| Summary: | In the present study, an approach of determining the standard Gibbs energy of formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> was proposed firstly, then the standard Gibbs energies of formation of a variety of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> were determined experimentally, and finally, a calculating model of the standard Gibbs energy of formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> was established. The detailed results are as follows: (1) the standard Gibbs energy of formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> can be determined successfully by two steps; the first is to measure the chemical potential of Fe in Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> under fixed oxygen partial pressure, the second is to derive the chemical potential of V in Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> by Gibbs–Duhem relation; (2) the standard Gibbs energies of formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> are mainly decided by the Fe/V molar ratio, and almost not influenced by the oxygen partial pressure in the range from 2.39 × 10<sup>−12</sup> to 3.83 × 10<sup>−11</sup> atm; (3) in this oxygen partial pressure range, the standard Gibbs energies of formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> can be calculated satisfactorily by the following model: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>f</mi></msub><msubsup><mi>G</mi><mrow><mi>F</mi><msub><mi>e</mi><mrow><mn>3</mn><mo>−</mo><mi>x</mi></mrow></msub><msub><mi>V</mi><mi>x</mi></msub><msub><mi>O</mi><mn>4</mn></msub></mrow><mi>θ</mi></msubsup><mfenced><mrow><mi>J</mi><mo>/</mo><mi>m</mi><mi>o</mi><mi>l</mi></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><msub><mo>Δ</mo><mi>f</mi></msub><msubsup><mi>G</mi><mrow><mi>F</mi><msub><mi>e</mi><mn>3</mn></msub><msub><mi>O</mi><mn>4</mn></msub></mrow><mi>θ</mi></msubsup><mo>+</mo><mfenced><mrow><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><msub><mo>Δ</mo><mi>f</mi></msub><msubsup><mi>G</mi><mrow><mi>F</mi><mi>e</mi><msub><mi>V</mi><mn>2</mn></msub><msub><mi>O</mi><mn>4</mn></msub></mrow><mi>θ</mi></msubsup><mo>+</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><mi>R</mi><mi>T</mi><mi>l</mi><mi>n</mi><mfenced><mrow><mn>1</mn><mo>−</mo><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><mi>R</mi><mi>T</mi><mi>l</mi><mi>n</mi><mfenced><mrow><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mo>−</mo><mo> </mo><mn>168627.48</mn><mfenced><mrow><mn>1</mn><mo>−</mo><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>/</mo><mn>2</mn></mrow></mfenced></mrow></semantics></math></inline-formula>.
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