## 4 Results
### Sensor Characterization  
As described in Section 3.2.1, and shown quantitatively in Figure 5, the pH sensor is characterized in two phases: Figure 5a, using a multimeter and Figure 5b, employing the instrumentation described in this work. During the first ten seconds, refer to Figure 5, the sensor remains outside of the sample, and then the electrode is exposed (i.e., introduced) to the solution under test. It is important to note that this was performed for both configurations. Then, we let the sensor stabilize and perform the measurements for a period of 60 s, while acquiring data every 0.25 s. Table 1 presents, for both sensor characterization phases, the statistical measures obtained for voltage and pH after the aforementioned 60 s period. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Phase I. Multimeter** & **Phase II. Instrumentation** \\ \hline pH * & E[V] [mV] *** & E[V] [V] & \(\sigma\)[V] [V] \\ \hline
4 & 164.74302 & 3.04761449 & 0.000487422 \\
7 & 4.48031 & 2.5272936 & 0.000456076 \\
10 & \(-\)166.07790 & 2.01269855 & 0.000459554 \\ \hline \hline \end{tabular}
* The certified (Batch)/Product Numbers: B38W00/5657, B35W06/5656, and B35W00/5655) pH values of the buffer solutions utilized in this work were 3.99, 6.98, and 10.00. The systematic uncertainty of the pH of buffer solutions establishes a limit in the precision (in the 0.01 range) of pH measurements that can be achieved with this method. ** Here, E[V] and \(\sigma\)[V] stand for expected value and standard deviation of random variable \(V\), which represents the measured voltage or electrical potential in mV or V. *** The measurement range for the voltage meter was set to automatic, and did not surpass \(\pm\)400 mV. From the manufacturer datasheet, the precision of the readings is expected to be 0.5% within this range.  
\end{table} 
Table 1: Statistical parameters derived from pH sensor characterizations: Phase I and Phase II. As noted in Section 4.1, from Table 1 and Figure 5, we confirm that, for our sensor, the response to neutral pH solutions is practically centered at 0 V. Additionally, for the configuration of the instrument, the bias voltage was measured to be 840 mV. Thus, the expected quantitative voltage for a neutral solution, at the instrument output, is straightforwardly determined to be 2.52 V, which matches precisely the measured value. Considering that the instrument will bestow information comparable to that shown in Table 1, the calibration curve is obtained by performing a linear regression to this data. In Equation (5), the linear regression is presented. Furthermore, in Figure 6, we depict the calibration curve for our pH sensor. \[\text{pH}=-5.791\ V_{out}+21.647 \tag{5}\]  
where \(V_{out}\) represents the output instrument voltage in [V]. Figure 5: The sensor characterization is performed in two different phases: (**a**) utilizing a multimeter and (**b**) employing the instrumentation described in this proposal. Figure 6: The calibration curve enables the direct measurement of pH from the instrument output. In Section 3.1.2, the importance of the instrument impedance to obtain accurate measurements was emphasized. Additionally, in the design proposed in this work, we placed special emphasis on this respect. In fact, the multimeter datasheet (Steren, Ciudad de Mexico, Mexico, MUL-605) reports an input impedance of 10 M\(\Omega\), which is significantly lower than the impedance in our proposal. By carefully following the procedure for Phase II, described in the preceding section, the instrument (without offset and amplification effects) sensitivity can be calculated. This information is shown in Table 2.  
A device exhibiting Nernstian response would have a detection range of \(\pm\)177 mV, ideally centered at 0 V, for a pH range of \(\pm\)3 units. Comparing the theoretical Nernstian response to the values presented in Table 2, a maximum deviation of 6 mV for the proposed instrument is observed.