DC Polarographic and Plane Polarographic investigation of the reduction of Thallium ( I )-Aqueous systems at dropping mercury electrode

1 Department of Chemistry, CNCS, Meklle University, Mekelle, Ethiopia 2 Govt. Arts College (Retd.), Bharathiar University, Tamilnadu (*pasubramanian@gmail.com) ABSTRACT The reduction behavior Thallium (I) at DME has been studied by several authors with different equivalent circuits and arrived at varying results. The complexity is due to the rapid reduction process and the adsorption behavior in the mercury solution interface. So, a thorough investigation was carried out on the reduction behavior of Thallium(I) at DME using DC polarographic and impedance methods assuming Randles and Laitinen (1955) basic equivalent circuit to hold good. The investigation was carried out in three different supporting electrolytes, sodium perchlorate, potassium nitrate and potassium chloride and for four different concentrations of depolariser. The double layer capacity was obtained by extrapolation method for all the systems. The reactant adsorption was established in the supporting electrolytes, potassium nitrate and potassium chloride. In the case of sodium perchlorate a different behavior was observed. Further theoretical phase sensitive ac polarograms are drawn to confirm the results. In all the systems, Thallium (I) proceeds with high degree of reversibility and the values of Ksh were found to be greater than one.


INTRODUCTION
The faradaic impedance technique is the best choice for the determination of kinetic parameters for rapid electrode processes like the reduction of Thallium(I).Randles(1947) first showed that the reduction of Thallium(I) proceeds reversibly by impedance technique.But they could not determine K sh value.Later they investigated the problem with Laitinen and reported a value for K sh as 1.8 in 1M perchloric acid as supporting electrolyte assuming a different equivalent circuit (Randles and Laitinen, 1955).Tamamushi and Tanaka (1961) reported that the anomaly in cot φ in Thallium(I) must be due to adsorption of Tl(I) ions at the mercury solution interface.The effect of adsorption on the faradaic process has been considered by several investigators (Llopis et al., 1959;Senda et al., 1961;Lorenzand salie 1961).Baticle and Perdu (1967)rigorously treated Thallium(I) system on the basis of Senda and Delahay's (1961) circuit and conducted six experiments (Baticleet al., 1967).In three experiments they could get only zero and in the remaining two, a very low value for the charge transfer resistance.Timmer et al. (1968) expressed the view that simple Randles and Laitinen (1955) circuit holds good only in the case of weak adsorption and in the case of strong adsorption they recommended a different equivalent Subramanian, P. A and Kalyanasundaram, R (MEJS) Volume 5( 1 (Sridhar and subramanya , 2010).
In the present paper it is proposed to study Thallium(I)-aqueous systems in three different supporting electrolytes using the basic and simple Randles and Laitinen(1955) equivalent circuit.
The same system in 50%methanol-water mixtures has been reported recently (Subramanian and Kalyanasundaram, 2012).The determination of double layer capacity 'C d ' in the presence of reactant adsorption is very difficult to ascertain and many earlier investigators failed in this regard.So, they referred to many complicated equivalent circuits to determine the charge transfer resistance.In this work it will be done by graphical extrapolation method (Smith et al., 1966;Somayaji et al., 1969).The C d of the supporting electrolyte will be different from that of the solution in the presence of reactant adsorption.Experimental parallel capacity 'C P ' values are plotted against 1/ ω and the limiting value as ω → ∞can be found on the 'C P ' axis on extrapolation.The C d of supporting electrolyte can be directly measured.Theoretical phase sensitive ac polarograms are drawn to ascertain the reactant adsorption.The charge transfer resistance Θ and Warburg coefficient σ can be obtained from the plots drawn with faradaic impedances Z ' f and Z '' f versus 1/√ω.

Apparatus and Chemicals
Recording DC Polarograph: DC polarograms were obtained using 'Systronics' make(Model:1632, India) console using three electrode assembly and a recorder.Pure nitrogen gas was used to purge the dissolved Oxygen gas.Saturated calomel electrode was used as reference electrode.

Complex plane polarography
A manual Impedance measurement bridge of Wien bridge type was used to measure the cell impedance.The equivalent circuit of the cell is given by double layer capacitance in series with the solution resistance.Systronics make (model:1013) function generator was used to superimpose a small amplitude sine wave signal(peak to peak 10mV The log plots were drawn and the slope values are calculated.Complex plane polarography of 0.3mM Thallium(I) was obtained at 750Hz.in the potential range corresponding to the rising portion of the wave in DC polarograms.'q' is determined from the equation = 1/Y' el and it is plotted against potential.The minimum in the plot corresponds to the peak potential.
The frequency variation experiments were conducted from 400Hz to 10,000Hz for four different concentrations, 0.3, 0.4, 0.5 and 0.6mM of Thallium (I) in all the three supporting electrolytes at the peak potentials.
The series resistance R Ω is an important parameter and it is determined by three different methods and compared.
The Randles and Laitinen (1955) equivalent circuit followed in this work is given below.Parallel capacity, Cp Vs ω -1 plots: Somayaji and Subramanya (1969) showed that the double layer capacity can be determined by plotting parallel capacity against ω -1 plots.This is possible even in the case of reactant adsorption.C p can be determined directly by adjusting the bridge network slightly or it can be obtained by circuit analysis.The circuit analysis is given in the figure below.
It is calculated using the following equations.
Both the methods were attempted and identical results were obtained.For all the four concentrations of Thallium(I) plots are made in the same plot.As ω -1 → 0, all the four plots tend to come closer and intercept at the same point on the C p axis.
Therefore a plot of Z' f Vs ω -1/2 will yield a straight line and on extrapolation, Θ m can be obtained from intercept and σ m from the slope.Plotting Z'' f Vs ω -1/2 in the same plot will give a straight line parallel to Z' f Vs ω -1/2 plot and passing through the origin.Thus both Θ m and σ m can be obtained.

DC Polarography
DC Polarograms of Thallium(I) in all the three supporting electrolytes were well defined and the E 1/2 values are given in the (Table 1).For all the three systems E 3/4 -E 1/4 was found to be 55mV.
The log plots resulted in a straight line and the slope value for all the systems were found to be 60mV, which is the theoretical value corresponding to a single electron reversible reduction.The polarograms and the log plots are given in the figure 1.The shape of the polarograms and the slope values from the log-plot very clearly shows the reversible nature of reduction in all the three systems.The value of transfer coefficient, 'α' was determined from the equation, Table1.DC Polarographic data and E P of Thallium(I)-Aqueous systems.Since the peak potential was found to be equal to half wave potential, the value of transfer coefficient was found to be 0.5 in all the three systems.The values are provided in (Table 1).

Complex plane Polarography
Potential variation experiments were carried out at a fixed frequency of 750 Hz in the potential range corresponding to the rising portion of the wave in DC polarogram for all the respective systems and the q Vs potential plots were drawn and given in figure 2. The Experimental values for all the systems are given in (Table 2).The minimum of the curves corresponds to the peak potential (Table 1).
Frequency variation experiments were carried out at the respective peak potentials for all the systems.The experimental values with other calculated parameters are given for 0.4mM Thallium(I)-0.5MNaClO 4 only for want of space in (Table 3).The mass and drop time of mercury are provided on the top of the table.

Series resistance
The series resistance R Ω was calculated for all systems by the three methods described above.It is quite remarkable that the values determined by the three different methods are in fair agreement.The series resistance is provided along with the data for the frequency variation experiments.The plots for Thallium(I)-0.5MNaClO 4 are given in figure 3. The plots are similar for other systems.

Determination of double layer capacity
1. C P Vs ω -1 Plots: The plots are given in the figures 4 and 5 for all the three systems.For a given system the plots for four different concentrations of Thallium (I) were drawn on the same plot (fig.4).In the case of Thallium(I)-0.5MNaClO 4 system, at higher values of ω -1 , C P was found to be concentration dependent.As ω -1 → 0, all the four plots tend to become closer and intercept at the same point.This shows that the double layer capacity is independent of depolarizer concentration and the C d is found to be 30 μF/ cm 2 .
For the systems, Thallium(I)-0.5MKNO 3 and Thallium (I)-0.5MKCl at higher values of ω -1 , C P was found to be concentration dependent.This behavior persists and becomes permanent even when ω -1 → 0. The plots of four different concentrations make four different intercepts.This fact shows that C d is dependent on the concentration of the depolarizer.C d values are reported in (Table 4).different from that of Z'-Z'' plane which was originally used but it is easier to handle and its relation to the theory is more direct (Sluyters-Rehbach and Sluyter, 1963a&b).The C d obtained in this mode of analysis was found to be 30 μF/ cm 2 for the Thallium (I)-0.5MNaClO 4 system.For the systems, Thallium(I)-0.5MKNO 3 and Thallium(I)-0.5MKCl the C d has already been found to be dependent on depolarizer concentration.This plot is expected to give only the C d of the blank solution.The values are tabulated (

Determination of Θ m and σ m at the peak potentials
The real and imaginary components of faradaic impedance, Z' f and Z'' f as described earlier.
were drawn against ω -1/2 in the same plot.The plot of Z'' f Vs ω -1/2 must result in a straight line and pass through the origin and the plot of Z' f Vs ω -1/2 must be parallel to that and make an intercept.In the case of Thallium (I)-0.5MNaClO 4 system, computation of Z' f and Z'' f using Volume 5(1):129-147, 2013 © CNCS, Mekelle University 132 ISSN: 2220-184X Various parameters of impedance used in this work and their relations are given below.Experimentally determined values: Resistance = R E ; Capacitance = C E ,; Real component of cell impedance Z' = AR E ; A = area of mercury drop, ; Imaginary component of cell impedance Z'' = A/[2ΠfC E ] ; f = frequency; Real component of Electrode impedance Z' el = Z' -R Ω ; R Ω = Series Resistance; Imaginary component of Electrode impedance Z'' el = Z''; Real component of electrode admittance Y' el = Z' el /(Z' el 2 + z'' el 2 ); Imaginary component of electrode admittance Y'' el = Z'' el /(Z' el 2 + z'' el 2 ) ; Real component of faradaic impedance Z' f = Y' el /( Y' el 2 +Y'' el 2 ) Imaginary component of faradaic impedance Z'' f = Y'' el /( Y' el 2 +Y'' el 2 ); Y' el and Y'' el are related by the equation, Y'' el = [Y' el /[p+1]] + ω C d where p = Θ/[σω -1/2 ] Double layer capacity: Double layer capacity, C d at the peak potential in the presence of depolarizer was determined by four different methods.
Subramanian, P. A and Kalyanasundaram, R (MEJS)    Volume 5(1):129-147, 2013 © CNCS, Mekelle University 133 ISSN: 2220-184X From electrode admittance plots: If C d remains constant Y'' el Vs Y' el plot will result in a straight line., the slope yielding the value of 'p' and intercept that of C d.The plot of Y'' el /ω Vs Y' el /ω will also result in a straight line and C d can be obtained from intercept.In the Y'' el Vs depolarizer concentration plot, ω C d can be obtained from the intercept upon extrapolation to zero concentration.Calculation of Θ m and σ m : Charge transfer resistance and the Warburg coefficient at the peak potential (Θ m , σ m ) were obtained from Z' f and Z'' f plot.The real and imaginary components of faradaic impedance are related to faradaic admittance by the following equations.
Vs Y' el Plots: These plots for different concentrations of the depolarizer at fixed frequency are given in figures 5. If C d remains constant, a plot of Y'' el against Y' el will result in a straight line and the slope gives the value of C d .This method is not principally Subramanian, P. A and Kalyanasundaram, R (MEJS) Volume 5(1):129-147, 2013 © CNCS, Mekelle University 137 ISSN: 2220-184X

Table 4 .
Table.4).3.Y'' el /ω Vs Y' el /ω Plots with different depolarizer concentrations at fixed frequencies: In this plot C d will be obtained by extrapolation to zero admittance which is practically equal to zero metal ion concentration.In general such plots will give the double layer capacity of the blank solution.Y'' el Vs depolarizer concentration plot is also similar to this.Therefore, such plots are not attempted for the systems whose C d depends on the concentration of the depolarizer.The values are tabulated(Table.4).4.Y'' el Vs depolarizer concentration plot: This plot was drawn only for Thallium (I)-0.5MNaClO 4 system.The intercept gives ω C d .Such plots for various frequencies are given in figure .The value has been found to be 30 μF/ cm 2 .At the same peak potential, C d of the blank solution (test solution without depolarizer) was also determined and tabulated (Table.4).Double layer capacity from various methods -C d μF/cm 2 .

Table 5 .
Θ m C, σ m C and K s,h values of different systems.Plots for determination of series resistance R Ω .