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## Application of Van't Hoff Equation to Phase Equilibrium

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Abstract

The applications of Van't Hoff equation of phase equilibrium, a special case of chemical equilibrium, in simplifying the deduction of some relevant thermodynamic equations are discussed in the paper.

Keywords： Van't Hoff equation ; Phase equilibrium constant ; Deduction of thermodynamic equations

FAN Sen, ZHU Yuanhai. Application of Van't Hoff Equation to Phase Equilibrium. University Chemistry[J], 2018, 33(3): 70-73 doi:10.3866/PKU.DXHX201711022

## 1 相平衡常数

${{K}^{\ominus}}(T)=\frac{{{a}_{\rm{B}}}\rm{(}\beta \rm{)}}{{{a}_{\rm{B}}}\rm{(}\alpha \rm{)}}$

$\frac{{{\rm{d}}\ln {K^{\rm{\ominus}}}}}{{{\rm{d}}T}}=\frac{\Delta _{\alpha }^{\beta }H_{\rm{m}}^{\ominus}}{R{{T}^{2}}}$

## 2 凝固点降低和沸点升高公式推导

$\frac{{{\rm{d}}\ln {x_{\rm{A}}}}}{{{\rm{d}}T}}=\frac{{{\Delta }_{\rm{fus}}}H_{\rm{m}}^{\ominus}}{R{{T}^{2}}}$

$-\frac{{{\rm{d}}\ln {x_{\rm{A}}}}}{{{\rm{d}}T}}=\frac{{{\Delta }_{\rm{vap}}}H_{\rm{m}}^{\ominus}}{R{{T}^{2}}}$

## 3 克-克方程和露点线方程

$\frac{{{\rm{d}}\ln {p_{\rm{A}}}}}{{{\rm{d}}T}}=\frac{{{\Delta }_{\rm{vap}}}H_{\rm{m}}^{\ominus}}{R{{T}^{2}}}$

$\frac{{{\rm{d}}\ln {p_{\rm{A}}}}}{{{\rm{d}}T}}=\frac{{{\Delta }_{\rm{vap}}}H_{\rm{m}}^{*}}{R{{T}^{2}}}$

$\frac{{{\rm{d}}\ln {x_{\rm{A}}}}}{{{\rm{d}}T}}=\frac{{{\Delta }_{\rm{vap}}}H_{\rm{m}}^{*}}{R{{T}^{2}}}$

## 4 纯气体溶解度随温度的变化与溶解熵

${{\left( \frac{\partial \ln {{x}_{\rm{B}}}}{\partial T} \right)}_{p}}=\frac{{{\Delta }_{\rm{sol}}}H_{\rm{m}}^{\ominus}}{R{{T}^{2}}}$

${{\Delta }_{\rm{sol}}}H_{\rm{m}}^{\ominus}(\rm{B})$是溶质B的标准态溶解焓。在气相视为理想气体，溶液视为理想溶液的条件下，标准溶解焓与平衡溶解焓一样，${{\Delta }_{\rm{sol}}}H_{\rm{m}}^{\ominus}(\rm{B})={\Delta _{{\rm{sol}}}}\mathit{H}_{\rm{m}}^{}({\rm{B}})$。溶解熵${{\Delta }_{\rm{sol}}}S_{\rm{m}}^{{}}(\rm{B})={\Delta _{{\rm{sol}}}}\mathit{H}_{\rm{m}}^{}({\rm{B}})/\mathit{T}$，即：

${{\Delta }_{\rm{sol}}}S_{\rm{m}}^{{}}=R{{\left( \frac{\partial \ln {{x}_{\rm{B}}}}{\partial \ln T} \right)}_{p}}$

## 5 固-气吸附平衡压力随温度的变化

${K^ \ominus }(T,\mathit{\Gamma }) = {\left( {{p_{\rm{B}}}/{p^ \ominus }} \right)^{ - 1}}$

${{\left( \frac{\partial \ln {{p}_{\rm{B}}}}{\partial T} \right)}_{\mathit{\Gamma}}}=-\frac{{{\Delta }_{\rm{ads}}}H_{\rm{m}}^{\ominus}(\mathit{\Gamma})}{R{{T}^{2}}}$

${{\left( \frac{\partial \ln {{p}_{\rm{B}}}}{\partial T} \right)}_{n}}=-\frac{{{\Delta }_{\rm{ads}}}H_{\rm{m}}^{{}}}{R{{T}^{2}}}$

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