On the Determination of the Surface of a Drop of Ammonium Amalgam Foam
Abstract Generated abstract
This paper proposes a method for estimating the average working surface of a drop of ammonium amalgam foam during electrochemical accumulation analysis, a quantity not previously determined experimentally. The method relates the electrolysis current, derived from the anodic peak area, to impurity concentration and an electrolysis constant, with a correction for additional stirring caused by gas evolution. Experiments with lead in ammonium chloride solutions gave an average foam-drop surface of about 0.382 square centimeters, close to an independent estimate of 0.44 square centimeters from surface-time integration. The results suggest that the increased anodic peak under these conditions is mainly due to an approximately 9.55-fold increase in working surface, supplemented by a 1.3-fold increase in the electrolysis constant.
Full Text
On the Determination of the Surface of a Drop of Ammonium Amalgam Foam
A. V. KONKOVA
Until now (in particular, in [1]) the increase in the anodic peak of an impurity due to EAA has been explained by an increase in the effective electrolysis constant
\[ K_{\mathrm{ef}} = K_{\mathrm{e}} \frac{S_2}{S_1}, \tag{1} \]
where
\(K_{\mathrm{e}}\) is the actual electrolysis constant, characterizing the stirring conditions;
\(S_2\) and \(S_1\) are, respectively, the electrode surfaces at the stage of accumulation of the impurity being determined and at the stage of its anodic dissolution.
No methods have been proposed for an experimental estimate of the surface of a drop of ammonium amalgam foam (\(S_2\)). Meanwhile, such an estimate is of considerable interest.
In the present work, a method is proposed for experimentally estimating the average working surface of a drop of ammonium amalgam foam on the basis of the known expression for the electrolysis current in a stirred solution:
\[ i_{\mathrm{e}} = K_{\mathrm{e}} C_{\mathrm{i}} \overline{S}, \tag{2} \]
where \(i_{\mathrm{e}}\) is the part of the total electrolysis current under EAA conditions caused by the ions of the impurity being determined;
\(\overline{S}\) is the time-averaged working surface of a drop of ammonium amalgam foam\(^1\), on which accumulation of the impurity is carried out;
\(C_{\mathrm{i}}\) is the impurity concentration in the solution.
It follows from equation (2) that, in order to determine the average surface, it is necessary to find experimentally the quantities \(i_{\mathrm{e}}\) and \(K_{\mathrm{e}}\). The value of the electrolysis current of the element being determined in the presence of EAA is readily determined from the area under the anodic peak:
\[ i_{\mathrm{e}} = \frac{Q}{\tau}, \tag{3} \]
where \(Q\) is the area under the anodic peak, expressed in coulombs;
\(\tau\) is the electrolysis time, sec.
\(^1\) In the presence of EAA, accumulation of the impurity at different moments of electrolysis is carried out on different electrode surfaces. This necessitates introducing the term “average surface.”
The value of the electrolysis constant, without knowing \(\overline S\), cannot be determined directly from experiment; however, it can be estimated by another method. Under identical experimental conditions, the electrolysis constant in the presence of EAA (\(K_{\mathrm e}\)) may differ from the electrolysis constant without EAA (\(K'_{\mathrm e}\)) owing to the additional stirring of the near-electrode layer of solution by the gas bubbles being evolved. To estimate this difference it is necessary to obtain the anodic peaks of some element on one and the same surface \(S_0\) (all other conditions being equal), both when gas bubbles are evolved from the electrode surface and when they are not. The ratio of these peaks will characterize the difference between the electrolysis constants:
\[ \frac{I}{I'}=\frac{K_{\mathrm e}}{K'_{\mathrm e}}. \]
Such peaks can be obtained, for example, in a KCl solution at electrolysis potentials equal to the potentials in experiments with EAA and without EAA. In this case the additional stirring of the near-electrode layer of the KCl solution occurs as a result of the evolution of gaseous hydrogen.
Of course, such a determination introduces some error into the estimate of \(K_{\mathrm e}\) (since the amount of hydrogen evolved during the electrolysis of KCl and \(NH_4Cl\) may be different); however, this error is comparatively small, because the change in \(K_{\mathrm e}\) due to bubble evolution cannot be large.
Experiments showed that the value \(K_{\mathrm e}/K'_{\mathrm e}\) is approximately equal to 1.3 (lead peaks in 0.1 N KCl at voltages of 4.0 and 1.0 volts proved to be equal: \(I=5.8\cdot 10^{-8}\ a\) and \(I'=4.5\cdot 10^{-8}\ a\)).
Thus, the mean surface of a foamed drop of ammonium amalgam can be found from the expression
\[ \overline S=\frac{Q}{1.3K'_{\mathrm e}\tau C_{\mathrm i}}. \tag{4} \]
The experimental determination of the quantities \(K_{\mathrm e}\) and \(S\) was carried out by us under the following experimental conditions: solution volume \(V=5\ ml\); concentration of ammonium ions in the solution \(C_{NH_4^+}=10^{-4}\ g\text{-ion}/cm^3\); \(\mathrm{pH}=5.6\); \(T=290^\circ K\); initial drop radius \(r_0=0.055\ cm\); without EAA, the voltage applied to the cell was \(E=1.0\ v\) and the electrolysis time \(\tau=30\ min\); with EAA, \(E=4.0\ v\) and \(\tau=5\ min\). Lead was taken as the element to be determined, at a concentration of \(1.4\cdot 10^{-9}\ M\); the anodic peaks were obtained at a polarograph sensitivity of \(4\cdot 10^{-9}\ a/mm\).
Under these conditions, the lead peak obtained without EAA had height \(H'=13\ mm\); the area under the peak was \(Q'=0.87\cdot 10^{-6}\ coulomb\). Under EAA conditions the lead peak had height \(H=30\ mm\); \(Q=1.81\cdot 10^{-6}\ coulomb\). Taking into account that the electrolysis time with EAA is 6 times shorter, we find an increase in the peak of \(6H/H'=13.8\). From formula (3) we find the values \(i_{\mathrm e}\) and \(i'_{\mathrm e}\). They are, respectively, \(6\cdot 10^{-9}\ a\) and \(4.83\cdot 10^{-10}\ a\). Hence
\[ K'_{\mathrm e}=\frac{i'_{\mathrm e}}{4\pi r_0^2 C_4}=8.63\cdot 10^3\ a\,cm^2/g\text{-ion} \tag{5} \]
and \(K_{\mathrm e}=1.3K'_{\mathrm e}=11.2\cdot 10^3\ a\,cm^2/g\text{-ion}\). The mean surface on which accumulation proceeded under EAA conditions, determined by formula (4), was
\[ \overline S_1=\frac{1.81\cdot 10^{-6}}{1.3\cdot 8.63\cdot 10^3\cdot 300\cdot 1.4\cdot 10^{-12}}=0.382\ cm^2. \]
Now let us estimate the average surface \(\overline{S}_2\) from the expression:
\[ \overline{S}_2=\frac{1}{\tau}\int_0^\tau S\,d\tau . \tag{6} \]
On the graph in the coordinates \(S_1\tau\), the integral \(\int_0^\tau S\,d\tau\) represents the area under the curve, while \(\overline{S}_2\) is the height of an equivalent rectangle with base \(\tau\). The \(\overline{S}_2\) obtained in this way is equal to \(0.44\ \mathrm{cm}^2\), i.e., only 1.1 times greater than \(\overline{S}_1\).
Thus, on the basis of the data obtained, the following conclusions may be drawn:
1) the values of the average working surface of an ammonium amalgam drop, estimated experimentally \((\overline{S}_2)\) and theoretically \((\overline{S}_1)\), practically coincide;
2) the additional increase in the surface of the drop due to its porosity is approximately equal to its decrease due to screening by gas bubbles. The increase in the average surface in comparison with the initial one in these experiments was:
\[ \overline{S}/S_0=0.382/0.04\simeq 9.55\ \text{times}. \]
Consequently, the observed increase in the current \(i_3/i'_3=12.4\) is due to an increase in the working surface (by a factor of 9.55) and to an increase in the electrolysis constant (by a factor of 1.3).
From a comparison of the numerical estimates of the increase in the lead electrolysis current (12.4) and the increase in the height of its anodic peak (13.8), we see that the height of the anodic peak in the presence of EAA increases somewhat more (by a factor of 1.11) than the corresponding electrolysis current. Obviously, this is explained by the cementation of lead by ammonium, which in the present case is quite possible, or by experimental error (\(\sim 10\%\)).
REFERENCES
- Yu. A. Karbanov. Candidate’s dissertation. Tomsk, 1965.