熔化热

常见物质的熔化热

(卡路里/)
Heat of fusion
(千焦耳/千克)
79.8 334[5]

30.09 126.39[11]

25
H
52
47.8-52.6 200–220

与溶解度的关系

${\displaystyle \ln x_{2}=-{\frac {\Delta H_{\mathit {fus}}^{\circ }}{R}}\left({\frac {1}{T}}-{\frac {1}{T_{\mathit {fus}}}}\right)}$

${\displaystyle x_{2}=\exp {\left(-{\frac {28100{\mbox{ J mol}}^{-1}}{8.314{\mbox{ J K}}^{-1}{\mbox{ mol}}^{-1}}}\left({\frac {1}{298}}-{\frac {1}{442}}\right)\right)}=0.0248}$

${\displaystyle {\frac {0.0248*{\frac {1000\mathrm {g} }{18.053\mathrm {mol^{-1}} }}}{1-0.0248}}*151.17{\mbox{ mol}}^{-1}=213.4}$

证明

${\displaystyle \mu _{solid}^{\circ }=\mu _{solution}^{\circ }\,}$

${\displaystyle \mu _{solid}^{\circ }=\mu _{liquid}^{\circ }+RT\ln X_{2}\,}$

${\displaystyle RT\ln X_{2}=-(\mu _{liquid}^{\circ }-\mu _{solid}^{\circ })\,}$

${\displaystyle \Delta G_{\mathit {fus}}^{\circ }=-(\mu _{liquid}^{\circ }-\mu _{solid}^{\circ })\,}$

${\displaystyle RT\ln X_{2}=-(\Delta G_{\mathit {fus}}^{\circ })\,}$

${\displaystyle \left({\frac {\partial ({\frac {\Delta G_{\mathit {fus}}^{\circ }}{T}})}{\partial T}}\right)_{p\,}=-{\frac {\Delta H_{\mathit {fus}}^{\circ }}{T^{2}}}}$

${\displaystyle \left({\frac {\partial (\ln X_{2})}{\partial T}}\right)={\frac {\Delta H_{\mathit {fus}}^{\circ }}{RT^{2}}}}$

${\displaystyle \mathrm {d} (\ln X_{2})={\frac {\Delta H_{\mathit {fus}}^{\circ }}{RT^{2}}}*\mathrm {d} T}$

${\displaystyle \int _{X_{2}=1}^{X_{2}=x_{2}}\mathrm {d} (\ln X_{2})=\ln x_{2}=\int _{T_{\mathit {fus}}}^{T}{\frac {\Delta H_{\mathit {fus}}^{\circ }}{RT^{2}}}*\mathrm {d} T}$

${\displaystyle \ln x_{2}=-{\frac {\Delta H_{\mathit {fus}}^{\circ }}{R}}\left({\frac {1}{T}}-{\frac {1}{T_{\mathit {fus}}}}\right)}$

参考资料

1. 沈晨. 更高更妙的物理 第四版. 浙江大学出版社. 2006: P124. ISBN 978-7-308-04609-1.
2. ^ 赵志敏. 高中物理竞赛教程.拓展篇. 复旦大学出版社. 2011年10月: P222. ISBN 978-7-309-08250-0.
3. ^ Atkins & Jones 2008，第236頁.
4. ^ Ott & Boerio-Goates 2000，第92–93頁.
5. ^ 存档副本. [2015-02-05]. （原始内容存档于2021-01-19）.
6. ^ 存档副本. [2015-02-05]. （原始内容存档于2018-12-26）.
7. ^ 存档副本. [2015-02-05]. （原始内容存档于2013-07-07）.
8. ^ 存档副本. [2015-02-05]. （原始内容存档于2020-12-12）.
9. ^ 化学品数据库.乙酸. [2015-01-28]. （原始内容存档于2021-02-05）.
10. ^ 化学品数据库.丙酮. [2015-01-28]. （原始内容存档于2020-04-11）.
11. ^ 化学品数据库.苯. [2015-01-28]. （原始内容存档于2021-02-04）.
12. ^ Measurement and Prediction of Solubility of Paracetamol in Water-Isopropanol Solution. Part 2. Prediction H. Hojjati and S. Rohani Org. Process Res. Dev.; 2006; 10(6) pp 1110–1118; (Article) doi:10.1021/op060074g
• Atkins, Peter; Jones, Loretta, Chemical Principles: The Quest for Insight 4th, W. H. Freeman and Company: 236, 2008, ISBN 0-7167-7355-4
• Ott, J. Bevan; Boerio-Goates, Juliana, Chemical Thermodynamics: Advanced Applications, Academic Press, 2000, ISBN 0-12-530985-6