Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K
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</...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Metals |
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| Online Access: | https://www.mdpi.com/2075-4701/13/8/1498 |
| _version_ | 1797583850144006144 |
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| author | Qingdong Miao Ming Li Baijun Yan |
| author_facet | Qingdong Miao Ming Li Baijun Yan |
| author_sort | Qingdong Miao |
| collection | DOAJ |
| description | 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>. |
| first_indexed | 2024-03-10T23:43:50Z |
| format | Article |
| id | doaj.art-a0a3169bde2446daaea3d600401f83ae |
| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-03-10T23:43:50Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metals |
| spelling | doaj.art-a0a3169bde2446daaea3d600401f83ae2023-11-19T02:12:11ZengMDPI AGMetals2075-47012023-08-01138149810.3390/met13081498Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 KQingdong Miao0Ming Li1Baijun Yan2State Key Laboratory for Comprehensive Utilization of Vanadium and Titanium Resources, Pangang Group Institute Co., Ltd., Panzhihua 617000, ChinaState Key Laboratory for Comprehensive Utilization of Vanadium and Titanium Resources, Pangang Group Institute Co., Ltd., Panzhihua 617000, ChinaState Key Laboratory of Advanced Metallurgy, Beijing 100083, ChinaIn 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>.https://www.mdpi.com/2075-4701/13/8/1498Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub>Gibbs energymeasurementmodelingGibbs–Duhem relation |
| spellingShingle | Qingdong Miao Ming Li Baijun Yan Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K Metals Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> Gibbs energy measurement modeling Gibbs–Duhem relation |
| title | Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K |
| title_full | Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K |
| title_fullStr | Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K |
| title_full_unstemmed | Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K |
| title_short | Experimental Determination of the Standard Gibbs Energy of Formation of Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> at 1473 K |
| title_sort | experimental determination of the standard gibbs energy of formation of fe sub 3 x sub v sub x sub o sub 4 sub at 1473 k |
| topic | Fe<sub>3–x</sub>V<sub>x</sub>O<sub>4</sub> Gibbs energy measurement modeling Gibbs–Duhem relation |
| url | https://www.mdpi.com/2075-4701/13/8/1498 |
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