## 3 Results and Discussion
### Nernst Parameters  
For determination of the concentration of a select ion, the Nernst Equation (1) was used. Where \(E\) is potential in mV, \(E_{0}\) is standard potential in mV, \(\alpha\) is the Nernst slope, and \(I_{i}\) is the effective activity of the ion of interest. Interferences can be caused by either other ionic species impacting the activity of the ion of interest, species interfering with the membrane itself, or physical degradation of the ISE membrane. Interferences are broadly grouped in the term \(\sum_{j:j\
eq i}^{k}I_{j}\), \(I_{i}\) is excluded as it is the ion of interest. \[E=E_{0}+\alpha\times\ln\left[I_{i}+\sum_{j:j\
eq i}^{k}I_{j}\right] \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Location** & \begin{tabular}{c} **Ca** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **Cl** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **Fe** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **Ni** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **S** \\ **(ppm)** \\ \end{tabular} & \
\begin{tabular}{c} **Sr** \\ **(ppm)** \\ \end{tabular} &
\begin{tabular}{c} **NO3** \\ **(ppm)** \\ \end{tabular} \\ \hline
**Inlet** & 950 & 5210 & 5.86 & 0.81 & 2229 & 9.92 & 1.50 \\ \hline
**Primary Clarifier** & 1080 & 3400 & - & 0.15 & 1810 & 7.98 & 1.18 \\ \hline
**Equalization Tank** & 1010 & 3400 & - & 0.15 & 1771 & 8.17 & 1.17 \\ \hline
**Secondary Clarifier** & 1090 & 3760 & - & 0.14 & 1862 & 7.82 & 1.02 \\ \hline
**Discharge** & 1100 & 2900 & - & 0.15 & 1883 & 7.76 & 1.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Concentration of Select Species in flue gas desulfurization (FGD) Wastewater in parts per million by mass (PPM). For ions with a charge magnitude of 1 an ideal \(\alpha\) value is \(\pm 25.6\) mV/decade, and an ion with a charge magnitude of 2 will have an \(\alpha\) value of \(\pm 12.8\) mV/decade. Decade in this definition is a change of an order of magnitude in the activity of the ion of interest in the natural log scale (i.e., from an effective 0.01 M to 0.001 M would be a decade in the base 10 scale, or 2.3 decades in the natural log scale). Nernst parameters were found for the ions nitrate, nitrite, calcium, and chloride using the respective ISE's. These parameters are shown in Table 3 and are fit to Equation (1). These values deviate severely from the expected values for monovalent and divalent ions, but this was expected for ion selective electrodes. These regressions were found to be accurate for ionic strengths below 0.1 M, after which the activity and concentration of each ion began deviating severely. Additional correlations with new experimental data were made using the Nernst equation to account for changes in temperature, as the FGD wastewater treatment system has varying temperatures throughout the process. The modified Nernst parameters are shown in Table 4.  
Modified Nernst parameters were derived by regression of linearized functions describing the slope and intercept. These linearizing functions were considered as constants, exponential, and logarithmic, which are expected behaviors for these systems [9]. These Nernst based relationships show that the calcium ISE is the most sensitive to temperature, as its slope changes drastically from 7.2 to 12 mV/decade at 25 and 50 \({}^{\circ}\)C, respectively. The other ISEs are only slightly affected with temperature. While there are corrections readily available (such as Nikolsky-Eisenman style equations) to account for factors such as ionic strength of solution, these factors were found to not accurately describe the composition of the actual FGD wastewater, and thus are not included in detail here [9]. Additional experiments were conducted to display the failures of this model to properly account for ionic strength interference. Residuals of the predicted versus the actual signal are compared to concentration of the target ions in Figure 2. The experimental sets with only varying ionic strength are encircled.