# 活度系数

（重定向自活度因子

## 定义

${\displaystyle x_{i}={\frac {p_{i}}{p_{i}^{\star }}}}$

${\displaystyle \mu _{i}=\mu _{i}^{\ominus }+RT\ln x_{i}}$

${\displaystyle a_{x,i}=\gamma _{x,i}x_{i}}$

${\displaystyle a_{x,i}=\gamma _{x,i}x_{i}=\gamma _{x,i}{\frac {p_{i}}{p_{i}^{\star }}}}$

${\displaystyle \mu _{i}=\mu _{i}^{\ominus }+RT\ln a_{i}}$

## 平衡常数的修正

${\displaystyle \Delta _{r}G=\sigma \mu _{S}+\tau \mu _{T}-(\alpha \mu _{A}+\beta \mu _{B})=0\,}$

${\displaystyle \Delta _{r}G=\sigma \mu _{S}^{\ominus }+\sigma RT\ln a_{S}+\tau \mu _{T}^{\ominus }+\tau RT\ln a_{T}-(\alpha \mu _{A}^{\ominus }+\alpha RT\ln a_{A}+\beta \mu _{B}^{\ominus }+\beta RT\ln a_{B})=0}$
${\displaystyle \Delta _{r}G=\left(\sigma \mu _{S}^{\ominus }+\tau \mu _{T}^{\ominus }-\alpha \mu _{A}^{\ominus }-\beta \mu _{B}^{\ominus }\right)+RT\ln {\frac {a_{S}^{\sigma }a_{T}^{\tau }}{a_{A}^{\alpha }a_{B}^{\beta }}}=0}$

${\displaystyle \Delta _{r}G=\Delta _{r}G^{\ominus }+RT\ln {\frac {a_{S}^{\sigma }a_{T}^{\tau }}{a_{A}^{\alpha }a_{B}^{\beta }}}}$

${\displaystyle K={\frac {[S]^{\sigma }[T]^{\tau }}{[A]^{\alpha }[B]^{\beta }}}\times {\frac {\gamma _{S}^{\sigma }\gamma _{T}^{\tau }}{\gamma _{A}^{\alpha }\gamma _{B}^{\beta }}}}$

## 活性系数的测量和计算方法

### 蒸汽压法

${\displaystyle a_{x,i}=x_{i}\gamma _{x,i}={\frac {p_{i}}{p_{i}^{\star }}}}$

### 德拜-休克尔极限公式法

${\displaystyle \ln(\gamma _{i})=-Az_{i}^{2}{\sqrt {I}}}$ [3]

### 图解积分法

${\displaystyle x_{1}\mathrm {d} \mu _{1}+x_{2}\mathrm {d} \mu _{2}=0}$

${\displaystyle \mu _{1}=\mu _{1}^{\ominus }+RT\ln \gamma _{1}x_{1}}$

${\displaystyle \mathrm {d} \mu _{1}=RT\mathrm {d} \ln \gamma _{1}+RT\mathrm {d} \ln x_{1}}$

${\displaystyle x_{1}\mathrm {d} \ln \gamma _{1}+x_{2}\mathrm {d} \ln \gamma _{2}+x_{1}\mathrm {d} \ln x_{1}+x_{2}\mathrm {d} \ln x_{2}=0}$

${\displaystyle \mathrm {d} \ln x_{1}={\frac {\mathrm {d} x_{1}}{x_{1}}},\mathrm {d} x_{1}=-\mathrm {d} x_{2}}$

${\displaystyle x_{1}\mathrm {d} \ln \gamma _{1}+x_{2}\mathrm {d} \ln \gamma _{2}=0}$

## 参考文献

1. ^ （英文）國際純粹與應用化學聯合會．"Activity coefficient"．《化学术语总目录》在线版．
2. ^ Jorge G. Ibanez; Margarita Hernandez-Esparza, Carmen Doria-Serrano, Mono Mohan Singh. Environmental Chemistry: Fundamentals. Springer. 2007. ISBN 978-0-387-26061-7.
3. ^ 傅献彩等. 物理化学（下） 第五版. 高等教育出版社. 2005年7月: 37页.
4. ^ C.W. Davies, Ion Association,Butterworths, 1962
5. ^ I. Grenthe and H. Wanner, Guidelines for the extrapolation to zero ionic strength, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
6. ^ 傅献彩等. 物理化学（上） 第五版. 高等教育出版社. 2005年7月: 251页.