## 1 Introduction
[1]  
The equilibrium constant can also be related to the standard mol Gibbs free energy of a reaction at any temperature and pressure by the following equation:  
\[\mathrm{lnK_{r}}=\frac{-\mathrm{\Delta G_{r}^{0}}}{\mathrm{RT}} \tag{5}\]  
\[\mathrm{\Delta G_{r}^{0}}\mathrm{=\Delta G_{r,P_{r},T_{r}}^{0}-\mathrm{\Delta G _{r,PIn the reaction (1), the quantities of the reactants A and B, and the products C and D are represented as activities, \(a_{i}\), and not as concentrations, \(C_{i}\), with respect to a species, \(i\). The activity of a species is related to its concentration at a specific ionic strength by the following equation:  
\[\text{a}_{i}=\gamma_{i}\cdot C_{i} \tag{7}\]  
The activity coefficient, \(\gamma_{i}\), is an ion-specific correction factor describing the interactions among charged ions in an aqueous solution. Because the activity coefficient is a nonlinear function of ionic strength given by the Davies, modified Debye-Huckel, or Pitzer equations, the activity is also a nonlinear function of concentration. When the ionic strength reaches 0.1 mol/kg, the activity of a chemical species in aqueous solution decreases due to the interaction among the charged ions. The activity decreases with an increase in the ionic strength, and is always lower than the concentration. Therefore, the activity coefficient is less than 1. It can be concluded that the decrease in activity will be more pronounced at higher ion concentrations and higher ion valences. In an infinitely dilute solution, the interaction between ions will approach zero; therefore, the activity coefficient will be 1, and the activity will be equal to the concentration [1]. In [PERSON]'s law, the conditions of an ideal solution are based on the assumption that chemical interactions between bonded molecules are equal, but the interactive forces between ions are zero. However, in real solutions, attractive forces such as adhesive and cohesive forces are not uniform between the molecules, thus causing real solutions to deviate from [PERSON]'s law. Consider the effect of ion interaction on the activity of an electrolytic solution; the ionic strength, I, represents the collective concentration level of all of the ions in the solution. \[\text{I}=\frac{1}{2}\sum_{i}C_{i}Z_{i}^{2} \tag{8}\]  
where \(C_{i}\) is the mol concentration of ion \(i\) (mol/kgw), \(Z_{i}\) is the charge number of ion \(i\), and \(\Sigma\) is summation of the charge numbers of all of the ions in the solution. In general, an activity coefficient varies with the concentration of a solution. Different activity coefficient models may yield significantly varied activity coefficients. In this study, we first reviewed the theory of the activity coefficient and compare the applicable concentration range of the activity coefficient models. 1. Debye-Huckel Theory  
The Debye-Huckel theory [8] states that the activity of a solution is affected by the mutual electrostatic forces between the ions. Thus, the activity coefficient \(\gamma\) is introduced in order to calculate the correct activity of an ion in a solution, and the Debye-Huckel extended equation can be expressed as follows:  
\[\log\gamma_{i}=\frac{-AZ_{i}^{2}\sqrt{\text{I}}}{1+Ba_{i}\sqrt{\text{I}}} \tag{9}\]  
where \(A\) and \(B\) are temperature-dependent constants, and \(a_{i}\) is the diameter of ion \(i\). The Debye-Huckel limiting law is simplified to (3) in a dilute solution. \[\log\gamma_{i}=-AZ_{i}^{2}\sqrt{\text{I}} \tag{10}\]  
The Debye-Huckel equation is commonly used to estimate the activity coefficient of a dilute single-ion solution. The Davies equation and modified Debye-Huckel equation are used to describe complicated ionic interactions in high-concentration solutions, and these equations are extensively applied to determine activity coefficients at different concentrations. 2.