Model Mathematics

\frac{d}{d time} (q_OH_i) = - v_R56_CHE \frac{d}{d time} (q_OH_o) = v_R12_CHE \frac{d}{d time} (q_Cl_i) = v_R45_CHE \frac{d}{d time} (q_Cl_o) = - v_R23_CHE

cOH_i = \frac{q_OH_i}{w_i} cOH_o = \frac{q_OH_o}{w_o} pH_i = 14 + \log_{10} cOH_i pH_o = 14 + \log_{10} cOH_o

mu_OH_i = R T \ln (K_OH_i q_OH_i) mu_OH_o = R T \ln (K_OH_o q_OH_o) mu_Cl_i = R T \ln (K_Cl_i q_Cl_i) mu_Cl_o = R T \ln (K_Cl_o q_Cl_o) mu_S1_CHE = R T \ln (K_S1_CHE q_S1_CHE) mu_S2_CHE = R T \ln (K_S2_CHE q_S2_CHE) mu_S3_CHE = R T \ln (K_S3_CHE q_S3_CHE) mu_S4_CHE = R T \ln (K_S4_CHE q_S4_CHE) mu_S5_CHE = R T \ln (K_S5_CHE q_S5_CHE) mu_S6_CHE = R T \ln (K_S6_CHE q_S6_CHE) v_R61_CHE = kappa_R61_CHE (ⅇ^{\frac{mu_S6_CHE}{R T}} - (ⅇ^{\frac{mu_S1_CHE}{R T}})) v_R12_CHE = kappa_R12_CHE (ⅇ^{\frac{mu_S1_CHE}{R T}} - (ⅇ^{\frac{mu_S2_CHE + mu_OH_o}{R T}})) v_R23_CHE = kappa_R23_CHE (ⅇ^{\frac{mu_S2_CHE + mu_Cl_o}{R T}} - (ⅇ^{\frac{mu_S3_CHE}{R T}})) v_R34_CHE = kappa_R34_CHE (ⅇ^{\frac{mu_S3_CHE}{R T}} - (ⅇ^{\frac{mu_S4_CHE}{R T}})) v_R45_CHE = kappa_R45_CHE (ⅇ^{\frac{mu_S4_CHE}{R T}} - (ⅇ^{\frac{mu_S5_CHE + mu_Cl_i}{R T}})) v_R56_CHE = kappa_R56_CHE (ⅇ^{\frac{mu_S5_CHE + mu_OH_i}{R T}} - (ⅇ^{\frac{mu_S6_CHE}{R T}})) \frac{d}{d time} (q_S1_CHE) = v_R61_CHE - v_R12_CHE \frac{d}{d time} (q_S2_CHE) = v_R12_CHE - v_R23_CHE \frac{d}{d time} (q_S3_CHE) = v_R23_CHE - v_R34_CHE \frac{d}{d time} (q_S4_CHE) = v_R34_CHE - v_R45_CHE \frac{d}{d time} (q_S5_CHE) = v_R45_CHE - v_R56_CHE \frac{d}{d time} (q_S6_CHE) = v_R56_CHE - v_R61_CHE