Dependence of the Growth Kinetics of an Ammonium Amalgam Droplet on the Concentration of Ammonium Ions in Solution

A. V. Konkova

The concentration of ammonium ions in solution \((C_{\mathrm{NH}_4^+})\) is one of the factors exerting the strongest influence on the ammonium amalgam effect (AAE),¹ since the growth kinetics of an ammonium amalgam droplet, i.e., the mean working surface, and consequently the height of the peak of the impurity being determined, depend on the value of \(C_{\mathrm{NH}_4^+}\).

The total number of discharged ammonium ions over a given electrolysis time \(\tau\) is proportional to the concentration (more precisely, the activity) of ammonium ions in solution:

\[ M = K_{\mathrm{A}}\cdot f \cdot C_{\mathrm{NH}_4^+}, \tag{1} \]

where \(M\) is the total number of discharged ammonium ions during the electrolysis time \(\tau\);

\(K_{\mathrm{A}}\) is the proportionality coefficient;

\(f\) and \(C_{\mathrm{NH}_4^+}\) are the activity coefficient and the concentration of ammonium ions.

Taking into account that only a fraction \(m=\alpha M\) of the total number \(M\) of discharged ammonium radicals participates in the formation of ammonium amalgam, and expressing \(m\) in terms of the radius of the ammonium amalgam droplet, we obtain

\[ m=\frac{4\pi P}{3\cdot 1.5RT}\,(r^3-r_0^3), \tag{2} \]

where \(P\) is the gas pressure in the gas bubble, atm;

\(T\) is the temperature in degrees Kelvin;

\(R\) is the universal gas constant;

\(r\) and \(r_0\) are the radius of the amalgam droplet at the electrolysis time \(\tau\) and at \(\tau=0\), respectively.

And further:

\[ \frac{P\,\frac{4}{3}\pi\,(r^3-r_0^3)}{1.5RT} = K_{\mathrm{A}}\alpha\cdot f C_{\mathrm{NH}_4^+}. \tag{3} \]

(\(\alpha\) is the fraction of ammonium radicals participating in the formation of ammonium amalgam, out of the total number of discharged radicals.) Let us express the quantity \(r^3\) from equation (3):

\[ r^3 = r_0^3 + A_C f \cdot C_{\mathrm{NH}_4^+}, \tag{4} \]

[1]^2

\[ A_c=\frac{3K_A a\,1.5RT}{4\pi P} \tag{5} \]

is a quantity independent of \(C_{\mathrm{NH}_4^+}\), but dependent on the time of electrolysis. The dependence of \(A_c\) on the time of electrolysis is due to the change with time of the quantity \(K_A\), which from (1) is equal to

\[ K_A=\frac{M}{f\cdot C_{\mathrm{NH}_4^+}}, \]

where \(M\) is a function of time: \(M=K_\tau\cdot \tau\) (\(K\) is a proportionality coefficient). Accordingly, the quantity \(A_c\) may be written as

\[ A_c=a'\tau, \tag{6} \]

where

\[ a'=\frac{3\cdot 1.5RT\,aK_\tau}{4\pi P a_{\mathrm{NH}_4^+}}. \tag{7} \]

The graphical expression of equation (4) should, in the coordinates \(r^3,\, a_{\mathrm{NH}_4^+}\), be a series of straight lines emerging from a point on the ordinate axis corresponding to the value \(r_0^3\). From the slope of such a straight line one can determine the quantity \(A_c\) for a given moment of electrolysis time. The experimental dependence of \(A_c\) on \(\tau\) should be a straight line passing through the origin.

For an experimental verification of expressions (4) and (6), experiments were carried out, the results of which are presented in Table 1. A description of the apparatus and of the experimental procedure is given in [3]. Buffer mixtures \(\mathrm{NH_4Cl}+\mathrm{NH_4OH}\) with the greatest buffer capacity (\(\mathrm{pH}=9\)) were subjected to electrolysis at a constant pH value and at different values of \(C_{\mathrm{NH_4Cl}}\). General experimental conditions: solution volume 10 ml; voltage applied to the cell, 4 volts; temperature \(20^\circ\mathrm{C}\).

Table 1

Radius of an ammonium amalgam droplet after 1, 2, 3, and 4 min of electrolysis in \(\mathrm{NH_4Cl}\) solutions of different concentration

If, using the data of Table 1, a graph is constructed in the coordinates \(r^3,\, a_{\mathrm{NH}_4^+}\), it can be seen that the dependence \(r^3,\, a_{\mathrm{NH}_4^+}\) in dilute solutions is indeed represented by straight lines emerging from a single point on the ordinate axis, which coincides with the experimental value of the cube of the initial radius of the mercury droplet, \(r_0^3=0.36\ \mathrm{mm}^3\). In concentrated solutions a deviation from the obtained dependence is observed. This is explained by the fact that the experiments on the influence of the concentration of ammonium ion in solution on the growth kinetics of an ammonium amalgam droplet were carried out at constant external voltage, and not at constant cathode potential\(^{2)}\).

\(^{2)}\) The cathode potential depends on \(C_{\mathrm{NH}_4^+}\) and, in concentrated solutions, changes with time more strongly than in dilute solutions.

It is also evident from Table 1 that, with increasing concentration of ammonium ions in the solution, the growth rate of the ammonium amalgam droplet increases, which once again confirms the conclusions we drew earlier in [3].

Table 2 gives data on the dependence of \(A_c\) on the electrolysis time. The values of \(A_c\) were determined as the slopes of straight lines on the plot of \(r^3, a_{\mathrm{NH}_4^+}\), constructed from the data of Table 1. The results presented in Table 2 confirm the validity of equation (6).

Table 2

Values of \(A_c\) at different moments of electrolysis time

The agreement observed between the theoretical expressions (4) and (6) and the experimental data may apparently indicate the validity of the expressions obtained and makes it possible, by changing the concentration of ammonium ions in the solution, to control to a certain extent the process of the ammonium amalgam effect.

LITERATURE

1. Yu. A. Karbainov, A. G. Stromberg. ZhAKh 20, 769, 1965.
2. A. V. Konkova. ZhAKh 23, no. 3, 451, 1968.
3. A. V. Konkova, A. G. Stromberg. Izv. TPI, 164, 147, 1967.

1. The essence of the AAE is set forth in previous works [1–3]. ↩