Thermodynamic properties of molybdate ion: reaction cycles and experiments

Heinz Gamsjäger; Masao Morishita

doi:10.1515/pac-2014-1105

Publicly Available Published by De Gruyter March 12, 2015

Thermodynamic properties of molybdate ion: reaction cycles and experiments

Heinz Gamsjäger and Masao Morishita

From the journal Pure and Applied Chemistry

https://doi.org/10.1515/pac-2014-1105

Abstract

Standard molar quantities of molybdate ion entropy, Sm0, enthalpy of formation, ΔfHmo, and Gibbs energy of formation, ΔfGmo, are key data for the thermodynamic properties of molybdenum compounds and complexes, which are at present investigated by an OECD NEA review project. The most reliable method to determine ΔfHmo of molybdate ion and alkali molybdates directly consists in measuring calorimetrically the enthalpy of dissolution of crystallized molybdenum trioxide and anhydrous alkali molybdates in corresponding aqueous alkali metal hydroxide solutions. Solubility equilibria of sparingly soluble alkaline earth molybdates and silver molybdate lead to trustworthy data for ΔfGmo of molybdate ion. Thereby the Gibbs energies of the metal molybdates and the corresponding metal ions are combined with the Gibbs energies of dissolution. As reliable values are available for ΔfGmo of the relevant metal ions the problem reduces to select the best values of solubility constants and ΔfGmo of alkaline earth molybdates and silver molybdate. There are two independent possibilities to achieve the latter task. (1) ΔfHmo for alkaline earth molybdates and silver molybdate have been determined by solution calorimetry. Entropy data of molybdenum have been compiled and evaluated recently. CODATA key values are available for Smo of the other elements involved. Whereas Smo(CaMoO4, cr) is well known since decades, low-temperature heat capacity measurements had to be performed recently, but now reliable values for Smo of Ag₂MoO₄(cr), BaMoO₄(cr) and SrMoO₄(cr) are available. (2) ΔfHmo(BaMoO4, cr), for example, can be obtained from high temperature equilibria also, but the result is less accurate than that of the first method. Once Gibbs energy of formation, ΔfGmo, and enthalpy of formation, ΔfHmo, of molybdate ion are known its standard entropy, Smo, can be calculated.

Keywords: enthalpy; entropy; ISSP-16; molybdate ion; thermodynamics

Present status of Δ_fH^o, Δ_fG^o and S^o(MoO₄^2–)

Thermodynamic standard data of MoO₄^2– are listed in Table 1. Latimer’s [1] values are clearly obsolete compared to those selected by Dellien et al. [2] and Wagman et al. [3]. While enthalpies and Gibbs energies of formation of [2] and [3] agree quite well the entropies differ by more than 10 J·K^–1·mol^–1, thus a re-evaluation within the framework of the OECD NEA Review Project on “Chemical Thermodynamics of Molybdenum” seemed appropriate. The final deliverable of Phase III of this Thermodynamic Data Base project is the “Chemical Thermodynamics of Iron, Part 1” [4], which is freely downloadable from the Internet. In sections Background, Focus of the review and Review procedure and results of this and the other chemical thermodynamics volumes background and procedure of the OECD-NEA reviews are explained. Thermodynamic properties of molybdate ion investigated and evaluated in this work are key data controlling solution chemistry of molybdenum compounds.

Table 1

Present status of Δ_fH^o, Δ_fG^o, S^o (MoO₄^2–) at T_ref = 298.15 K.

References	Δ_fH^o/kJ·mol^–1	Δ_fG^o/kJ·mol^–1	S ^o/J·K^–1·mol^–1
Latimer [1]	–1063.99	–915.46	58.60
Dellien et al. [2]	–997.05	–838.47	37.70
Wagman et al. [3]	–997.9	–836.3	27.2

Standard molar enthalpy of formation of molybdate ion and alkali molybdates

Enthalpy of dissolution of molybdenum trioxide in dilute aqueous alkali hydroxide

Graham and Hepler [5] constructed a high precision calorimeter and derived Δ_fH^o (Na₂MoO₄, cr, 298.15 K) as well as Δ_fH^o (MoO₄^2–, 298.15 K) by measuring the enthalpies of solution of the following reactions.

(1) MoO 3 ( cr ) + 2 NaOH ( 0.531 mol dm − 3 ) = soln . I + H 2 O ( l ) (1)

(2) soln . I = Na 2 MoO 4 ( cr ) (2)

(1) + (2) = (3) MoO 3 ( cr ) + 2 NaOH ( 0.531 mol dm − 3 ) = Na 2 MoO 4 ( cr ) + H 2 O ( l ) (1) + (2) = (3)

A detailed calorimetric balance is given in Table 2. Interconversion between amount ratio (mole ratio) r(H₂O/B) and molality m_B is achieved by eq. (4), where MH2O is the molar mass of H₂O.

Table 2

Calorimetric determination of ΔfH°(MoO42−, 298.15 K),r(H₂O/NaOH) = 104.4, m(NaOH) ≈ 0.53 mol·kg^–1 [5].

Reaction	(Δ_rH°± dΔ_rH°)/kJ·mol^–1
MoO₃(cr) + 50 (NaOH·104.4H₂O) = Na₂MoO₄·48NaOH·5221H₂O	–78.868 ± 0.837 (2r1)
Na₂MoO₄·48NaOH·5221H₂O = Na₂MoO₄·208.84H₂O + 48(NaOH·104.42H₂O)	0 ± 0.40 (2r2)
48(NaOH·104.42H₂O) = 48(NaOH·104.4H₂O) + 0.96H₂O(l)	0 ± 0.021 (2r3)
2(NaOH·∞H₂O) = 2(NaOH·104.4H₂O) + (∞ –208.8)H₂O(l)	0.938 ± 0.10 (2r4)
Na₂MoO₄·208.84H₂O + (∞ -208.84)H₂O(l) = Na₂MoO₄·∞H₂O	–0.309 ± 0.20 (2r5)

MoO₃(cr) + 2(NaOH·∞H₂O) = Na₂MoO₄·∞H₂O + H₂O(l)
MoO₃(cr) + 2OH^- = MoO₄^2- + H₂O(l)	–78.239±0.954(2r6)

(4) r ( H 2 O / B ) = 1 / ( M H 2 O m B ) (4)

(5) Δ f H m o ( MoO 4 2 − ) = Δ 2 r 6 H m o + Δ f H m o ( MoO 3 , cr ) [ 6 ] + 2 Δ f H m o ( OH − ) (Tab . 14) − Δ f H m o ( H 2 O,l ) (Tab . 14) Δ f H o ( MoO 4 2 − ) / kJ ⋅ mol − 1 = − ( 997 . 42 ± 1.13 ) (5)

The value for Δ_fH^o(MoO₃, cr, 298.15 K) has been compiled and evaluated recently [6], for this and all other auxiliary data used see section “Auxiliary data”. The values for Δ_2r4H^o and Δ_2r5H^o in Table 2 have been derived from [3], see Figs. 1a, b and 2. Enthalpies of dilution for Na₂MoO₄ have not been determined experimentally, but have been estimated by assuming analogue behavior as observed with Na₂SO₄ (Δ_2r5H^o). At ≈ 0.2 mol·dm^–3 NaOH (r(H₂O/NaOH = 273.8, r(H₂O/Na₂SO₄ = 547.8) corresponding values for Δ_r4H^o and Δ_r5H^o practically cancel each other, see the numerical values in red in Figs. 1a and 2.

$Fig. 1 (a) Calculation of ΔfHmo[r(H2O/NaOH)]${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}[r({{\rm{H}}_2}{\rm{O/NaOH)]}}$ for 50≤r≤500. (b) Calculation of ΔfHmo[r(H2O/NaOH)]${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}[r({{\rm{H}}_2}{\rm{O/NaOH)]}}$ for 50≤r≤200.$

Fig. 1

(a) Calculation of ΔfHmo[r(H2O/NaOH)] for 50≤r≤500. (b) Calculation of ΔfHmo[r(H2O/NaOH)] for 50≤r≤200.

$Fig. 2 Calculation of ΔfHmo[r(H2O/Na2SO4)].${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}[r({{\rm{H}}_2}{\rm{O/N}}{{\rm{a}}_2}{\rm{S}}{{\rm{O}}_4}{\rm{)]}}{\rm{.}}$ For 160≤r≤600.$

Fig. 2

Calculation of ΔfHmo[r(H2O/Na2SO4)]. For 160≤r≤600.

Crouch-Baker and Dickens [7] dissolved MoO₃(cr) in 0.20 mol·kg^–1 NaOH, thus there is only a minute difference between the recalculated values of Δ_r1H^o and Δ_r6H^o, see Table 3.

Table 3

Standard enthalpy of reaction MoO₃(cr) + 2OH^– = MoO₄^2– + H₂O(l).

Alkali metal	Δ_r1H^o/kJ·mol^–1	Δ_r6H^o/kJ·mol^–1	Reference
Li	–77.579 ± 0.661	–78.178 ± 0.661	[10]
Li	–77.091 ± 0.569	–77.718 ± 0.569	[12]
Na	–78.868 ± 0.954	–78.239 ± 0.954	[5]
Na	–78.099 ± 0.963	–78.088 ± 0.963	[7]
Rb	–77.870±0.635	–77.090±0.635	[9]
Cs	–78.025±0.655	–77.026±0.655	[8]

O’Hare and his coworkers determined Δ_fH^o (MoO₄^2–, 298.15 K) as well as Δ_fH^o (Ma₂MoO₄, 298.15 K), where Ma = Cs, Rb or Li, by measuring the enthalpy of solution of MoO₃(cr) and Ma₂MoO₄(cr) in ≈ 0.24 mol·dm^–3 CsOH [8], ≈ 0.2 mol·dm^–3 RbOH [9], and ≈ 0.2 mol·dm^–3 LiOH [10]. In each case a detailed calorimetric balance of the reaction cycle analogous to Table 2 was presented. Enthalpies of dilution for Cs₂MoO₄, etc. should be known. In [9] Δ_rH^o for reactions analogous to (2r2) and (2r3) were set to zero and Δ_rH^o for reactions analogous to (2r4) and (2r5) were assumed to cancel each other. The latter assumption, however, turned out to be approximately true only for sodium sulfate (r = 547.8). Thus corrections were applied assuming that dilution enthalpies of cesium, rubidium and lithium molybdates can be approximated by calculating the dilution enthalpies of the corresponding sulfates.

Similar experiments have been carried out by Suponitskii et al. [11] when MoO₃(cr) was dissolved in 0.32 mol·dm^–3 NaOH. The enthalpies of solution obtained Δ_r1H^o/kJ·mol^–1 = –(78.01 ± 1.17) and Δ_r6H^o/kJ·mol^–1 = –(77.86 ± 1.25) agree quite well with the other determinations of this quantity [5, 7–10, 12]. However, the radiation correction given in Table 1 of [11] could not be assigned properly. In addition 0.32 mol·dm^–3 NaOH equals r(H₂O/NaOH) = 173.25 and not r(H₂O/NaOH) = 185, thus Δ_r6H^o given in [11] was excluded from calculation of the weighted mean.

Shukla et al. [12] determined ΔslnHmo values of MoO₃(cr), Li₂MoO₄(cr) and of [Li₂O(cr) + MoO₃(cr)] in LiOH(aq, 0.1 mol·dm^–3) at 298.15 K using an isoperibol solution calorimeter. From these data ΔfHmo (Li₂MoO₄, cr) and ΔfHmo (MoO₄^2–) were obtained. Results of references [5, 8–10], and [12] have been evaluated in a manner similar to that described for Na₂MoO₄(cr).

In Table 3 the weighted mean of Δ_r1H^o and Δ_r6H^o has been calculated. Δ_r1H^o and Δ_r6H^o differ only by a quarter of the 2σ values, but Δ_r6H^o is considered to be more reliable, and thus has been used for all further calculations.

Weighted mean: (Δ_r1H^o ± 2σ)/kJ·mol^–1 = –(77.759 ± 0.569), (Δ_r6H^o ± 2σ)/kJ·mol^–1 = –(77.625 ± 0.569) selected!

Equation (5) leads to the selected value:

Δ f H o ( MoO 4 2 − , 298.15 K ) / kJ ⋅ mol − 1 = − ( 996.807 ± 0.826 )

In principle Δ_fH^o(MoO₄^2–, 298.15 K) can be obtained also from eq. (6):

(6) Δ f H o (MoO 4 2 − ) = − R ( ∂ ln K s0 o / ∂ T − 1 ) p − n Δ f H o ( M 2 + / n ) + Δ f H o ( M n MoO 4 , cr ) (6)

Only Ks0o of Ag₂MoO₄(cr) has been measured in a temperature range which allows to calculate (∂lnKs0o/∂T−1)p reliably. For silver molybdate −R(∂lnKs0o/∂T−1)p = (58.4 ± 3.7) kJ⋅mol−1 [13], Δ_fH^o(Ag₂MoO₄, cr) = –(838.16 ± 2.00) kJ·mol^–1 [14]. For Δ_fH^o(Ag⁺) see section “Auxiliary data”. These data lead to Δ_fH^o(MoO₄^2–, 298.15 K = –(991.3 ± 4.2) kJ·mol^–1, and this value almost overlaps with the one determined by solution calorimetry of LiOH, NaOH, RbOH CsOH and MoO₃(s). As its uncertainty is ≈ 4.5 times higher, it was disregarded for the calculation of the weighted mean.

Standard molar enthalpy of formation of anhydrous sodium molybdate

The enthalpies of formation of alkali molybdates play an important role for the determination of formation enthalpies for silver, barium and strontium molybdate. Thus, in this section methods to obtain Δ_fH^o(Na₂MoO₄, cr) will be discussed. As pointed out in subsection “Enthalpy of dissolution of molybdenum trioxide in dilute aqueous alkali hydroxide”, Graham and Hepler [5] and O’Hare et al. [8–10] determined Δ_fH^o (Ma₂MoO₄, cr, 298.15 K), where Ma = Cs, Rb, Na or Li, by measuring the enthalpy of solution of MoO₃(cr) and Ma₂MoO₄(cr) in dilute aqueous solutions of the corresponding alkali hydroxide. The detailed calorimetric balance leading to Δ_fH^o(Na₂MoO₄, cr) is given in Table 4.

Table 4

Reaction scheme and thermochemical data of Δ_fH^o(Na₂MoO₄, cr, 298.15 K).

Reaction [5]	(Δ_rH^o ± δΔ_rH^o)/kJ·mol^–1
MoO₃(cr) + 50 (NaOH·104.4H₂O) = Na₂MoO₄·48NaOH·5221H₂O (r1)
Na₂MoO₄·48NaOH·5221H₂O = Na₂MoO₄(cr) + 48(NaOH·104.42H₂O) (r2)	–69.141 ± 0.804 (4r1 + 4r2)
50(NaOH·104.42H₂O) = 50(NaOH·104.4H₂O) + H₂O(l)	0 ± 0.02 (4r3)
2(NaOH·∞H₂O) = 2(NaOH·104.42 H₂O) + (∞ –208.84) H₂O(l)	0.938 ± 0.10 (4r4)

MoO₃(cr) + 2(NaOH·∞H₂O) = Na₂MoO₄(cr) + H₂O(l)	–68.203 ± 0.810 (4r5)
MoO₃(cr) + 2Na⁺ + 2OH^- = Na₂MoO₄(cr) + H₂O(l)

(7) Δ f H m o (Na 2 MoO 4 , cr) = Δ 4r5 H m o − Δ f H m o ( H 2 O, l) + 2 Δ f H m o (NaOH ⋅ ∞ H 2 O)[3] + Δ f H m o (MoO 3 , cr) Δ f H m o (Na 2 MoO 4 ,cr) = − ( 1467.574 ± 1.014 ) / kJ · mol − 1 (7)

As the enthalpies of dilution have been taken from [3], so was the value for ΔfHmo(NaOH⋅∞H2O), the uncertainty assigned to it was obtained by combining the values listed for ±δΔfHmo(Na+) and ±δΔfHmo(OH−) in [15].

Koehler et al. [16] adopted a different reaction scheme for the solution calorimetric determination of ΔfHmo(Na2MoO4, cr), see Table 5:

Table 5

Calorimetric reaction scheme for ΔfHmo(Na2MoO4, cr).

Eq.	Reaction [16]	Δ_5rH_303.15/kJ·mol^–1
(5r1)	MoO₃(cr) + 2OH^–(sol) = MoO₄^2–(sol) + H₂O(sol)	–77.188 ± 0.133
(5r2)	2NaCl(cr) = 2Na⁺(sol) + 2Cl^–(sol)	7.448 ± 0.030
(5r3)	26.462H₂O(l) = 26.462H₂O(sol)	0.042 ± 0.042
(5r4)	2Na⁺(sol) + MoO₄^2–(sol) = Na₂MoO₄(cr)	10.572 ± 0.043
(5r5)	2 Cl^–(sol) + 27.462H₂O(sol) = 2(HCl·12.731H₂O)(l) + 2OH^–(sol)	117.727 ± 0.575

(5r6)	MoO₃(cr) + 2NaCl(cr) + 26.462H₂O(l) = Na₂MoO₄(cr) + 2(HCl·12.731H₂O)(l)	58.601 ± 0.594 Δ_5r6H_298.15/kJ·mol^–1 59.897 ± 0.594

(8) Δ f H m o (Na 2 MoO 4 , cr) = Δ 5r6 H m o − 2 Δ f H m o (HCl, r = 12.731 )[3] + 2 Δ f H m o (NaCl, cr)(Tab . 14) + Δ f H m o (H 2 O , l) + Δ f H m o (MoO 3 , cr) (8)

The value for ΔfHmo(HCl, r = 12.731)/kJ⋅mol−1 = −(162.421 ± 0.209) has been calculated from enthalpies of dilution listed in [3], see Fig. 3, the uncertainty was taken from [16].

$Fig. 3 Calculation of ΔfHmo[r(H2O/HCl)].${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}[r({{\rm{H}}_2}{\rm{O/HCl)]}}{\rm{.}}$ for 8≤r≤26.$

Fig. 3

Calculation of ΔfHmo[r(H2O/HCl)]. for 8≤r≤26.

As the calorimetric experiments were carried out at T = 303.15 K the authors [16] corrected Δ5r6Hmo to T = 298.15 K. This correction was accepted, but for calculating the weighted mean the uncertainty was increased by a factor of 1.5, δΔfHmo(Na2MoO4, cr) = ± (1.5⋅0.968)kJ⋅mol−1.

Δ f H m o (Na 2 MoO 4 , cr, 298 .15 K)/kJ ⋅ mol − 1 = − (1468 .593 ± 1 .452)

Tangri et al. [17] synthesized Na₂MoO₄(cr) from stoichiometric quantities of sodium carbonate and molybdenum trioxide by means of a pyrometallurgical technique, and measured its molar enthalpy of solution at 298.15 K using an isoperibol calorimeter. Dash and Shukla [18] carried out similar calorimetric experiments, but prepared anhydrous sodium molybdate by heating of Na₂MoO₄·2H₂O at 450 K for 8 h under a stream of high purity argon. To convert Δ_slnH_m (Table 6, column 4) into ΔslnHmo (Table 6, column 5) the Debye-Hückel limiting law according to eq. (9) was used, where v is the sum of stoichiometric numbers of ions, z₊ and z_– are cation and anion charge numbers, respectively, and A_H/RT = 0.80185 (kg·mol^–1)^0.5 has been taken from [19].

Table 6

Enthalpy of solution of Na₂MoO₄(cr).

Refs.	Na₂MoO₄m/mol·kg^–1	(I_m/mol·kg^–1)^0.5	Δ_slnH_m (r > 1000)/kJ·mol^–1	Δ sln H m o ( r = ∞ ) / k J ⋅ m o l − 1
[17]	0.01158	0.18639	–10.464	–11.575
	0.01170	0.18735	–11.122	–12.240
	0.01005	0.17364	–10.129	–11.165
	0.01125	0.18371	–11.419	–12.515
	0.01019	0.17484	–10.662	–11.705
	0.01053	0.17774	–10.361	–11.421
			(Δ_slnH^o ± 2σ)/kJ·mol^–1 = –10.693 ± 0.977	(Δ_slnH^o ± 2σ)/kJ·mol^–1 = –11.770 ± 1.022
[18]	0.003690	0.10522	–9.848	–10.475
	0.002331	0.08362	–9.684	–10.183
	0.002137	0.08006	–10.043	–10.520
	0.002914	0.09349	–10.022	–10.580
			(Δ_slnH^o ± 2σ)/kJ·mol^–1 = –9.899 ± 0.336	(Δ_slnH^o ± 2σ)/kJ·mol^–1 = –10.440 ± 0.353

(9) Δ sln H m = Δ sln H m o + A H ν 2 | z + z − | I m 0.5 (9)

In [18] it is argued that at amount ratio r(H₂O/Na₂MoO₄) > 1000 the measured heat of solution equals the heat at infinite dilution. Table 6, however, shows that ΔslnHmo(r = ∞) – Δ_slnH_m (r ≈ 5000) ≈ –1 kJ·mol^–1 andΔslnHmo(r = ∞) – Δ_slnH_m (r ≈ 20 000) ≈ –0.5 kJ·mol^–1, thus these differences are by no means negligible.

As ΔslnHmo refers to reaction Na₂MoO₄(cr) 2Na⁺ + MoO₄^2– the standard molar enthalpy of sodium molybdate formation can be obtained by eq. (10).

(10) Δ f H m o (Na 2 MoO 4 , cr) = 2 Δ f H m o (Na + )[15] + Δ f H m o (MoO 4 2 − ) − Δ sln H m o (10)

Δ f H m o (Na 2 MoO 4 , cr)/kJ ⋅ mol − 1 = − (1465.717 ± 2 ⋅ 1 .320) [17]

= − ( 1467.047 ± 0.906 ) [18]

The atomic ratio of anhydrous sodium molybdate Na₂MoO₄(cr) synthesized and studied by [17] r(Na/Mo) = 1.999 ± 0.052, this scatter might be the reason that in this work the value for ΔfHmo(Na2MoO4, cr) is slightly higher than those found by [5, 16] and [18]. Thus for calculating the weighted mean the uncertainty was increased by a factor of 2, δΔfHmo(Na2MoO4) = ± 2.64 kJ⋅mol−1.

For further calculations the weighted mean of ΔfHmo(Na2MoO4, cr) from the results of [5, 16–18] was selected:

Δ f H m o (Na 2 MoO 4 , cr, 298 .15 K) = − (1467 .423 ± 0 .597) kJ ⋅ mol − 1 .

Standard molar Gibbs energy of formation of molybdate ion

Determination of ΔfGmo(MoO42−) using solubility data of crystalline calcium, strontium, barium, and silver molybdate

O’Hare et al. [10] derived Δ_fG^o (MoO₄^2–, 298.15 K) using Ks0o data obtained from solubility equilibria, M_nMoO₄(cr) nM^2/n+(aq) + MoO₄^2–(aq), and eq. (11). In the present application M_nMoO₄ stands for calcium, strontium, barium, and silver molybdate. CODATA key values [15] and NEA selected auxiliary data [20] are available for the corresponding Gibbs energies of metal ion formation Δ_fG^o(M^2+/n). Corresponding Ks0o values have been reviewed recently [13].

(11) Δ f G o (MoO 4 2 − ) = − R T ref ln K s0 o − n Δ f G o ( M 2 + / n ) + Δ f G o ( M n MoO 4 , cr ) (11)

One way to obtain Δ_fG^o(M_nMoO₄, cr) is by eqs. (12) and (13).

(12) Δ f S o (M n MoO 4 , cr ) = S o ( M n MoO 4 , cr ) − n S o ( M, cr ) − 2 S o ( O 2 , g ) − S o ( Mo, cr ) (12)

(13) Δ f G o (M n MoO 4 , cr ) = Δ f H o (M n MoO 4 , cr ) − T ref Δ f S o (M n MoO 4 , cr ) (13)

For S^o(M, cr) and S^o(O₂, g) again CODATA key values [15] and NEA selected auxiliary data [20] are available, whereas S^o(Mo, cr) has been compiled and evaluated recently [6]. Low-temperature heat capacity measurements of Morishita and his group led to standard entropies of Ag₂MoO₄(cr) (Morishita, private communication), BaMoO₄(cr) (Morishita, private communication) and SrMoO₄(cr) [21], which differ from those accepted so far by 7–15 J·K^–1·mol^–1, see Table 7 [3, 22]. The new value of Smo(CaMoO4(cr, 298.15)) (Morishita, private communication) agrees within experimental uncertainties with the one obtained by Weller and King [23], (122.6 ± 0.8) J·K^–1·mol^–1.

Table 7

Standard molar entropies of sparingly soluble molybdates.

Solid molybdates	S m o / J ⋅ K − 1 ⋅ mol − 1			Δ f S m o / J ⋅ K − 1 ⋅ m o l − 1
Solid molybdates	Ref. [3]	Ref. [22]	Ref. [(Morishita, private communication), 21]	Refs. [6, 15, 20, 21(Morishita, private communication)]
Ag₂MoO₄(cr)	213	–	220.80 ± 2.21	–303.18 ± 2.25
BaMoO₄(cr)	138	146.9 ± 4.6	152.69 ± 1.53	–348.62 ± 1.75
SrMoO₄(cr)	–	128.9 ± 5.0	136.56 ± 1.37	–358.02 ± 1.39
CaMoO₄(cr)	122.6	122.6 ± 1.0	121.69 ± 1.22	–358.78 ± 1.29

Muldrow and Hepler determined Δ_fH^o(Ag₂MoO₄, cr) [14] and Δ_fH^o(CaMoO₄, cr) [24] by measuring solution enthalpies of reactions (14r), (16r), (18r), and (20eff) in their high precision calorimeter.

Silver molybdate

In the 1^st series of calorimetric experiments [14] the enthalpy of reaction of crystalline Na₂MoO₄ with dilute solutions of AgNO₃ in excess was measured to determine the enthalpy of precipitation of Ag₂MoO₄. The calorimetric reaction has been written as eq. (14r)

(14r) Na 2 MoO 4 ( cr ) + AgNO 3 ( excess dil . sln . ) = Ag 2 MoO 4 ( cr ) + AgNO 3 ( dil . sln . ) + NaNO 3 ( dil . sln . ) → Δ 14 H m o (14r)

The enthalpies of dilution of NaNO₃ and AgNO₃ have been ignored because in these dilute solutions the respective heat effects are small and tend to cancel each other. Thus the calorimetric equation used effectively can be written as

(14eff) Na 2 MoO 4 ( cr ) + 2 Ag + = Ag 2 MoO 4 ( cr ) + 2 Na + → Δ 14 H m o / kJ ⋅ mol − 1 = − ( 61.086 ± 2.292 ) , mean of 8 data sets (14eff)

(15) Δ f H m o (Ag 2 MoO 4 , cr) = Δ 14 H m o − 2 Δ f H m o (Na + ) + 2 Δ f H m o (Ag + )[15] + Δ f H m o (Na 2 MoO 4 , cr) Δ f H m o (Na 2 MoO 4 , cr, 298 .15 K) / kJ ⋅ mol − 1 = − ( 1467.42 ± 0.60 ) [this work] Δ f H m o (Ag 2 MoO 4 , cr) / kJ · mol − 1 = − ( 836.246 ± 2.378 ) (15)

In the 2^nd series of calorimetric experiments [14] the enthalpy of reaction of excess crystalline AgNO₃ with dilute solutions of Na₂MoO₄ was measured to determine the enthalpy of precipitation of Ag₂MoO₄. The calorimetric reaction has been written as eq. (16r).

(16r) AgNO 3 ( cr , excess ) + Na 2 MoO 4 ( dil . sln ) = Ag 2 MoO 4 ( cr ) + AgNO 3 ( dil . sln ) + NaNO 3 ( dil . sln ) → Δ 16 H m (16r)

To calculate the actual value of ΔcrslnHmo(AgNO3) subtract ΔfHmo(AgNO3, cr) [3] from ΔfHmo(AgNO3, sln) at the corresponding value of r(H₂O/AgNO₃). An analytical function of ΔfHmo(AgNO3, sln) = f[r(H2O)/AgNO3)] can be obtained, just as the curves plotted in Figs. 1–3, by nonlinear regression of respective data listed in [3]. When the enthalpy of solution of excess AgNO₃(cr) had been taken into account, the calorimetric equation used effectively was simplified to

(16eff) 2 AgNO 3 ( c r ) + M o O 4 2 − = Ag 2 MoO 4 ( cr ) + 2 NO 3 − → Δ 16 H m o / kJ ⋅ mol − 1 = − ( 10.84 ± 3.34 ) , mean of 4 data sets (16eff)

(17) Δ f H m o ( AgMoO 4 , cr) = Δ 16 H m o − 2 Δ f H m o ( NO 3 − ) [ 15 ] + Δ f H m o ( MoO 4 2 − ) + 2 Δ f H m o ( AgNO 3 , cr ) [ 3 ] (17)

Δ f H m o (MoO 4 2 − ) /kJ·mol^–1 = –(996.762 ± 0.843) [this work], uncertainty of ΔfHmo(AgNO3, cr) has been estimated by analogy to similar data in [20].

Δ f H m o (Ag 2 MoO 4 , cr)/kJ ⋅ mol − 1 = − (842 .73 ± 3 .67)

The weighted mean of eq. (15) and eq. (17) is the revised result of [14], which is based on auxiliary data accepted at present:

Δ f H o ( Ag 2 MoO 4 , cr , 298.15 K = − ( 838.16 ± 2.00 ) kJ ⋅ mol − 1 .

Calcium molybdate

In the 1^st series of calorimetric experiments [24] the enthalpy of reaction of excess crystalline Ca(NO₃)₂ with dilute solutions of Na₂MoO₄ was measured to determine the enthalpy of precipitation of CaMoO₄. The calorimetric reaction has been written as eq. (18r)

(18r) Ca ( NO 3 ) 2 ( cr , excess ) + Na 2 MoO 4 ( dil . sln ) = CaMoO 4 ( cr ) + Ca ( NO 3 ) 2 ( dil . sln ) + 2 NaNO 3 ( dil . sln ) (18r)

The actual value of ΔcrslnHmo[Ca(NO3)2] was calculated by the same method as was ΔcrslnHmo(AgNO3). When the enthalpy of solution of Ca(NO₃)₂(cr) had been taken into account, the calorimetric equation used effectively was simplified to

(18eff) Ca ( NO 3 ) 2 ( cr , excess ) + MoO 4 2 − = CaMoO 4 ( cr ) + 2 NO 3 − → Δ 18 H m o kJ ⋅ mol − 1 = − ( 12 .67 ± 2.37 ) , mean of 3 data sets (18eff)

(19) Δ f H m o ( CaMoO 4 , cr) = Δ 18 H m o − 2 Δ f H m o ( NO 3 − ) + Δ f H m o ( MoO 4 2 − ) + Δ f H m o [ Ca(NO 3 ) 2 , cr ] [3] Δ f H m o ( CaMoO 4 , cr) / kJ · mol − 1 = − ( 1534.17 ± 2.94 ) (19)

In the 2^nd series of calorimetric experiments [24] the enthalpy of reaction of crystalline Na₂MoO₄ with dilute solutions of Ca(NO₃)₂ was measured to determine the enthalpy of precipitation of CaMoO₄. The calorimetric reaction has been written as eq. (20eff).

(20eff) Na 2 MoO 4 ( cr ) + Ca 2 + = CaMoO 4 ( cr ) + 2 Na + → Δ 20 H m o / kJ ⋅ mol − 1 = − ( 7.05 ± 0.16 ) , mean of 4 data sets (20eff)

(21) Δ f H m o (CaMoO 4 , cr) = Δ 20 H m o − 2 Δ f H m o (Na + ) + Δ f H m o (Na 2 MoO 4 , cr) + Δ f H m o (Ca 2 + )[14] Δ f H m o (CaMoO 4 , cr) / kJ · mol − 1 = − ( 1536.793 ± 1.182 ) (21)

The weighted mean of series 1 and 2 results in: ΔfHmo(CaMoO₄, cr, 298.15 K) = – (1536.43 ± 1.10) kJ·mol^–1. This value agrees perfectly with the original result of [24] ΔfHmo(CaMoO₄, cr, 298.15 K) = –(1536.79 ± 3.77) kJ·mol^–1. Taking into account the difference in ΔcrslnHmo[Ca(NO3)2] measured by preliminary experiments of [24] and given by [3] it is suggested to keep the original uncertainty.

Δ f H m o (CaMoO 4 , cr) / k J · m o l – 1 = – ( 1536.43 ± 3.77 )

Barany [25] determined Δ_fH^o (CaMoO₄, cr) by solution calorimetry using the reaction scheme given in Table 8.

Table 8

Calorimetric reaction scheme for CaMoO₄(cr).

Eq.	Reaction	Δ_8rH/kJ·mol^–1
(8r1)	MoO₃(cr, 25 °C) + H₂O(sol, 73.7 °C) = MoO₄^2–(sol,73.7 °C) + 2H⁺(sol, 73.7 °C)	–25.557 ± 0.128
(8r2)	CaO(cr, 25 °C) + 2HF(sol, 73.7 °C) = CaF₂(s, 73.7 °C) + H₂O(sol, 73.7 °C)	–232.329 ± 0.371
(8r3)	CaF₂(sol, 73.7 °C) + MoO₄^2–(sol, 73.7 °C) + 2H⁺(sol, 73.7 °C) = CaMoO₄(cr, 25 °C) + 2HF(sol, 73.7 °C)	92.153 ± 0.144

(8r4)	CaO(cr, 25 °C) + MoO₃(cr, 25) = CaMoO₄(cr, 25)	–165.733 ± 0.418

(22) Δ f H m o (CaMoO 4 , cr) = Δ 8r4 H m o + Δ f H m o (MoO 3 , cr) + Δ f H m o (CaO , cr)[15] Δ f H m o (CaMoO 4 , cr) / kJ · mol − 1 = − ( 1545.635 ± 1.156 ) (22)

Barium molybdate, strontium molybdate

O’Hare [26] selected for the determination of Δ_fH^o(BaMoO₄, cr, 298.15 K) the reaction

Cs₂MoO₄(cr) + BaCl₂(sln, pH ≈ 10) BaMoO₄(cr) + 2CsCl(sln). When alkali molybdate is added to an excess of a barium salt solution at pH ≈ 10, pure BaMoO₄ precipitates quantitatively. The calorimetric scheme of three sets of measurements is summarized in Table 9.

Table 9

Reaction scheme for determination of ΔfHmo(BaMoO4,cr, 298.15 K).

Reaction	(Δ_rH^o ± δΔ_rH^o)/kJ·mol^–1
Cs₂MoO₄(cr) + 20(Ba²⁺·2Cl^–·NH₄OH·532H₂O) = BaMoO₄(cr) + (19Ba²⁺·20NH₄OH·40Cl^–·2Cs⁺·10640H₂O)	–(11.450 ± 0.310) (9r1)
(19Ba²⁺·20NH₄OH·40Cl^–·2Cs⁺·10640H₂O) = (19Ba²⁺·20NH₄OH·38Cl^–·10640H₂O) + 2CsCl(cr)	–(34.748 ± 0.070) (9r2)
(19Ba²⁺·20NH₄OH·38Cl^–·10640H₂O) + BaCl₂(cr) = 20(Ba²⁺·2Cl^–·NH₄OH·532H₂O)	–(12.349 ± 0.057) (9r3)

Cs₂MoO₄(cr) + BaCl₂(cr) = BaMoO₄(cr) + 2CsCl(cr)	–(58.547 ± 0.323) (9r4)

(23) Δ f H m o (BaMoO 4 , cr) = Δ 9r4 H m o − 2 Δ f H m o ( CsCl, cr ) [ 20 ] + Δ f H m o (BaCl 2 , cr)[20] + Δ f H m o (Cs 2 MoO 4 , cr)[6] (23)

Recalculated value:

Δ f H o ( B a M o O 4 , c r , 298.15 K ) / k J · m o l – 1 = – ( 1543.50 ± 2.81 )

Shukla et al. [27] determined the standard molar enthalpies of formation, ΔfHmo, at T = 298.15 K of BaMoO₄(cr) and SrMoO₄(cr) by a quite similar method, measuring the enthalpies of precipitation of these molybdates due to the reaction between Na₂MoO₄(cr) and ammoniacal solutions of barium or strontium nitrate in an isoperibol solution calorimeter. Molybdates of barium and strontium both have very low solubilities at pH = 10 and when an alkali molybdate is added to a barium or strontium salt solution, quantitative precipitation of barium or strontium molybdate takes place. The reaction can be represented as

Na₂MoO₄(cr) + M(NO₃)₂(aq, pH = 10) = MMoO₄(cr) + 2NaNO₃(aq), (M = Ba or Sr). This reaction was used to derive the enthalpy of formation of BaMoO₄ and SrMoO₄. The quantities required include the enthalpies of solution/reaction of Ba(NO₃)₂, Sr(NO₃)₂, NaNO₃, and Na₂MoO₄ in ammoniacal solutions (pH = 10) of Ba(NO₃)₂ or Sr(NO₃)₂, enthalpies of formation of these four compounds, and the enthalpies of precipitation of BaMoO₄ and SrMoO₄ from ammoniacal Ba(NO₃)₂ or Sr(NO₃)₂ solutions.

The standard molar enthalpies of formation ΔfHmo at T = 298.15 K of Ba(NO₃)₂(cr), Sr(NO₃)₂(cr), and NaNO₃(cr) required for evaluating ΔfHmo values of BaMoO₄(cr) and SrMoO₄(cr) are available from [3] without their uncertainties. Hence in [27] it was attempted to measure these standard enthalpies of solution at 298.15 K in distilled water.

Plotting of Δ_slnH_mvs. Im0.5, showed that the extrapolation to zero ionic strength was faulty, see Fig. 4. Comparison with data selected by [3] showed discrepancies of 0.3–1 kJ·mol^–1. Correct application of eq. (9) improved the result, but a slight discrepancy remained. In view of this analysis it was decided to take auxiliary quantities (i) Δ_fH^o(Sr(NO₃)₂, cr), and Δ_fH^o(NaNO₃, cr) as well as their uncertainties from [20], (ii) Δ_fH^o(Na₂MoO₄, cr) from this work, (iii) Δ_fH^o[Ba(NO₃)₂, cr] from [3], and the uncertainties of the latter from [27]. The reaction schemes for the determination of formation enhalpies of barium and strontium molybdate are summarized in Tables 10 and 11, respectively.

Fig. 4

Enthalpy of solution of NaNO₃ at 298.15 K.

Table 10

Reaction scheme for determination of ΔfHmo(BaMoO4,cr, 298.15 K).

Reaction	(Δ_rH^o ± dΔ_rH^o)/kJ·mol^–1
Ba(NO₃)₂(cr) + sln A₁ = sln B₁	(37.217 ± 0.054) (10r1)
sln C₁ = 2NaNO₃(cr) + sln A₁	–(40.354 ± 0.116) (10r2)
Na₂MoO₄(cr) + sln B₁ = BaMoO₄(cr) + sln C₁	–(20.631 ± 0.039) (10r3)

Ba(NO₃)₂(cr) + Na₂MoO₄(cr) = BaMoO₄(cr) + 2NaNO₃(cr)	–(23.768 ± 0.134) (10r4)

Table 11

Reaction scheme for determination of ΔfHmo(SrMoO4,cr, 298.15 K).

Reaction	(Δ_rH^o ± δΔ_rH^o)/kJ·mol^–1
Sr(NO₃)₂(cr) + sln A₂ = sln B₂	(18.388 ± 0.067) (11r1)
sln C₂ = 2NaNO₃(cr) + sln A₂	–(40.510 ± 0.101) (11r2)
Na₂MoO₄(cr) + sln B₂ = SrMoO₄(cr) + sln C₂	–(11.359 ± 0.012) (11r3)

Sr(NO₃)₂(cr) + Na₂MoO₄(cr) = SrMoO₄(cr) + 2NaNO₃(cr)	–(33.481 ± 0.122) (11r4)

(24) Δ f H m o (BaMoO 4 , cr) = Δ 10r4 H m o − 2 Δ f H m o ( NaNO 3 , cr) + Δ f H m o (Na 2 MoO 4 , cr) + Δ f H m o [Ba(NO 3 ) 2 , cr] [3] (24)

(25) Δ f H m o (SrMoO 4 , cr) = Δ 11r4 H m o − 2 Δ f H m o ( NaNO 3 , cr) + Δ f H m o (Na 2 MoO 4 , cr) + Δ f H m o [Sr(NO 3 ) 2 , cr] [20] (25)

Recalculated values:

Δ f H m o ( BaMoO 4 , cr , 298.15 K ) / kJ · mol − 1 = − ( 1548.10 ± 1.36 )

Δ f H m o ( SrMoO 4 , cr , 298.15 K ) / kJ · mol − 1 = − ( 1548.10 ± 1.30 )

Standard Gibbs energies of formation have been calculated using these enthalpies of formation and the entropies of formation listed in Table 7, see Table 12.

Table 12

Calculation of standard Gibbs energies of metal molybdate formation at T_ref = 298.15 K.

Metal molybdate	Δ f H m o / kJ ⋅ mol − 1	Δ f S m o / J ⋅ K − 1 ⋅ mol − 1	Δ f G m o / kJ ⋅ mol − 1	Refs.
Ag₂MoO₄	–838.16 ± 2.00	–303.18 ± 2.25	–747.765 ± 2.109	[14]
BaMoO₄	–1543.50 ± 2.81	–348.62 ± 1.75	–1439.560 ± 2.858	[26]
BaMoO₄	–1548.10 ± 1.36	–348.62 ± 1.75	–1444.160 ± 1.456	[27]
BaMoO₄ weighted mean	–1547.23 ± 1.22	–348.62 ± 1.75	–1443.387 ± 1.333	this work
SrMoO₄	–1548.10 ± 1.30	–358.02 ± 1.39	–1441.355 ± 1.364	[27]
CaMoO₄	–1545.64 ± 1.16	–358.78 ± 1.28	–1438.668 ± 1.222	[25]
CaMoO₄	–1536.43 ± 3.77	–358.78 ± 1.28	–1429.458 ± 3.789	[24]
CaMoO₄, eq. (26)	–1542.59 ± 3.14	–358.78 ± 1.28	–1437.872 ± 3.114	this work
CaMoO₄ weighted mean	–1544.59 ± 1.05	–358.78 ± 1.28	–1437.621 ± 1.113	this work

The weighted mean of ΔfHmo(BaMoO₄, cr) determined by [26] and [27] and the corresponding value of ΔfGmo(BaMoO₄, cr) have been calculated, because eqs. (26) and (27) lead to independent values of ΔfGmo(Ag₂MoO₄, cr) and ΔfGmo(CaMoO4, cr). The solubility products Ks0o of Ag₂MoO₄(cr), CaMoO₄(cr), and BaMoO₄(cr) are well known [13] and ΔslnGmo = −RTreflnKs0o.ΔfGmo(Ag2MoO4, cr) = ΔslnGmo(BaMoO4)−ΔslnGmo(Ag2MoO4)−ΔfGmo(Ba2+) + 2ΔfGmo(Ag+) + ΔfGmo(BaMoO4, cr) (26)

(27) Δ f G m o (CaMoO 4 , cr) = Δ sln G m o ( BaMoO 4 ) − Δ sln G m o ( CaMoO 4 ) − Δ f G m o ( Ba 2 + ) + Δ f G m o ( Ca 2 + ) + Δ f G m o (BaMoO 4 , cr) (27)

Now the standard Gibbs energy of molybdate ion can be calculated employing eq. (11), see Table 13. Selected value:

Table 13

Calculation of standard Gibbs energy of molybdate ion at T_ref = 298.15 K using eq. (11).

Metal molybdate	Δ sln G m o /kJ ⋅ mol − 1	n Δ f G m o ( M 2 + / n ) /kJ ⋅ mol − 1	Δ f G m o / k J ⋅ mol − 1	Δ f G m o ( MoO 4 2 − ) / kJ ⋅ mol − 1
Ag₂MoO₄	66.16 ± 0.30	154.192 ± 0.312	–747.765 ± 2.109	–835.797 ± 2.153
Ag₂MoO₄, eq. (26)	66.16 ± 0.30	154.192 ± 0.312	–749.089 ± 2.627	–837.121 ± 2.663
BaMoO₄	48.51 ± 0.22	–557.656 ± 2.582	–1439.560 ± 2.858	–833.394 ± 3.858
BaMoO₄	48.51 ± 0.22	–557.656 ± 2.582	–1444.160 ± 1.456	–837.994 ± 2.973
SrMoO₄	45.00 ± 1.40	–563.864 ± 0.781	–1441.355 ± 1.364	–832.491 ± 2.105
CaMoO₄	45.69 ± 0.32	–552.806 ± 1.050	–1438.668 ± 1.222	–840.1725 ± 1.642
CaMoO₄	45.69 ± 0.32	–552.806 ± 1.050	–1429.458 ± 3.789	–830.962 ± 3.945
CaMoO₄, eq. (27)	45.69 ± 0.32	–552.806 ± 1.050	–1435.617 ± 3.113	–837.121 ± 3.301
			Weighted mean = –836.542 ± 0.881

Δ f G m o ( MoO 4 2 − , 298 .15 K ) /kJ ⋅ mol − 1 = − ( 836. 54 2 ± 0.881 )

This result agrees perfectly with that of O’Hare et al. [10].

Determination of ΔfHmo(BaMoO4, cr) from high-temperature equilibria

Singh et al. [28] determined the standard Gibbs energy of the reaction (I)

(I) BaMoO 3 ( cr ) + 0.5 O 2 ( g ) = BaMoO 4 ( cr ) (I)

by measuring the potential difference of the electrochemical cell Pt|[BaMoO₃(cr) + BaMoO₄(cr)]|CSZ|air(p(O₂) = 21.21 kPa)|Pt where CSZ represents zirconia stabilized with x(CaO) = 0.15, see Fig. 5. While enthalpy increment data for BaMoO₄(cr) are available [29], these data as well as low-temperature heat capacity data are lacking for BaMoO₃(cr). Thus a reliable third law analysis of reaction (I) is not feasible.

Fig. 5

Gibbs energy of reaction (I).

Dash et al. [30] investigated reaction (II)

(II) BaMoO 3 ( cr ) + 2 Cr ( cr ) = Ba ( g ) + Mo ( cr ) + Cr 2 O 3 ( cr ) (II)

by measuring the equilibrium vapor pressure of barium employing the Knudsen-effusion mass-loss technique, see Fig. 6. When the results of [28] and [30] are combined, see Fig. 7, second and third law analyses can be applied to reaction (III).

Fig. 6

Gibbs energy of reaction (II).

Fig. 7

Gibbs energy of reaction (III).

(III) Ba ( g ) + Mo ( cr ) + Cr 2 O 3 ( cr ) + 0.5 O 2 ( g ) = BaMoO 4 ( cr ) + 2 Cr ( cr ) (III)

Consulting the NIST-JANAF Tables [31], however, shows that ΔfHmo(Cr2O3, cr, 298.15 K)/kJ⋅mol−1 = −(1134.7 ± 8.4). The second law value ΔrIIIHmo/kJ·mol^–1 = –(285.92 ± 2.49), see Fig. 7, thus the uncertainty of ΔfHmo(BaMoO₄, cr, 298.15 K) derived from high-temperature equilibria will amount to ≈ ±9 kJ·mol^–1, regardless of the method of evaluation. Consequently ΔfGmo(MoO42−) was based only on solution calorimetric experiments.

Calculation of Smo(MoO42−)

When ΔfHmo(MoO42−), see subsection “Enthalpy of dissolution of molybdenum trioxide in dilute aqueous alkali hydroxide” and ΔfGmo(MoO42−), see subsection “Determination of ΔfGmo(MoO42−) using solubility data of crystalline calcium, strontium, barium, and silver molybdate” are known the calculation of Smo(MoO42−) is straightforward according to eqs. (28) and (29).

(28) Δ f S m o (MoO 4 2 − ) = [ Δ f H m o (MoO 4 2 − ) − Δ f G m o (MoO 4 2 − ) ] / T ref (28)

(29) S m o (MoO 4 2 − ) = Δ f S m o (MoO 4 2 − ) + S m o ( Mo , cr ) + 2 S m o ( O 2 , g ) + S m o ( H 2 , g ) Δ f S m o (MoO 4 2 − ) / J · K − 1 · mol − 1 = 1000 · [ − ( 996.807 ± 0.826 ) + ( 836. 542 ± 0.881 ) ] / T ref (29)

The value recommended for selection is

S m o (MoO 4 2 − ) / J · K − 1 · mol − 1 = ( 32.03 ± 4.05 )

Auxiliary data

Auxiliary data and references used in this work are listed in Table 14.

Table 14

List of auxiliary data and references.

Compound/Species	Δ f H m o / kJ ⋅ mol − 1	Reference	Element	S m o / J ⋅ K − 1 ⋅ m o l − 1	Reference
MoO₃(cr)	–(744.982 ± 0.592)	[6]	Mo(cr)	28.581 ± 0.050	[6]
OH^–	–(230.015 ± 0.040)	[15]	O₂(g)	205.152 ± 0.005	[15]
H₂O(l)	–(285.830 ± 0.040)	[15]	H₂(g)	130.680 ± 0.003	[15]
Na⁺	–(240.340 ± 0.060)	[15]	Ag(cr)	42.55 ± 0.20	[15]
NaOH⋅ ∞ H₂O	–(470.110 ± 0.070)	[3]	Ca(cr)	41.59 ± 0.40	[15]
NaCl(cr)	–(411.260 ± 0.120)	[20]	Sr(cr)	55.70 ± 0.21	[20]
Ag⁺	(105.790 ± 0.080)	[15]	Ba(cr)	62.42 ± 0.84	[20]
AgNO₃(cr)	–(124.390 ± 0.500)	[3]
NaNO₃(cr)	–(467.580 ± 0.410)	[20]
Ca(NO₃)₂(cr)	–(938.390 ± 1.300)	[3]
Sr(NO₃)₂(cr)	–(982.360 ± 0.800)	[20]
Ba(NO₃)₂(cr)	–(992.070 ± 0.900)	[3]
NO₃^–	–(206.850 ± 0.400)	[15]
CaO(cr)	–(634.920 ± 0.900)	[15]
Ca²⁺	–(543.000 ± 1.000)	[15]
Sr²⁺	–(550.900 ± 0.500)	[20]
Ba²⁺	–(534.800 ± 2.500)	[20]
BaCl₂(cr)	–(855.200 ± 2.500)	[20]
CsCl(cr)	–(442.310 ± 0.160)	[20]

Selected data

Thermodynamic properties selected in this work, which will finally go in the OECD NEA Thermochemical Database (TDB) review on the inorganic compounds and aqueous complexes of molybdenum, are listed in Table 15. The data selected for Ag₂ MoO₄(cr) are the weighted mean of [14] and eq. (26), see Tables 12 and 13.

Table 15

List of selected data at T_ref = 298.15 K.

Compound/Species	Δ f H m o / kJ ⋅ mol − 1	Δ f G m o / kJ ⋅ mol − 1	S m o / J ⋅ K − 1 ⋅ mol − 1
MoO₄^2–	–(996.807 ± 0.826)	–(836.542 ± 0.881)	32.03 ± 4.05
Na₂MoO₄(cr)	–(1467.423 ± 0.597)
Cs₂MoO₄(cr)	–(1514.374 ± 1.206)
Ag₂MoO₄(cr)	–(838.627 ± 1.609)	–(748.232 ± 1.743)	220.80 ± 2.21
CaMoO₄(cr)	–(1544.593 ± 1.045)	–(1437.621 ± 1.113)	121.69 ± 1.22
SrMoO₄(cr)	–(1548.100 ± 1.300)	–(1441.355 ± 1.364)	136.56 ± 1.37
BaMoO₄(cr)	–(1547.227 ± 1.224)	–(1443.287 ± 1.330)	152.69 ± 1.53

Article note

A collection of invited papers based on presentations at the 16^th International Symposium on Solubility Phenomena and Related Equilibrium Processes (ISSP-16), Karlsruhe, Germany, July 21–25, 2014.

Corresponding author: Heinz Gamsjäger, Montanuniversität, Lehrstuhl für Physikalische Chemie, 8700 Leoben, Austria, e-mail: gamsjaeg@unileoben.ac.at

Acknowledgments

We are grateful to the OECD-NEA-TDB Review Team on Mo for stimulating discussions on solid state and solution chemistry of molybdenum and its inorganic compounds. Thanks are also due to both reviewers whose thoughtful and constructive comments improved the quality of this paper.

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Published Online: 2015-03-12

Published in Print: 2015-05-01

Thermodynamic properties of molybdate ion: reaction cycles and experiments

Abstract

Present status of Δ_fH^o, Δ_fG^o and S^o(MoO₄^2–)

Standard molar enthalpy of formation of molybdate ion and alkali molybdates

Enthalpy of dissolution of molybdenum trioxide in dilute aqueous alkali hydroxide

Standard molar enthalpy of formation of anhydrous sodium molybdate

Standard molar Gibbs energy of formation of molybdate ion