Thermodynamic properties of the ternary oxides in the Eu–Ru–O system by using solid-state electrochemical cells

Abstract

The Gibbs free energies of formation of Eu₃RuO₇(s) and Eu₂Ru₂O₇(s) have been determined using solid-state electrochemical technique employing oxide ion conducting electrolyte. The reversible electromotive force (e.m.f.) of the following solid-state electrochemical cells have been measured:

$$Cell{\left( I \right)}:{{\left( - \right)}Pt} \mathord{\left/ {\vphantom {{{\left( - \right)}Pt} {{\left\{ {Eu_{3} RuO_{7} {\left( s \right)} + Eu_{2} O_{3} {\left( s \right)} + Ru{\left( s \right)}} \right\}}}}} \right. \kern-\nulldelimiterspace} {{\left\{ {Eu_{3} RuO_{7} {\left( s \right)} + Eu_{2} O_{3} {\left( s \right)} + Ru{\left( s \right)}} \right\}}}//CSZ//O_{2} {{\left( {p{\left( {O_{2} } \right)} = 21.21 kPa} \right)}} \mathord{\left/ {\vphantom {{{\left( {p{\left( {O_{2} } \right)} = 21.21 kPa} \right)}} {Pt{\left( + \right)}}}} \right. \kern-\nulldelimiterspace} {Pt{\left( + \right)}}$$

$$Cell{\left( {II} \right)}:{{\left( - \right)}Pt} \mathord{\left/ {\vphantom {{{\left( - \right)}Pt} {{\left\{ {Eu_{3} RuO_{7} {\left( s \right)} + Eu_{2} Ru_{2} O_{7} {\left( s \right)} + Ru{\left( s \right)}} \right\}}}}} \right. \kern-\nulldelimiterspace} {{\left\{ {Eu_{3} RuO_{7} {\left( s \right)} + Eu_{2} Ru_{2} O_{7} {\left( s \right)} + Ru{\left( s \right)}} \right\}}}//CSZ//O_{2} {{\left( {p{\left( {O_{2} } \right)} = 21.21 kPa} \right)}} \mathord{\left/ {\vphantom {{{\left( {p{\left( {O_{2} } \right)} = 21.21 kPa} \right)}} {Pt{\left( + \right)}}}} \right. \kern-\nulldelimiterspace} {Pt{\left( + \right)}}$$

The Gibbs free energies of formation of Eu₃RuO₇(s) and Eu₂Ru₂O₇(s) from elements in their standard state, calculated by the least squares regression analysis of the data obtained in the present study, can be given, respectively, by:

$$\left\{ {\Delta _{f} G^{o} } \right.\left. {{{\left( {Eu_{3} RuO_{7} , s} \right)}} \mathord{\left/ {\vphantom {{{\left( {Eu_{3} RuO_{7} , s} \right)}} {{\left( {kJ \cdot mol^{{ - 1}} } \right)} \pm 2.5}}} \right. \kern-\nulldelimiterspace} {{\left( {kJ \cdot mol^{{ - 1}} } \right)} \pm 2.5}} \right) = - 2,785.2 + 0.567 \cdot {\left( {T \mathord{\left/ {\vphantom {T K}} \right. \kern-\nulldelimiterspace} K} \right)}; {\left( {{922.5 \leqslant T} \mathord{\left/ {\vphantom {{922.5 \leqslant T} {K \leqslant 1194.9}}} \right. \kern-\nulldelimiterspace} {K \leqslant 1194.9}} \right)}.$$

$$\left\{ {\Delta _{f} G^{o} } \right.\left. {{{\left( {Eu_{3} Ru_{2} O_{7} , s} \right)}} \mathord{\left/ {\vphantom {{{\left( {Eu_{3} Ru_{2} O_{7} , s} \right)}} {{\left( {kJ \cdot mol^{{ - 1}} } \right)} \pm 2.9}}} \right. \kern-\nulldelimiterspace} {{\left( {kJ \cdot mol^{{ - 1}} } \right)} \pm 2.9}} \right) = - 2,256.6 + 0.579 \cdot {\left( {T \mathord{\left/ {\vphantom {T K}} \right. \kern-\nulldelimiterspace} K} \right)}; {\left( {{995.3 \leqslant T} \mathord{\left/ {\vphantom {{995.3 \leqslant T} {K \leqslant 1260.6}}} \right. \kern-\nulldelimiterspace} {K \leqslant 1260.6}} \right)}.$$

The uncertainty estimates for Δ_f G ^o(T) include the standard deviation in e.m.f. and uncertainty in the data taken from the literature.