Study of intermetallic Compounds in Mercury by the APN Method
Abstract Generated abstract
This paper develops theoretical graphical procedures for determining the phase composition of amalgams containing binary intermetallic compounds in mercury when only one of the two metals produces an anodic notch in the APN method. It derives diagnostic linear relationships for cases where the compound exists either as a sparingly soluble solid precipitate, characterized by a solubility product, or as a sparingly dissociating soluble compound, characterized by a dissociation constant. The authors also propose a complementary potentiometric graphical method using amalgam concentration cells to distinguish these cases and to calculate the corresponding equilibrium constants. The work clarifies practical limitations of the APN approach, including the need for independently known compound stoichiometry and possible equilibrium shifts during anodic-wave recording.
Full Text
STUDY OF INTERMETALLIC COMPOUNDS IN MERCURY BY THE APN METHOD. III. THEORY. COMPARATIVE CALCULATIONS BY THE APN METHOD AND BY POTENTIOMETRY. ONLY ONE METAL GIVES AN ANODIC NOTCH
M. S. ZAKHAROV, A. G. STROMBERG, N. A. MESYATS
(Presented by the scientific-methodological seminar of the CTF)
In the preceding article [1] a procedure was set forth for determining the phase composition of amalgams for the case when both metals that form an intermetallic compound with each other in mercury give anodic notches. However, in the practice of the APN method one more often encounters cases when only one element gives an anodic notch. The present work is devoted to the development of a procedure of the APN method for studying the phase composition of amalgams for cases in which, of the two elements forming an intermetallic compound with each other, only one element gives an anodic notch.
Let two elements interact with each other in mercury with the formation of an intermetallic compound:
\[ A+nB \rightleftarrows AB_n . \tag{1} \]
If the intermetallic compound exists in mercury in the form of a sparingly soluble precipitate, then the equilibrium in the system is characterized by the solubility product. For such a system A. G. Stromberg and A. E. Gorodovykh [2] obtained the expression:
\[ \lg y=\lg K-n\lg z, \tag{2} \]
where
\[ y=\frac{c_1}{^{\circ}c_1}; \qquad K=\frac{L_p}{^{\circ}c^{\,n+1}}; \qquad z=\frac{c_2}{^{\circ}c_1}, \]
\(c_1\), \(^{\circ}c_1\), \(c_2\) are the concentrations, in gram-atoms/l, respectively, of element \(A\) in the absence of element \(B\), of \(A\) in the presence of \(B\), and of \(B\) in the presence of \(A\) in the amalgam. \(L_p\) is the solubility product of the intermetallic compound.
From equation (2) it is evident that a plot in the coordinates \(\lg y\)—\(\lg z\) is a straight line. Thus, if it turns out that the plot constructed from experimental data in the indicated coordinates is a straight line, then the intermetallic compound exists in mercury in the form of a solid precipitate. To construct the plot, it is convenient to express \(y\) and \(z\) through quantities known from experiment [2]:
\[ y=\frac{I_1}{^{\circ}I_1}; \qquad z=\left[x-\frac{n}{K'}(1-y)\right]; \qquad x=\frac{{}^{\times}c_2}{{}^{\times}C_1}; \tag{3} \]
\[ K'=\frac{K_2}{K_1}; \qquad K_1=\frac{I'_1}{zF\,{}^{\times}C_1}; \qquad K_2=\frac{I'_2}{zF\,{}^{\times}C_2}, \]
where \(^{\circ}I_1\), \(I_1\) are the depth of the anodic notch of element \(A\) in the absence and presence—
in the presence of component \(B\); \(^{\times}C_2\) and \(^{\times}C_1\) are the concentrations of ions of, respectively, \(B\) and \(A\) in the solution \((^{\times}C_1=\mathrm{const})\); \(K_1\) and \(K_2\) are the electrolysis constants for \(B\) and \(A\), respectively; \(z\) is the number of electrons participating in the electrode process per ion; \(F\) is the Faraday number; \(I'_1\) and \(I'_2\) are the electrolysis currents for \(B\) and \(A\), respectively. In the experimental determination of \(I'_1\) and \(I'_2\), \(^{\times}C_1\) and \(^{\times}C_2\) in the solution must be taken not lower than \(10^{-3}\) gram-ion/l, so that the residual current is not comparable with the Faradaic current.
The intercept cut off by straight line (2) on the abscissa axis is numerically equal to \(\lg K\). Hence one can calculate the solubility product of the intermetallic compound under study:
\[ L_p = K^\circ C^{n+1}. \tag{4} \]
If the intermetallic compound exists in mercury in the form of a sparingly dissociating soluble compound, then the equilibrium in the system will be characterized by the dissociation constant. For the system under consideration the expression for the dissociation constant \((K_{\mathrm{d}})\) is written as
\[ K_{\mathrm{d}}=\frac{C_1\cdot C_2^n}{C_3}, \tag{5} \]
where \(C_3\) is the concentration of the intermetallic compound in mercury. It can be expressed as follows:
\[ C_3 = {}^\circ C_1 - C_1. \tag{6} \]
Dividing the left- and right-hand sides of equation (5) by the quantity \({}^\circ C_1^n\), we obtain
\[ \frac{K_{\mathrm{d}}}{{}^\circ C_1^n} = \frac{C_1}{({}^\circ C_1-C_1)}\cdot \frac{C_2^n}{{}^\circ C_1^n}, \tag{7} \]
Putting
\[ \frac{K_{\mathrm{d}}}{{}^\circ C_1^n}=K;\qquad \frac{C_1}{{}^\circ C_1-C_1}=y';\qquad \frac{C_2^n}{{}^\circ C_1^n}=Z^n, \]
and taking logarithms, we have
\[ \lg y'=\lg K-n\lg Z. \tag{8} \]
This equation represents a straight line in the coordinates \(\lg y'—\lg z\). Consequently, if a graph constructed from experimental data in the coordinates \(\lg y'—\lg z\) proves to be a straight line, then the intermetallic compound in mercury exists in the form of a sparingly dissociating liquid compound.
To construct the graph, the value \(z\) is determined from equation (3), and \(y'\) is calculated from the expression:
\[ y'=\frac{I_1}{{}^\circ I_1-I_1}. \tag{9} \]
The intercept cut off by straight line (8) on the abscissa axis is equal to \(\lg K\). Hence one can calculate the dissociation constant of the intermetallic compound under study:
\[ K_{\mathrm{d}}=K^\circ C_1^n. \tag{10} \]
Theoretically, it may be expected that, when the amalgam dissolves during the recording of anodic notches by the APN method, the equilibrium in the amalgam system will shift from right to left.
If the intermetallic compound exists in mercury in the form of a solid precipitate, then the shift of equilibrium will be less noticeable because of the low rate of dissolution of the precipitate (amalgams are based on this principle—
gamma-polarographic methods for determining the solubility of sparingly soluble metals in mercury).
When an intermetallic compound exists in mercury in the form of a sparingly dissociating soluble compound, the shift of equilibrium upon removal of the anodic wave will be more significant. In this case, both in the coordinates \(\lg y — \lg z\) and in the coordinates \(\lg y_1 — \lg z\), a straight line may fail to be obtained. Under these conditions, as indicated in [1], it is necessary to increase the rate of potential change when removing the anodic wave to such a value that a straight line is obtained in one of the coordinate systems. High rates of potential change with a linear potential sweep can be obtained on a TsLA-design oscillographic polarograph. To construct the above-mentioned graphs it is necessary to know the value of \(n\), i.e., the composition of the intermetallic compound. In the case where, of the two elements being studied, only one element gives an anodic wave, it does not yet appear possible to determine the value of \(n\) by the APN method. Therefore, for the intermetallic compounds studied, the value of \(n\) must be taken from the literature; for unstudied intermetallic compounds, the value of \(n\) must be determined by the potentiometric method or by the electrical-conductivity method. The latter methods make it possible to determine \(n\) independently of the phase composition of the amalgam.
The question of the phase composition of an amalgam can be solved more fruitfully by applying, in addition to the APN method, other methods as well, in particular the potentiometric method. Zebreva [3] proposed judging the phase composition of amalgams from the constancy of the solubility product or the dissociation constant calculated from potentiometric measurements. However, Kozin [4] showed that such a method does not make it possible to solve the question under consideration.
To determine the phase composition of amalgams from potentiometric data we propose a graphical procedure which, in our opinion, is more illustrative than the procedure proposed by Zebreva.
To study intermetallic compounds in mercury by the potentiometric method, an amalgam concentration cell of the following type is assembled:
\[ \underset{C_1'}{A(\mathrm{Hg})}\,(A^{n+}X_n^-)\,\underset{C_1\,C_2}{AB(\mathrm{Hg})}. \tag{11} \]
In this cell the right-hand electrode is the electrode under investigation. Its amalgam contains a definite amount of the electropositive element \(B\) and variable amounts of the electronegative element \(A\). In the left-hand electrode (the reference electrode) there is an amalgam of the electronegative element \(A\) of definite concentration. The emf of cell (11) is described by the equation
\[ E = b \ln \frac{C_1'}{C_1}, \tag{12} \]
where
\[ b = \frac{RT}{nF}. \]
If in the ternary system \(AB\mathrm{Hg}\) an interaction occurs between the elements \(A\) and \(B\), then the emf of cell (11) will be greater than it should be at \(C_1\).
Let us suppose that the intermetallic compound being formed is present in mercury in a solid phase. In this case the state
equilibrium in the amalgam will be characterized by the solubility product:
\[ L_{\mathrm p}=C_1\cdot C_2^n . \tag{13} \]
In studying intermetallic compounds in mercury, the concentrations of components \(A\) and \(B\) are usually small (\(10^{-3}—10^{-4}\) g-atom/l). Therefore one may take \(f_1=f'_1=1\) or \(f_1=f'_1\ne 1\). In both cases, in the expression for the e.m.f. (12) the ratio \(\dfrac{f'_1}{f_1}=1\). Taking these considerations into account, the following may be written:
\[ E=b\lg\frac{a'_1}{a_1}=b\lg\frac{f_1 C'_1}{f_1 C_1}\simeq b\lg\frac{C'_1}{C_1}, \tag{12a} \]
i.e., \(C_1\) and \(C_2\) can be used in the calculations without making the assumption that the solution (amalgam) is ideal. In addition, one may regard \(f_1\), \(f_2\), and \(f_3\simeq \mathrm{const}\) and include them in the constants \(L_{\mathrm p}\) or \(K_{\mathrm d}\). In this case \(C_1\) and \(C_2\) can also be used in the calculations without making the assumption that the solution is ideal, but the numerical value of \(L_{\mathrm p}\) and \(K_{\mathrm d}\) will differ somewhat from the true value.
Taking the logarithm of expression (13), we obtain
\[ \lg C_1=\lg L_{\mathrm p}-n\lg C_2 . \tag{14} \]
Equation (14) is the equation of a straight line (for \(C_2=\mathrm{const}\) and \(C'_1=\mathrm{const}\)). Consequently, if a plot constructed in the coordinates \(\lg C_1—\lg C_2\) turns out to be a straight line, then the equilibrium state in the system is characterized by the solubility product, and the intermetallic compound in mercury under the conditions studied is present in the form of a sparingly soluble precipitate. The value \(\lg C_1\) is calculated from the experimental data (\(C'_1\) and \(E\)) from the expression:
\[ \lg C_1=\lg C'_1-\frac{E}{b'}, \tag{15} \]
where
\[ b'=\frac{2.3RT}{nF}. \]
On the basis of simple considerations, the value \(C_2\) can be expressed as follows:
\[ C_2={}^{\circ}C_2-n({}^{\circ}C_1-C_1), \tag{16} \]
where \({}^{\circ}C_2\) is the initial concentration of element \(B\) in the right-hand electrode; \({}^{\circ}C_1\) is the concentration of component \(A\) in the right-hand electrode in the absence of interaction between \(A\) and \(B\).
The intercept \((a)\) cut off by the straight line on the abscissa axis is numerically equal to \(\lg L_{\mathrm p}\). Hence, from potentiometric-measurement data one can calculate the solubility product of the intermetallic compound:
\[ L_{\mathrm p}=10^a . \tag{17} \]
Now let us suppose that the intermetallic compound forming in mercury is in the liquid phase. In this case the equilibrium will be characterized by the dissociation constant (see 5).
Taking the logarithm of expression (5), we obtain
\[ \lg P=\lg K_{\mathrm d}-n\lg C_2, \tag{18} \]
where
\[ P=\frac{C_2}{C_3}. \]
From equation (18) it is seen that if a plot in the coordinates \(\lg P—\lg C_2\) turns out to be a straight line (for \({}^{\circ}C_2=\mathrm{const}\) and \(C'_1=\mathrm{const}\)),
then the state of equilibrium in the system is characterized by the dissociation constant, and the intermetallic compound in mercury under the conditions studied is in the liquid phase.
The value \(C_3\), from the experimental data, can be calculated from the equation:
\[ C_3 = C_1^{0} - C_1 e^{-\frac{E}{b}}. \tag{19} \]
The value \(C_1\), from the experimental data, is calculated from expression (15).
The value of the dissociation constant of the intermetallic compound is calculated from the expression:
\[ K_{\mathrm{d}} = 10^{l}, \tag{20} \]
where \(l\) is the segment cut off by the straight line on the abscissa axis.
Conclusions
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A graphical method is proposed for studying the phase composition of amalgams by the APN method when intermetallic compounds of two elements are formed in them, of which only one element gives an anodic wave. The proposed method makes it possible to calculate \(L_p\) or \(K_{\mathrm{d}}\) of the intermetallic compound.
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A graphical procedure is proposed for studying the phase composition of amalgams by the potentiometric method when binary intermetallic compounds are formed in them. The proposed procedure makes it possible to calculate \(L_p\) or \(K_{\mathrm{d}}\) of the intermetallic compound.
References
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A. G. Stromberg, M. S. Zakharov, N. A. Mesyats. The present collection, 172.
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A. G. Stromberg, V. E. Gorodovykh. Journal of Inorganic Chemistry, 8, 2355 (1963).
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A. I. Zebreva. ZhFKh, 35, 948 (1961).
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L. F. Kozin. Physicochemical Principles of Amalgam Metallurgy. Publishing House of the Academy of Sciences of the Kazakh SSR, Alma-Ata, p. 185 (1964).