Thermodynamic properties of molybdate ion: reaction cycles and experiments

Standard molar quantities of molybdate ion entropy, $S_{\rm{m}}^0,$ enthalpy of formation, ${\Delta _{\rm{f}}}H_m^{\rm{o}},$ and Gibbs energy of formation, ${\Delta _{\rm{f}}}G_{\rm{m}}^{\rm{o}},$ 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 ${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}$ 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 ${\Delta _{\rm{f}}}G_{\rm{m}}^{\rm{o}}$ 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 ${\Delta _{\rm{f}}}G_{\rm{m}}^{\rm{o}}$ of the relevant metal ions the problem reduces to select the best values of solubility constants and ${\Delta _{\rm{f}}}G_{\rm{m}}^{\rm{o}}$ of alkaline earth molybdates and silver molybdate. There are two independent possibilities to achieve the latter task. (1) ${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}$ 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 $S_{\rm{m}}^{\rm{o}}$ of the other elements involved. Whereas $S_{\rm{m}}^{\rm{o}}({\rm{CaMo}}{{\rm{O}}_4},{\rm{ cr}})$ is well known since decades, low-temperature heat capacity measurements had to be performed recently, but now reliable values for $S_{\rm{m}}^{\rm{o}}$ of Ag2MoO4(cr), BaMoO4(cr) and SrMoO4(cr) are available. (2) ${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}}({\rm{BaMo}}{{\rm{O}}_4},{\rm{ cr}}),$ 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, ${\Delta _{\rm{f}}}G_{\rm{m}}^{\rm{o}},$ and enthalpy of formation, ${\Delta _{\rm{f}}}H_{\rm{m}}^{\rm{o}},$ of molybdate ion are known its standard entropy, $S_{\rm{m}}^{\rm{o}},$ can be calculated.