南开大学物理化学2-1第七章——化学平衡公式合集
第七章
1. 化学平衡的基础概念
- \((\frac{\partial{U}}{\partial\zeta})_{S,V}=(\frac{\partial{H}}{\partial\zeta})_{S,p}=(\frac{\partial{A}}{\partial\zeta})_{T,V}=(\frac{\partial{G}}{\partial\zeta})_{T,p}=\sum\limits_{B}\nu_B\mu_B\leq0\)
- \((\frac{\partial{G}}{\partial\zeta})_{T,p}=\sum\limits_B\nu_B\mu_B^{\theta}+RT\ln\prod\limits_B(\frac{p_B}{p^\theta})^{\nu_B}=\Delta_rG_m^\theta+RT\ln{Q_p^\theta}\) 理想气体
- \(Q_p^\theta\) 判断反应方向
- \(Q_p^\theta<K_p^\theta\) 反应正向进行
- \(Q_p^\theta>K_p^\theta\) 反应反向进行
- \(Q_p^\theta=K_p^\theta\) 反应平衡
- \(\Delta_rG_m^\infty\)与\(\Delta_rG_m\)的区别 理想气体
- \(\Delta_rG_m^\infty=\sum\limits_B\nu_B\mu_B\)
- \(\Delta_rG_m=\frac{G_2-G_1}{\zeta_2-\zeta_1}=\sum\limits_B\nu_B\mu_B^\theta(T)+\frac{RT}{\zeta_2-\zeta_1}\sum\limits_B[n_B(0)+\nu_B\zeta_2]\ln\frac{n_B(0)+\nu_B\zeta_2}{\sum\limits_B[n_B(0)+\nu_B\zeta_2]}\\-\frac{RT}{\zeta_2-\zeta_1}\sum\limits_B[n_B(0)+\nu_B\zeta_1]\ln\frac{n_B(0)+\nu_B\zeta_1}{\sum\limits_B[n_B(0)+\nu_B\zeta_1]}+RT\sum\limits_B\nu_B\ln\frac{p}{p^\theta}\)
- \(\Delta_rG_m^\theta=-RT\ln{K_p^\theta}\) 理想气体
2. 理想气体的化学平衡
- 各类平衡常数
- \(K_c^\theta=\prod\limits_B(\frac{c_{B,eq}}{c^\theta})^{\nu_B}\) \(K_p^\theta\), \(K_c^\theta\)为T的函数
- \(K_p=\prod\limits_B(p_{B,eq})^{\nu_B}\) T的函数
- \(K_c=\prod\limits_B(c_{B,eq})^{\nu_B}\) T的函数
- \(K_x=\prod\limits_B(x_{B,eq})^{\nu_B}\) T, p的函数
- \(K_n=\prod\limits_B(n_{B,eq})^{\nu_B}\) T, p的函数K
- 各类平衡常数相互关系
- \(K_c^\theta=K_p^\theta\cdot(\frac{p^\theta}{c^\theta{R}T})^{\sum\limits_B\nu_B}\)
- \(K_p^\theta=K_c^\theta\cdot(\frac{c^\theta{R}T}{p^\theta})^{\sum\limits_B\nu_B}\)
- \(K_p=K_p^\theta\cdot(p^\theta)^{\sum\limits_B\nu_B}\)
- \(K_c=K_c^\theta\cdot(c^\theta)^{\sum\limits_B\nu_B}\)
- \(K_p=K_c\cdot(RT)^{\sum\limits_B\nu_B}\)
- \(K_c=K_p\cdot(RT)^{-\sum\limits_B\nu_B}\)
- \(K_p=K_n\cdot(\frac{p}{\sum\limits_Bn_{B,eq}})^{\sum\limits_B\nu_B}\)
- \(K_p=K_x\cdot(p)^{\sum\limits_B\nu_B}\)
- 转化率的定义
- \(\alpha=\frac{\Delta{n}}{n_0}\times{100\%}\)
- \(\ln\frac{K_p^\theta(T_2)}{K_p^\theta(T_1)}=\frac{\Delta_rH_m^\theta}{R}(\frac{1}{T_1}-\frac{1}{T_2})\)
- \(\ln\frac{K_c^\theta(T_2)}{K_c^\theta(T_1)}=\frac{\Delta_rU_m^\theta}{R}(\frac{1}{T_1}-\frac{1}{T_2})\)
- \(\frac{d\ln{K_p^\theta}}{dT}=\frac{\Delta_rH_m^\theta}{RT^2}\)
- \(\frac{d\ln{K_c^\theta}}{dT}=\frac{\Delta_rU_m^\theta}{RT^2}\)
- \(\frac{d\ln{K_p^\theta}}{dp}=0\)
- \(\frac{d\ln{K_c^\theta}}{dp}=0\)
3. 真实气体化学平衡
- 真实气体的反应
- \(K_f^\theta=\prod\limits_B(\frac{f_{B,eq}}{p^\theta})^{\nu_B}=K_\gamma\cdot{K_p^\theta}\)
- \(K_\gamma=\prod\limits_B(\gamma_B)^{\nu_B}\)
- \(K_f=K_f^\theta(p^\theta)^{\sum\limits_B\nu_B}=K_\gamma\cdot{K_p}\)
- \(\frac{d\ln{K_f^\theta}}{dT}=\frac{\Delta_rH_m^\theta}{RT^2}\)
- \(\Delta_rG_m^\theta=-RT\ln{K_f^\theta}\)
4. 液体混合物的化学平衡
-
理想液体混合物的反应
- \(\Delta_rG_m^\theta=-RT\ln{K_x^\theta}\)
- \(\Delta_rG_m^\infty=-RT\ln{K_x^\theta}+RT\ln{Q_x^\theta}\)
- \(\frac{d\ln{K_x^\theta}}{dT}=\frac{\Delta_rH_m^\theta}{RT^2}\)
-
非理想液体混合物的反应
- \(\Delta_rG_m^\theta=-RT\ln{K_a^\theta}\)
5. 稀溶液的化学平衡
-
非理想稀溶液的反应
- \(K_a^\theta=(\gamma_A^{eq}x_A^{eq})^{\nu_A}\prod\limits_{B\neq{A}}(\frac{\gamma_{m,B}^{eq}m_B^{eq}}{m^\theta})^{\nu_B}\approx{\prod\limits_{B\neq{A}}(a_{m,B}^{eq})^{\nu_B}}\)
- \(K_{a,c}^\theta=\prod\limits_{B\neq{A}}(\frac{\gamma_{m,B}^{eq}c_B^{eq}}{c^\theta})^{\nu_B}\)
- \(K_{a,x}^\theta=\prod\limits_{B\neq{A}}(\gamma_{m,B}^{eq}x_B^{eq})^{\nu_B}\)
- \(\Delta_rG_m^\theta=-RT\ln{K_a^\theta}\)
-
理想稀溶液的反应
- \(K_m^\theta=(x_A^{eq})^{\nu_A}\prod\limits_{B\neq{A}}(\frac{m_B^{eq}}{m^\theta})^{\nu_B}\approx{\prod\limits_{B\neq{A}}(\frac{m_{B}^{eq}}{m^\theta})^{\nu_B}}\)
- \(K_{c}^\theta=(x_A^{eq})^{\nu_A}\prod\limits_{B\neq{A}}(\frac{c_B^{eq}}{c^\theta})^{\nu_B}\approx{\prod\limits_{B\neq{A}}(\frac{c_{B}^{eq}}{c^\theta})^{\nu_B}}\)
- \(K_{x}^\theta=\prod\limits_{B\neq{A}}(x_B^{eq})^{\nu_B}\)
- \(K_m=\prod\limits_{B\neq{A}}(m_{B}^{eq})^{\nu_B}\)
- \(K_c=\prod\limits_{B\neq{A}}(c_{B}^{eq})^{\nu_B}\)
- \(K_x=\prod\limits_{B\neq{A}}(x_{B}^{eq})^{\nu_B}\)
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