Toward a Method for Quantitative Assessment of the Influence of Eh and pH on the Content of Trace Components in Natural Waters

B. I. Shestakov

(Presented by the scientific seminar of the Department of Hydrogeology and Engineering Geology and the Problem Geological Laboratory of TPI)

The significance of oxidation and reduction potential in the migration of many elements is now generally known [1, 2, 3, 4, et al.]. However, the use of a well-developed theory for the practical interpretation of the influence of $Eh$ on changes in the contents of elements encounters considerable difficulties. Even when $Eh$ is correctly determined (and measuring natural $Eh$ is far from simple [2]), it is practically impossible to determine from its value the probable contents of elements. The main reasons for this situation are as follows. First, all known reference equations and diagrams have been calculated for cases in which the presence of only one form of occurrence of an element is initially assumed, for example $\mathrm{Fe}^{2+}$, and then its change in the course of changes in $Eh$ and pH is considered. In reality, however, in natural waters an element may occur simultaneously in several forms (for example, iron at pH 7, in the form of $\mathrm{Fe}^{3+}$, $\mathrm{Fe(OH)}^{2+}$, $\mathrm{Fe(OH)}$, $\mathrm{Fe(OH)}_3$ [5]. In addition, the presence of various complex ions (chloride, sulfate, thiosulfate, polythionate, organic, and others) is not taken into account. Besides these basic causes, there are also other reasons for discrepancies between practically observed contents and theoretically calculated ones, many of which may still be unknown to science. In the practice of interpreting hydrogeochemical investigations it is extremely important to establish exactly how quantitatively $Eh$ and pH and the contents of an element in natural waters are related in a specific geological setting, and how great their influence is on the migration of one or another element. To solve this problem, in interpreting data from hydrogeochemical investigations in the northeastern part of Salair, the author used a multiple linear regression model between the content of certain elements, pH, and $Eh$ of natural waters.

Proceeding from the Nernst equation, the relationship between the indicated quantities was sought in the form

$$ Eh = b_1 + b_2 \mathrm{pH} + b_n \lg [M], \tag{1} $$

where $[M]$ is the concentration of the metal (in view of the low mineralization—up to 0.8 mg/l of the waters—and the microgram contents of the elements, the concentration is taken as equal to the activity), and $b_1$, $b_2$, $b_n$ are coefficients.

The technique for calculating coefficients in expressions of type (1) is described in detail by Ya. I. Lukomskii [6]. Directly for our case it consists of the following operations:

1) From the initial tables of analyses, the following quantities are calculated:

\[ \overline{x_i}=\frac{\sum_1^N x_n}{N}; \qquad S_i=\sqrt{\frac{\sum_1^N x_n^2}{N-1}-\overline{x_i}^{\,2}}; \qquad r_{ij}=\frac{\sum_1^N x_n x_m}{\sqrt{\sum_1^N x_n^2\cdot \sum x_m^2}}, \]

where

\[ \begin{aligned} \overline{x_i}&\text{ is the arithmetic mean of } Eh,\ \mathrm{pH},\ \lg[M],\\ x_m,\ x_n&\text{ are specific values of } Eh,\ \mathrm{pH},\ \lg[M],\\ S_i&\text{ are the root-mean-square deviations of } Eh,\ \mathrm{pH},\ \lg[M],\\ r_{ij}&\text{ are the correlation coefficients between } Eh,\ \mathrm{pH},\ \lg[M]. \end{aligned} \]

All calculation results are recorded in Table 1.

Table 1

2) The data of Table 1 make it possible to determine the coefficients of the equations:

\[ \widetilde{Eh}=\beta_2\widetilde{\mathrm{pH}}+\beta_1\widetilde{\lg[M]}, \tag{2} \]

where \(\widetilde{Eh}\), \(\widetilde{\mathrm{pH}}\), and \(\widetilde{\lg[M]}\) are standardized values of the corresponding quantities; \(\beta_1\) and \(\beta_2\) are coefficients calculated from the system of equations:

\[ r_{12}=\beta_2+\beta_1 r_{2n} \]

\[ r_{1n}=\beta_2 r_{2n}+\beta_1, \tag{3} \]

As a result of the calculations in items 1 and 2, the following equations were compiled:

\[ \widetilde{\lg[\mathrm{Pb}]}=1,21\,\widetilde{\mathrm{pH}}+1,23\,\widetilde{Eh}; \qquad R=0,90 \tag{4} \]

\[ \widetilde{\lg[\mathrm{Cu}]}=3,28\,\widetilde{\mathrm{pH}}+5,33\,\widetilde{Eh}; \qquad R=0,60 \tag{5} \]

\[ \widetilde{\lg[\mathrm{Zn}]}=2,40\,\widetilde{\mathrm{pH}}+4,33\,\widetilde{Eh}; \qquad R=0,61 \tag{6} \]

\[ \widetilde{\lg[\mathrm{Ag}]}=-6,16\,\widetilde{\mathrm{pH}}-11,16\,\widetilde{Eh}; \qquad R=0,58 \tag{7} \]

\[ \widetilde{\lg[\mathrm{Ba}]}=4,21\,\widetilde{\mathrm{pH}}+7,09\,\widetilde{Eh}; \qquad R=0,59 \tag{8} \]

\[ \widetilde{\lg[\mathrm{Mn}]}=-5,15\,\widetilde{\mathrm{pH}}-9,27\,\widetilde{Eh}; \qquad R=0,58 \tag{9} \]

\[ \widetilde{\lg[\mathrm{Ti}]}=-3,62\,\widetilde{\mathrm{pH}}-6,23\,\widetilde{Eh}; \qquad R=0,59 \tag{10} \]

Here \(R\) is the coefficient of multiple correlation, calculated by the formula

\[ R=\sqrt{\beta_2 r_{12}+\beta_1 r_{1n}}; \]

the remaining notation has been explained above.

Equations (4)—(10) make it possible to draw conclusions about the influence of $Eh$ and pH on the content of trace components within the range of $Eh$ and pH characteristic of the study area.

High values of the multiple correlation coefficients $R$ indicate the very large role of $Eh$ and pH in the migration of trace components. Roughly speaking, if the influence of all factors (geological, hydrogeological, climatic, etc.) is taken in total as unity, then the coefficient $R$ shows what part of this unity is constituted by the influence of $Eh$ and pH. On the basis of the values of $R$, all the elements listed in equations (4)—(10), in decreasing order of the influence of $Eh$ and pH, may be arranged in the following series:

$$ \mathrm{Pb},\ \mathrm{Zn},\ \mathrm{Cu},\ \mathrm{Ti},\ \mathrm{Ba},\ \mathrm{Mn},\ \mathrm{Ag}. $$

A separate assessment of the influence of each factor can be approached on the basis of the coefficients before $Eh$ and pH in equations (4)—(10). These coefficients show by how many standard deviations $\lg[\mathrm{M}]$ will change if $Eh$ or pH changes by one standard deviation; moreover, the sign “+” before a coefficient indicates that, with an increase in the value of the corresponding factor, the content of the given element will increase, while the sign “−” indicates the opposite.

The signs of the coefficients show that, with increasing pH, the contents of Pb, Cu, Zn, and Ba increase, with the greatest influence of pH being manifested for barium. This regularity agrees well for Cu, Pb, and Zn with the hypothesis of hydrocarbonate [7] and complex (in the form of $\mathrm{MOH}^{+}$ [5]) migration forms of these elements. A negative influence of pH is found for Ti, Mn, and Ag (for the latter to the greatest degree), which may be explained by the formation of practically insoluble hydroxides of these metals [8].

An increase in $Eh$ positively affects the migration of elements with constant valence—Pb, Zn, Ba—which fully agrees with the existing theory of oxidation–reduction reactions in natural waters [7, 2], etc. The increase in Cu contents with increasing $Eh$ is explained by the good migration capacity of the $\mathrm{Cu}^{2+}$ ion under oxidizing conditions; the decrease in Ti and Mn contents with increasing $Eh$ is explained by the low mobility of the oxidized forms of these elements ($\mathrm{Mn}^{3+}$, $\mathrm{Mn}^{4+}$, and $\mathrm{Ti}^{4+}$). The increase in Ag content with decreasing $Eh$ should apparently be explained from the standpoint of a complex form of migration. From equations (4)—(10) one can pass to equations in the natural values of variables of type (1) by the formulas:

$$ b_2=\beta_2\frac{S_{Eh}}{S_{\mathrm{pH}}};\qquad b_n=\beta_n\frac{S_{Eh}}{S_{\lg[\mathrm{M}]}};\qquad b_1=\overline{Eh}-b_2\overline{\mathrm{pH}}-b_n\overline{\lg[\mathrm{M}]}, \tag{11} $$

where $\overline{Eh}$, $\overline{\mathrm{pH}}$, and $\overline{\lg[\mathrm{M}]}$ are arithmetic mean values.

These equations are written as follows:

$$ Eh=0.42-0.06\,\mathrm{pH}+0.05\,\lg[\mathrm{Pb}] \tag{12} $$

$$ Eh=0.38-0.04\,\mathrm{pH}+0.02\,\lg[\mathrm{Cu}] \tag{13} $$

$$ Eh=0.37-0.03\,\mathrm{pH}-0.02\,\lg[\mathrm{Zn}] \tag{14} $$

$$ Eh=0.36-0.04\,\mathrm{pH}+0.0005\,\lg[\mathrm{Ba}] \tag{15} $$

$$ Eh=0.36-0.03\,\mathrm{pH}-0.0002\,\lg[\mathrm{Ag}] \tag{16} $$

$$ Eh=0.36-0.03\,\mathrm{pH}+0.0003\,\lg[\mathrm{Mn}] \tag{17} $$

$$ Eh=0.36-0.04\,\mathrm{pH}-0.0006\,\lg[\mathrm{Ti}] \tag{18} $$

The difference between the theoretically calculated [2, 9, etc.] and the practically established equations (12)—(18) is explained by the difference between natural conditions and standard ones, and by the reasons given at the beginning of the paper.

Thus, the proposed method makes it possible to quantitatively assess the influence of $Eh$ and pH on the content of trace components and to draw important geochemical conclusions.

References

1. L. G. M. Baas-Becking et al. Limits of variation of pH and oxidation-reduction potentials of natural environments. In: Geochemistry of Lithogenesis, IL, 1963.

2. R. Garrels. Mineral Equilibria. IL, 1962.

3. W. Latimer. Oxidation States and Their Potential in Aqueous Solutions. IL, 1964.

4. G. Tischendorf and H. Ungethüm. On the significance of the oxidation-reduction potential ($Eh$) and the concentration of hydrogen ions (pH) for geochemistry and for the study of mineral deposits. Translation from German No. 44299/4, VINITI Translation Bureau, 1965.

5. S. A. Brusilovskii. On the migration forms of elements in natural waters. Hydrogeochemical Materials, vol. XXXV, Publishing House of the Academy of Sciences of the USSR, 1963.

6. Ya. I. Lukomskii. Correlation Theory and Its Application to Production Analysis. Gosstatizdat, Moscow, 1958.

7. A. I. Perel’man. Geochemistry of Epigenetic Processes. Nedra Publishing House, Moscow, 1966.

8. I. P. Onufrienok. On the question of the limits of saturation of natural waters with metal ions. In: Experience in Developing Hydrochemical Methods for Prospecting Ore Deposits. Gosgeoltekhizdat, Moscow, 1959.

9. Chemist’s Handbook, vol. 3. Khimiya Publishing House, Moscow, 1964.