-Na2WO4 ternary systems

The phase diagrams of the NaBO₂-NaCl-Na₂CO₃, NaBO₂-Na₂CO₃-Na₂MoO₄, NaBO₂- Na₂CO₃-Na₂WO₄, and NaBO₂-NaCl-Na₂WO₄ ternary systems were studied by a calculation-experimental method and differential thermal analysis. The coordinates of ternary eutectics were determined: E ₁: 612°C, 16 mol % NaBO₂, 42 mol % NaCl, and 42 mol % Na₂CO₃; E ₂: 568°C, 12 mol % NaBO₂, 28 mol % Na₂CO₃, and 60 mol % Na₂MoO₄; E ₃: 575°C, 12 mol % NaBO₂, 32 mol % Na₂CO₃, and 56 mol % Na₂WO₄; E ₄: 628°C, 8 mol % NaBO₂, 20 mol % NaCl, and 72 mol % Na₂WO₄; and E ₅: 655°C, 9 mol % NaBO₂, 53 mol % NaCl, and 38 mol % Na₂WO₄.     

Kinetics of Absorption of Carbon Dioxide into Sodium Metaborate Solution

Carbon dioxide capture potential of sodium metaborate, which is the main product of the process by means of which hydrogen is obtained from sodium borohydride, was investigated. This work aims at both carbon dioxide capture and finding an alternative use for sodium metaborate. The products of this chemical absorption are sodium carbonate, sodium bicarbonate, and boric acid; all of which are industrially important chemicals. In this study, the kinetics of the reaction between sodium metaborate and carbon dioxide was investigated at atmospheric pressure and temperatures between 17 and 50°C while initial sodium metaborate concentration was changed as 0.5, 1, and 2.5 wt%. The frequency factor and activation energy for this reaction were found as 1.97 × 10⁻³ m³/mol‐s and 18,062 J/mol, respectively.     

Investigation of the reaction mechanism and kinetics of production of anhydrous sodium metaborate (NaBO2) by a solid-state reaction

In this study, the solid-state reaction mechanism and kinetics were investigated for production of anhydrous sodium metaborate (NaBO₂), an industrially and technologically important boron compound. To assess the kinetics of solid-state production of NaBO₂, the chemical reaction between borax (Na₂B₄O₇) and sodium hydroxide (NaOH) was investigated by use of the thermal analysis techniques thermogravimetry (TG) and differential thermal analysis (DTA). DTA curves obtained under non-isothermal conditions at different heating rates (5, 10 and 20 °C/min), revealed five endothermic peaks corresponding to five solid-state reactions occurring at 70, 130, 295, 463, and 595 °C. The stages of the solid-state reaction used for production NaBO₂ were also analyzed by XRD, which showed that at 70 and 130 °C, Na₂B₄O₇ and NaOH particles contacted between the grains, and diffusion was initiated at the interface. However, there was not yet any observable formation of NaBO₂. Formation of NaBO₂ was initiated and sustained from 295 to 463 °C, and then completed at 595 °C; the product was anhydrous NaBO₂. Activation energies (E _a) of the solid-state reactions were calculated from the weight loss based on the Arrhenius model; it was found that in the initial stages of the solid-state reaction E _a values were lower than in the last three steps.     

Nucleophilic and electrophilic promotion of ligand substitution reactions in oxo‐bridged,dinuclear chromium(III) complexes

Base hydrolysis reactions of [Cr(tmpa)(NCSe)]₂O²⁺, [Cr(tmpa)(N₃)]₂O²⁺, [Cr₂(tmpa)₂(μ−O)(μ−PhPO₄)]⁴⁺ and [Cr₂(tmpa)₂(μ−O)(μ−CO₃)]²⁺ follow the pseudo‐first‐order relationship (excess OH⁻): k_obsd=k_o+k_bQ_p[OH⁻]/(1+Q_p[OH⁻]). For the CO₃²⁻ complex, k_b(60°C)=(1.50±0.03)×10⁻² s⁻¹; ΔH‡=61±2 kJ/mol, ΔS‡=−99±7 J/mol K; Q_p(60°C)=(3.8±0.3)×10¹ M⁻¹; ΔH°=67±2 kJ/mol, ΔS°=230±7 J/mol K (I=1.0 M). An isokinetic relationship among k_OH(=k_bQ_p) activation parameters for five (tmpa)CrOCr(tmpa) complexes shows that all follow essentially the same pathway. Activated complex formation is thought to require nucleophilic attack of coordinated OH⁻ at the chromium‐leaving group bond in the k_b step, accompanied by reattachment of a tmpa pyridyl arm displaced by OH⁻ in the Q_p preequilibrium. Abstraction of both thiocyanate ligands was observed upon mixing [Cr(tmpa)(NCS)]₂O²⁺ with [Pd(CH₃CN)₄]²⁺ in CH₃CN solution. The proposed mechanism requires rapid complexation of both reactant thiocyanate ligands by Pd(II) (K_p(25°C)=(4.5±0.2)×10⁸ M⁻²; ΔH°=−32±6 kJ/mol, ΔS°=59±19 J/mol K) prior to rate‐limiting Cr NCS bond‐breaking (k₂(25°C)=(1.17±0.02)×10⁻³ s⁻¹; ΔH‡=98±2 kJ/mol, ΔS‡=27±5 J/mol K). Pd(II)‐assisted NCS⁻ abstraction is not driven by weakening of the Cr( )NCS⁻ bond through ligation of the sulfur atom to palladium, but rather by a favorable ΔS‡ resulting from the release of Pd(NCS)⁺ fragments and weak solvation of the activated complex in CH₃CN solution. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 351–356, 1999     

Desorption behavior of a surfactant in a linear low‐density polyethylene blend at elevated temperatures

The desorption behavior of a surfactant in a linear low‐density polyethylene (LLDPE) blend at elevated temperatures of 50, 70, and 80 °C was studied with Fourier transform infrared spectroscopy. The composition of the LLDPE blend was 70:30 LLDPE/low‐density polyethylene. Three different specimens (II, III, and IV) were prepared with various compositions of a small molecular penetrant, sorbitan palmitate (SPAN‐40), and a migration controller, poly(ethylene acrylic acid) (EAA), in the LLDPE blend. The calculated diffusion coefficient (D) of SPAN‐40 in specimens II, III, and IV, between 50 and 80 °C, varied from 1.74 × 10^?11 to 6.79 × 10^?11 cm²/s, from 1.10 × 10^?11 to 5.75 × 10^?11 cm²/s, and from 0.58 × 10^?11 to 4.75 × 10^?11 cm²/s, respectively. In addition, the calculated activation energies (E_D) of specimens II, III, and IV, from the plotting of ln D versus 1/T between 50 and 80 °C, were 42.9, 52.7, and 65.6 kJ/mol, respectively. These values were different from those obtained between 25 and 50 °C and were believed to have been influenced by the interference of Tinuvin (a UV stabilizer) at elevated temperatures higher than 50 °C. Although the desorption rate of SPAN‐40 increased with the temperature and decreased with the EAA content, the observed spectral behavior did not depend on the temperature and time. For all specimens stored over 50 °C, the peak at 1739 cm^?1 decreased in a few days and subsequently increased with a peak shift toward 1730 cm^?1. This arose from the carbonyl stretching vibration of Tinuvin, possibly because of oxidation or degradation at elevated temperatures. In addition, the incorporation of EAA into the LLDPE blend suppressed the desorption rate of SPAN‐40 and retarded the appearance of the 1730 cm^?1 peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1114–1126, 2004     

NaCl-NaBO2-Na2CO3-NaMoO4 quaternary system

The NaCl-NaBO₂-Na₂CO₃-Na₂MoO₄ quaternary system was studied by a calculation-experimental method and differential thermal analysis. The coordinates of one ternary eutectic and two quaternary eutectics were determined: E ₇: 572°C, 29 mol % NaCl, 10 mol % NaBO₂, 32 mol % Na₂CO₃, and 29 mol % Na₂MoO₄; ɛ₁: 562°C, 36 mol % NaCl, 10 mol % NaBO₂, 30.5 mol % Na₂CO₃, and 23.5 mol % Na₂MoO₄; and ɛ₂: 536°C, 17 mol % NaCl, 10 mol % NaBO₂, 27 mol % Na₂CO₃, and 46 mol % Na₂MoO₄.     

CO oxidation with oxygen of the catalyst and gas-phase oxygen over (0.5−15)%СоО/СеО<Subscript>2</Subscript>

The CO adsorption species on Co₃O₄ and (0.5-15%)CoO/CeO₂ catalysts have been investigated by temperature-programmed desorption and IR spectroscopy. At 20°C, the largest amount of CO is adsorbed on the 5%CoO/CeO₂ sample to form, on Co_m²⁺O_n²⁺ clusters, hydrogen-containing, bidentate, and monodentate carbonate complexes, whose decomposition is accompanied by CO₂ desorption at 300 and 450°C (1.1 × 10²⁰ g^–1). The formation of the carbonates is accompanied by the formation of Co⁺ cations and Co⁰, on which carbonyls form. The latter decompose at 20, 90, and 170°C to release CO (2.7 × 10¹⁹ g^–1). Part of the carbonyls oxidizes to CO₂ upon oxygen adsorption, and the CO₂ undergoes desorption at 20°C. Adsorbed oxygen decreases the decomposition temperature of the H-containing and bidentate carbonates from 300 to 100-170°C and maintains the sample in the oxidized state, which is active in subsequent CO adsorption and oxidation. CO oxidation by oxygen of the catalyst diminishes the activity of the sample in these processes and increases the decomposition temperature of the carbonate complexes. Taking into account the properties of the adsorption complexes, we concluded that the H-containing and bidentate carbonates are involved in CO oxidation by oxygen of the catalyst at ~170°C under isothermal conditions. The rate limiting step is the decomposition of the carbonates, a process whose activation energy is 65-74 kJ/mol.     

Ternary reciprocal systems Na,K||BO<Subscript>2</Subscript>,CO<Subscript>3</Subscript> and Na,K||BO<Subscript>2</Subscript>,Cl

The phase diagrams of the ternary reciprocal systems Na,K||BO₂,CO₃ and Na,K||BO₂,Cl were studied for the first time by a calculation-experimental method and by differential thermal analysis. Analytical models of phase equilibrium states were derived, and the coordinates of eutectics were found to be (680°C, 32 mol % NaBO₂, 68 mol % KCl) and (648°C, 9 mol % NaBO₂, 45.5 mol % NaCl, 45.5 mol % KCl). Binary solid solutions based on metaborates and carbonates of sodium and potassium were shown to be stable. The possibility of synthesizing tungsten oxide bronzes in a eutectic melt in the ternary system NaBO₂–NaCl–КCl was revealed.     

Isothermal and nonisothermal crystallization kinetics of nylon‐46

Isothermal and nonisothermal crystallization kinetics of nylon‐46 were investigated with differential scanning calorimetry. The equilibrium melting enthalpy and the equilibrium melting temperature of nylon‐46 were determined to be 155.58 J/g and 307.10 °C, respectively. The isothermal crystallization process was described by the Avrami equation. The lateral surface free energy and the end surface free energy of nylon‐46 were calculated to be 8.28 and 138.54 erg/cm², respectively. The work of chain folding was determined to be 7.12 kcal/mol. The activation energies were determined to be 568.25 and 337.80 kJ/mol for isothermal and nonisothermal crystallization, respectively. A convenient method was applied to describe the nonisothermal crystallization kinetics of nylon‐46 by a combination of the Avrami and Ozawa equations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1784–1793, 2002     

Vinylic polymerization of norbornene by neutral nickel(II)‐based catalysts

Neutral Ni(II) salicylaldiminato complexes activated with modified methylaluminoxane as catalysts were used for the vinylic polymerization of norbornene. Catalyst activities of up to 7.08 × 10⁴ kg_pol/(mol_Ni · h) and viscosity‐average molecular weights of polymer up to 1.5 × 10⁶ g/mol were observed at optimum conditions. Polynorbornenes are amorphous, soluble in organic solvents, highly stable, and show glass‐transition temperatures around 390 °C. Catalyst activity, polymer yield, and polymer molecular weight can be controlled over a wide range by the variation of the reaction parameters such as the Al/Ni ratio, monomer/catalyst ratio, monomer concentration, polymerization reaction temperature, and time. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2680–2685, 2002     

The kinetics and mechanism of polymer-based NHC-Pd-pyridine catalyzed heterogeneous Suzuki reaction in aqueous media

One of the most important challenges of the Suzuki reaction is a green synthesis of reaction products. In terms of economy and ecology, the Suzuki reaction details must be characterized for the industrial-scale Suzuki reaction processes. In this paper, for the first time, a kinetic and mechanistic study on the Suzuki reaction catalyzed with hydrogel-supported PEPPSI (pyridine-enhanced precatalyst preparation stabilization (and) initiation) type NHC-Pd-pyridine composite has been investigated. To determine the rate-limiting step, the effects of reactants and experimental conditions on the heterogeneous Suzuki reaction have been experimentally defined. The experimental results demonstrated that it is possible to reach 100% yield under the optimum reaction conditions, which were found as 75 × 10⁻³ mol/L of phenylboronic acid (FBA), 50 × 10⁻³ mol/L of bromoacetophenone (Brac), 125 × 10⁻³ mol/L of K₂CO₃, 1 g/L of catalyst, 80°C of reaction temperature, 400 rpm of mixing rate, and 3 h of reaction time. The transmetalation step in the cycle was defined as the rate-limiting step. On the basis of kinetic results, a mathematical reaction rate expression was presented assuming the steady-state approach to steps of the catalytic cycle. The activation energy (E_a) of the reaction was estimated to be 34.88 kJ/mol.     

Solid electrolytes with cesium cation conductivity in the Ga<Subscript>2</Subscript>O<Subscript>3</Subscript>-TiO<Subscript>2</Subscript>-Cs<Subscript>2</Subscript>O system

Solid solutions based on cesium monogallate CsGaO₂ are synthesized in the Ga₂O₃-TiO₂-Cs₂O system. Their crystalline structure and also temperature and concentration conductivity dependences are studied. The cesium cation character of conductivity is confirmed. The most conducting samples contain an excess of cesium oxide and have the structure of high-temperature γ-modification of KAlO₂. Their specific conductivity is (5.0–6.7) × 10^?3 S cm^?1 at 400 °C, (2.5–5.0) × 10^?2 S cm^?1 at 700°C at the activation energy of 33–35 kJ/mol^?1.     

Controlled Synthesis of a Vacancy‐Defect Single‐Atom Catalyst for Boosting CO2 Electroreduction

The reaction of precursors containing both nitrogen and oxygen atoms with Ni^II under 500 °C can generate a N/O mixing coordinated Ni‐N₃O single‐atom catalyst (SAC) in which the oxygen atom can be gradually removed under high temperature due to the weaker Ni?O interaction, resulting in a vacancy‐defect Ni‐N₃‐V SAC at Ni site under 800 °C. For the reaction of Ni^II with the precursor simply containing nitrogen atoms, only a no‐vacancy‐defect Ni‐N₄ SAC was obtained. Experimental and DFT calculations reveal that the presence of a vacancy‐defect in Ni‐N₃‐V SAC can dramatically boost the electrocatalytic activity for CO₂ reduction, with extremely high CO₂ reduction current density of 65 mA cm^?2 and high Faradaic efficiency over 90 % at ?0.9 V vs. RHE, as well as a record high turnover frequency of 1.35×10⁵ h^?1, much higher than those of Ni‐N₄ SAC, and being one of the best reported electrocatalysts for CO₂‐to‐CO conversion to date.     

Controlled radical polymerization of styrene mediated by the C‐phenyl‐N‐tert‐butylnitrone/AIBN pair: Kinetics and electron spin resonance analysis

Kinetics of the free radical polymerization of styrene at 110 °C has been investigated in the presence of C‐phenyl‐N‐tert‐butylnitrone (PBN) and 2,2′‐azobis(isobutyronitrile) (AIBN) after prereaction in toluene at 85 °C. The effect of the prereaction time and the PBN/AIBN molar ratio on the in situ formation of nitroxides and alkoxyamines (at 85 °C), and ultimately on the control of the styrene polymerization at 110 °C, has been investigated. As a rule, the styrene radical polymerization is controlled, and the mechanism is one of the classical nitroxide‐mediated polymerization. Only one type of nitroxide (low‐molecular‐mass nitroxide) is formed whatever the prereaction conditions at 85 °C, and the equilibrium constant (K) between active and dormant species is 8.7 × 10^?10 mol L^?1 at 110 °C. At this temperature, the dissociation rate constant (k_d) is 3.7 × 10^?3 s^?1, the recombination rate constant (k_c) is 4.3 × 10⁶ L mol^?1 s^?1, whereas the activation energy (E_a,diss.), for the dissociation of the alkoxyamine at the chain‐end is ～125 kJ mol^?1. Importantly, the propagation rate at 110 °C, which does not change significantly with the prereaction time and the PBN/AIBN molar ratio at 85 °C, is higher than that for the thermal polymerization at 110 °C. This propagation rate directly depends on the equilibrium constant K and on the alkoxyamine and nitroxide concentrations, as well. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1219–1235, 2007     

Efficient Ni-based catalysts for low-temperature reverse water-gas shift (RWGS) reaction

CO₂ hydrogenation for syngas can alleviate the pressure of un-controlled emissions of CO₂ and bring enormous economic benefits. Advantageous Ni-catalysts have good CO₂ hydrogenation activity and high CO selectivity merely over 700 °C. Herein, we introduced Cu into Ni catalysts, which were evaluated by H₂-TPR, XRD, BET, in-situ XPS and CO₂-TPD, and their CO₂ hydrogenation activity and CO selectivity were significantly affected by the Ni/Cu ratios, which was rationalized by the synergistic effect of bimetallic catalysts. In addition, the reduction temperatures of studied catalysts apparently affected the CO₂ hydrogenation, which were caused by the number and dispersion of the active species. It's found that the Ni₁Cu₁-400 had good stability, high CO selectivity (up to 90%), and fast formation rate (1.81×10⁻⁵ mol/g_cat/s) at 400 °C, which demonstrated a good potential as a superior catalyst for reverse water-gas shift (RWGS) reaction.     

Kinetics of low temperature CO oxidation over Pt/SnO2 catalyst

In a CO−O₂ stoichiometric mixture, the kinetic parameters, reaction order, rate constant and activation energy of CO oxidation over a Pt/SnO₂ catalyst have been measured using a fixed bed flow reactor near 0°C. The results show that it is a first-order reaction. The activation energy of CO oxidation over Pt/SnO₂ prepared with SnO₂ calcined at 300°C was approximately 21 kJ/mol. The activation energy of CO oxidation over Pt/SnO₂ changed slowly with SnO₂ calcination temperature above 400°C, and reached approximately 45 kJ/mol.     

Polymerized ionic liquids: Effects of counter‐anions on ion conduction and polymerization kinetics

A novel imidazolium‐containing monomer, 1‐[ω‐methacryloyloxydecyl]‐3‐(n‐butyl)‐imidazolium (1BDIMA), was synthesized and polymerized using free radical and controlled free radical polymerization followed by post‐polymerization ion exchange with bromide (Br), tetrafluoroborate (BF₄), hexafluorophosphate (PF₆), or bis(trifluoromethylsulfonyl)imide (Tf₂N). The thermal properties and ionic conductivity of the polymers showed a strong dependence on the counter‐ions and had glass transition temperatures (T_g) and ion conductivities at room temperature ranging from 10 °C to −42 °C and 2.09 × 10⁻⁷ S cm⁻¹ to 2.45 × 10⁻⁵ S cm⁻¹. In particular, PILs with Tf₂N counter‐ions showed excellent ion conductivity of 2.45 × 10⁻⁵ S cm⁻¹ at room temperature without additional ionic liquids (ILs) being added to the system, making them suitable for further study as electro‐responsive materials. In addition to the counter‐ions, solvent was found to have a significant effect on the reversible addition‐fragmentation chain‐transfer polymerization (RAFT) for 1BDIMA with different counter‐ions. For example, 1BDIMATf₂N would not polymerize in acetonitrile (MeCN) at 65 °C and only achieved low monomer conversion (< 5%) at 75 °C. However, 1BDIMA‐Tf₂N proceeded to high conversion in dimethylformamide (DMF) at 65 °C and 1BDIMABr polymerized significantly faster in DMF compared to MeCN. NMR diffusometry was used to investigate the kinetic differences by probing the diffusion coefficients for each monomer and counter‐ion in MeCN and DMF. These results indicate that the reaction rates are not diffusion limited, and point to a need for deeper understanding of the role electrostatics plays in the kinetics of free radical polymerizations. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1346–1357     

A consistent model for the thermal decomposition of NCN3 and the singlet– triplet relaxation of NCN

The thermal decomposition of cyanogen azide (NCN₃) and the subsequent collision‐induced intersystem crossing (CIISC) process of cyanonitrene (NCN) have been investigated by monitoring excited electronic state ¹NCN and ground state ³NCN radicals. NCN was generated by the pyrolysis of NCN₃ behind shock waves and by the photolysis of NCN₃ at room temperature. Falloff rate constants of the thermal unimolecular decomposition of NCN₃ in argon have been extracted from ¹NCN concentration–time profiles in the temperature range 617 K <T< 927 K and at two different total densities: k(ρ ≈ 3 × 10^?6 mol/cm³)/s^?1=4.9 × 10⁹ × exp (?71±14 kJ mol^?1/RT) (± 30%); k(ρ ≈ 6 × 10^?6 mol/cm³)/s^?1=7.5 × 10⁹ × exp (‐71±14 kJ mol^?1/RT) (± 30%). In addition, high‐temperature ¹NCN absorption cross sections have been determined in the temperature range 618 K <T< 1231 K and can be expressed by σ /(cm²/mol)= 1.0 × 10⁸ ?6.3 × 10⁴ K^?1 × T (± 50%). Rate constants for the CIISC process have been measured by monitoring ³NCN in the temperature range 701 K <T< 1256 K resulting in k_CIISC (ρ ≈ 1.8 ×10^?6 mol/cm³)/ s^?1=2.6 × 10⁶× exp (‐36±10 kJ mol^?1/RT) (± 20%), k_CIISC (ρ ≈ 3.5×10^?6 mol/cm³)/ s^?1 = 2.0 × 10⁶ × exp (?31±10 kJ mol^?1/RT) (± 20%), k_CIISC (ρ ≈ 7.0×10^?6 mol/cm³)/ s^?1=1.4 × 10⁶ × exp (?25±10 kJ mol^?1/RT) (± 20%). These values are in good agreement with CIISC rate constants extracted from corresponding ¹NCN measurements. The observed nonlinear pressure dependences reveal a pressure saturation effect of the CIISC process. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 30–40, 2013     

Thermochemical Properties and Decomposition Kinetics of Ammonium Magnesium Phosphate Monohydrate

Ammonium magnesium phosphate monohydrate NH4MgPO4·H2O was prepared via solid state reaction at room temperature and characterized by XRD, FT-IR and SEM. Thermochemical study was performed by an isoperibol solution calorimeter, non-isothermal measurement was used in a multivariate non-linear regression analysis to determine the kinetic reaction parameters. The results show that the molar enthalpy of reaction above is （28.795 ± 0.182） kJ/mol （298.15 K）, and the standard molar enthalpy of formation of the title complex is （-2185.43 ± 13.80） kJ/mol （298.15 K）. Kinetics analysis shows that the second decomposition of NH4MgPO4·H2O acts as a double-step reaction： an nth-order reaction （Fn） with n=4.28, E1=147.35 kJ/mol, A1=3.63×10^13 s^-1 is followed by a second-order reaction （F2） with E2=212.71 kJ/mol, A2= 1.82 × 10^18 s^-1.     

Interaction of salts in ionic melts of the ternary reciprocal systems Na,K‖BO2,MoO4 and Na,K‖BO2,WO4

The phase diagrams of the ternary reciprocal systems Na,K‖BO₂,MoO₄ and Na,K‖BO₂,WO₄ were studied for the first time by a calculation-experimental method and differential thermal analysis. The coordinates were determined for binary eutectics of the diagonal stable sections NaBO₂-K₂MoO₄(K₂WO₄) and the ternary invariant points e(55 mol % NaBO₂, 45 mol % K₂MoO₄, 740°C), e(55 mol % NaBO₂, 45 mol % K₂WO₄, 730°C), E(4.5 mol % NaBO₂, 78 mol % Na₂MoO₄, 17.5 mol % K₂MoO₄, 652°C), E(4.5 mol % NaBO₂, 78 mol % Na₂WO₄, 17.5 mol % K₂WO₄, 643°C), P₂(5 mol % NaBO₂, 56 mol % Na₂MoO₄, 39 mol % K₂MoO₄, 673°C), P₂(5 mol % NaBO₂, 56 mol % Na₂WO₄, 39 mol % K₂WO₄, 671°C). Binary solid solutions based on sodium and potassium metaborates were shown to be stable. Analytical models of phase equilibrium states of the ternary reciprocal systems Na,K‖BO₂,MoO₄(WO₄) were obtained, which enable one to calculate melting (crystallization) points and construct isotherms at any given composition. The specific heats of melting of samples of invariant compositions were found by quantitative differential thermal analysis.