3.1. Determination of pKa in Ethanolic Medium
After experimenting with the methyl red indicator, the pH values of each withdrawn aliquot were corrected by applying Equation (1) (see
Section 2.1);
.
We found a value of ΔpH equal to −0.43, close to the one presented by Battes for the mixture of ethanol and 90% water, −0.40. For each pH value measured by the conventional glass electrode, 0.43 must be discounted to obtain the pH value corrected for the effect of the liquid junction potential, as shown in
Table 4 [
19].
For each aliquot of the ethanolic solution containing the indicator, the reading was performed on the spectrophotometer, as shown in
Figure 4. It can be observed the absorbance peaks (A
maximum) present at λ = 413 nm, referring to the basic species of the indicator, which presented a yellow color, and the peaks presented at λ = 510 nm, referring to the acidic species of the indicator, whose color was red. Another important aspect was the presence of the isoabsorbed point (isobestic); that is, the wavelength at which all absorbing species had the same absorptivity, so Beer’s law was not affected by equilibrium at λ = 438 nm, evidencing the presence of two species in equilibrium.
To find the
pKa value, the spectrophotometric principles presented above were applied. From the collected absorbance values and the maximum absorption wavelengths, for the acidic and basic forms of the indicator, it was possible to apply the mathematical expression presented in Equation (2) (Henderson–Hasselbalch equation) [
30] and its graphical representation of the log ratio [A
Ind−/A
Hind] as a function of corrected pH, as shown in
Figure 5 [
19,
31].
Starting from Equation (2) and graphically representing the corrected pH values as a function of the values of
, as shown in
Figure 5, it was possible to find the value of pKa from the intercept of the curve with the Y-axis, a situation in which pH = pKa, which, for the methyl red indicator, is equal to 6.98.
To determine the turning interval, in addition to the careful observation of the operator to reveal the interval, it was also accompanied by graphically obtaining the beginning and end values of the indicator turning process. In
Figure 6, the normalized absorbance values for the indicator as a function of the corrected pH are shown. The extrapolation obtained from the dotted curve provides the lower and upper pH limits for the turning of the indicator, where the points in yellow were the ones that obtained the best correlation, 99.93%. Consequently, these will be the points used to perform the curve extrapolation [
19].
Using the Excel statistical software, based on analysis of variance, both linear regression and the intercept of the calibration plot were significant (
p < 0.05). Therefore, the value of the intercept (linear coefficient), −1.5701, and the slope of the line, 0.3099, were found using an unweighted linear fit, Equation (3), where
y represents absorbance and
x is pH.
where
α represents the linear coefficient and
β the slope, we obtain the following Equation (4):
To determine the values of the extrapolation of the line, that is, where it crosses the y -axis at 0 and 1, as they are normalized values, using Equation (4), and solving for pH, Equations (5) and (6):
Thus, it was possible to determine the values of the indicator turning interval for the ethanolic medium, which in the case of methyl red starts at 5.06 and ends at 8.29, with a pKa of 6.98. This procedure was carried out for the other indicators used, obtaining new pKa and pH values from their respective turning intervals. The equation obtained for each of the indicators and the new range values are described in
Table 5.
3.2. Construction of the New Glass Electrode
Based on the results of the experiments in
Table 6, it was noticeable that two experiments (9 and 10) reached values very close to each other as well as to the expected value. Analyzing these two experiments, it was observed that only the level of variable 3, corresponding to temperature, was changed. The same occurred when we compared experiments 7 and 8, and 11 and 12, showing that when the value for variables 1 and 2 was maintained and the value of variable 3 was changed, the results were very similar. This behavior demonstrated that variable 3 (temperature) was not statistically significant for the experiment, besides the
p-value being higher than 0.05. Otherwise, the results of the cited experiments would present a more significant variation between them.
When comparing experiments where the levels of variables 1 and 3 were maintained, the value of variable 2 (ionic strength) is altered, evidencing that variable 2 had great relevance for the experiment. The variable 1 (buffer solution composition) had great relevance for the experiment due to the great difference in the results due to its level changing.
After evaluating the results, the optimized condition was used in experiment 9, where a buffer solution with a concentration of 0.050 molal, ionic strength of 0.1 molal, and temperature of 20 °C was used. Although the temperature was not relevant to the experiment, we chose to keep the temperature at 20 °C for the experiments in the next section.
3.3. Studies Carried out with the Optimized Electrode
As mentioned before, to correct the net junction potential, it is necessary to deduct 0.43 from each pH value measured by electrode A. This value was experimentally determined by measuring the value of the net junction potential (E
lj) established between the internal and external region of the reference electrode and later converted to the respective value expressed in pH, as discussed above. The corrected values for electrode A are shown in
Table 7 and are used from now on for electrode A.
For a significant level of 0.05, and based on parametric and nonparametric tests, it was possible to evaluate and compare the results from electrode A (ASTM), electrode B (ABNT), and the optimized electrode C,
Table 8.
The determination of the pH values of different aqueous solutions using acid and basic indicators was the first method used to determine this important parameter, before the development of potentiometers and glasses electrodes. Thus, for this reason the method was adapted and applied for the determination of the pH and pKa of the indicators prepared in an ethanolic solution of HFE. The concept of Henderson–Hasselbalch was applied, considering that indicators as defined as weak organic bases or acids and, for the most part, are soluble in ethanol. Thus, for this research, a reference system was prepared using a set of ethanol-soluble indicators. This set was applied to generate a reference system for pH measurement in ethanol independent of any electronic system composed of a pH meter and glass electrode. The pH values of the ethanolic solutions were determined by applying the turning ranges of each indicator to different aliquots of the ethanolic solution (HEF) as shown in
Table 5. Methyl red indicator was used as an example for others due to its impeccable physicochemical behavior. The spectrum shown in
Figure 7a was obtained by the methyl red indicator for an acidified HEF solution, a blue curve; a basified HEF solution, a black curve; and for the ethanolic buffer solution, a red curve, which was intended to determine its pH value.
The spectral behavior analysis was based on observing the values of maximum λ of absorbance in the bands of each solution, as shown in
Figure 7a. The acidified and basified solutions had maximum absorbance peaks at 510 nm and 413 nm, respectively. The presence of two bands, simultaneously, was noticeable, showing that the pH of the solution is between its turning range, which in this case was from 5.06 to 8.29 (experimental data available on
Table 5), with an average pH value close to 6.67. It should be noted that the spectral behavior of the buffer solution differed from the other indicators (acid or basic) concerning the isoabsorptive point [
32,
33]. This statement was ratified through the analysis of the curve deconvolution, using Software Origin 7.0, in which the presence of the basic (415 nm) and acidic (504 nm) species was clearly demonstrated, as shown in
Figure 7b. It was noticeable that the color of the tube that contained the sample of buffer solution presents an orange color, as shown in
Figure 7c., the result of the mixture of the yellow color, the basic species, with red, the acidic species, thus showing the presence of the two species of the indicator; that is, the sample pH was close to the average value of the used indicator range, which is 6.67, which corroborated the spectral behavior discussed earlier.
Table 9 presented the spectra obtained, and the visual results of the experiments carried out simultaneously. The colors developed by the dyes (pH indicators) were observed for the same experimental conditions in test tubes for visual comparison. Falcon tubes can be seen from left to right, respectively: (i) the acidified HEF solution; (ii) the buffer solution to be determined for pH, and (iii) the basified HEF solution.
For the xylenol orange, the presence of the acid species, with a maximum at λ = 433 nm, and of the basic species, with a maximum at 588 nm, was perceptible. When the behavior of the buffer solution was analyzed, its similarity in behavior with the acidic species was evident due to the partial overlap, which is what indicated that the pH of the buffer solution was below the acid turning range of this indicator, as shown in
Table 5; that is, the pH of the solution is less than 6.96. Furthermore, the visual perception showed that the buffer solution was very similar to the acidified solution, with a yellow color, thus assuming it agreed with the spectral result, a pH ≤ 6.96.
Next, for the bromophenol blue, the presence of two bands very close to the peaks of the acidic and basic species was visualized. However, the peak at 602 nm was noticeably higher; that is, it had a higher absorbance. The visual inspection for the buffer solution was bluish green, showing a greater contribution of the basic species (a blue tone) than the acid species, which had a yellow color. From these results, it was possible to infer that the pH of the solution must be above the middle of the range, 6.18, and below the basic range, 7.22, as shown in
Table 5.
Finally, for the bromocresol green, the presence of two bands was visible, indicating the presence of acidic and basic species. Thus, considering the equivalence of the absorbance of the acid and basic species, the pH of the solution must be close to the middle of the range, as shown in
Table 5, with a pH = 6.72, a value very close to that found by the methyl red (6.67). The same result was obtained in the visual perception, where the coloring of the buffer solution presented a shade of green (tube in the middle), evidencing the mixture of a blue and yellow color.
The pH results obtained by the indicators, investigated into the ethanolic buffer solution, considering the spectra and visual inspection, were grouped, as shown in
Table 10. The most relevant results were obtained by the methyl red and bromocresol green indicators, as both reveal that the pH in the middle of their ranges and values are very similar. From these results, it was possible to narrow the pH range of the buffer solution, indicating that the pH of the solution is very close to the range from 6.67 to 6.72.
Using the pH range determined using the pH indicators, it was possible to compare the results obtained by the three different electrodes, A, B, and C. As mentioned before, the distributions of electrodes A and B were Gaussian; therefore, the mean value was used. On the other hand, for the electrode C, the median was used, as shown in
Table 11.
Comparing the mean and median values, as shown in
Table 11, with the values of the pH intervals found by the indicators, it was noticeable that the closest was the value obtained by the median of the distribution of electrode C. It was even very close to the values found by methyl red and bromocresol green, thus demonstrating efficiency in the measurement using the optimized electrode.
This study using the pH indicators found a pH for the buffer solution close to the range from 6.67 to 6.72. When comparing the mean values obtained for electrodes A and B, 6.48 and 6.59, respectively, and the median value for electrode C, 6.71, it was evident that the result that best fitted the indicators was the result obtained by electrode C.
Finally, the values found in
Table 3 were graphically recorded in
Figure 8. Since the angular coefficient of the regression was 59.48, a value referring to 100.5% of Nernst’s ideal response, 59.16 to 25 °C, it was an indication of an adequate sensitivity of the optimized electrode [
19].