# 活度系数

## 定义

$x_i= \frac{p_i} {p^{\star}_i}$

$\mu_i = \mu_{i}^{\ominus} + RT \ln x_i$

$a_{x,i} =\gamma_{x,i} x_i$

$a_{x,i}=\gamma_{x,i} x_i = \frac{p_i} {p^{\star}_i}$

$\mu_i = \mu_{i}^{\ominus} + RT \ln a_i$

## 平衡常数的修正

$\Delta_r G = \sigma \mu_S + \tau \mu_T - (\alpha \mu_A + \beta \mu_B) = 0\,$

$\Delta_r G = \sigma \mu_S^\ominus - \sigma RT \ln a_S + \tau \mu_T^\ominus - \tau RT \ln a_T -(\alpha \mu_A^\ominus-\alpha RT \ln a_A + \beta \mu_B^\ominus-\beta RT \ln a_B)=0$
$\Delta_r G =\left(\sigma \mu_S^\ominus+\tau \mu_T^\ominus -\alpha \mu_A^\ominus- \beta \mu_B^\ominus \right) + RT \ln \frac{a_S^\sigma a_T^\tau} {a_A^\alpha a_B^\beta} =0$

$\Delta_r G = \Delta_r G^\ominus - RT \ln \frac{a_S^\sigma a_T^\tau} {a_A^\alpha a_B^\beta}$

$K= \frac{[S]^\sigma[T]^\tau}{[A]^\alpha[B]^\beta} \times \frac{\gamma_S^\sigma \gamma_T^\tau}{\gamma_A^\alpha \gamma_B^\beta}$

## 活度系数的测量和计算方法

### 蒸汽压法

$a_{x,i}= x_i \gamma_{x,i} = \frac{p_i} {p^{\star}_i}$

### 德拜-休克尔极限公式法

$\ln(\gamma_i) = - A z_i^2 \sqrt{I}$[3]

### 图解积分法

$x_1 \mathrm{d}\mu_1 + x_2 \mathrm{d}\mu_2 = 0$

$\mu_1 = \mu_{1}^{\ominus} + RT \ln \gamma_1 x_1$

$\mathrm{d}\mu_1 = RT \mathrm{d} \ln \gamma_1 + RT \mathrm{d} \ln x_1$

$x_1 \mathrm{d}\ln \gamma_1 + x_2 \mathrm{d}\ln \gamma_2 + x_1 \mathrm{d}\ln x_1 + x_2 \mathrm{d} \ln x_2 = 0$

$\mathrm{d}\ln x_1 = \frac {\mathrm{d} x_1} {x_1}, \mathrm{d}x_1 = -\mathrm{d} x_2$

$x_1 \mathrm{d}\ln \gamma_1 + x_2 \mathrm{d}\ln \gamma_2 = 0$

## 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 在线版本．
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.