Potentiometric measurement of redox potential in acidic rivers around Mutsu Hiuchi Dake Volcano, Japan Open Access

Various anthropogenic factors can affect the water quality of streams and rivers. Bieroza et al. (2023) highlighted the importance of high-frequency water quality measurements to improve the database for water quality management. Although high-frequency water quality monitoring is designed for measuring specific parameters (⁠⁠, pH, DO, and temperature), they typically do not include Eh values. A possible reason for the exclusion of redox potential (Eh) values is likely the fact that it remains unknown which chemical species control those values. The Eh value in dilute natural waters is believed to have limited significance and cannot be used for quantitative modeling of the transport properties of redox-sensitive species from bulk analysis (Stefánsson et al. 2005). However, Linnik et al. (2023) reported the importance of Eh values as an essential characteristic for evaluating the chemical and biological status of surface water bodies. Additionally, in acid mine water, high concentrations of Fe²⁺ and Fe³⁺ control the Eh values, making it usable for measuring the redox potential using WATEQ2, a computerized ion association model (Nordstrom et al. 1979). Nordstrom et al. (1979) used platinum electrodes to measure the redox potential and Macalady et al. (1990) reported that lab and field Eh measurements using Pt or wax-impregnated-graphite electrodes can provide Nernstian potentials in the presence of measurable Fe²⁺ at pH as high as 6.6. Kumar & Riyazuddin (2012) indicated that 41% of the Eh values calculated from the Fe³⁺/Fe²⁺ redox couple agree with measured Eh values within ±30 mV, which represents the uncertainty of Pt-electrode measurements in shallow groundwater. These findings indicate the importance of using platinum electrodes to measure the redox potential in acidic rivers or streams occurring in volcanic regions. However, such studies are limited. Moreover, the calculated Fe²⁺ and measured Fe²⁺ concentrations in acidic rivers have seldom been compared. Therefore, the present study aimed to compare the Eh values calculated from Fe³⁺/Fe²⁺ ratios with those obtained from electrode measurements in acidic river waters of the Ohaka and Koaka rivers flowing through the Mutsu Hiuchi Dake volcanic region. Additionally, the study includes a comparison of calculated and measured Eh values for other detected redox species, specifically O₂/H₂O and as redox couples. We further aimed to compare the calculated Fe²⁺ with the measured Fe²⁺ concentrations.

The inset map shows the sampling locations and is modified from the topographical map of the Geospatial Information Authority of Japan.

Unfiltered samples were used for laboratory measurements of alkalinity. Water samples for the determination of alkalinity were collected in 100-mL polyethylene bottles. Filtered (polytetrafluoroethylene filter; DISMIC-25_HP; pore size: 0.2 μm) splits were collected for in-field measurement of Fe²⁺ using a colorimeter (model DR890, Hach, USA), and the laboratory measurement of dissolved organic carbon (DOC), cation and anion concentrations in the river water samples. To analyze Fe, Mn, Cu, Zn, Ni, and Al, subsamples of the filtered water were transferred to 100-mL polyethylene bottles and acidified to pH < 2 using ultrapure HNO₃. Unacidified splits were retained in 100-mL polyethylene bottles to analyze cations (Na⁺, ⁠, K⁺, Mg²⁺, and Ca²⁺) and anions (F^–, Cl^–, ⁠, and ⁠); subsamples were kept in 50 mL glass vials for the estimation of DOC.

Elemental analyses were performed at the Geothermal Engineering Laboratory at Hirosaki University, Japan. Fe, Mn, Cu, Zn, Ni, and Al concentrations were determined using inductively coupled plasma (ICP)-optical emission spectrometry (ICP-OES; Optima 7000DV, PerkinElmer Co. Ltd, USA). The concentrations of Na⁺, ⁠, K⁺, Mg²⁺, and Ca²⁺ were determined via ion chromatography with conductivity detection using an ICS-1100 instrument (Thermo Fisher Scientific Inc., Waltham, MA, USA), and the concentrations of F^–, Cl^–, ⁠, and were determined using an ICS-2100 instrument (Thermo Fisher Scientific Inc.). The DOC values were measured using a total organic carbon (TOC) analyzer (TOC-V_CPH, Shimadzu Co., Kyoto, Japan). Alkalinity measurements at pH 4.8, involving titration, were conducted using 876 Dosimat Plus (Metrohm AG, Switzerland) and N/50 H₂SO₄. Thus, alkalinity measurements were not performed on samples with a pH <4.8. The obtained alkalinity values were expressed in terms of the concentration. The Fe³⁺ concentrations were calculated from the Fe concentrations analyzed using ICP-OES. The analytical precision (coefficients of variation for triplicate measurements) was within 1% for Na⁺, K⁺, Mg²⁺, Ca²⁺, F⁻, Cl⁻, NO₃⁻, ⁠, Zn, and Al; 2% for Fe²⁺, Fe, and Mn; 4% for and DOC; and within 15% for Cu and Ni. The error in the charge balance between the cations and anions was calculated using the aqueous speciation code PHREEQC ver.3 with the WATEQ4f.dat database (Parkhurst & Appelo 2013) was <± 3.3% in all the samples. PHREEQC (Parkhurst & Appelo 2013) is a widely used geochemical modeling software developed by the United States Geological Survey and distributed freely to the public (Lu et al. 2022).

The redox reactions considered for the in situ Eh calculation for comparison with the measured Eh in this study are listed in Table 1. Since the valence of the manganese ion could not be clarified, the manganese redox couple was not considered. The data listed in Table 1 are part of the thermodynamic database from WATEQ4f used with the GWB program (Bethke 2022). Log K values were corrected against the in situ temperature. Constants were calculated based on the van't Hoff equation using Log K and the standard enthalpy of the reaction (Table 1). The activity required to calculate Eh from the chemical species-related redox reactions was determined using PHREEQC ver.3 with WATEQ4f.dat (Parkhurst & Appelo 2013). The river water results (Table 2) were used as input data for the calculation of activities, except for Fe and DOC concentrations. PHREEQC ver.3 with WATEQ4f.dat (Parkhurst & Appelo 2013) was used to calculate the Fe²⁺ concentration from the results presented in Table 2, excluding the Fe²⁺, Fe³⁺, and DOC concentrations as input data.

Table 1

Reactions and equilibrium constants at 25 °C for the calculation of Eh

Reaction .	.	Log K .	ΔrH° (kcal/mol) .
		–13.02	9.68
		–86.08	134.79
		–119.077	187.055

Reaction .	.	Log K .	ΔrH° (kcal/mol) .
		–13.02	9.68
		–86.08	134.79
		–119.077	187.055

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Table 2

Results of chemical analysis of the water samples in 2017

.	.	Ohaka River .				Koaka River .
		27-Apr .	2-Jul .	27-Jul .	30-Nov .	27-Apr .	2-Jul .	27-Jul .	30-Nov .
pH		3.87	3.50	3.47	3.91	4.55	4.64	4.65	5.17
Eh	(mV)	645	683	684	687	559	553	549	464
Temp.	(°C)	11.7	20.3	19.4	4.8	11.2	20.0	20.6	2.8
DO	(mg/L)	NM	8.1	9.2	NM	NM	8.3	9.3	NM
DOC	(mg/L)	0.10	0.15	0.17	0.22	0.147	0.20	0.25	0.21
F–	(mg/L)	0.069	0.157	0.151	0.094	0.044	0.059	0.057	0.041
Cl–	(mg/L)	11.6	16.6	15.7	14.2	10.1	11.0	10.9	12.2
	(mg/L)	0.559	0.169	0.182	0.300	0.717	0.254	0.300	0.584
	(mg/L)	74.3	140	138	98.8	62.8	77.6	73.5	56.5
	(mg/L)	NM	NM	NM	NM	NM	NM	NM	0.83
Na+	(mg/L)	9.79	15.5	15.1	12.0	8.26	10.5	10.3	9.3
	(mg/L)	0.016	0.048	0.052	0.026	<0.01	0.012	0.014	0.010
K+	(mg/L)	0.906	1.60	1.57	1.08	0.744	1.06	1.06	0.973
Mg2+	(mg/L)	4.16	7.39	7.27	5.68	3.23	4.45	4.31	3.49
Ca2+	(mg/L)	13.3	21.7	21.7	17.9	11.7	16.0	15.6	13.0
Fe2+	(mg/L)	0.91	0.98	0.86	0.64	0.71	0.38	0.37	0.54
Fe3+	(mg/L)	0.37	0.82	0.94	1.05	0.033	0.060	0.043	0.02
Fe	(mg/L)	1.28	1.8	1.8	1.69	0.743	0.44	0.413	0.56
Mn	(mg/L)	0.24	0.424	0.435	0.322	0.173	0.30	0.29	0.218
Cu	(mg/L)	0.006	0.008	0.008	0.006	<0.004	<0.004	<0.004	<0.004
Zn	(mg/L)	0.017	0.030	0.030	0.024	0.016	0.020	0.019	0.014
Ni	(mg/L)	<0.004	0.004	0.005	<0.004	<0.004	<0.004	<0.004	<0.004
Al	(mg/L)	2.69	5.61	5.61	3.74	3.25	2.54	2.07	1.97

.	.	Ohaka River .				Koaka River .
		27-Apr .	2-Jul .	27-Jul .	30-Nov .	27-Apr .	2-Jul .	27-Jul .	30-Nov .
pH		3.87	3.50	3.47	3.91	4.55	4.64	4.65	5.17
Eh	(mV)	645	683	684	687	559	553	549	464
Temp.	(°C)	11.7	20.3	19.4	4.8	11.2	20.0	20.6	2.8
DO	(mg/L)	NM	8.1	9.2	NM	NM	8.3	9.3	NM
DOC	(mg/L)	0.10	0.15	0.17	0.22	0.147	0.20	0.25	0.21
F–	(mg/L)	0.069	0.157	0.151	0.094	0.044	0.059	0.057	0.041
Cl–	(mg/L)	11.6	16.6	15.7	14.2	10.1	11.0	10.9	12.2
	(mg/L)	0.559	0.169	0.182	0.300	0.717	0.254	0.300	0.584
	(mg/L)	74.3	140	138	98.8	62.8	77.6	73.5	56.5
	(mg/L)	NM	NM	NM	NM	NM	NM	NM	0.83
Na+	(mg/L)	9.79	15.5	15.1	12.0	8.26	10.5	10.3	9.3
	(mg/L)	0.016	0.048	0.052	0.026	<0.01	0.012	0.014	0.010
K+	(mg/L)	0.906	1.60	1.57	1.08	0.744	1.06	1.06	0.973
Mg2+	(mg/L)	4.16	7.39	7.27	5.68	3.23	4.45	4.31	3.49
Ca2+	(mg/L)	13.3	21.7	21.7	17.9	11.7	16.0	15.6	13.0
Fe2+	(mg/L)	0.91	0.98	0.86	0.64	0.71	0.38	0.37	0.54
Fe3+	(mg/L)	0.37	0.82	0.94	1.05	0.033	0.060	0.043	0.02
Fe	(mg/L)	1.28	1.8	1.8	1.69	0.743	0.44	0.413	0.56
Mn	(mg/L)	0.24	0.424	0.435	0.322	0.173	0.30	0.29	0.218
Cu	(mg/L)	0.006	0.008	0.008	0.006	<0.004	<0.004	<0.004	<0.004
Zn	(mg/L)	0.017	0.030	0.030	0.024	0.016	0.020	0.019	0.014
Ni	(mg/L)	<0.004	0.004	0.005	<0.004	<0.004	<0.004	<0.004	<0.004
Al	(mg/L)	2.69	5.61	5.61	3.74	3.25	2.54	2.07	1.97

Note. NM, no measurement.

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Table 2 presents the pH, measured Eh, temperature, DO concentration, and water quality (DOC, F^–, Cl^–, ⁠, ⁠, ⁠, Na⁺, ⁠, K⁺, Mg²⁺, Ca²⁺, Fe²⁺, Fe³⁺, Fe, Mn, Cu, Zn, Ni, and Al) for the Ohaka and Koaka rivers. The pH of the Ohaka and Koaka rivers ranged from 3.47 to 3.91 and 4.55 to 5.17, respectively, with the Ohaka River being more acidic. The measured Eh values of the Ohaka and Koaka rivers ranged from 645 to 687 and 464 to 559 mV, respectively. The water temperature of the Ohaka and Koaka rivers ranged from 4.6 to 20.3 and 2.8 to 20.6 °C, respectively. Although a slight difference was observed in the maximum water temperature, the minimum water temperature was ∼2 °C lower in the Koaka River. A slight difference was observed in the DO concentrations between the two rivers, ranging from 8.1 to 9.3 mg/L. The DOC values of the Ohaka and Koaka rivers ranged from 0.11 to 0.22 and 0.147 to 0.25 mg/L, respectively. The F^–, Cl^–, ⁠, Na⁺, ⁠, K⁺, Mg²⁺, Ca²⁺, Fe²⁺, Fe³⁺, Fe, Mn, Cu, Zn, Ni, and Al concentrations of the Ohaka River were higher than those of the Koaka River except for the and Al concentrations collected on 27 April. The Fe²⁺ concentration ranged from 0.64 to 0.98 mg/L in the Ohaka River and 0.37 to 0.71 mg/L in the Koaka River, whereas the Fe³⁺ concentration ranged from 0.37 to 1.05 mg/L in the Ohaka River and 0.02 to 0.060 mg/L in the Koaka River. In addition, the concentration ranged from 0.169 to 0.559 mg/L in the Ohaka River and 0.254 to 0.717 mg/L in the Koaka River, whereas the concentration ranged from 0.016 to 0.052 mg/L in the Ohaka River and <0.01 to 0.014 mg/L in the Koaka River.

Using the redox couples listed in Table 1, the vertical error bars indicate the considered analytical error. A solid line indicates the 1:1 ratio between measured Eh and calculated Eh values.

The calculated Eh values of Fe³⁺/Fe²⁺ redox couple in the Ohaka River were within ±10 mV of the measured Eh at the three campaigns and within ±12 mV at the fourth campaign (30 November 2017), while the values in the Koaka River were within ±5 mV at the fourth campaign (30 November 2017) and within ±40 mV at the other three campaigns compared with measured Eh values (Figure 3).

In contrast, Nordstrom (2000) reported that when the total dissolved iron concentrations in acid mine waters were in the range from 10^–7 to 10^–5 mol/kg (0.006–0.56 mg/kg), the difference between the measured and calculated Eh was within ±50 mV. Although the analytical results in this study are expressed in mg/L, considering a slight difference between mg/L and mg/kg in low-salinity solutions, which have total dissolved solids of <10,000 mg/L (Clark 2015), the comparative results of the Koaka River were considered similar to those of Nordstrom (2000).

These results are believed to be associated with the potentiometric measurement of Eh values, which operates within an effective range determined by the concentration of electroactive components, as indicated by Yalin & Shenker (2022). The monitoring results in acidic rivers around Mutsu Hiuchi Dake Volcano indicated that Fe²⁺ and Fe³⁺ concentrations of ∼10^–5 mol/L (∼0.56 mg/L) or higher are the effective range. However, since acidic rivers and streams in other volcanic regions have considerably lower pH values and higher iron concentrations than those in this study (Markússon & Stefánsson 2011; Björke et al. 2015), we believe that it is necessary to validate the effectiveness of Eh measurements under various conditions.

The calculated Eh values of the O₂/H₂O redox couple were much higher than the measured Eh values in all sampling campaigns of the Ohaka and Koaka Rivers. This is consistent with Stefánsson et al. (2005), who calculated the Eh values of the O₂/H₂O redox for streams and rivers. The RMSE for the measured Eh and calculated Eh values of the O₂/H₂O redox couple was 496 mV.

The calculated Eh values of the redox couple in the Ohaka River were within 30 mV during the first campaign (27 April 2017) and above 50 mV during the other campaigns compared with the measured Eh values. Meanwhile, those of the redox couple in the Koaka River were within 5 mV during the second and third campaigns (2 July 2017, and 27 July 2017) and above 80 mV during the fourth campaign (30 November 2017) compared with the measured Eh values. The RMSE for the measured Eh and calculated Eh values of the redox couple was 49 mV. In this study, the difference between the calculated and measured Eh of the redox couple was within ±10 mV, inconsistent with previous studies that measured Eh in rivers or streams (Stefánsson et al. 2005). Furthermore, the and concentrations in Figure 2 did not exceed ∼10^–5 mole/L (∼0.63 mg/L as and 0.19 mg/L as ⁠). Thus, it can be suggested that the and distributions may not have reached equilibrium and were controlled by source transport.

The relationship between the measured and calculated Fe²⁺ concentrations is shown in Figure 6. The solid line in Figure 6 indicates a 1:1 relationship, while the dotted lines indicate ±10%. The mV values associated with the circles plotted in Figure 6 indicate the calculated Eh minus the measured Eh. Temperature in °C is the in situ temperature. These results show that when the calculated Eh minus the measured Eh is within ±10 mV, the Fe²⁺ concentrations calculated using the measured Eh values and the analyzed Fe concentrations show good agreement with the measured Fe²⁺ concentrations, with the calculated Fe²⁺ concentrations plotting within ±10% of the measured Fe²⁺ concentrations.

On the other hand, considering the vertical error bars shown in Figure 6, which take into account the accuracy range (±10 mV) for ORP measurements obtained using platinum electrodes, the measured and calculated Fe²⁺ concentrations were within ±10% when the measured Fe²⁺ concentrations were ∼0.56 mg/L (10⁻⁵ mol/L) or higher. This suggests that a concentration of ∼10⁻⁵ mol/L or higher is required to measure Eh, as highlighted above.

The black circle is the Ohaka River. The white circle is the Koaka River. The horizontal error bars indicate the Fe²⁺ measurement precision of ±0.02 mg/L, and the vertical error bars indicate the values considered in the accuracy range (±10 mV) for ORP measurements obtained using platinum electrodes.

The Eh values were calculated by using the data in Table 1. The blue color indicated the Fe³⁺/Fe²⁺ activity ratio of 0.000001–0.00001, white indicated the range of 0.00001–0.0001, gray indicated the range 0.0001–0.001, yellow indicated the range 0.001–0.01, and red indicated the range 0.01–0.1.

The Eh values were calculated by using the data in Table 4. The pH was fixed at 3.5. Blue color indicates the activity ratio of 0.01–1, white indicates the range of 1–100, gray indicates the range of 100–10,000, and yellow indicates the range of 10,000–1,000,000. The data listed in Table 4 are part of the thermodynamic database from WATEQ4f used within the GWB program (Bethke 2022).

Table 4

Reaction and equilibrium constant at 25 °C for the calculation of Eh

Reaction .	.	Log K .	ΔrH° (kcal/mol) .
		–40.644	65.44

Reaction .	.	Log K .	ΔrH° (kcal/mol) .
		–40.644	65.44

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Comparison of the calculated Eh from Fe³⁺/Fe²⁺, O₂/H₂O, redox couples with the measured Eh at water temperatures ranging from 2.8 to 20.6 °C in acidic river water of the Ohaka and Koaka Rivers in volcanic regions indicated that the Fe³⁺/Fe²⁺ redox couple controls the measured Eh in the Ohaka River. Fe²⁺ and Fe³⁺ concentrations required 10^–5 mole/L (∼0.56 mg/L) or more to maintain the difference between the calculated and measured Eh within ±12 mV. In addition, the Fe²⁺ concentrations calculated using the measured Eh values and the analyzed Fe concentrations were within ±10% of the analyzed Fe²⁺ concentrations when considering the difference between the calculated and measured Eh within ±10 mV. We conclude that in volcanic regions, Eh monitoring of acidic rivers containing Fe²⁺ and Fe³⁺ concentrations of ∼10^–5 mol/L (∼0.56 mg/L) or higher is effective. It will be necessary to conduct research in volcanic regions with higher Fe²⁺ and Fe³⁺ concentrations than in the current study area to validate our results.

We would like to thank Editage (Cactus Communications K. K.) for English language editing.

This work was partially supported by JSPS KAKENHI Grant Number JP26281053.

S.I. wrote the original draft, reviewed and edited the article, visualized the project, validated the process, developed the Methodology, investigated the work, rendered support in formal analysis and data curation, conceptualized the project. Y.S. investigated the work, reviewed and edited the article. H.M. investigated the work, reviewed and edited the article, rendered support in funding acquisition. S.W. reviewed and edited the article.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.