# 熔化热

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

30.09 126.39[11]

## 与溶解度的关系

$\ln x_2 = - \frac {\Delta H^\circ_{\mathit{fus}}}{R} \left(\frac{1}{T}- \frac{1}{T_{\mathit{fus}}}\right)$

$x_2 = \exp {\left(- \frac {28100 \mbox{ J mol}^{-1}} {8.314 \mbox{ J K}^{-1} \mbox{ mol}^{-1}}\left(\frac{1}{298}- \frac{1}{442}\right)\right)}= 0.0248$

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

### 证明

$\mu^\circ_{solid} = \mu^\circ_{solution}\,$

$\mu^\circ_{solid} = \mu^\circ_{liquid} + RT\ln X_2\,$

$RT\ln X_2 = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,$

$\Delta G^\circ_{\mathit{fus}} = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,$

$RT\ln X_2 = - ( \Delta G^\circ_{\mathit{fus}})\,$

$\left( \frac{\partial ( \frac{\Delta G^\circ_{\mathit{fus}} } {T} ) } {\partial T} \right)_{p\,} = - \frac {\Delta H^\circ_{\mathit{fus}}} {T^2}$

$\left( \frac{\partial ( \ln X_2 ) } {\partial T} \right) = \frac {\Delta H^\circ_{\mathit{fus}}} {RT^2}$

$\partial \ln X_2 = \frac {\Delta H^\circ_{\mathit{fus}}} {RT^2}*\delta T$

$\int^{x_2=x_2}_{x_2 = 1} \delta \ln X_2 = \ln x_2 = \int_{T_{\mathit{fus}}}^T \frac {\Delta H^\circ_{\mathit{fus}}} {RT^2}*\Delta T$

$\ln x_2 = - \frac {\Delta H^\circ_{\mathit{fus}}} {R}\left(\frac{1}{T}- \frac{1}{T_{\mathit{fus}}}\right)$

## 参考资料

1. ^ 1.0 1.1 1.2 沈晨. 更高更妙的物理 第四版. 浙江大学出版社. : 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, p. 236.
4. ^ Ott & Boerio-Goates 2000, pp. 92–93.
5. ^ [1]
6. ^ [2]
7. ^ [3]
8. ^ [4]
9. ^ 化学品数据库.乙酸. [2015-01-28].
10. ^ 化学品数据库.丙酮. [2015-01-28].
11. ^ 化学品数据库.苯. [2015-01-28].
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