A Simple and Accurate Approach for Determining the VFA Concentration in Anaerobic Digestion Liquors, Relying on Two Titration Points and an External Inorganic Carbon Analysis

: A new analytic approach is presented for determining the total volatile fatty acids (VFA T ) concentration in anaerobic digesters. The approach relies on external determination of the inorganic carbon concentration (C T ) in the analyzed solution, along with two strong-acid titration points. The C T concentration can be determined by either a direct analysis (e.g., by using a TOC device) or by estimating it from the recorded partial pressure of CO 2 (g) in the biogas (often a routine analysis in anaerobic digesters). The titration is carried out to pH 5.25 and then to pH 4.25. The two titration results are plugged into an alkalinity-mass-based equation and then the two terms are subtracted from each other to yield an equation in which VFA T is the sole unknown (since C T is known and the effect of the total orthophosphate and ammonia concentrations is shown to be small at this pH range). The development of the algorithm and its veriﬁcation on four anaerobic reactor liquors is presented, on both the raw water and on acetic acid-spiked samples. The results show the method to be both accurate (up to 2.5% of the expected value for VFA T /Alkalinity >0.2) and repetitive when the total orthophosphate and ammonia concentrations are known, and fairly accurate ( ± 5% for VFA T >5 mM) when these are completely neglected. PHREEQC-assisted computation of C T from the knowledge of the partial pressure of CO 2 (g) in the biogas (and pH, EC and temperature in the liquor) resulted in a very good estimation of the C T value ( ± 3%), indicating that this technique is adequate for the purpose of determining VFA T for alarming operators in case of process deterioration and imminent failure.


Introduction
The control of anaerobic reactors via titrimetric analysis, applied to determine the sum of the volatile fatty acids concentrations (VFA T , namely the sum of the acetate, propionate and butyrate systems in solution), has been addressed in many publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. More than a few algorithms have been developed in the past to interpret titration results aimed at VFA T concentration determination [5], ranging from methods relying on two [4,7,14,15] through eight [11] titration points, and almost anything in between [8,9]. Some of the methods entail (external) analytical knowledge of the concentrations of other, dominant, weak-acid systems present in the water, such as orthophosphate (P T ) and ammonia (N T ) [8,11,13], while others [1,2,6,7,10,15] ignore the presence of these species, a practice that often yields only approximate results. The major difficulty in accurately determining the VFA T concentration through titration lies in the fact that the buffer capacity curves of the carbonate system (pKC 1 = 6.375) and the VFA system (pK a = 4.75) overlap close to the pH range where the buffering capacity of the VFA system is dominant. This is particularly true under the water composition that develops in intensive anaerobic digesters, which is often characterized by a very high total inorganic carbon concentration (C T ), such as, e.g., in thermophilic and mesophilic anaerobic digesters. The fact that the buffering capacity of the carbonate system is often much higher than that of the VFA system at that pH range (4.5 < pH < 6) leads to camouflaging of the titration signal that arises from the VFA species, which can only be overcome by relatively unwieldy titration methods, which often require the execution of multiple titration points. More specifically, most of the methods that have been suggested thus far, e.g., [8,11,16,17] have considered the problem to consist of two unknowns (VFA T and C T ), which need to be determined simultaneously, while assuming that P T and N T had been determined by an external analysis (and thus their effects on the titration interpretation can be calculated and included in the algorithm). Such an approach, although certainly possible and capable of resulting in accurate VFA T results, invariably leads to cumbersome and lengthy titration procedures. Other approaches exist that attempt to separate C T from VFA T by acidification and boiling [1] or by neglecting the effect of C T in a particular pH range [2,4,15]. Each of these methods has its advantages and disadvantages, elaboration on which can be (partly) found in [12,17].
The current work assumed a different approach, according to which the total inorganic carbon concentration (C T ) is analyzed on the same sample, however separately from the titration method that is performed to determine the VFA T concentration. Once C T is determined (e.g., via a TOC analyzer), a very simple and easy to execute 2-point titration procedure can be performed to yield accurate VFA T concentration results, and, as shown in this paper, this can be done without the need to analyze the P T and N T concentrations, as is often required in other titration methods.

Development of the Titration-Data Interpretation Algorithm
Similarly to previous approaches [4,8,11] the fundamental algorithm equation involves equating an equivalent-based term of the overall alkalinity species in solution (relative to the reference species defined below) in terms of the volume of the standard strong acid titrant added (left hand side of Equation (1)) with an equivalent-based term of alkalinity expressed in terms of the concentrations of all proton accepting species likely to be present in the water, i.e., proton accepting species of the carbonate, orthophosphate, ammonia and VFA systems following the addition of a certain equivalent mass, x, of strong acid (right hand side of Equation (1)). The utilized alkalinity equation was formulated against the following reference species: H 2 CO 3 * , H 3 PO 4, NH 4 + and CH 3 COOH (representing all the acidic species of the various VFA weak acid systems).
where: V e = volume of titrant (strong acid) required to the equivalence point (L); V x = volume of titrant added to yield pH x (L); V s = the volume of the sample (L); C a = concentration of the titrant (eq/L) and the subscript x represents the concentration of the individual species following the dosage of V x liter of strong acid to the solution. Equation (1) can be written explicitly as a function of the total concentration of the various weak acid systems (C T , P T , N T , VFA T ), pH x and the apparent equilibrium constants: where: K C , K P , K N and K Ac are the thermodynamic equilibrium constants of the carbonate, orthophosphate, ammonia and acetate systems, respectively, adjusted for ionic strength and temperature. Note that in order to consider the original C T , VFA T , P T and N T values in the water, they are multiplied in the algorithm by the dilution factor emanating from the titrated volume. For brevity and comprehensibility reasons, this dilution factor is not shown in Equation (2) through (6), but it is of course included in the computerized algorithm (see code in Appendix B).
If C T is known and two titration points (i.e., two V x /pH x pairs) are chosen such that the alkalinity components of the phosphate and ammonia systems hardly change when the two formed equations are subtracted from each other, only one unknown, VFA T , remains, since V e is also eliminated. Following [8,11] the two chosen titration points should be located roughly half a pH unit on either side of the pK Ac of acetic acid (i.e., the titration is carried out to pH 5.25 and then to pH 4.25). These areas in the pH scale support stable and accurate pH measurements and the relatively large amount of strong acid that needs to be added between them (when the VFA and carbonate concentrations are substantial) allows for high accuracy, particularly when the VFA T concentration increases, which is exactly the eventuality for which the method is developed. When the VFA T concentration is very low (i.e., lower than 120 mg/L as CH 3 COOH), the accuracy (in % of the true VFA T concentration) may be lower, but this is perceived inconsequential for anaerobic processes control.
Equations (3)-(5) depict the formation of two equations from Equation (2) following titration to the two pH points (V x1 , pH 5.25 and V x2 , pH 4.25), and the isolation of VFA T (Equation (4)) following the subtraction of Equation (3) from Equation (4). For demonstration purposes the values of respective thermodynamic equilibrium constants [16] are shown in these equations, however in the practical algorithm developed in this paper these values are adjusted to reflect the solution's ionic strength and temperature effects [18]. It is noted that in the practical execution of the method there is no need to titrate precisely to pH 5.25 and pH 4.25 but only to their vicinity.
10 −15.75 +K P 1 10 −10.5 +K P 1 K P 2 10 −5.25 +K P 1 K P 2 K P 3 10 −12.75 +K P 1 10 −8.5 +K P 1 K P 2 10 −4.25 +K P 1 K P 2 K P 3 Subtracting Equation (3) from Equation (4) and isolating VFA T yields: 10 −12.75 +K P 1 10 −8.5 +K P 1 K P 2 10 −4.25 +K P 1 10 −15.75 +K P 1 10 −10.5 +K P 1 K P 2 10 −5.25 +K P 1 To substantiate that the P T and N T alkalinity-related component concentrations can indeed be neglected in Equation (5) without a significant loss of accuracy, let us consider a fairly typical anaerobic digester water composition, characterized by three typical orthophosphate (P T ) concentrations (100, 150 and 200 mgP/L) and one total ammonia (N T ) concentration of 32.1 mM (450 mgN/L) [19]. Figure 1 shows the buffering capacity curves of the various weak acid systems in solution at the relevant pH range, assuming three VFA T values and C T = 51.1 mM. For the derivation of the buffer capacity terms see Lahav and Birnhack (2019) [18]. Since the integration of a buffering capacity curve between two pH values gives, by definition, the overall alkalinity concentration between these values, one can perform a separate integration of each weak acid system and determine from it the a fairly typical anaerobic digester water composition, characterized by three typical orthophosphate (PT) concentrations (100, 150 and 200 mgP/L) and one total ammonia (NT) concentration of 32.1 mM (450 mgN/L) [19]. Figure 1 shows the buffering capacity curves of the various weak acid systems in solution at the relevant pH range, assuming three VFAT values and CT = 51.1 mM. For the derivation of the buffer capacity terms see Lahav and Birnhack (2019) [18]. Since the integration of a buffering capacity curve between two pH values gives, by definition, the overall alkalinity concentration between these values, one can perform a separate integration of each weak acid system and determine from it the theoretical error in the VFAT concentration that would arise from ignoring the NT and PT values in the calculation represented by Equation (5).   Table 1 shows the overall theoretical error incurred from neglecting N T and P T . While the effect of N T on VFA T is outright negligible (as also demonstrated by the very small the area under the N T buffer intensity curve), the effect of P T cannot be considered as such, but it is still small and, as shown in Table 1, it becomes smaller as the total VFA concentration (VFA T ) reaches high (and alarming, from the anaerobic digester operation standpoint) concentrations. For example, the error in determining a VFA T concentration of 8 mM (480 mg/L as CH 3 COOH) was merely 3.3% when N T and P T were 450 mgP/L and 200 mgN/L, respectively. Therefore, for the sake of execution simplicity and for anaerobic reactor control purposes both N T and P T can be ignored without loss of essential information. This said, if P T and N T concentrations are known, even roughly, they could be plugged into the algorithm to attain better accuracy. This is mostly important when P T reaches very high concentrations, such as 700 mgP/L, which has been reported in some locations [20]. Table 1. The error induced in VFA T calculation (Equation (5)) by neglecting the alkalinity components related to the ammonia and orthophosphate weak-acid systems.

Titration Procedure
All titrations were performed in a sealed 220-mL glass container, equipped with a cap with perforated holes for placing pH and electrical conductivity (EC) probes, along with a port used for acid dosage. The titration was performed using a digital burette (Dosimat To obtain good results with the method it is essential to use a high-quality, sensitive pH electrode, which shows a stabilized reading in less than 30 s.

Titration of Synthetic Solutions
To compare the results of the new developed algorithm with the previously published 5-and 8-point methods [8,11], six synthetic solutions with varying VFA T concentration (mg/L as CaCO 3 ) and carbonate alkalinity concentration (mg/L as CaCO 3 ) ratios were titrated using the 8-point titration procedure [11], which consists in it both the 5-point and the 2-point titration points (note that the VFA unit of concentration is shown here as mg/L as CaCO 3 , for calculating the VFA to carbonate alkalinity ratio using similar units). The VFA T concentration was 1 mM in all the synthetic solutions, simulating a dilution factor of 3.3 with deionized water (DIW) for an initial VFA T concentration of 200 mg/L as HAc. To substantiate the premise that the method is accurate for all VFAs that have a pKa value close to 4.75, a synthetic solution of butyric acid with a VFA T to alkalinity ratio of 0.31 and a VFA T concentration of 1 mM was also prepared and tested using the same method.

Titration of Anaerobic Liquor Solutions
The dilution of the sample was done inside the sealed container, using a large as possible solution volume to reduce the head space to a minimum, to restrict the CO 2 mass that could potentially escape from the aqueous phase during the titration. Titrations were performed with an acid concentration of 0.05 N. The initial temperature and EC values are recorded prior to the titration. For detailed guidelines for sample collection and step-bystep execution of the procedure the reader is referred to the first section in the results and to Appendix A.

Synthetic Solutions
The measured parameters (temperature; EC; C T ; dilution factor; initial solution volume and the acid concentration) and the titration results for each synthetic solution were plugged in the program developed by Lahav and Morgan, 2002 [11] and the new excel program developed in the current work. The Excel program can be downloaded from the Supplementary Material.

Anaerobic Liquors
All the measured parameters (temperature; EC; C T ; N T ; P T ; dilution factor; initial solution volume and the acid concentration) and the titration results (two acid volumes and pH values) were plugged into a custom written excel function (see details of the VFA code in Appendix B) to yield the VFA T concentration (in M).

Calculating C T from the Knowledge of the CO 2(g) Partial Pressure
To determine the C T concentration from the biogas-CO 2 partial pressure, the PHREEQC [21] software was used (database = phreeqc.dat). The solution characteristics were plugged into the initial solution sheet and the inorganic carbon (C T ) was set to equilibrate with the measured partial pressure (Pp) of CO 2(g) in the biogas. The initial solution C T was set at equilibrium with a given CO 2 Pp and only the speciation results of the solution were used. The Excel program can be downloaded from the Supplementary Material.

Sample Preparation
Synthetic solutions: sodium acetate, butyric acid and sodium bicarbonate were used to simulate the VFA T and carbonate alkalinity, respectively. The VFA T concentration was determined prior to addition of the carbonate alkalinity using TOC analyzer and Gran's titration for total alkalinity. C T was determined using a TOC analyzer. All the chemicals were of analytical grade, salts were dried at 60 • C overnight and kept in a desiccator prior to use.
Anaerobic liquor: (1) for the VFA T analysis: samples of anaerobic digester liquor were centrifuged (6000 rpm for 20 min), filtered through a No. 1 Whatman filter paper and refrigerated (4 • C) until analysis and (2) C T , N T and P T determination: samples of the anaerobic digester liquor were immediately centrifuged at 6000 RPM for 20 min after sampling and the clear supernatant was diluted (1:250) and filtered via a 45 µm syringe filter.

Analyses
Analyses: Ammonia was determined using the salicylate method [22]. Phosphate was determined using the metol method [23]. Inorganic carbon concentration (C T ) was determined by a Sievers M5310C (Suez Water Technologies, Boulder Co, USA) TOC Analyzer with a detection range of 0.04-50 mg/L. pH, temperature and electrical conductivity (EC) were measured using a Metrohm 914 pH meter equipped with a pH electrode with a Pt1000 sensor (Unitrode with Pt1000, Metrohm) and an EC electrode (conductivity measuring cell, Metrohm).
Statistical analyses: All the empirical results were analyzed statistically by JMP Pro ® , SAS Institute Inc. α = 0.05 was used in all calculations. Table 2 presents the titration results and relative error (%) obtained with three titration methods, as compared to a known VFA T and C T concentrations, at six VFA T to alkalinity dimensionless ratios (mg/L as CaCO 3 to mg/L as CaCO 3 ).  Table 2 shows that all the three methods yield accurate results down to VFA T /alkalinity ratio of 0.12 (relative error of 4.5%) while when the ratio dropped to 0.1, the relative error rose to 10%. The reason for the drop in accuracy at the low ratios stems from the fact that even a small error in the analysis of the (high) C T concentration yield a high error in the (low) VFA T concentration. To overcome this inherent drawback, the user is advised to spike the solution with an accurate volume of sodium acetate solution, to increase the ratio to above 0.2. This will ensure the accuracy of the results (in all three methods). At the end of the procedure the known dosed concentration should be subtracted from the result. To make sure that the obtained results are accurate, the user should follow the following guidelines: (1) the VFA T concentration in the titrated solution should be at least one 1 mM (i.e., 60 mg/L as CH 3 COOH); (2) if the VFA T concentration is lower than 60 mg/L, it is suggested to spike the solution with a known concentration of acetic acid to attain at least 1 mM while also keeping in mind the VFA T /alkalinity ratio (note that you will need to add the volume of the dosed acetic acid to the total volume, correct the P T and N T concentrations, etc.) and (3) an initial titration can be performed to assess the volume of acid required to reach the two pH points. The titration after that can be faster thereby reducing the potential change in C T due to CO 2 release from the solution to the beaker's headspace; (4) the volume of the titrated acid is crucial to the accurate execution of the method. Choose an acid concentration that will allow for at least 2 mL of titrant between the two pH points. More guidelines and instructions appear in Appendix A. Figure 2 shows the VFA T concentrations (average of triplicate measurements with lower and upper 95% confidence intervals) obtained by the proposed method upon its execution on four types of both thermophilic (Shafdan, Acre) and mesophilic (Haifa) anaerobic digestion waters treating sludge from a municipal WWTP and another set of measurements performed on a mesophilic anaerobic digester treating winery wastes (Zichron). In all cases the raw water was diluted to obtain a solution with an alkalinity concentration in the range 300-400 mg/L as CaCO 3 ; C T (and also N T and P T ) was determined by external analysis and two titration points were executed. The raw results of all the analyses are listed in Tables A1-A4 in Appendix C. As shown in Figure 2, the method was found to be very accurate (an average error lower than 1.5%, relative to the expected, spiked values) in determining the VFA T concentration of the spiked samples, and also in predicting (via extrapolation of the spiked samples' results) the raw-water VFA T concentration (compare the free term in the linear regression equations with the raw VFA T results that appear in Table 3). The slope of all four linear regression equations is very close to 1 (with p value < 0.01), demonstrating the accuracy of the method. The raw VFA T concentration in two of the solutions (the mesophilic reactors, Haifa and Zichron) was lower, with concentrations of 12 and 28 mg/L as HAc, respectively, while in the thermophilic reactors (Shafdan and Acre) the recorded concentrations were 250 and 580 mg/L as HAc, respectively. The results that appeared in Figure 2 were obtained by plugging the measured C T , N T and P T concentrations into Equation (5), in addition to the results of the two titration points. Table 3 lists the VFA T results that were returned by Equation (5) when P T and N T were neglected (i.e., assuming that both concentrations are zero). As shown, the resulting difference was not larger than 5% when the VFA T concentration was higher than 5 mM. When the VFA T concentration was increased to concentrations commonly perceived to be of concern (>8 mM) to the stability of anaerobic digesters, the error induced by neglecting N T and P T dropped to 1-5%. Most importantly for VFA T concentration control purposes, the slope of the increase in the VFA T concentrations remained the same when P T and N T were neglected, which means that, although from a global perspective less accurate VFA T results were obtained, the method continues to serve its main purpose, which is to alert the operator on a possible decline in the methanogenic bacteria activity. ceived to be of concern (>8 mM) to the stability of anaerobic digesters, the er by neglecting NT and PT dropped to 1-5%. Most importantly for VFAT concen trol purposes, the slope of the increase in the VFAT concentrations remaine when PT and NT were neglected, which means that, although from a global less accurate VFAT results were obtained, the method continues to serve its ma which is to alert the operator on a possible decline in the methanogenic bacter

Determining VFAT Using CT Values Estimated from CO2(g) Partial Pressure Va Measured in the Biogas
TOC analyzers may not be available in the (often) rudimentary laborator erate within WWTPs. Since the knowledge of CT is obligatory for executing th method, the authors warmly suggest that such device would be available. How absence, CT can be estimated via a simulation program (PHREEQC or a simila

Determining VFA T Using C T Values Estimated from CO 2 (g) Partial Pressure Values Measured in the Biogas
TOC analyzers may not be available in the (often) rudimentary laboratories that operate within WWTPs. Since the knowledge of C T is obligatory for executing the presented method, the authors warmly suggest that such device would be available. However, in its absence, C T can be estimated via a simulation program (PHREEQC or a similar tool) from the knowledge of the CO 2(g) partial pressure in the biogas, which is measured routinely in many anaerobic digesters, in addition to the electrical conductivity, pH and temperature prevailing in the anaerobic digester liquor. Such calculation relies on two assumptions: (1) the aqueous phase in the reactor is completely mixed and (2) the aqueous phase tends towards equilibrium with the biogas. The two assumptions, although reasonable, are clearly not entirely correct, but for the purpose of estimating C T for use in the suggested method, our hypothesis was that the emanating error would be relatively low, and more importantly, the trend in the increase in the VFA T concentration can be expected to be obtained accurately regardless of the inaccuracy in the nominal VFA T concentrations, which is sufficient for raising a red flag in the case of an alarming rise in the VFA T concentration.
To assess whether such estimation is valid, seven anaerobic digesters in the Shafdan WWTP and one in the Acre WWTP were sampled for the percentage of CO 2(g) and the overall pressure in the (dry) biogas, along with the required parameters (pH, EC and temperature) in the aqueous phase. PHREEQC was used to calculate the C T concentrations from these data, and these were compared with measured C T values obtained from the same samples via a TOC-based analysis. The results are presented in Table 4, which shows that the C T values obtained from the calculations were very close to the TOC-measured C T (an average difference of 0.4% and STDV of 2.8%). Such deviations in the C T concentration can be expected to yield only a small error in the computed VFA T concentration of several tens of mgHAc/L at the maximum, which translates into inconsequential error in VFA T when the measured concentration was high (e.g., 8 mM). It can be hence concluded that estimating the C T value via the CO 2(g) partial pressure and its use within Equation (5) is a viable method for determining the trend of the VFA T concentration, despite the slightly lower accuracy.

Conclusions
A new, titration-based, simple to execute and accurate analytical method for VFA T analysis in anaerobic digester waters is presented and verified. The method differs from previous techniques by the fact that the total inorganic carbon concentration is analyzed on the same sample, but by an external method, preferably using a TOC analyzer. The titration method consists of only two points, carried out to pH values in the vicinity of pH 5.25 and pH 4.25. The buffer capacity area between these pH values is dominated by the VFA T and carbonate weak-acid systems, with only a minor effect of the ammonia and orthophosphate systems, hence these weak-acid systems can be neglected in the analysis without significant loss of accuracy, particularly when the VFA T concentration is high (VFA T > 8 mM). The method was shown to yield results that are comparable with the 5-point and 8-point methods in terms of accuracy and reproducibility. The method was further tested on four anaerobic liquors and was shown to yield accurate and consistent results, with both raw and spiked samples. The inclusion of the orthophosphate (and to a lesser extent the ammonia) concentration increases the obtained accuracy, however if these are not known, the loss of accuracy is inconsequential (not more than a few percent) when the VFA T concentration reaches values of concern. A PHREEQC-based procedure was developed for estimating the total inorganic carbon concentration based on the measured partial pressure of CO 2 in the biogas, for possible use in the case that a direct C T analysis is not available. This technique was shown to yield accurate C T values with an average error of 0.4% ± 2.8%. The resulting VFA T computation may only slightly deviate from the correct value, indicating that this approximated technique is valid for determining the VFA T trend, and hence adequate as a monitoring tool for the performance of anaerobic digesters. This said, for obtaining the most accurate and reliable VFA T results the writers recommend using externally measured C T and P T values. N T can be neglected altogether because its effect on the VFA T value is almost negligible. The presented method is ideal for use by researchers working on anaerobic processes, but it is also appropriate as a routine tool for controlling full-scale anaerobic digesters. The Excel-based interpretation program and the PHRREQC-based procedure for estimating C T from Pp (CO 2 ) can be downloaded from the Supplementary Material.

1.
Fill the test tube slowly, by letting the liquor outlet tube fill the test-tube from its bottom.

2.
Let the liquor to overflow for at least one volume of the test tube and then seal the tube tightly.

3.
After the centrifuge step, the test tubes kept closed until the titration. 4.
Only the supernatant part of the centrifuge step is used in the titration.

5.
If C T analysis is carried out using a TOC analyzer, the centrifuge supernatant should be sampled for this purpose.

Appendix A.3. Titration
The following set of conditions must be met for attaining stable and accurate results: • The titration must be performed in a sealed, gently magnetically stirred beaker (see Figure A1).

•
The inlet holes for the pH and EC electrodes and for the acid tube or burette should be sealed as tightly as possible.

•
Only analytical grade acid (HCl) ampules of a known concentration (diluted to a concentration of 0.05-0.2 eq/L) should be used.

•
The pH and EC electrodes must be calibrated and be in a good working condition.

•
From experience, to obtain accurate results, the alkalinity of the titrated solution (after dilution) should be around 300-400 mg/L as CaCO 3 . The sample should be diluted to meet this condition. • A minimal head space should be left in the sealed beaker for allowing the addition of acid with a small safety margin.
Place the required volume of deionized water for the required dilution in the beaker.

2.
Close the beaker cover. Insert the EC and pH electrodes in their designated inlet holes.

3.
Gently open the centrifuged test tube and take the required volume of the supernatant by using a pipette.

4.
Insert the volume of sample below the water level (to minimize CO 2 losses) through the inlet hole of the acid tube or burette in the cap of the sealed beaker.

5.
Place the acid tube or burette in place. 6.
Wait for the pH reading to stabilize. 7.
After stabilization, register the EC and temperature values (the temperature can be measured via the EC or pH meters). 8.
Start titrating the strong acid to pH = 5.25. Register the exact pH that was reached and the volume of strong acid that was titrated. These measurements are marked pH X1 and V X1 , respectively. 9.
Continue titrating the strong acid to pH = 4.25. Register the exact pH reached and the cumulative volume of strong acid up to that pH point. These measurements are marked pH X2 and V X2 , respectively. measured via the EC or pH meters). 8. Start titrating the strong acid to pH = 5.25. Register the exact pH that was reached and the volume of strong acid that was titrated. These measurements are marked pHX1 and VX1, respectively. 9. Continue titrating the strong acid to pH = 4.25. Register the exact pH reached and the cumulative volume of strong acid up to that pH point. These measurements are marked pHX2 and VX2, respectively. Figure A1. A sealed beaker with inlet holes for electrodes and for the acid titration tubing.