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

30.09 126.39

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

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

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

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

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

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

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

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

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

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

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