This paper evaluates crystallographic data and thermodynamic properties for sodium chromate, potassium chromate, sodium molybdate, potassium molybdate (K2MoO4), sodium tungstate, and potassium tungstate collected from the literature. A thorough literature review was carried out to obtain a good understanding of the available data, and a critical evaluation has been performed from room temperature to above the melting temperatures. Also, the solid–solid transition and melting properties of the six pure salts were measured by differential scanning calorimetry, and high-temperature x-ray powder diffraction measurements were performed to determine the crystal structures and space groups associated with the phases of K2MoO4. This work is the first step towards the development of a thermodynamic model for the Na+, K+//Cl, SO42−, CO32−, CrO42−, Cr2O72−, MoO42−, Mo2O72−, WO42−, W2O72−, O2− system that is relevant for high temperature corrosion in atmospheres containing O–H–S–C–Cl and alkali salts.

Combustion installations suffer from the problem of hot corrosion, which limits their efficiency.1–4 This phenomenon is an accelerated form of oxidation (from 600 to 950 °C)5,6 affecting equipment in the presence of high-temperature combustion gases (N2, CO2, CO, O2, H2O, etc.) containing impurities (SO2, Cl2, S2, HCl, etc.) and corrosive products (Na2O, K2O, NaOH, KOH, NaCl, KCl, etc.).3,4,7 The formation of ashes and corrosive gases is mainly due to the elements K, Na, Ca, Mg, Fe, Al, Si, P, S, Cl, C, H, and O.8,9 Stainless steels containing the alloying elements Ni, Cr, Mo, W, and V are particularly prone to this problem.2,4,10–12 They are frequently exposed to gaseous species generated during combustion (O2, CO2, SO2, H2O) or from the evaporation of ashes (KCl, NaCl, Na2SO4, K2SO4, Na2CO3, K2CO3).3,4,6,13

Oxides formed from these alloying elements, such as Cr2O3,10,14 MoO3, WO3, and V2O5,1,10,12 often react with the KCl, NaCl, Na2SO4, K2SO4, Na2CO3, and K2CO3 present during the operating conditions of these installations and/or originating from the fuel used. Those along with the quantity of air required for combustion contribute to the oxidation of the alloying elements. The literature reports that, under operating conditions, corrosive deposits in the form of Na2CrO4 and K2CrO414,15 may be formed on the walls of installations. Other salts can further enhance the corrosion, particularly sodium molybdate (Na2MoO4),15,16 potassium molybdate (K2MoO4), sodium tungstate (Na2WO4),15,17 and potassium tungstate (K2WO4). These may be present in solid or liquid form.

Studies by Misra and Stearns11 and Fryberg et al.16 revealed the complete conversion of Na2SO4 to Na2CrO4 before the onset of catastrophic corrosion for Mo-containing superalloys. Initiation of catastrophic corrosion was characterized by the conversion of Na2CrO4 to Na2MoO4 observed in the MoO3-rich layer at the scale-metal interface, related to fluxing by the Na2MoO4–MoO3 mixture.

Catastrophic corrosion is attributable to the formation of Na2MoO4 and a Na2MoO4–MoO3 mixture, but its mechanisms are still unclear. The presence of sodium in the MoO3–WO3 zones reduces the melting temperature by forming Na2MoO4–Na2WO4.16 Furthermore, Bourhis and Saint-John18 reported catastrophic corrosion in Mo-containing superalloys related to fluxing by MoO3, which forms at the scale-metal interface.

In this context, predicting potential corrosion products to ensure the preservation of equipment while maximizing the rate of conversion into electrical energy is extremely important. Indeed, the various deposits, rich in salts, are generally very corrosive and, when present in liquid form, often dissolve the protective oxide layers and attack the metal surface.19 

A thermodynamic model for the Na+, K+//Cl, SO42−, CO32−, CrO42−, Cr2O72−, MoO42−, Mo2O72−, WO42−, W2O72−, O2− system is being developed. This will permit us to make phase equilibrium calculations, and thus assess the limiting conditions under which deposits are susceptible to form and then prevent their formation. As a first step, it is necessary to investigate the crystal structures and thermodynamic properties (including solid–solid transitions and fusion) of all relevant pure salts. The present article is devoted to a thorough literature review for the sodium and potassium chromates, molybdates, and tungstates. The sodium and potassium dichromates, dimolybdates and ditungstates will be discussed in a subsequent paper. For the six compounds considered in this work, literature data are sometimes lacking or contradictory. Therefore, differential scanning calorimetry (DSC) was used to measure the temperature and enthalpy change for the solid–solid transitions and fusion of the various compounds investigated. In addition, high temperature x-ray diffraction (XRD) measurements were conducted for K2MoO4.

2.1.1. Materials and measurements

The initial reagents used in this study were 99.999% pure Ar (gas) from Oy Linde Gas AB (Finland), Na2CrO4 · 4H2O, K2CrO4, Na2MoO4, K2MoO4, Na2WO4 · 2H2O, and K2WO4. The following Table presents the supplier’s name, Chemical Abstracts Service (CAS) number, and purity for each solid reagent.

Chemical formula Supplier CAS number Purity (%)
Na2CrO4 · 4H2 Sigma-Aldrich  10034-82-9  99.0 
K2CrO4  Alfa-Aesar  7789-00-6  99.9 
Na2MoO4  Sigma-Aldrich  7631-95-0  99.9 
K2MoO4  Sigma-Aldrich  13446-49-6  98 
Na2WO4 · 2H2 Sigma-Aldrich  10213-10-2  99.995 
K2WO4  Alfa-Aesar  7790-60-5  99.5 
Chemical formula Supplier CAS number Purity (%)
Na2CrO4 · 4H2 Sigma-Aldrich  10034-82-9  99.0 
K2CrO4  Alfa-Aesar  7789-00-6  99.9 
Na2MoO4  Sigma-Aldrich  7631-95-0  99.9 
K2MoO4  Sigma-Aldrich  13446-49-6  98 
Na2WO4 · 2H2 Sigma-Aldrich  10213-10-2  99.995 
K2WO4  Alfa-Aesar  7790-60-5  99.5 

DSC/TGA experiments were conducted to measure the temperature and enthalpy change for the solid–solid transitions and fusion of the pure compounds Na2CrO4, K2CrO4, Na2MoO4, K2MoO4, Na2WO4, and K2WO4. These measurements were performed using a NETZSCH STA 449 F1 Jupiter® simultaneous DSC-TGA equipment.

The calibration of the DSC apparatus was performed using the known enthalpy changes and transition temperatures of the following reference substances (ultra-pure salts):
BaC O 3 ( purity of  99.98 % )  with  T trs ( I II ) = 808 ° C;
CsCl ( purity of  99.99 % )  with  T trs ( I II ) = 476 ° C;
A g 2 S O 4 ( purity of  99.999 % )  with  T trs ( I II ) = 426 ° C;
and
C 6 H 5 COOH  ( purity of  99.5 % )  with  T trs ( sol L ) = 122 ° C.

Variations recorded during the calibration measurements were used to estimate the experimental error for the temperatures and enthalpy changes as ±1 °C and ±10% minimum, respectively.

A dehydration treatment of all pure compounds was performed prior to the DSC measurements. This operation was performed in a Vulcan oven temperature (Model: 3-130) to eliminate water absorbed by the samples during their storage, and also most of the water present in the initial reagents Na2CrO4 · 4H2O and Na2WO4 · 2H2O. All reagents were heated for 3 h at 200 °C and then cooled to 25 °C.

About 45 mg of the dehydrated samples were added in a Pt/Rh (80/20) crucible, and a flow rate of 70 ml/min of Ar was used as a protective gas in all runs.

Initial heating was performed from room temperature to 40 °C, followed by a 10 min isothermal hold to ensure thermal stability of the sample and reference. Three consecutive heating–cooling cycles were then conducted for each sample, with a heating/cooling rate of 10 °C/min.

The maximum temperature investigated was always 49 °C above the predetermined melting temperature of each compound while the minimum temperature investigated was at least 50 °C below the temperature of the first solid–solid transition, with a holding time of 1 min in each case. The maximum temperature selected was low enough to avoid vaporization of the compound, but high enough to ensure complete fusion.

Thermogravimetric analysis (TGA) was conducted to monitor mass loss or volatilization. Mass loss and heat flux were both measured continuously throughout the DSC experiments. A maximum mass loss of −3% was always targeted during the experiments. For each pure compound, the overall mass loss was monitored at the end of each DSC experiment: −1.08% for Na2CrO4, −1.01% for K2CrO4, −0.12% for Na2MoO4, −0.1% for K2MoO4, −0.02% for Na2WO4, and −0.63% for K2WO4.

Each solid–solid transition and melting temperature was defined as the temperature at the onset of the peak. The first heating/cooling cycle was always discarded owing to non-reproducible data (i.e., thermal history of the sample).

2.1.2. Setting up the baseline

The first requirement is to establish a baseline before making the actual measurement for a sample. This can be obtained from the signal recorded during a temperature cycle applied to two empty crucibles.

The difference between the baseline and the signal obtained, under the same experimental conditions (i.e., nature of crucibles, temperature profile, heating/cooling rate, and flow rate of gas), depends on the material whose thermal behavior is to be studied. It is essential to have a suitable baseline for each analysis program. Pt/Rh (80/20) crucibles with the same mass were used for the baseline (blank run), the sapphire holder, and the sample holder in all DSC-TGA experiments.

XRD patterns for K2MoO4 were determined using a 98% purity commercial sample in powder form purchased from Sigma-Aldrich, Germany.

The powder was ground in an agate mortar to ∼50 µm particle size to ensure cohesion and then spread evenly on a flat sample holder. The used XRD device was X’Pert Pro MPD Powder model (by Malvern Panalytical), which was connected to a high-temperature chamber Anton Paar HTK 1200N and temperature controller TCU1000N. This setup enabled autonomous temperature control and diffraction measurements. Tube gave CuKα radiation and was set at 40 kV and 40 mA.

The sample holder was equipped with an alumina ring as the sample crucible and Pt–10%Rh thermocouple (type-S) to provide good correspondence between actual and set temperatures. Measurements were carried out at 25, 350, 465, and 500 °C, with a heating rate of 10 °C/min between set points. After the measurement at 500 °C, the sample was cooled to 25 °C and the measurement was repeated at this temperature to confirm the stability of the sample. Measurements were done in a normal air atmosphere and using a secondary monochromator. Measurement angles were from 10° to 70° for a total duration of 1 h per temperature point. The sample was held at a temperature set point for 1 h before being scanned so that it had time to react or change morphology.

A critical review of the literature related to the crystal structures and space groups of the six pure compounds is provided in this section.

Crystal structure information for phases of Na2CrO4 and K2CrO4 is summarized in Tables 1 and 2, respectively.

TABLE 1.

Crystallographic data for phases of Na2CrO4

Phase Crystal structure T (°C) Space group Reference
Na2CrO4(I)  Orthorhombic  <419  D 2 h 6 -Pbnn  20  
Cmcm  21  
22  
23  
24  
25  
Na2CrO4(II)  Hexagonal  419–793  P63mc  23  
P63/mmc  26  
Phase Crystal structure T (°C) Space group Reference
Na2CrO4(I)  Orthorhombic  <419  D 2 h 6 -Pbnn  20  
Cmcm  21  
22  
23  
24  
25  
Na2CrO4(II)  Hexagonal  419–793  P63mc  23  
P63/mmc  26  
TABLE 2.

Crystallographic data for phases of K2CrO4

Phase Crystal structure T (°C) Space group Reference
K2CrO4(I)  Orthorhombic  <669  Pcmn  23  
Pnam  27  
⋯  28  
K2CrO4(II)  Hexagonal  669–976  P63mc  23  
P6/mmc, P6mc, P 6 ̄ 2c, P 3 ̄ 1 ̄ c, P31c  27  
Phase Crystal structure T (°C) Space group Reference
K2CrO4(I)  Orthorhombic  <669  Pcmn  23  
Pnam  27  
⋯  28  
K2CrO4(II)  Hexagonal  669–976  P63mc  23  
P6/mmc, P6mc, P 6 ̄ 2c, P 3 ̄ 1 ̄ c, P31c  27  

Miller’s20 visual estimation in single-crystal x-ray oscillation intensities showed that Na2CrO4(I) (low-temperature phase) is orthorhombic with D 2 h 6 -Pbnn space group. This study was subsequently reviewed by Fischmeister,21 Niggli,22 Goldberg et al.,23 Nimmo,24 and Amirthalingam and Venkateswarlu25 who confirmed a different space group, Cmcm.

The crystal structure of K2CrO4(I) at room temperature has been investigated by XRD.23,26,27 An orthorhombic structure has been reported with space group Pnam26,27 or Pcmn.23 

The high-temperature phases Na2CrO4(II) and K2CrO4(II) exhibit hexagonal structures. The analysis of high-temperature XRD diffractograms of A2BX4-type compounds suggests the space group P63mc for both phases with the presence of c-glide;29 the two structures are isostructural with that of α-Ca2SiO4.23 For Na2CrO4(II), Ferrante et al.26 reported the space group P6/mmc. The XRD analysis of Pistorius27 suggested that K2CrO4(II) has the same space group as K2SO4: P6/mmc, P6mc, P 6 ̄ 2c, P 3 ̄ 1 ̄ c, or P31c.

Crystal structure information for phases of Na2MoO4 is summarized in Table 3.

TABLE 3.

Crystallographic data for phases of Na2MoO4

Phase Crystal structure T (°C) Space group Reference
Na2MoO4(I)  Cubic  <458  ⋯  30  
Fd3m  31  
⋯  32  
Fd 3 ̄ 33  
34  
35  
Na2MoO4(II)  Orthorhombic  458–592  ⋯  32  
Pbn21  Reference 10 in Ref. 36  
Na2MoO4(III)  Orthorhombic  592–641  ⋯  32  
Fddd  Reference 10 in Ref. 36  
34  
Na2MoO4(IV)  Hexagonal  641–687  P63/mmc  Reference 10 in Ref. 36  
34  
⋯  32  
Phase Crystal structure T (°C) Space group Reference
Na2MoO4(I)  Cubic  <458  ⋯  30  
Fd3m  31  
⋯  32  
Fd 3 ̄ 33  
34  
35  
Na2MoO4(II)  Orthorhombic  458–592  ⋯  32  
Pbn21  Reference 10 in Ref. 36  
Na2MoO4(III)  Orthorhombic  592–641  ⋯  32  
Fddd  Reference 10 in Ref. 36  
34  
Na2MoO4(IV)  Hexagonal  641–687  P63/mmc  Reference 10 in Ref. 36  
34  
⋯  32  

The structure of the low-temperature phase (I) of Na2MoO4 is a spinel according to Lindqvist et al.,30 with cubic crystal structure.30–35 XRD revealed the Fd 3 ̄ m space group,34 and further studies by Raman spectroscopy33 and neutron powder diffraction35 yielded the same space group. Swanson31 reported the Fd3m space group. XRD patterns showed that the second phase (II) of Na2MoO4 is orthorhombic32,36 with space group Pbn21.36 The transition from II to III yielded the same crystal structure32,34,36 with the Fddd space group.34,36 The high-temperature phase IV is hexagonal32,34,36 with space group P63/mmc.34,36

Crystal structure information for phases of K2MoO4 is summarized in Table 4.

TABLE 4.

Crystallographic data for phases of K2MoO4

Phase Crystal structure T (°C) Space group Reference
K2MoO4(I)  Monoclinic  <324  C2/m  This work 
37  
38  
⋯  39  
C2/m  40  
K2MoO4(II)  Orthorhombic  324–455  Ccmm  This work 
⋯  39  
Ccmm  41  
K2MoO4(III)  Trigonal  455–928  P 3 ̄ m1  This work 
⋯  39  
P 3 ̄ m1  42  
Phase Crystal structure T (°C) Space group Reference
K2MoO4(I)  Monoclinic  <324  C2/m  This work 
37  
38  
⋯  39  
C2/m  40  
K2MoO4(II)  Orthorhombic  324–455  Ccmm  This work 
⋯  39  
Ccmm  41  
K2MoO4(III)  Trigonal  455–928  P 3 ̄ m1  This work 
⋯  39  
P 3 ̄ m1  42  

K2MoO4 exhibits three phases. The low-temperature form I is monoclinic. Our XRD analysis, the measurements of Ref. 37 (who performed three-dimensional Patterson and Fourier syntheses that were refined by least squares techniques) and those of Refs. 38–40 confirmed C2/m as the space group.

Our high-temperature XRD analysis showed that II is orthorhombic, in agreement with Refs. 40 and 41. The space group identified by us (Ccmm) agrees with that reported by Van Den Berg et al.41 

III has also been studied by us using high-temperature XRD up to 500 °C; analysis of the diffractogram indicated a trigonal structure. Van Den Akker et al.42 erroneously reported an hexagonal structure. According to our results, the space group is P 3 ̄ m1, in agreement with Van Den Akker et al.42 

According to Warczewski,39 the transition from the intermediate-temperature phase II to the high-temperature pseudohexagonal phase III involves two modulated intermediate structures (incommensurable), which are orthorhombic and pseudohexagonal, respectively. Based on these data, K2MoO4 exhibits four phases, and the high-temperature form (IV) is hexagonal. However, as will be explained later, this fourth phase was not observed in our high-temperature XRD analysis (at 465 and 500 °C). Therefore, only three phases were considered for K2MoO4 in the present work.

Crystal structure information for phases of Na2WO4 is summarized in Table 5.

TABLE 5.

Crystallographic data for phases of Na2WO4

Phase Crystal structure T (°C) Space group Reference
Na2WO4(I)  Cubic  <588  Fd3m  43  
Fd 3 ̄ 44  
33  
35  
45  
Na2WO4(II)  Tetragonal (tentative)  588–589  I41/amd (tentative)  45  
Na2WO4(III)  Orthorhombic  589–694  Pnam D 2 h 16   43  
Fddd  45  
Phase Crystal structure T (°C) Space group Reference
Na2WO4(I)  Cubic  <588  Fd3m  43  
Fd 3 ̄ 44  
33  
35  
45  
Na2WO4(II)  Tetragonal (tentative)  588–589  I41/amd (tentative)  45  
Na2WO4(III)  Orthorhombic  589–694  Pnam D 2 h 16   43  
Fddd  45  

There are some uncertainties in the literature regarding the number of phases for Na2WO4, as well as their crystal structures and space groups.33,36,43,46–48 XRD analyses conducted by Pistorius43 and Temperature-Programmed x-ray powder Diffraction (TPXRD) by Hämmer and Höppe45 suggested the presence of three phases. However, the XRD analyses performed by Pistorius43 have only identified with certainty two phases (I and III). For Na2WO4(II), the diffraction pattern was of rather poor quality.

XRD analysis,49 Raman spectroscopy33 and neutron diffraction35 confirmed that the low-temperature phase Na2WO4(I) is cubic with Fd 3 ̄ m space group. At room temperature, only Na2MoO4 and Na2WO4 exhibit an ordinary spinel structure among alkali metal sulfates, chromates, molybdates and tungstates.30,35 The work of Hämmer and Höppe45 was the only one able to characterize the phase II using TPXRD; Austin and Pierce47 had indicated that both solid–solid transitions were displaced and non-reconstructive. Therefore, obtaining single crystals of the high-temperature phases of Na2WO4 by quenching was impossible, as well as the use of Rietveld refinement and DSC. Based on TPXRD data, it is suggested that Na2WO4(II) has a tetragonal unit cell with lattice parameters a = 1707.2 pm, c = 1293.6 pm, and a space group consistent with symmetry relationships to Na2WO4(I), i.e., I41/amd.45 The latter is assumed to be a maximal subgroup of Fd 3 ̄ m and a direct supergroup of Fddd (space group of the phase III).45 Even with indexing and Pawley fitting (RBragg = 0.013, Rwp = 0.058), the structure of II was not reliably determined. Thus, Na2WO4(II) was assumed to crystallize in the I41/amd space group, with no symmetry relationship derivable between Na2WO4(I) and Na2WO4(III), and no proposed unit cell fitting into such a structure.45 Very limited high-temperature XRD studies have been conducted to identify the structure and space group of the phase III; Pistorius43 and Hämmer and Höppe45 reported an orthorhombic structure with different space groups (Pnam and Fddd, respectively).

Crystal structure information for phases of K2WO4 is summarized in Table 6.

TABLE 6.

Crystallographic data for phases of K2WO4

Phase Crystal structure T (°C) Space group Reference
K2WO4(I)  Monoclinic  <364  ⋯  50  
C2/m  42  
⋯  39  
K2WO4(II)  Orthorhombic (β-K2SO4 type)  364–458  ⋯  42  
K2WO4(III)  Trigonal  458–927  P 3 ̄ m1  42  
⋯  39  
Phase Crystal structure T (°C) Space group Reference
K2WO4(I)  Monoclinic  <364  ⋯  50  
C2/m  42  
⋯  39  
K2WO4(II)  Orthorhombic (β-K2SO4 type)  364–458  ⋯  42  
K2WO4(III)  Trigonal  458–927  P 3 ̄ m1  42  
⋯  39  

K2WO4 displays three phases. The crystal structure was studied at room temperature by Raman spectroscopy50 and XRD,39,42 and was found to be monoclinic with C2/m space group.42 The phase II was examined by XRD only by Van Den Akker et al.,42 who suggested a β-K2SO4 type structure. However, the structure has not been reliably identified, and these authors indicated that most potassium salt phases have an orthorhombic structure (β-K2SO4 type).

For the phase III, the XRD analyses of Warczewski39 and Van Den Akker et al.42 revealed a trigonal structure with P 3 ̄ m1 space group.42 Note that Refs. 39 and 42 incorrectly reported a hexagonal structure.

4.1.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transition (I → II) for Na2CrO4

To measure the temperature and enthalpy change for the solid–solid transition of Na2CrO4, DSC measurements were conducted in this work. In addition, data acquired by various experimental techniques were collected from the literature and are shown in Table 7.

TABLE 7.

Transition temperature and enthalpy change of solid–solid transition for Na2CrO4

Ttrs (I → II) (°C) Δ H t r s I II (kJ mol−1) Experimental method Reference
417.3  8.49a  DSC (second heating) at 10 °C/min  This work 
417.6  8.27a  DSC (third heating) at 10 °C/min  This work 
413a  ⋯  Cooling curves  51  
421 ± 4  ⋯  DTAb  52  
420  10.04  DTA  53  
420.9 ± 3  9.58 ± 0.42  Ice calorimetry, drop method  54  
419  8.87a  DTA  23  
427a  9.47  Calorimetry, drop method  26  
419.4  10.06 (cooling)  DSC at 10 °C/min  55  
9.60 (heating) 
419.1 ± 2.7  9.6 ± 0.6  Weighted average  This work 
Ttrs (I → II) (°C) Δ H t r s I II (kJ mol−1) Experimental method Reference
417.3  8.49a  DSC (second heating) at 10 °C/min  This work 
417.6  8.27a  DSC (third heating) at 10 °C/min  This work 
413a  ⋯  Cooling curves  51  
421 ± 4  ⋯  DTAb  52  
420  10.04  DTA  53  
420.9 ± 3  9.58 ± 0.42  Ice calorimetry, drop method  54  
419  8.87a  DTA  23  
427a  9.47  Calorimetry, drop method  26  
419.4  10.06 (cooling)  DSC at 10 °C/min  55  
9.60 (heating) 
419.1 ± 2.7  9.6 ± 0.6  Weighted average  This work 
a

Outlier.

b

The purity of salt is 99.5%.

4.1.2. Temperature (Tfus) and enthalpy of fusion (ΔHfus) for Na2CrO4

The thermodynamic properties of fusion (temperature and enthalpy change) were measured by Refs. 26, 51, 53, 54, and 5664. The heat of fusion was obtained by drop calorimetry26,54 and DTA.53 In this work, DSC measurements were conducted. As an example, the DSC thermogram (second and third heating/cooling cycles only) for Na2CrO4 is shown in Fig. 1. The DSC thermograms for all other compounds are presented in the supplementary material. All data collected from the literature and obtained in the present work are presented in Table 8.

FIG. 1.

DSC thermogram for Na2CrO4 (second and third heating/cooling cycles only). Blue: second heating, dark green: third heating, light green: second cooling, black: third cooling.

FIG. 1.

DSC thermogram for Na2CrO4 (second and third heating/cooling cycles only). Blue: second heating, dark green: third heating, light green: second cooling, black: third cooling.

Close modal
TABLE 8.

Transition temperature and enthalpy of fusion for Na2CrO4

Tfus (II → L) (°C) ΔHfus (II → L) (kJ mol−1) Experimental method Reference
783a  18.48a  DSC (second heating) at 10 °C/min  This work 
783.4a  19.60a  DSC (third heating) at 10 °C/min  This work 
792  ⋯  Cooling curves  51  
780a  ⋯  Pt/Pt–Rh thermocouple; visual  56  
794.5  ⋯  Cooling curves  57  
792  ⋯  Calibrated TC; recorder potentiometer  58  
791.9  ⋯  DTA  59  
793  ⋯  Pt/Pt–Rh thermocouple; visual  60  
796  25.15  DTA  53  
792.4 ± 1  ⋯  DTA; high-T microscopy  61  
794  ⋯  Visual-polythermal method  62  
796.9 ± 2  24.23 ± 0.42  Ice calorimetry, drop method  54  
792  24.31  Calorimetryb, drop method  26  
785.6a  ⋯  DTA  63  
795.1  ⋯  DTA  64  
793.3 ± 3.2  24.3 ± 0.9  Weighted average  This work 
Tfus (II → L) (°C) ΔHfus (II → L) (kJ mol−1) Experimental method Reference
783a  18.48a  DSC (second heating) at 10 °C/min  This work 
783.4a  19.60a  DSC (third heating) at 10 °C/min  This work 
792  ⋯  Cooling curves  51  
780a  ⋯  Pt/Pt–Rh thermocouple; visual  56  
794.5  ⋯  Cooling curves  57  
792  ⋯  Calibrated TC; recorder potentiometer  58  
791.9  ⋯  DTA  59  
793  ⋯  Pt/Pt–Rh thermocouple; visual  60  
796  25.15  DTA  53  
792.4 ± 1  ⋯  DTA; high-T microscopy  61  
794  ⋯  Visual-polythermal method  62  
796.9 ± 2  24.23 ± 0.42  Ice calorimetry, drop method  54  
792  24.31  Calorimetryb, drop method  26  
785.6a  ⋯  DTA  63  
795.1  ⋯  DTA  64  
793.3 ± 3.2  24.3 ± 0.9  Weighted average  This work 
a

Outlier.

b

The standard error is 0.07% for the determination, and the absolute uncertainty of the enthalpy is estimated to be ±0.3%.

4.1.3. Recommended thermodynamic data for sodium chromate Na2CrO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° , and CP) for sodium chromate (Na2CrO4) are provided in Table 9. For the pure liquid, below the temperature of fusion, the heat capacity (as a function of temperature) over a given temperature range was taken identical to that of the solid phase stable over this specific temperature range (i.e., CP of the low-temperature phase I between 298.15 and 692.3 K, and CP of the high-temperature phase II between 692.3 and 1066.4 K). Similarly, for solid II, below the temperature of the solid–solid transition, the heat capacity was taken identical to that of solid I. For all three phases, the heat capacity above the maximum temperature Tmax of the highest temperature range in Table 9 is assumed to be constant and equal to the value of CP at Tmax.

TABLE 9.

Selected thermodynamic properties of Na2CrO4

Phase T range (K) Δ f H 298 ° (kJ mol−1)a S 298 ° (J mol−1 K−1)b CP (J mol−1 K−1) Reference
Na2CrO4(I)  298.15  −1341.49      This work 
  176.62    26  
298.15–692.3      101.07 + 0.139 99T/K  54  
Na2CrO4(II)  298.15  −1331.86  190.52    This work 
298.15–692.3      101.07 + 0.139 99T/K  54  
692.3–1066.4      149.94 + 0.051 59T/K  54  
Na2CrO4(L)  298.15  −1307.53  213.34    This work 
298.15–692.3      101.07 + 0.139 99T/K  54  
692.3–1066.4      149.94 + 0.051 59T/K 
1066.4–2000      204.78 
Phase T range (K) Δ f H 298 ° (kJ mol−1)a S 298 ° (J mol−1 K−1)b CP (J mol−1 K−1) Reference
Na2CrO4(I)  298.15  −1341.49      This work 
  176.62    26  
298.15–692.3      101.07 + 0.139 99T/K  54  
Na2CrO4(II)  298.15  −1331.86  190.52    This work 
298.15–692.3      101.07 + 0.139 99T/K  54  
692.3–1066.4      149.94 + 0.051 59T/K  54  
Na2CrO4(L)  298.15  −1307.53  213.34    This work 
298.15–692.3      101.07 + 0.139 99T/K  54  
692.3–1066.4      149.94 + 0.051 59T/K 
1066.4–2000      204.78 
a

Enthalpy relative to the enthalpy of the elements in their stable standard states at 298.15 K.

b

Absolute (third law) entropy.

The same approach was used for all other compounds considered in this work, even when there were more than two solid phases. More details on the thermodynamic properties selected for Na2CrO4 are given below.

The available measurements for the temperature and enthalpy change of the (I → II) and (II → L) transitions for Na2CrO4 are shown in Tables 7 and 8, respectively. For each property, the measured values were plotted as a function of the experiment number in order to identify visually outliers (see Figures S6–S9 in the supplementary material). A weighted average was then calculated from the retained measurements, with a weighting based on the expected accuracy of each experimental technique. The weighting factors used for the temperature and enthalpy change are given in Tables S3 and S4, respectively, in the supplementary material. The standard deviation σ was then calculated.

The outliers are identified by the letter “a” in Tables 7 and 8 and are shown in red color in Tables S1 and S2 in the supplementary material, and as empty circles in Figs. S6–S9 in the supplementary material. In these scatter plots, the weighted average is shown as a solid line while the two dashed lines correspond to (weighted average ±2σ). It was checked that all outliers lie outside this range. The reported uncertainties in Tables 7 and 8 correspond to ±2σ. A similar approach was used for all other compounds investigated in this work.

The value of the standard enthalpy at 298.15 K ( Δ f H 298 ° ) for Na2CrO4(I) was estimated as follows. The enthalpy of dissolution in water of Na2CrO4(I) ( N a 2 Cr O 4 I 2 Na aq + + CrO 4 aq 2 ) was measured by calorimetry65 as −19.12 kJ mol−1. According to the most recent databases of the FactSage software package,66, Δ f H 298 ° ( Na aq + ) = −239.73 kJ mol−1 and Δ f H 298 ° ( CrO 4 aq 2 ) = −881.15 kJ mol−1. The obtained value of −1341.49 kJ mol−1 for Δ f H 298 ° [Na2CrO4(I)] is very close to that of −1342.20 kJ mol−1 recommended in Barin’s compilation.67 The Open Quantum Materials Database (OQMD)68,69 reported an enthalpy of formation at 0 K of −1331.21 kJ mol−1 derived from Density Functional Theory (DFT) calculations. The corresponding value given in Materials Project70 is −1343.37 kJ mol−1.

The standard entropy at 298.15 K ( S 298 ° ) of Na2CrO4(I) was derived by Ferrante et al.26 as 176.62 J mol−1 K−1 by integration of their experimental CP values from 5.5 to 308.5 K using adiabatic calorimetry. This value is identical to that recommended in Barin’s compilation (176.61 J mol−1 K−1).67 

To our knowledge, no other direct heat capacity measurements are available for Na2CrO4. Denielou et al.54 carried out heat content measurements using drop calorimetry in an ice calorimeter. The salts were then analyzed using XRD to confirm that they were in their stable form. Enthalpy variations HTH273 as a function of temperature were obtained as follows. For Na2CrO4(I), 9 measurements were performed between 370 and 665 K, and the following fit was provided by Denielou et al.:54, HTH273 = 6.999 × 10−5 T2 + 10.107 × 10−2T − 32.78 kJ mol−1 (0.4%, empirical standard deviation of 0.03 kJ).54 For Na2CrO4(II), 11 measurements were conducted between 698 and 1065 K, with the following fit: HTH273 = 2.580 × 10−5 T2 + 14.994 × 10−2T − 35.84 kJ mol−1 (0.15%, empirical standard deviation of 0.03 kJ).54 Finally, for Na2CrO4(L), at least 11 measurements were made above 1091 K, with the following fit: HTH273 = 20.478 × 10−2 T − 40.74 kJ mol−1 (0.11%, empirical standard deviation of 0.05 kJ).54 

For each phase of Na2CrO4, the heat capacity expression (as a function of temperature) was derived by us from the fits of HTH273 provided by Denielou et al.54 Calculated values of HTH298 are compared to the available data in Fig. 2. This figure includes the heat contents HTH298 measured by Ferrante et al.26 as well as the HTH298 values obtained by conversion of the HTH273 data of Denielou et al.54 [HTH298 = (HTH273) − (H298H273)]. These two series of data are in good agreement.

FIG. 2.

Calculated heat content HTH298 for Na2CrO4 (enthalpies of transition are the weighted average of all available data presented in Tables 7 and 8). Experimental data from Refs. 26 ( ) and 54 (○).

FIG. 2.

Calculated heat content HTH298 for Na2CrO4 (enthalpies of transition are the weighted average of all available data presented in Tables 7 and 8). Experimental data from Refs. 26 ( ) and 54 (○).

Close modal

4.2.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transition (I → II) for K2CrO4

The temperature and enthalpy change for the solid–solid transition of K2CrO4 was measured by DSC in the present work. These data along with all measurements collected from the literature (and obtained using various experimental techniques) are gathered in Table 10. Our experimental DSC thermogram is provided in the supplementary material (Fig. S1).

TABLE 10.

Transition temperature and enthalpy change of solid–solid transition for K2CrO4

Ttrs (I → II) (°C) Δ H t r s I II (kJ mol−1) Experimental method Reference
670.7  7.201  DSC (second heating) at 10 °C/min  This work 
671.2  7.123  DSC (third heating) at 10 °C/min  This work 
666  ⋯  Heating or cooling curves  71  
679a  ⋯  Pyrometry  72  
669  ⋯  Cooling curves  51  
666  ⋯  Cooling curves; visual  73  
664  10.251a  Heating or cooling curves  74  
666.8  ⋯  Thermocouple Pt–Rh  75  
669  ⋯  Cooling curves  76  
663  ⋯  Resistance technique  27  
671  7.155  DTA  53  
665  10.2a  ⋯  77  
668.5 ± 3  ⋯  DTAb  78  
675  ⋯  DTAc  79  
662.9 ± 3  9.954 ± 0.502a  Ice calorimeter, enthalpimetry  80  
674  6.583  DSCd at 5 °C/min  81  
5.243a  DTAd at 5 °C/min 
670.2 ± 3  7.2 ± 0.25  DSC  82  
6.908e  10 °C/min (heating) 
  40 °C/min (cooling) 
668.9  ⋯  Elect conduct (single crystal)  83  
669.2 ± 7.1  7.0 ± 0.5  Weighted average  This work 
Ttrs (I → II) (°C) Δ H t r s I II (kJ mol−1) Experimental method Reference
670.7  7.201  DSC (second heating) at 10 °C/min  This work 
671.2  7.123  DSC (third heating) at 10 °C/min  This work 
666  ⋯  Heating or cooling curves  71  
679a  ⋯  Pyrometry  72  
669  ⋯  Cooling curves  51  
666  ⋯  Cooling curves; visual  73  
664  10.251a  Heating or cooling curves  74  
666.8  ⋯  Thermocouple Pt–Rh  75  
669  ⋯  Cooling curves  76  
663  ⋯  Resistance technique  27  
671  7.155  DTA  53  
665  10.2a  ⋯  77  
668.5 ± 3  ⋯  DTAb  78  
675  ⋯  DTAc  79  
662.9 ± 3  9.954 ± 0.502a  Ice calorimeter, enthalpimetry  80  
674  6.583  DSCd at 5 °C/min  81  
5.243a  DTAd at 5 °C/min 
670.2 ± 3  7.2 ± 0.25  DSC  82  
6.908e  10 °C/min (heating) 
  40 °C/min (cooling) 
668.9  ⋯  Elect conduct (single crystal)  83  
669.2 ± 7.1  7.0 ± 0.5  Weighted average  This work 
a

Outlier.

b

The purity of this salt is 99.8%.

c

The purity of this salt is 99.96%.

d

The purity of this salt is 99.87%.

e

Questionable according to the authors.

4.2.2. Temperature (Tf) and enthalpy of fusion (ΔHf) for K2CrO4

The temperature and enthalpy of fusion have been measured by Refs. 51, 53, 59, 61, 7173, 75, 77, 80, and 8488. The heat of fusion was obtained by enthalpimetric analysis80 and DTA.53 All data from the literature and our DSC measurements are given in Table 11.

TABLE 11.

Transition temperature and enthalpy of fusion for K2CrO4

Tfus (II → L) (°C) ΔHfus (II → L) (kJ mol−1) Experimental method Reference
977.2  32.896  DSC (second heating) at 10 °C/min  This work 
976.4  34.197  DSC (third heating) at 10 °C/min  This work 
971  ⋯  Heating or cooling curves  71  
984  ⋯  Pyrometry  72  
976  ⋯  Cooling curves  51  
978  ⋯  Cooling curves; visual  73  
968.3  ⋯  Thermocouple Pt–Rh  75  
970.9  ⋯  Cooling curves  84  
976  ⋯  DTA  59  
972  ⋯  Visual-polythermal method  85  
979  31.547  DTA  53  
984  28.9a  ⋯  77  
980  ⋯  DTA and high-temperature microscopy  61  
984  ⋯  DTA  86  
976  ⋯  Visual-polythermal method  87  
968  ⋯  Pt/Pt–Rh thermocouple; visual  88  
973.9 ± 4  32.991 ± 0.669  Ice calorimeter, enthalpimetry  80  
975.9 ± 9.9  33.1 ± 1.8  Weighted average  This work 
Tfus (II → L) (°C) ΔHfus (II → L) (kJ mol−1) Experimental method Reference
977.2  32.896  DSC (second heating) at 10 °C/min  This work 
976.4  34.197  DSC (third heating) at 10 °C/min  This work 
971  ⋯  Heating or cooling curves  71  
984  ⋯  Pyrometry  72  
976  ⋯  Cooling curves  51  
978  ⋯  Cooling curves; visual  73  
968.3  ⋯  Thermocouple Pt–Rh  75  
970.9  ⋯  Cooling curves  84  
976  ⋯  DTA  59  
972  ⋯  Visual-polythermal method  85  
979  31.547  DTA  53  
984  28.9a  ⋯  77  
980  ⋯  DTA and high-temperature microscopy  61  
984  ⋯  DTA  86  
976  ⋯  Visual-polythermal method  87  
968  ⋯  Pt/Pt–Rh thermocouple; visual  88  
973.9 ± 4  32.991 ± 0.669  Ice calorimeter, enthalpimetry  80  
975.9 ± 9.9  33.1 ± 1.8  Weighted average  This work 
a

Outlier.

4.2.3. Recommended thermodynamic data for potassium chromate K2CrO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° , and CP) for potassium chromate (K2CrO4) are given in Table 12.

TABLE 12.

Selected thermodynamic properties of K2CrO4

Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2CrO4(I)  298.15  −1403.70      89  
  199.99    90  
298.15–942.4      144.28 + 0.061 19T/K  80  
K2CrO4(II)  298.15  −1396.66  207.47    This work 
298.15–942.4      144.28 + 0.061 19T/K  80  
942.4–1249.1      44.89 + 0.153 39T/K 
1249.1–2000a      212.01 
K2CrO4(L)  298.15  −1363.55  233.97    This work 
298.15–942.4      144.28 + 0.061 19T/K  80  
942.4–1249.1      44.89 + 0.153 39T/K 
1249.1–2000      212.01 
Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2CrO4(I)  298.15  −1403.70      89  
  199.99    90  
298.15–942.4      144.28 + 0.061 19T/K  80  
K2CrO4(II)  298.15  −1396.66  207.47    This work 
298.15–942.4      144.28 + 0.061 19T/K  80  
942.4–1249.1      44.89 + 0.153 39T/K 
1249.1–2000a      212.01 
K2CrO4(L)  298.15  −1363.55  233.97    This work 
298.15–942.4      144.28 + 0.061 19T/K  80  
942.4–1249.1      44.89 + 0.153 39T/K 
1249.1–2000      212.01 
a

Above the temperature of fusion, the heat capacity of K2CrO4(II) was assumed to be equal to that of K2CrO4(L) to ensure a reasonable extrapolation of the Gibbs energy at high temperatures. In absence of this additional CP range, the high-temperature phase would be calculated to be more stable than the pure liquid above 6814 K.

The standard enthalpy at 298.15 K of −1403.70 kJ mol−1 for K2CrO4(I) was taken directly from the National Bureau of Standards (NBS) Tables of chemical thermodynamic properties of Wagman et al.,89 since no experimental values were found in the literature. OQMD68,69 reported an enthalpy of formation at 0 K of −1362.95 kJ mol−1 using DFT calculations. The corresponding value given in Materials Project70 is −1394.70 kJ mol−1.

The standard entropy at 298.15 K ( S 298 ° ) reported by Popov and Kolesov90 (see Table 12) is in very good agreement with that in the book edited by Lax77 (i.e., 200 J mol−1 K−1), and also with that from Barin67 (i.e., 199.99 J mol−1 K−1). The value from Popov and Kolesov is the only experimental value found in the literature; it was obtained by integration of 0 K 298.15 K C P T dT , where the low-temperature heat capacity was measured by calorimetry.

To our knowledge, there are no other direct CP measurements for K2CrO4 available in the literature. Heat content (HTH298) measurements were conducted by Sirousse-Zia80 using 99.5% certified material and enthalpimetric analysis in an ice calorimeter. This author obtained 11 experimental values for each phase (K2CrO4(I), K2CrO4(II), and K2CrO4(L)), and derived a fit of HTH298 as a function of temperature. For I, between 517 and 888 K, HTH298 = 3.622 × 10−8T3 − 2.227 × 10−5T2 + 16.336 × 10−2T − 45.89 kJ mol−1 (0.7%, empirical standard deviation of 0.06 kJ). The corresponding value is 1.776 kJ mol−1 at 298.15 K. The following new fit, which is null at 298.15 K, was obtained by us: 3.059 523 × 10−5 (T − 298.15)2 + 1.625 099 × 10−1 (T − 298.15) kJ mol−1.

Sirousse-Zia80 also derived the following fits: for II, between 942 and 1202 K, HTH298 = 7.669 × 10−5T2 + 4.489 × 10−2T + 17.95 kJ mol−1 (0.4%, empirical standard deviation of 0.05 kJ); for the pure liquid, above 1261 K, HTH298 = 2.120 × 10−1T − 38.17 kJ mol−1 (0.4%, empirical standard deviation of 0.05 kJ). For each phase of K2CrO4, the heat capacity expression (as a function of temperature) was derived (see Table 12) from the fits of HTH298 given previously. Calculated values of HTH298 are shown along with the available data in Fig. 3. Our calculations somewhat underestimate the measurements of Sirousse-Zia80 for the high-temperature phase and the pure liquid since the selected enthalpy changes for the solid–solid transition and the fusion are weighted averages of all available data from the literature and of our own DSC measurements.

FIG. 3.

Calculated heat content HTH298 for K2CrO4 (enthalpies of transition are the weighted average of all available data presented in Tables 10 and 11). Experimental data from Ref. 80 (○).

FIG. 3.

Calculated heat content HTH298 for K2CrO4 (enthalpies of transition are the weighted average of all available data presented in Tables 10 and 11). Experimental data from Ref. 80 (○).

Close modal

4.3.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transitions (I → II, II → III, and III → IV) for Na2MoO4

The temperatures and enthalpy changes for the various solid–solid transitions (I → II, II → III, and III → IV) of Na2MoO4 were measured by DSC in this work. These data along with all measurements available in the literature are shown in Tables 1315, respectively. Our experimental DSC thermogram is presented in the supplementary material (Fig. S2).

TABLE 13.

Transition temperature and enthalpy change of transition I → II for Na2MoO4

Ttrs (I → II) (°C) ΔHtrs (I → II) (kJ mol−1) Experimental method Reference
455.8  22.447  DSC (second heating) at 10 °C/min  This work 
456.7  22.097  DSC (third heating) at 10 °C/min  This work 
440a  61.086a  Heating or cooling curves  74  
457.9 ± 2  26.65  DTA  53  
454.9 ± 1  ⋯  DTA at 5 °C/min  91  
444.9 ± 2a  21.76 ± 0.38  Calorimetry, drop method  54  
460.9  ⋯  DSC (cooling) at 3 °C/min  36  
440.9 (run 1)a  ⋯     
435.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
441.9 (run 3)a  ⋯     
459.9  ⋯  DTA (heating) at 10 °C/min  32  
457.85  ⋯  DSC at 10 °C/min 
509.9–529.9a  ⋯  Raman spectroscopy  33  
456.9 ± 1  26.78 ± 0.38  DSC at (10, 5 and 2 °C/min)  93  
457.6 ± 3.7  23.1 ± 4.9  Weighted average  This work 
Ttrs (I → II) (°C) ΔHtrs (I → II) (kJ mol−1) Experimental method Reference
455.8  22.447  DSC (second heating) at 10 °C/min  This work 
456.7  22.097  DSC (third heating) at 10 °C/min  This work 
440a  61.086a  Heating or cooling curves  74  
457.9 ± 2  26.65  DTA  53  
454.9 ± 1  ⋯  DTA at 5 °C/min  91  
444.9 ± 2a  21.76 ± 0.38  Calorimetry, drop method  54  
460.9  ⋯  DSC (cooling) at 3 °C/min  36  
440.9 (run 1)a  ⋯     
435.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
441.9 (run 3)a  ⋯     
459.9  ⋯  DTA (heating) at 10 °C/min  32  
457.85  ⋯  DSC at 10 °C/min 
509.9–529.9a  ⋯  Raman spectroscopy  33  
456.9 ± 1  26.78 ± 0.38  DSC at (10, 5 and 2 °C/min)  93  
457.6 ± 3.7  23.1 ± 4.9  Weighted average  This work 
a

Outlier.

TABLE 14.

Transition temperature and enthalpy change of transition II → III for Na2MoO4

Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
591.4  1.685  DSC (second heating) at 10 °C/min  This work 
591.4  1.700  DSC (third heating) at 10 °C/min  This work 
590.9 ± 2  1.88  DTA  53  
579.9 ± 2a  ⋯  DTA at 5 °C/min  91  
592.9 ± 3  2.09 ± 0.38  Calorimetry, drop method  54  
591.9  ⋯  DSC (cooling) at 3 °C/min  36  
571.9 (run 1)a  ⋯     
574.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
569.9 (run 3)a  ⋯     
579.9a  ⋯  DTA (heating) at 10 °C/min  32  
591.9  ⋯  DSC at 10 °C/min 
549.9–639.9  ⋯  Raman spectroscopy  33  
592.9 ± 1  2.01 ± 0.33  DSC at (10, 5 and 2 °C/min)  93  
591.8 ± 2.5  1.9 ± 0.3  Weighted average  This work 
Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
591.4  1.685  DSC (second heating) at 10 °C/min  This work 
591.4  1.700  DSC (third heating) at 10 °C/min  This work 
590.9 ± 2  1.88  DTA  53  
579.9 ± 2a  ⋯  DTA at 5 °C/min  91  
592.9 ± 3  2.09 ± 0.38  Calorimetry, drop method  54  
591.9  ⋯  DSC (cooling) at 3 °C/min  36  
571.9 (run 1)a  ⋯     
574.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
569.9 (run 3)a  ⋯     
579.9a  ⋯  DTA (heating) at 10 °C/min  32  
591.9  ⋯  DSC at 10 °C/min 
549.9–639.9  ⋯  Raman spectroscopy  33  
592.9 ± 1  2.01 ± 0.33  DSC at (10, 5 and 2 °C/min)  93  
591.8 ± 2.5  1.9 ± 0.3  Weighted average  This work 
a

Outlier.

TABLE 15.

Transition temperature and enthalpy change of transition III → IV for Na2MoO4

Ttrs (III → IV) (°C) Δ H t r s III IV (kJ mol−1) Experimental method Reference
642.4  8.316  DSC (second heating) at 10 °C/min  This work 
642.4  8.248  DSC (third heating) at 10 °C/min  This work 
641.9 ± 2  10.84a  DTA  53  
637.9 ± 2  ⋯  DTA at 5 °C/min  91  
641.9 ± 2  8.28 ± 0.46  Calorimetry, drop method  54  
639.9  ⋯  DSC (cooling) at 3 °C/min  36  
641.9 ± 2  8.3 ± 0.4  Calorimetry; spectroscopy  94  
622.9 (run 1)a  ⋯     
625.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
618.9 (run 3)a  ⋯     
641.85  ⋯  DTA (heating) at 10 °C/min  32  
637.9  ⋯  DSC at 10 °C/min 
669.9–676.9a  ⋯  Raman spectroscopy  33  
639.9 ± 1  7.81 ± 1.25  DSC at (10, 5 and 2 °C/min)  93  
640.6 ± 3.4  8.2 ± 0.4  Weighted average  This work 
Ttrs (III → IV) (°C) Δ H t r s III IV (kJ mol−1) Experimental method Reference
642.4  8.316  DSC (second heating) at 10 °C/min  This work 
642.4  8.248  DSC (third heating) at 10 °C/min  This work 
641.9 ± 2  10.84a  DTA  53  
637.9 ± 2  ⋯  DTA at 5 °C/min  91  
641.9 ± 2  8.28 ± 0.46  Calorimetry, drop method  54  
639.9  ⋯  DSC (cooling) at 3 °C/min  36  
641.9 ± 2  8.3 ± 0.4  Calorimetry; spectroscopy  94  
622.9 (run 1)a  ⋯     
625.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
618.9 (run 3)a  ⋯     
641.85  ⋯  DTA (heating) at 10 °C/min  32  
637.9  ⋯  DSC at 10 °C/min 
669.9–676.9a  ⋯  Raman spectroscopy  33  
639.9 ± 1  7.81 ± 1.25  DSC at (10, 5 and 2 °C/min)  93  
640.6 ± 3.4  8.2 ± 0.4  Weighted average  This work 
a

Outlier.

4.3.2. Temperature (Tfus) and enthalpy of fusion (ΔHfus) for Na2MoO4

The properties of fusion (temperature and enthalpy change) were measured by Refs. 32, 36, 53, 54, and 9197. The enthalpy of fusion was obtained using DTA,53 drop calorimetry,54 calorimetry,94 and DSC.93 All data collected from the literature and our own DSC measurements are displayed in Table 16.

TABLE 16.

Transition temperature and enthalpy of fusion for Na2MoO4

Tfus (IV → L) (°C) ΔHfus (IV → L) (kJ mol−1) Experimental method Reference
688.2  18.637  DSC (second heating) at 10 °C/min  This work 
686.9  18.495  DSC (third heating) at 10 °C/min  This work 
688  ⋯  Visual-polythermal method  95  
690  ⋯  DTA  96  
692.9 ± 2a  24.43a  DTA  53  
686.9 ± 1  ⋯  DTA at 5 °C/min  91  
688.9 ± 3  21.42 ± 0.5  Calorimetry, drop method  54  
688.9  ⋯  DSC (cooling) at 3 °C/min  36  
685.9 ± 2  20.4 ± 0.4  Calorimetry; spectroscopy  94  
687  ⋯  Thermal analysis  97  
671.9 (run 1)a  ⋯     
674.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
667.9 (run 3)a  ⋯     
679.9a  ⋯  DSC at 10 °C/min  32  
684.9  ⋯  DTA at 10 °C/min 
683.9 ± 1  20.73 ± 1.14  DSC at (10, 5 and 2 °C/min)  93  
687.1 ± 3.5  20.4 ± 2.5  Weighted average  This work 
Tfus (IV → L) (°C) ΔHfus (IV → L) (kJ mol−1) Experimental method Reference
688.2  18.637  DSC (second heating) at 10 °C/min  This work 
686.9  18.495  DSC (third heating) at 10 °C/min  This work 
688  ⋯  Visual-polythermal method  95  
690  ⋯  DTA  96  
692.9 ± 2a  24.43a  DTA  53  
686.9 ± 1  ⋯  DTA at 5 °C/min  91  
688.9 ± 3  21.42 ± 0.5  Calorimetry, drop method  54  
688.9  ⋯  DSC (cooling) at 3 °C/min  36  
685.9 ± 2  20.4 ± 0.4  Calorimetry; spectroscopy  94  
687  ⋯  Thermal analysis  97  
671.9 (run 1)a  ⋯     
674.9 (run 2)a  ⋯  DTA (1.8 and 10.2 °C/min)  92  
667.9 (run 3)a  ⋯     
679.9a  ⋯  DSC at 10 °C/min  32  
684.9  ⋯  DTA at 10 °C/min 
683.9 ± 1  20.73 ± 1.14  DSC at (10, 5 and 2 °C/min)  93  
687.1 ± 3.5  20.4 ± 2.5  Weighted average  This work 
a

Outlier.

4.3.3. Recommended thermodynamic data for sodium molybdate Na2MoO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° , and CP) for sodium molybdate (Na2MoO4) are shown in Table 17.

TABLE 17.

Selected thermodynamic properties of Na2MoO4

Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
Na2MoO4(I)  298.15  −1465.87      98  
  159.41    99  
298.15–730.7      125.34 + 0.078 58T/K  54  
Na2MoO4(II)  298.15  −1442.80  190.98    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
Na2MoO4(III)  298.15  −1440.86  193.22    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
Na2MoO4(IV)  298.15  −1432.63  202.23    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
913.7–960.2      208.30 
Na2MoO4(L)  298.15  −1412.26  223.45    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
913.7–960.2      208.30 
960.2–2000      213.00  54  
Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
Na2MoO4(I)  298.15  −1465.87      98  
  159.41    99  
298.15–730.7      125.34 + 0.078 58T/K  54  
Na2MoO4(II)  298.15  −1442.80  190.98    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
Na2MoO4(III)  298.15  −1440.86  193.22    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
Na2MoO4(IV)  298.15  −1432.63  202.23    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
913.7–960.2      208.30 
Na2MoO4(L)  298.15  −1412.26  223.45    This work 
298.15–730.7      125.34 + 0.078 58T/K  54  
730.7–865      −215.46 + 0.506 43T/K 
865–913.7      202.30  This work 
913.7–960.2      208.30 
960.2–2000      213.00  54  

The molar enthalpy of dissolution of Na2MoO4 in a NaOH solution was measured at 298.15 K by Tangri et al. using an isoperibol calorimeter.98 The molar enthalpy of solution at infinite dilution was measured as −11.79 ± 0.51 kJ mol−1,98 and a standard enthalpy at 298.15 K of −1465.87 kJ mol−1 was then derived for Na2MoO4(I). Using a cycle of calorimetric reactions, Koehler et al.100 evaluated Δ f H 298 ° = −1467.75 kJ mol−1. The value recommended in Barin’s compilation tables67 is −1469.00 kJ mol−1. The Δ f H 298 ° value reported by Tangri et al.98 was selected in the present work. OQMD68,69 reported an enthalpy of formation at 0 K of −1560.17 kJ mol−1 using DFT. The corresponding value given in Materials Project70 is −1456.16 kJ mol−1.

For the standard entropy at 298.15 K ( S 298 ° ), Welle and King99 reported a value of 159.41 J mol−1 K−1, estimated by integration of their low-temperature heat capacity measurements obtained by calorimetry. The Einstein and Debye functions were used over the extrapolated temperature range of 0–51 K.

Using adiabatic calorimetry, Gavrichev et al.101 performed low-temperature CP measurements from 14 to 297 K, and derived a S 298 ° value of 149.9 ± 0.2 J mol−1 K−1.

Finally, the S 298 ° value obtained by Weller and King,99 which is close to the value of 159.41 J mol−1 K−1 recommended in Barin’s compilation tables,67 was selected in this work.

Using drop calorimetry in an ice calorimeter, Denielou et al.54 performed heat content measurements (HTH273) for Na2MoO4, and derived fits of their data along with CP expressions (as a function of temperature). The stability of the salts was verified by XRD analyses.

For Na2MoO4(I), based on 11 measurements between 427 and 709 K, HTH273 = 3.929 × 10−5T2 + 1.253 × 10−1T − 376.02 kJ mol−1 (0.3%, empirical standard deviation of 0.02 kJ). This fit was assumed to be valid from 298.15 K to our selected temperature of 730.7 K for the I → II transition.

Extrapolation to 296.5 K of the heat capacity expression CP(I) = 0.078 58T + 125.344 27 J mol−1 K−1 (valid from 427 to 709 K) given by Denielou et al.54 gives a value of 148.64 J mol−1 K−1, which agrees well with the heat capacity measurement of Weller and King.99 Gavrichev et al.101 measured at 298.15 K a value of 131.81 J mol−1 K−1, which is about 17 J mol−1 K−1 lower.

For Na2MoO4(II), based on 12 measurements between 734 and 857 K, HTH273 = 2.532 × 10−4T2 − 2.155 × 10−1T + 118.59 kJ mol−1 (0.13%, empirical standard deviation of 0.05 kJ). This fit was assumed to be valid from 730.7 K to our selected temperature of 865 K for the II → III transition.

For Na2MoO4(III), based on 10 measurements between 870 and 907 K, HTH273 = 4.456 × 10−4T2 − 5.895 × 10−1T + 300.54 kJ mol−1 (0.14%, empirical standard deviation of 0.04 kJ). This fit was assumed to be valid from 865 K to our selected temperature of 913.7 K for the III → IV transition.

A typo was detected in the article of Denielou et al.54 The original constant of 30.054 kJ mol−1 in the fit provided for Na2MoO4(III) corresponded to negative values of (HTH273). Adjusting this constant to 300.54 kJ mol−1 permitted us to reproduce (within the reported error bars) the experimental enthalpy changes of Denielou et al.54 for the II → III and III → IV transitions (the two temperatures used for these calculations were those reported by the authors).

For Na2MoO4(IV), based on 9 measurements between 920 and 960 K, HTH273 = −4.774 × 10−4T2 + 1.106T + 469.86 kJ mol−1 (0.16%, empirical standard deviation of 0.08 kJ). This fit was assumed to be valid from 913.7 K to our selected temperature of fusion of 960.2 K.

A marked decrease of CP as a function of temperature was observed between the phases III and IV, owing to the mathematical expressions of (HTH273) proposed by Denielou et al.54 Since the temperature ranges of validity were very limited (from 870 to 907 K for III, and from 920 to 960 K for IV), the corresponding values of (HTH273) were refitted by us using a linear expression (a + bT), thus leading to constant heat capacity values. Our new fits of (HTH273) are 2.023 × 10−1T − 51.169 (kJ mol−1) for III, and 2.083 × 10−1T − 48.12 (kJ mol−1) for IV. The corresponding CP values are 202.3 and 208.3 J mol−1 K−1, respectively (see Table 17).

For Na2MoO4(L), based on 14 measurements above 1091 K, HTH273 = 2.0478 × 10−1T − 40.74 kJ mol−1 (0.1%, empirical standard deviation of 0.12 kJ).

Calculated values of HTH298 are shown along with the available measurements in Fig. 4. This figure includes the heat contents HTH298 measured by Iyer et al.92 as well as the HTH298 values obtained by conversion of the HTH273 data of Denielou et al.54 [HTH298 = (HTH273) − (H298H273)]. These two series of data are in good agreement.

FIG. 4.

Calculated heat content HTH298 for Na2MoO4 (enthalpies of transition are the weighted average of all available data presented in Tables 1316). Experimental data from Refs. 54 (○) and 92 (). Red line: HTH298 fit of low-temperature heat capacity data shown in Fig. 5.

FIG. 4.

Calculated heat content HTH298 for Na2MoO4 (enthalpies of transition are the weighted average of all available data presented in Tables 1316). Experimental data from Refs. 54 (○) and 92 (). Red line: HTH298 fit of low-temperature heat capacity data shown in Fig. 5.

Close modal

The calculated heat capacity at low temperatures for Na2MoO4(I) is shown in Fig. 5 along with the measurements of Weller and King,99 Gavrichev et al.,101 and Zhidikova and Kuskov.102 

FIG. 5.

Calculated heat capacity at low temperatures for Na2MoO4(I). Experimental data from Refs. 99 (●), 101 (○), and 102 (◆). Red line: best linear fit of CP data above room temperature.

FIG. 5.

Calculated heat capacity at low temperatures for Na2MoO4(I). Experimental data from Refs. 99 (●), 101 (○), and 102 (◆). Red line: best linear fit of CP data above room temperature.

Close modal

In Fig. 4, the black full lines correspond to our final calculations while the red dashed line corresponds to heat contents HTH298 obtained from the fit of the low-temperature CP data measured by Refs. 99, 101, and 102, and shown in Fig. 5. An average deviation of about 3.7 kJ mol−1 is observed for the red dashed line, which is substantially higher than the error of about 0.02 kJ mol−1 reported by Ref. 54. This lends support to our final calculations displayed in Figs. 4 and 5.

The heat content measurements of Iyer et al.92 were carried out over the temperature range 335–760 K using drop calorimetry in a high-temperature Calvet calorimeter. These authors observed transitions at 520 ± 5 and 720 ± 5 K. The first transition (at about 520 K) has not been reported previously while the DTA study of the same authors from 300 to 973 K revealed the presence of three solid–solid transitions (at about 713, 845 and 896 K). According to Iyer et al.,92 the first transition (at about 520 K) was not observed in their calorimetric study owing to the sensitivity being insufficient to detect a small enthalpy change for a small sample size. For the second transition (at about 720 K), there is good agreement between the calorimetric and DTA studies of Iyer et al.,92 and also with the calorimetric measurements of Denielou et al.54 using drop calorimetry in an ice calorimeter. Finally, the transition at about 520 K reported by Iyer et al.92 was ignored in the present work, and only three solid–solid transitions (corresponding to the four phases I, II, III, and IV) were considered.

4.4.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transitions (I → II, II → III, and III → IV) for K2MoO4

The temperatures and enthalpy changes for the various solid–solid transitions (I → II, II → III, and III → IV) of K2MoO4 were measured by DSC in the present work. These measurements along with all data collected from the literature are displayed in Tables 1820, respectively. Our experimental DSC thermogram is provided in the supplementary material (Fig. S3).

TABLE 18.

Transition temperature and enthalpy change of transition I → II for K2MoO4

Ttrs (I → II) (°C) Δ H trs I II (kJ mol−1) Experimental method Reference
325.4  2.338a  DSC (second heating) at 10 °C/min  This work 
322.2  2.236a  DSC (third heating) at 10 °C/min  This work 
327 ± 1.5  ⋯  Thermal study  103  
323  ⋯  Thermal analysis (cooling)  104  
321  ⋯  Thermal analysis  59  
323  ⋯  DTA  91  
295.9 ± 2a  11.34  DTA  53  
282.9a  8.27 ± 0.10  DTA  105  
Heating 0.5 °C/min 
Cooling 0.42 °C/min 
322.9 ± 1  11.34 ± 1.62  DSC (5 and 10 °C/min)  40  
323.5 ± 3.8  10.6 ± 2.9  Weighted average  This work 
Ttrs (I → II) (°C) Δ H trs I II (kJ mol−1) Experimental method Reference
325.4  2.338a  DSC (second heating) at 10 °C/min  This work 
322.2  2.236a  DSC (third heating) at 10 °C/min  This work 
327 ± 1.5  ⋯  Thermal study  103  
323  ⋯  Thermal analysis (cooling)  104  
321  ⋯  Thermal analysis  59  
323  ⋯  DTA  91  
295.9 ± 2a  11.34  DTA  53  
282.9a  8.27 ± 0.10  DTA  105  
Heating 0.5 °C/min 
Cooling 0.42 °C/min 
322.9 ± 1  11.34 ± 1.62  DSC (5 and 10 °C/min)  40  
323.5 ± 3.8  10.6 ± 2.9  Weighted average  This work 
a

Outlier.

TABLE 19.

Transition temperature and enthalpy change of transition II → III for K2MoO4

Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
454.8  0.980  DSC (second heating) at 10 °C/min  This work 
455.1  0.978  DSC (third heating) at 10 °C/min  This work 
454 ± 1.5  ⋯  Thermal study  103  
458  ⋯  Thermal analysis (cooling)  104  
439a  ⋯  Thermal analysis  59  
438a  ⋯  DTA  91  
451.9 ± 2  1.13  DTA  53  
456.9  0.64 ± 0.03a  DTA  105  
Heating 0.5 °C/min 
Cooling 0.42 °C/min 
452.9 ± 2  1.04 ± 0.06  DSC (5 and 10 °C/min)  40  
454.7 ± 3.9  1.0 ± 0.1  Weighted average  This work 
Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
454.8  0.980  DSC (second heating) at 10 °C/min  This work 
455.1  0.978  DSC (third heating) at 10 °C/min  This work 
454 ± 1.5  ⋯  Thermal study  103  
458  ⋯  Thermal analysis (cooling)  104  
439a  ⋯  Thermal analysis  59  
438a  ⋯  DTA  91  
451.9 ± 2  1.13  DTA  53  
456.9  0.64 ± 0.03a  DTA  105  
Heating 0.5 °C/min 
Cooling 0.42 °C/min 
452.9 ± 2  1.04 ± 0.06  DSC (5 and 10 °C/min)  40  
454.7 ± 3.9  1.0 ± 0.1  Weighted average  This work 
a

Outlier.

TABLE 20.

Transition temperature and enthalpy change of transition III → IV for K2MoO4

Ttrs (III → IV) (°C) ΔHtrs (III → IV) (kJ mol−1) Experimental method Reference
⋯  ⋯  DSC (second heating) at 10 °C/min  This work 
⋯  ⋯  DSC (third heating) at 10 °C/min  This work 
479.0 ± 1.5  ⋯  Thermal study  103  
480  ⋯  Thermal analysis (cooling)  104  
475  ⋯  Thermal analysis  59  
462  ⋯  DTA  91 a 
475.9 ± 10  ⋯  ⋯  Reported from “V. P. Glushko (VINITI, Moscow, 1981–1982) volume 10” in Ref. 40  
479.9  0.024  DSC 5 °C/min  40  
Ttrs (III → IV) (°C) ΔHtrs (III → IV) (kJ mol−1) Experimental method Reference
⋯  ⋯  DSC (second heating) at 10 °C/min  This work 
⋯  ⋯  DSC (third heating) at 10 °C/min  This work 
479.0 ± 1.5  ⋯  Thermal study  103  
480  ⋯  Thermal analysis (cooling)  104  
475  ⋯  Thermal analysis  59  
462  ⋯  DTA  91 a 
475.9 ± 10  ⋯  ⋯  Reported from “V. P. Glushko (VINITI, Moscow, 1981–1982) volume 10” in Ref. 40  
479.9  0.024  DSC 5 °C/min  40  
a

Another solid–solid transition at 480 °C, which was not considered in this work, has been reported by Ref. 91.

The experimental data in Tables 1820 suggest that there are three different solid–solid transitions for K2MoO4. According to our high-temperature XRD measurements (at 465 and 500 °C), there are only two solid–solid transitions. Furthermore, in the second and third heating/cooling runs of our two DSC experiments, the III → IV transition was never observed. While performing DSC measurements with a heating/cooling rate of 5 K/min, Gavrichev et al.40 did observe the III → IV transition and reported an extremely low enthalpy change of 0.024 kJ mol−1.40 Other studies reported a similar transition temperature59,91,103,104 but did not measure the corresponding enthalpy change.

In most studies reporting the III → IV transition, the purity of the reagents was not indicated, and thus this transition may be due to the presence of impurities. Finally, based on our XRD and DSC measurements, only two solid–solid transitions were considered for K2MoO4 in the present work. Note that, if a III → IV transition were taken into account, it would have very little impact on our future calculations related to high temperature corrosion, since the corresponding enthalpy change would be very small (0.024 kJ mol−1) and the phase III would be stable over a limited temperature range of less than 25 °C (i.e., between about 455 and 478 °C).

4.4.2. Temperature (Tfus) and enthalpy of fusion (ΔHfus) for K2MoO4

The properties of fusion (temperature and enthalpy change) were measured by Refs. 40, 53, 59, 9497, and 103105.

The heat of fusion was measured by DTA,53,105 calorimetry,94 and DSC.40 All experimental data from the literature and our own DSC measurements are gathered in Table 21.

TABLE 21.

Transition temperature and enthalpy of fusion for K2MoO4

Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
927.1  30.460a  DSC (second heating) at 10 °C/min  This work 
927.8  28.983a  DSC (third heating) at 10 °C/min  This work 
819 ± 1.5a  ⋯  Thermal study  103  
926  ⋯  Thermal analysis (cooling)  104  
936  ⋯  Thermal analysis  59  
926  ⋯  Visual-polythermal method  95  
926  ⋯  Heating curves  96  
926  38.702  DTA  53  
925.9 ± 1  38.70  DTA  105  
Heating at 0.5 °C/min 
Cooling at 0.42 °C/min 
927.9 ± 2  34.70 ± 0.7  Calorimetry; spectroscopy  94  
926  ⋯  Thermal analysis  97  
930.9 ± 1  40.14 ± 1.25  DSC (5 and 10 °C/min)  40  
927.8 ± 5.9  36.6 ± 5.0  Weighted average  This work 
Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
927.1  30.460a  DSC (second heating) at 10 °C/min  This work 
927.8  28.983a  DSC (third heating) at 10 °C/min  This work 
819 ± 1.5a  ⋯  Thermal study  103  
926  ⋯  Thermal analysis (cooling)  104  
936  ⋯  Thermal analysis  59  
926  ⋯  Visual-polythermal method  95  
926  ⋯  Heating curves  96  
926  38.702  DTA  53  
925.9 ± 1  38.70  DTA  105  
Heating at 0.5 °C/min 
Cooling at 0.42 °C/min 
927.9 ± 2  34.70 ± 0.7  Calorimetry; spectroscopy  94  
926  ⋯  Thermal analysis  97  
930.9 ± 1  40.14 ± 1.25  DSC (5 and 10 °C/min)  40  
927.8 ± 5.9  36.6 ± 5.0  Weighted average  This work 
a

Outlier.

4.4.3. Recommended thermodynamic data for potassium molybdate K2MoO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° and CP) for potassium molybdate (K2MoO4) are shown in Table 22.

TABLE 22.

Selected thermodynamic properties of K2MoO4

Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2MoO4(I)  298.15  −1497.85      This work 
  199.30    40  
298.15–596.6      113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
K2MoO4(II)  298.15–727.9  −1487.27  217.02  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
K2MoO4(III)  298.15–730.7  −1486.26  218.42  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
730.7–865      −227.31 + 0.524 73 T/K + 729 689.6 (T/K)−2 
865–1201      196.45 + 0.018 30 T/K + 729 689.6 (T/K)−2 
K2MoO4(L)  298.15–730.7  −1449.67  248.88  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
730.7–865      −227.31 + 0.524 73 T/K + 729 689.6 (T/K)−2 
865–1201      196.45 + 0.018 30 T/K + 729 689.6 (T/K)−2 
1201–1500      204.67 + 0.015 06 T/K 
Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2MoO4(I)  298.15  −1497.85      This work 
  199.30    40  
298.15–596.6      113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
K2MoO4(II)  298.15–727.9  −1487.27  217.02  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
K2MoO4(III)  298.15–730.7  −1486.26  218.42  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
730.7–865      −227.31 + 0.524 73 T/K + 729 689.6 (T/K)−2 
865–1201      196.45 + 0.018 30 T/K + 729 689.6 (T/K)−2 
K2MoO4(L)  298.15–730.7  −1449.67  248.88  113.50 + 0.096 88 T/K + 729 689.6 (T/K)−2  This work 
730.7–865      −227.31 + 0.524 73 T/K + 729 689.6 (T/K)−2 
865–1201      196.45 + 0.018 30 T/K + 729 689.6 (T/K)−2 
1201–1500      204.67 + 0.015 06 T/K 

The standard enthalpy at 298.15 K ( Δ f H 298 ° ) of K2MoO4(I) was estimated as −1497.85 kJ mol−1 as follows. Nelson et al.65 measured by calorimetry the enthalpy of dissolution of K 2 Mo O 4 I in a 10−3 M OH aq solution. These authors reported an enthalpy change of −3.97 kJ mol−1 for the reaction K 2 Mo O 4 I 2 K aq + + MoO 4 aq 2 . According to the FactSage databases,66, Δ f H 298 ° ( K aq + ) = −251.97 kJ mol−1 and Δ f H 298 ° ( MoO 4 aq 2 ) = −997.88 kJ mol−1. There is no recommended value of Δ f H 298 ° for K2MoO4(I) in Barin’s compilation tables.67 OQMD68,69 reported an enthalpy of formation at 0 K of −1575.70 kJ mol−1 using DFT. The corresponding value given in Materials Project70 is −1493.30 kJ mol−1.

The standard entropy at 298.15 K ( S 298 ° ) of K2MoO4(I) was set to the value of 199.3 J mol−1 K−1 reported by Gavrichev et al.40 These authors derived this value by integration of 0 K 298.15 K C P T dT using their low-temperature heat capacity data obtained by adiabatic calorimetry. To our knowledge, this is the only experimental value available in the literature. S 298 ° was estimated by us using two different exchange reactions, for which ∆S = 0 was assumed at 298.15 K. We derived a value of 182.79 J mol−1 K−1 from the exchange reaction N a 2 Mo O 4 I + K 2 Cr O 4 I K 2 Mo O 4 I + N a 2 Cr O 4 I , and a value of 180.25 J mol−1 K−1 from the exchange reaction N a 2 Mo O 4 I + 2 KC l sol K 2 Mo O 4 I + 2 NaC l sol . The standard entropies at 298.15 K of Na2MoO4(I), K2CrO4(I) and Na2CrO4(I) were assessed by us in this work, and those of KCl(sol) and NaCl(sol) were taken from the FTsalt thermodynamic database.66 Our two derived S 298 ° values are very rough estimates. These are lower than the value reported by Gavrichev et al.40 

The latter value, which was selected in this work, is probably somewhat too low since the experimental S 298 ° value of Gavrichev et al.101 for Na2MoO4 was lower by about 10 J mol−1 K−1 than the values of Refs. 67 and 99 favored in this work.

To our knowledge, the low-temperature data of Gavrichev et al.40 are the only direct heat capacity measurements available for K2MoO4. In the present work, the heat capacity (as a function of temperature) of K2MoO4 was assessed from the following exchange reactions, assuming that ∆CP = 0 at all temperatures: N a 2 Mo O 4 sol + 2 KC l sol K 2 Mo O 4 sol + 2 NaC l sol for the solid phases (I, II, and III), and N a 2 Mo O 4 L + 2 KC l L K 2 Mo O 4 L + 2 NaC l L for the pure liquid. The heat capacity of Na2MoO4 was evaluated in the present work, and those of KCl and NaCl were taken from the FTsalt database.66 

In Fig. 6, the calculated heat capacity of solid K2MoO4 at low temperatures is compared to three series of measurements (3, 4, and 6) conducted by Gavrichev et al.40 using DSC. These authors performed six different series of measurements at low temperatures: series 1 between 78.83 and 215.59 K, series 2 between 132.27 and 215.40 K, series 3 between 8.97 and 75.08 K, series 4 between 174.38 and 342.90 K, series 5 between 245 and 257.31 K, and series 6 between 99.83 and 116.16 K. Agreement from room temperature to 342.90 K (maximum temperature investigated by Gavrichev et al.40) is satisfactory.

FIG. 6.

Calculated heat capacity at low temperatures for K2MoO4(I). Experimental data from Ref. 40 (series 3 :○, series 4 :●, and series 6 :◆).

FIG. 6.

Calculated heat capacity at low temperatures for K2MoO4(I). Experimental data from Ref. 40 (series 3 :○, series 4 :●, and series 6 :◆).

Close modal

4.5.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transitions (I → II and II → III) for Na2WO4

The temperatures and enthalpy changes for the solid–solid transitions (I → II and II → III) of Na2WO4 were measured by DSC in the present work. These measurements along with all data collected from the literature are displayed in Tables 23 and 24, respectively. Our experimental DSC thermogram is displayed in the supplementary material (Fig. S4).

TABLE 23.

Transition temperature and enthalpy change of transition I → II for Na2WO4

Ttrs (I → II) (°C) ΔHtrs (I → II) (kJ mol−1) Experimental method Reference
⋯  28.93  DSC (second heating) at 10 °C/min  This work 
⋯  28.66  DSC (third heating) at 10 °C/min  This work 
564a  ⋯  Cooling curves  46  
587  ⋯  Cooling curvesb  106  
587.6  30.851  DTA  107  
579a  39.790a  Heating or cooling curves  74  
588  31.380 ± 0.146  DTAc at 1 °C/min  86  
591  34.434  DTA  53  
585.9 ± 3  31.506 ± 0.502  Calorimetry, drop method  54  
587.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
559.9a  ⋯  Raman spectroscopy  33  
⋯  3.3a  Thermal analysis (DSC) at 8–10 °C/min  108  
589  ⋯  DSC (heating) at 0.1 °C/min  45  
588.3 ± 3.1  31.5 ± 5.9d  Weighted average  This work 
Ttrs (I → II) (°C) ΔHtrs (I → II) (kJ mol−1) Experimental method Reference
⋯  28.93  DSC (second heating) at 10 °C/min  This work 
⋯  28.66  DSC (third heating) at 10 °C/min  This work 
564a  ⋯  Cooling curves  46  
587  ⋯  Cooling curvesb  106  
587.6  30.851  DTA  107  
579a  39.790a  Heating or cooling curves  74  
588  31.380 ± 0.146  DTAc at 1 °C/min  86  
591  34.434  DTA  53  
585.9 ± 3  31.506 ± 0.502  Calorimetry, drop method  54  
587.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
559.9a  ⋯  Raman spectroscopy  33  
⋯  3.3a  Thermal analysis (DSC) at 8–10 °C/min  108  
589  ⋯  DSC (heating) at 0.1 °C/min  45  
588.3 ± 3.1  31.5 ± 5.9d  Weighted average  This work 
a

Outlier.

b

Cooling rates were not provided, but it was mentioned that various (slow) cooling rates were used.

c

Enthalpy changes were measured upon cooling while temperatures were measured upon heating.

d

See explanation in text.

TABLE 24.

Transition temperature and enthalpy change of transition II → III for Na2WO4

Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
⋯  ⋯  DSC (second heating) at 10 °C/min  This work 
⋯  ⋯  DSC (third heating) at 10 °C/min  This work 
564–588  ⋯  Cooling curves  46  
591  ⋯  Cooling curvesa  106  
588.8  4.113 ± 0.015  DTA  107  
589  4.142 ± 0.146  DTA at 1 °C/min  86  
589.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
591  ⋯  DSC (heating) at 0.1 °C/min  45  
Ttrs (II → III) (°C) ΔHtrs (II → III) (kJ mol−1) Experimental method Reference
⋯  ⋯  DSC (second heating) at 10 °C/min  This work 
⋯  ⋯  DSC (third heating) at 10 °C/min  This work 
564–588  ⋯  Cooling curves  46  
591  ⋯  Cooling curvesa  106  
588.8  4.113 ± 0.015  DTA  107  
589  4.142 ± 0.146  DTA at 1 °C/min  86  
589.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
591  ⋯  DSC (heating) at 0.1 °C/min  45  
a

Cooling rates were not provided, but it was mentioned that various (slow) cooling rates were used.

4.5.2. Temperature (Tfus) and enthalpy of fusion (ΔHfus) for Na2WO4

The properties of fusion (temperature and enthalpy change) were measured by Refs. 36, 46, 53, 54, 62, 86, 97, and 106109. The heat of fusion was obtained by DTA53,86,107,108 and drop calorimetry.54 All experimental data collected from the literature and our own DSC measurements are compiled in Table 25.

TABLE 25.

Transition temperature and enthalpy of fusion for Na2WO4

Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
690.8  24.47  DSC (second heating) at 10 °C/min  This work 
690.9  23.85  DSC (third heating) at 10 °C/min  This work 
698  ⋯  Cooling curves  46  
694  ⋯  Cooling curves  106  
695.5  23.799 ± 0.015  DTA  107  
698  ⋯  Visual-polythermal analysis  109  
696  31.254 ± 0.146  DTA at 1 °C/min  86  
698  31.464  DTA  53  
693  ⋯  Visual-polythermal analysis  62  
689  ⋯  Thermal analysis  97  
693.9 ± 2  27.865 ± 0.586  Calorimetry, drop method  54  
693.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
695.9 ± 2  34 ± 3.5a  Thermal analysis (DTA) at 8–10 °C/min  108  
694.2 ± 5.6  27.0 ± 6.6  Weighted average  This work 
Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
690.8  24.47  DSC (second heating) at 10 °C/min  This work 
690.9  23.85  DSC (third heating) at 10 °C/min  This work 
698  ⋯  Cooling curves  46  
694  ⋯  Cooling curves  106  
695.5  23.799 ± 0.015  DTA  107  
698  ⋯  Visual-polythermal analysis  109  
696  31.254 ± 0.146  DTA at 1 °C/min  86  
698  31.464  DTA  53  
693  ⋯  Visual-polythermal analysis  62  
689  ⋯  Thermal analysis  97  
693.9 ± 2  27.865 ± 0.586  Calorimetry, drop method  54  
693.9  ⋯  DSC (cooling) at 0.3 °C/min  36  
695.9 ± 2  34 ± 3.5a  Thermal analysis (DTA) at 8–10 °C/min  108  
694.2 ± 5.6  27.0 ± 6.6  Weighted average  This work 
a

Outlier.

4.5.3. Recommended thermodynamic data for sodium tungstate Na2WO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° , and CP) for sodium tungstate (Na2WO4) are given in Table 26.

TABLE 26.

Selected thermodynamic properties of Na2WO4

Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
Na2WO4(I)  298.15  −1544.73      110  
  161.08    111  
298.15–861.5      130.18 + 0.067 34 T/K  54  
Na2WO4(II)  298.15  −1513.26  197.61    This work 
298.15–861.5      130.18 + 0.067 34 T/K  54  
861.5–967.4      −29.72 + 0.255 81 T/K 
Na2WO4(L)  298.15  −1486.31  225.47    This work 
298.15–861.5      130.18 + 0.067 34 T/K  54  
861.5–967.4      −29.72 + 0.255 81 T/K 
967.4–2000      216.19 
Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
Na2WO4(I)  298.15  −1544.73      110  
  161.08    111  
298.15–861.5      130.18 + 0.067 34 T/K  54  
Na2WO4(II)  298.15  −1513.26  197.61    This work 
298.15–861.5      130.18 + 0.067 34 T/K  54  
861.5–967.4      −29.72 + 0.255 81 T/K 
Na2WO4(L)  298.15  −1486.31  225.47    This work 
298.15–861.5      130.18 + 0.067 34 T/K  54  
861.5–967.4      −29.72 + 0.255 81 T/K 
967.4–2000      216.19 

Various studies were conducted to identify the number of solid–solid transitions. Some authors reported a single solid–solid transition33,53,54,74,108 while others reported two such transitions.36,45,86,106,107

Denielou et al.54 used drop calorimetry to measure heat contents (HTH273) whereas Riccardi and Sinistri53 performed DTA measurements; both studies reported a single solid–solid transition (see Table 23). The DSC analyses of Bottelberghs and van Buren36 were able to separate the peaks corresponding to the I → II and II → III transitions using a very low heating rate of 0.3 °C/min. They estimated the temperature range of stability of the phase II to be only about 2 °C. According to Bottelberghs and van Buren,36 the previous studies did not observe the II → III transition because their calorimetric apparatuses were not calibrated with Zn, thus preventing them from measuring quantitatively and separately all solid–solid transitions.

Goranson and Kracek107 observed large overheating and undercooling effects for the II → III transition on their differential heating and cooling curves; they reported a difference of only 1.2 °C between their temperatures for the I → II and II → III transitions. Similarly, the DSC measurements of Hämmer and Höppe45 at a heating rate of 0.1 °C/min showed these two solid–solid transitions, with a temperature difference of only 2 °C.

Our DSC measurements for Na2WO4 were performed at a heating/cooling rate of 10 °C/min. One solid–solid transition was observed upon heating whereas two different solid–solid transitions were observed upon cooling. The presence of two exothermic events in our DSC cooling curves indicates that both phase transitions were reversible.45 

Our weighted averages of the temperatures for the I → II and II → III transitions are 588.3 and 589.6 °C (see Tables 23 and 24), respectively, with a temperature difference of only 1.3 °C. Hence, only two phases for Na2WO4 were considered in the present work: the low-temperature phase I and the high-temperature phase III (which was renamed II for the sake of clarity, as seen in Table 26). Nolte and Kordes,86 and Goranson and Kracek107 are the only authors who were able to measure the enthalpy changes of the I → II and II → III transitions. Our selected enthalpy change for the I → II transition (where the notation “II” now refers to the high-temperature phase III) is the sum of the two enthalpy changes for the I → II and II → III transitions reported in Refs. 86 and 107. (A weighted average of these two series of data was used).

For both Na2WO4 and Na2MoO4, the enthalpy change of the I → II transition is higher than the enthalpy of fusion. Therefore, for both compounds, the entropy change of the I → II transition exceeds the entropy of fusion. For Na2WO4, Goranson and Kracek107 estimated the volume changes related to the I → II transition and to the fusion using their calorimetric data and the Clausius-Clapeyron relation. Based on these values (see Table 27), the molar volume change associated with the I → II transition is larger than the molar volume change upon melting. This explains the ranking of the corresponding entropy changes. It is very likely that the same phenomenon occurs for Na2MoO4.

TABLE 27.

Volume change of Na2WO4

Transition Volume change (cm3 g−1) Volume change (cm3 mol−1) Reference
Na2WO4(I → II)  0.035  10.284  107  
Na2WO4(III → L)  0.018  5.289  107  
Transition Volume change (cm3 g−1) Volume change (cm3 mol−1) Reference
Na2WO4(I → II)  0.035  10.284  107  
Na2WO4(III → L)  0.018  5.289  107  

The standard enthalpy at 298.15 K ( Δ f H 298 ° ) of Na2WO4(I) was estimated by JANAF110 from the reaction H2WO4(sol) + 2 NaCl(sol) = Na2WO4(I) + 2 HCl(aq., 12.73 H2O), using Δ f H 298 ° ( H2WO4(sol)) = −1131.77 kJ mol−1 and Δ f H 298 ° (NaCl(sol)) = −411.12 kJ mol−1 both taken from Ref. 110, the heat of reaction Δ r H 303 ° = 81.34 ± 0.33 kJ mol−1 measured by Koehler et al.,100 and Δ f H 298 ° (HCl(aq.)) = −74.84 ± 62.76 kJ mol−1 provided in Ref. 112.

The enthalpy change at 298.15 K of the reaction W(sol) + 2 NaOH(aq) + 2 H2O(l) = Na2WO4(aq) + 3 H2(g) was measured by calorimetry as −29.29 ± 6.28 kJ mol−1.113 The heat of solution for the reaction Na2WO4(I) = Na2WO4(aq) was then measured as −7.11 ± 0.42 kJ mol−1, which finally permitted to derive a value of −1541.39 kJ mol−1 for Δ f H 298 ° (Na2WO4(I)). This latter value is close to the value of −1544.73 kJ mol−1 recommended by JANAF.110 

Using a cycle of calorimetric reactions, Koehler et al.100 estimated Δ f H 298 ° (Na2WO4(I)) as −1586.57 kJ mol−1.

Graham and Hepler114 measured by calorimetry at 298.15 K the enthalpy of dissolution of Na2WO4(I) in small concentrations of NaOH or in 0.005–0.01 M NH4OH, according to the reaction N a 2 W O 4 ( I ) 2 Na aq + + WO 4 aq 2 . From their experimental enthalpy change for the reaction H2WO4(sol) + 2 OH(aq) = WO 4 2 (aq) + 2 H2O(L) and the standard enthalpies at 298.15 K of H2WO4(sol), OH and H2O taken from Ref. 115, they first estimated Δ f H 298 ° ( WO 4 2 (aq)). The obtained value was consistent with that of the Bureau of Standards.115 Then, from the latter value, the standard enthalpy at 298.15 K of Na+(aq) provided by Ref. 115 and their measured enthalpy of dissolution of Na2WO4(I) (−6.69 ± 0.42 kJ mol−1), they assessed Δ f H 298 ° (Na2WO4(I)) as −1588.25 kJ mol−1.

Finally, the Δ f H 298 ° value recommended by JANAF110 was selected in this work. Indeed, according to JANAF,110 Koehler et al.100 and Graham and Hepler114 used an erroneous value of −1172.36 kJ mol−1 for Δ f H 298 ° (H2WO4(sol)). Also, note that U.S. Nat. Bur. Stand. Circ. 500115 reported a value of −1652.68 kJ mol−1 for Δ f H 298 ° (Na2WO4(I)). This value was derived from the experimental heat of reaction of tungsten powder using an excess of Na2O2. As mentioned in Ref. 110, this approach is most likely wrong owing to the possible formation of tungstate and complexes of peroxytungstate.

The standard enthalpy at 298.15 K of Na2WO4(I) was estimated by us using the method proposed by Hisham and Benson.116 These authors derived equations of the type 1 a Δ f H 298 ° M a X b = m Δ f H 298 ° MCl + 1 m 2 Δ f H 298 ° M 2 O + C , where m and C are two constants, and Δ f H 298 ° refers to the standard enthalpy at 298.15 K of the corresponding solid compound. They selected the corresponding chloride and oxide of a metal M as reference compounds since, for the majority of metals, the chloride and oxide values are known with good accuracy. For the alkali tungstates, Hisham and Benson116 obtained m = 2.93 and C = −426.35 kJ mol−1. Using the Δ f H 298 ° values for solid NaCl and Na2O from the FactSage thermodynamic databases,66, Δ f H 298 ° (Na2WO4(I)) was assessed as −1554.87 kJ mol−1, which is reasonably close to the value recommended by JANAF110 and selected in the present work. OQMD68,69 reported an enthalpy of formation at 0 K of −1637.84 kJ mol−1 using DFT. The corresponding value given in Materials Project70 is −1500.06 kJ mol−1.

Using calorimetry, King and Weller111 performed low-temperature heat capacity measurements for Na2WO4(I), and derived from them a value of 161.08 J mol−1 K−1 for the standard entropy at 298.15 K ( S 298 ° ). (The temperature range from 0 to 51 K was extrapolated using the Einstein and Debye functions.) This value, which is recommended by JANAF,110 was selected in the present work.

Na2WO4 was studied by Denielou et al.,54 using the same experimental technique that was previously discussed in detail for Na2CrO4 and Na2MoO4. These authors provided fits (as a function of temperature) for their heat content measurements (HTH273). For Na2WO4(I), based on 14 measurements between 345 and 849 K, HTH273 = 3.367 × 10−5T2 + 1.302 × 10−1T − 38.58 kJ mol−1 (0.4%, empirical standard variation of 0.03 kJ). This fit was assumed to be valid from 298.15 K to our selected temperature of 861.5 K for the I → II transition.

For Na2WO4(II), based on 9 measurements between 862 and 957 K, HTH273 = 1.279 × 10−4T2 − 2.972 × 10−2T + 60.75 kJ mol−1 (0.4%, empirical standard variation of 0.05 kJ). This fit was assumed to be valid from 861.5 K until our selected temperature of fusion of 967.4 K.

For Na2WO4(L), based on 12 measurements above 992 K, HTH273 = 2.162 × 10−1T − 29.61 kJ mol−1 (0.14%, empirical standard variation of 0.08 kJ).54 

In this work, the heat capacity expression (as a function of temperature) for Na2WO4 was selected in order to reproduce the heat content measurements (HTH273) of Denielou et al.54 Calculations are compared to the available data in Fig. 7. Also, the calculated heat capacity is shown along with the low-temperature measurements of King and Weller111 in Fig. 8. At room temperature, agreement is reasonable.

FIG. 7.

Calculated heat content HTH273 for Na2WO4 (enthalpies of transition are the weighted average of all available data presented in Tables 23 and 25). Experimental data from Ref. 54 (○). Red line: HTH273 fit of low-temperature heat capacity data shown in Fig. 8.

FIG. 7.

Calculated heat content HTH273 for Na2WO4 (enthalpies of transition are the weighted average of all available data presented in Tables 23 and 25). Experimental data from Ref. 54 (○). Red line: HTH273 fit of low-temperature heat capacity data shown in Fig. 8.

Close modal
FIG. 8.

Calculated heat capacity at low temperatures for Na2WO4(I). Experimental data from Ref. 111 ( ). Red line: best linear fit of room temperature CP data.

FIG. 8.

Calculated heat capacity at low temperatures for Na2WO4(I). Experimental data from Ref. 111 ( ). Red line: best linear fit of room temperature CP data.

Close modal

In Fig. 7, the black full lines represent our final calculations while the red dashed line refers to HTH273 heat contents obtained from the fit of the room temperature CP data of Ref. 111 displayed in Fig. 8. An average deviation of about 4 kJ mol−1 is calculated for the red dashed line, which is significantly higher than the experimental error of 0.03 kJ mol−1 reported by Ref. 54. This lends support to our final calculations shown in Figs. 7 and 8.

4.6.1. Transition temperature (Ttrs) and enthalpy change (ΔHtrs) of solid–solid transitions (I → II and II → III) for K2WO4

The temperatures and enthalpy changes for the solid–solid transitions (I → II and II → III) of K2WO4 were measured by DSC in the present work. These measurements along with all data from the literature are shown in Tables 28 and 29, respectively. Our experimental DSC thermogram is displayed in the supplementary material (Fig. S5). Some authors reported a single solid–solid transition86,117 while others reported two such transitions.42,53,91,108 Our DSC measurements at a heating/cooling rate of 10 °C/min confirmed that K2WO4 exhibits two different solid–solid transitions.

TABLE 28.

Transition temperature and enthalpy change of transition I → II for K2WO4

Ttrs (I → II) (°C) Δ H trs I II (kJ mol−1) Experimental method Reference
362.7  9.82  DSC (second heating) at 10 °C/min  This work 
361.7  9.84  DSC (third heating) at 10 °C/min  This work 
358  ⋯  Cooling curves  117  
350a  9.121 ± 0.146  DTA at 1 °C/min  86  
381a  11.464  DTA  53  
370  ⋯  DTA at 5 °C/min  91  
370  ⋯  XRDb  42  
⋯  12  Thermal analysis (DTA) at 8–10 °C/min  108  
364.1 ± 9.6  10.3 ± 2.2  Weighted average  This work 
Ttrs (I → II) (°C) Δ H trs I II (kJ mol−1) Experimental method Reference
362.7  9.82  DSC (second heating) at 10 °C/min  This work 
361.7  9.84  DSC (third heating) at 10 °C/min  This work 
358  ⋯  Cooling curves  117  
350a  9.121 ± 0.146  DTA at 1 °C/min  86  
381a  11.464  DTA  53  
370  ⋯  DTA at 5 °C/min  91  
370  ⋯  XRDb  42  
⋯  12  Thermal analysis (DTA) at 8–10 °C/min  108  
364.1 ± 9.6  10.3 ± 2.2  Weighted average  This work 
a

Outlier.

b

A high temperature focusing Guinier camera from Nonius was used with a calibrated thermocouple. The estimated error is about ±10 °C.

TABLE 29.

Transition temperature and enthalpy change of transition II → III for K2WO4

Ttrs (II → III) (°C) Δ H t r s II III (kJ mol−1) Experimental method Reference
461.1  1.031  DSC (second heating) at 10 °C/min  This work 
461.3  1.001  DSC (third heating) at 10 °C/min  This work 
456  1.046  DTA  53  
455  ⋯  DTA at 5 °C/min  91  
435a  ⋯  XRDb  42  
⋯  1.2  Thermal analysis (DTA) at 8–10 °C/min  108  
458.4 ± 5.7  1.1 ± 0.2  Weighted average  This work 
Ttrs (II → III) (°C) Δ H t r s II III (kJ mol−1) Experimental method Reference
461.1  1.031  DSC (second heating) at 10 °C/min  This work 
461.3  1.001  DSC (third heating) at 10 °C/min  This work 
456  1.046  DTA  53  
455  ⋯  DTA at 5 °C/min  91  
435a  ⋯  XRDb  42  
⋯  1.2  Thermal analysis (DTA) at 8–10 °C/min  108  
458.4 ± 5.7  1.1 ± 0.2  Weighted average  This work 
a

Outlier.

b

A high temperature focusing Guinier camera from Nonius was used with a calibrated thermocouple. The estimated error is about ±10 °C.

4.6.2. Temperature (Tfus) and enthalpy of fusion (ΔHfus) for K2WO4

The properties of fusion (temperature and enthalpy change) were determined by Refs. 53, 62, 73, 86, 97, 118, and 119. All experimental data from the literature and our own DSC measurements are presented in Table 30.

TABLE 30.

Transition temperature and enthalpy of fusion for K2WO4

Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
928.2  32.47  DSC (second heating) at 10 °C/min  This work 
927.7  32.57  DSC (third heating) at 10 °C/min  This work 
894a  ⋯  Cooling curves  73  
926  ⋯  Visual-polythermal analysis  118  
926  ⋯  Visual-polythermal analysis  119  
928  31.087 ± 0.146  DTA at 1 °C/min  86  
923  30.711  DTA  53  
919a  ⋯  Visual-polythermal analysis  62  
926  ⋯  Thermal analysis  97  
926.5 ± 3.3  32.0 ± 1.7  Weighted average  This work 
Tfus (III → L) (°C) ΔHfus (III → L) (kJ mol−1) Experimental method Reference
928.2  32.47  DSC (second heating) at 10 °C/min  This work 
927.7  32.57  DSC (third heating) at 10 °C/min  This work 
894a  ⋯  Cooling curves  73  
926  ⋯  Visual-polythermal analysis  118  
926  ⋯  Visual-polythermal analysis  119  
928  31.087 ± 0.146  DTA at 1 °C/min  86  
923  30.711  DTA  53  
919a  ⋯  Visual-polythermal analysis  62  
926  ⋯  Thermal analysis  97  
926.5 ± 3.3  32.0 ± 1.7  Weighted average  This work 
a

Outlier.

4.6.3. Recommended thermodynamic data for potassium tungstate K2WO4

Our selected thermodynamic data ( Δ f H 298 ° , S 298 ° , and CP) for potassium tungstate (K2WO4) are given in Table 31.

TABLE 31.

Selected thermodynamic properties of K2WO4

Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2WO4(I)  298.15  −1581.60  175.81    (FactSage, SGPS database66
298.15–637.3      113.39 + 0.125 52 T/K 
K2WO4(II)  298.15  −1571.33  191.92    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–731.5      194.56 
K2WO4(III)  298.15  −1570.28  193.36    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–1199.6      194.56 
K2WO4(L)  298.15  −1538.30  220.02    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–1199.6      194.56 
1199.6–2000      213.38 
Phase T range (K) Δ f H 298 ° (kJ mol−1) S 298 ° (J mol−1 K−1) CP (J mol−1 K−1) Reference
K2WO4(I)  298.15  −1581.60  175.81    (FactSage, SGPS database66
298.15–637.3      113.39 + 0.125 52 T/K 
K2WO4(II)  298.15  −1571.33  191.92    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–731.5      194.56 
K2WO4(III)  298.15  −1570.28  193.36    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–1199.6      194.56 
K2WO4(L)  298.15  −1538.30  220.02    This work 
298.15–637.3      113.39 + 0.125 52 T/K  (FactSage, SGPS database66
637.3–1199.6      194.56 
1199.6–2000      213.38 

The standard enthalpy at 298.15 K ( Δ f H 298 ° ) was taken directly from the SGPS database in FactSage.66 Indeed, this value (−1581.6 kJ mol−1) is close to the value of −1574.0 kJ mol−1 assessed using the equation of Hisham and Benson116 with an approach similar to that described previously for Na2WO4. The validity of this equation was confirmed by us for the compounds Na2CrO4, K2CrO4, Na2MoO4 and K2MoO4, for which there was good agreement between the estimated Δ f H 298 ° values and our selected values based on experimental data from the literature. For K2WO4, OQMD68,69 reported an enthalpy of formation at 0 K of −1645.27 kJ mol−1 using DFT. The corresponding value given in Materials Project70 is −1528.42 kJ mol−1.

The standard entropy at 298.15 K ( S 298 ° ) of K2WO4(I) was taken directly from the SGPS database in FactSage66 since no other values were available in the literature. Also, S 298 ° was roughly estimated from the exchange reactions N a 2 W O 4 I + K 2 Cr O 4 I K 2 W O 4 I + N a 2 Cr O 4 I and N a 2 W O 4 I + 2 KC l sol K 2 W O 4 I + 2 NaC l sol , for which ∆S was assumed to be null at 298.15 K. The corresponding estimates are 184.46 and 181.92 J mol−1 K−1, respectively, which compares reasonably well to our selected value of 175.81 J mol−1 K−1.

To our knowledge, no experimental data for the heat capacity of K2WO4 are published. Therefore, the heat capacity expression (as a function of temperature) for this compound was taken directly from the SGPS database of FactSage.66 

Table 32 provides a summary of all transition temperatures and enthalpies of transition estimated in the present work, along with their assessed uncertainties.

TABLE 32.

Summary table of recommended values

Transition Ttrs (°C) U(Ttrs) (°C) ΔHtrs (kJ mol−1) UHtrs) (kJ mol−1)
Na2CrO4(I → II)  419.1  2.7  9.6  0.6 
Na2CrO4(II → L)  793.3  3.2  24.3  0.9 
K2CrO4(I → II)  669.2  7.1  7.0  0.5 
K2CrO4(II → L)  975.9  9.9  33.1  1.8 
Na2MoO4(I → II)  457.6  3.7  23.1  4.9 
Na2MoO4 (II → III)  591.8  2.5  1.9  0.3 
Na2MoO4(III → IV)  640.6  3.4  8.2  0.4 
Na2MoO4(IV → L)  687.1  3.5  20.4  2.5 
K2MoO4(I → II)  323.5  3.8  10.6  2.9 
K2MoO4(II → III)  454.7  3.9  1.0  0.1 
K2MoO4(III → L)  927.8  5.9  36.6  5.0 
Na2WO4(I → II)  588.3  3.1  31.5  5.9 
Na2WO4(II → L)  694.2  5.6  27.0  6.6 
K2WO4(I → II)  364.1  9.6  10.3  2.2 
K2WO4(II → III)  458.4  5.7  1.1  0.2 
K2WO4(III → L)  926.5  3.3  32.0  1.7 
Transition Ttrs (°C) U(Ttrs) (°C) ΔHtrs (kJ mol−1) UHtrs) (kJ mol−1)
Na2CrO4(I → II)  419.1  2.7  9.6  0.6 
Na2CrO4(II → L)  793.3  3.2  24.3  0.9 
K2CrO4(I → II)  669.2  7.1  7.0  0.5 
K2CrO4(II → L)  975.9  9.9  33.1  1.8 
Na2MoO4(I → II)  457.6  3.7  23.1  4.9 
Na2MoO4 (II → III)  591.8  2.5  1.9  0.3 
Na2MoO4(III → IV)  640.6  3.4  8.2  0.4 
Na2MoO4(IV → L)  687.1  3.5  20.4  2.5 
K2MoO4(I → II)  323.5  3.8  10.6  2.9 
K2MoO4(II → III)  454.7  3.9  1.0  0.1 
K2MoO4(III → L)  927.8  5.9  36.6  5.0 
Na2WO4(I → II)  588.3  3.1  31.5  5.9 
Na2WO4(II → L)  694.2  5.6  27.0  6.6 
K2WO4(I → II)  364.1  9.6  10.3  2.2 
K2WO4(II → III)  458.4  5.7  1.1  0.2 
K2WO4(III → L)  926.5  3.3  32.0  1.7 

In this work, thermodynamic properties (standard enthalpy at 298.15 K, standard entropy at 298.15 K, heat capacity as a function of temperature) were selected for all condensed phases of the compounds Na2CrO4, K2CrO4, Na2MoO4, K2MoO4, Na2WO4 and K2WO4, based on a critical analysis of all available experimental data from the literature. In addition, for the six compounds, the temperatures and enthalpy changes of all solid–solid transitions and of fusion were measured by DSC. Those data were also considered for our selection of the thermodynamic properties. Crystal structures and space groups were collected from the literature for all phases of the six compounds. High-temperature XRD measurements permitted us to conclude that K2MoO4 displays three phases instead of the four reported in several publications.

The present work is the first step towards the development of a thermodynamic model for the Na+, K+//Cl, SO42−, CO32−, CrO42−, Cr2O72−, MoO42−, Mo2O72−, WO42−, W2O72−, O2− system that is relevant in the high temperature corrosion of equipment such as heat-transfer tubes. A critical evaluation of the thermodynamic properties of the compounds Na2Cr2O7, K2Cr2O7, Na2Mo2O7, K2Mo2O7, Na2W2O7 and K2W2O7 will be described in a subsequent paper. These compounds need to be considered since reactions of the type 2 A2MO4 ⇋ A2M2O7 + A2O (where A = Na, K and M = Cr, Mo, W) may partly occur. Through phase equilibria calculations (which will avoid a tedious and costly trial and error experimental approach), the developed thermodynamic model will permit us to better understand high temperature corrosion phenomena in the temperature range 600–950 °C. The developed thermodynamic model will also enable a better investigation of the chemistry of ash deposits and heat exchanger alloys since the combined ash/gas/alloy chemistry controls the melting behaviour of ashes.

See the supplementary material for DSC thermograms and scatter plots for Na2CrO4, K2CrO4, Na2MoO4, K2MoO4, Na2WO4, and K2WO4.

Ms. Sara Benalia would like to thank the Canada Research Chair in Computational Thermodynamics for High Temperature Sustainable Processes held by Professor Patrice Chartrand and the Johan Gadolin Process Chemistry Centre for the 5 month-mobility grant awarded for her stay at Åbo Akademi University (Turku, Finland). The authors would like to thank Mr. Peter Backman and Ms. Jaana Paananen for operating the DSC apparatus, Ms. Evguenia Sokolenko for helping locate old articles and for translating them into English, Dr. Paul Lafaye for fruitful discussions, and Mr. Maxime Aubé for his helpful comments on the manuscript.

The authors have no conflict to disclose.

The data that support the findings of this study are available within the article and its supplementary material.

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