# Studies on the Electrochemical Behavior of Sulfite on Incoloy 800 in a Neutral Environment
## 3 Results
### Electrochemical Impedance Spectroscopy  
The impedance spectra obtained for sulfite oxidation on Incoloy 800 in 1 mol L\({}^{-1}\) Na\({}_{2}\)SO\({}_{4}\) solution, at different electrode potentials and sulfite concentrations, are represented in Figure 6 as complex plane (Nyquist) plots and absolute impedance and phase angle versus frequency (Bode) plots. The Nyquist plots show two overlapped semicircles corresponding to two time constants, with the largest diameter semicircle decreasing as the potential and sulfite concentration increases. An additional feature is observed at low frequencies, which is connected to diffusion phenomena. The phase angle plots also indicate three maxima, a well-defined one around the frequency of 10 Hz with a shoulder at a higher frequency of about 10\({}^{3}\) Hz and a lower intensity maxima below 1 Hz. The experimental data were analyzed using two different equivalent electric circuits (EEC). The EEC shown in Figure 7c was applied for high sulfite concentrations (1 and 0.5 M), while the EEC in Figure 7d was used for low sulfite concentrations (10\({}^{-1}\), 10\({}^{-2}\), and 10\({}^{-3}\) M) to model the diffusion of sulfite ions at lower concentrations. In this equivalent circuit, \(R_{S}\) is used for the solution resistance, the constant phase element CPE\({}_{\text{dl}}\) is used for the double layer capacitance, and \(R_{ct}\) for the charge transfer resistance of sulfite oxidation. The mass transport process associated with sulfite electrooxidation is modeled with a finite length diffusion Warburg element, W. Additionally, a Gerischer element is included in the equivalent circuits to account for the two-step mechanism of sulfite electrooxidation, which consists of a single charge transfer step when sulfite radicals are formed (Equation (1)), followed by a chemical reaction in which the intermediate species form dithionate (Equation (2)). Figure 6: _Cont._  
Figure 7: Dependence of charge transfer resistance \(R_{ct}\) (**a**) and double layer capacitance \(C_{dl}\) (**b**) versus electrode potential at different sulfite concentrations. Electrical equivalent circuits used to model the impedance data for (**c**) high (1 and 0.5 M) and (**d**) low (10\({}^{-1}\), 10\({}^{-2}\), and 10\({}^{-3}\)) concentrations of sulfite. Because the capacitive behavior of real electrochemical systems frequently deviates from the ideal situation, the capacitance is commonly replaced by a constant phase element (CPE) whose impedance is provided by Equation (9):  
\[Z_{\text{CPE}}=1/T\;(\text{j}\omega)^{n} \tag{9}\]  
where \(T\) is a parameter connected to the capacitance, j is the imaginary unit, and \(\omega\) is the angular frequency in radians and \(n\) is an exponent between 0 and 1 that describes the CPE's constant phase angle, equal to -(\(n^{\ast}\)90). The true capacitance values can be determined based on [PERSON]'s model, using Equation (10) [43]:  
\[C_{dl}=T^{1/n}\;({R_{S}}^{-1}+{R_{ct}}^{-1})^{(n-1)/n} \tag{10}\]  
Equation (11) gives the impedance of the generalized finite-length Warburg element with a short-circuit terminus, which reflects the situation of diffusion regions with transmissive or permeable boundaries for the diffusing species:  
\[Z_{\text{W}}=[{R_{d}}/(\text{j}\omega\tau_{d})^{p}]\text{tanh}\;(\text{j} \omega\tau_{d})^{p} \tag{11}\]  
where \(R_{d}\) is the diffusion resistance (\(\Omega\;\text{cm}^{2}\)); \(\tau_{d}\) is the diffusion time constant (s) given as the ratio between the squared diffusion layer thickness and the diffusion coefficient, and p is an exponent between 0 and 1. The Gerischer element was initially introduced to describe electrochemical systems where a chemical reaction is preceding or following the electrochemical reaction. It is characteristic of an electrode-electrolyte interface where a homogeneous first-order chemical reaction in the diffusion layer is coupled to a heterogeneous electrochemical reaction.