EMF Measurements in the Liquid Pb/PbCl₂-KCl/Pb-Sb-Bi System

The Pb-SbBi alloys electrode potentials were defined by measuring the EMF of the following galvanic element in the temperature interval of 723–873 K:

Twenty compositions of the alloy, which are located at the secant lines of the concentration triangle with a constant Sb:Bi molar ratio of 1:3; 1:1; 3:1, were studied. Table I presents concentrations and weights of the alloy components.

Experiments were carried out in a cell, which is represented in Figure 1. The Pb-SbBi alloys with different Pb concentrations were placed into the molten KCl-PbCl₂ (50:50 mol %) mixture and served as a right half-cell. The lead electrode was used as a second half-cell. The electrolytes of two half-cells were separated by a porous diaphragm, which was impregnated by the salt of the same composition. Molybdenum rods (1 mm in diameter) screened by alundum tubes from the melt served as current leads to the metal electrodes. An alundum crucible was used as a container for the salt mixture. Extra pure argon provided inert atmosphere in the electrochemical cell. The alloys were prepared from antimony, bismuth and C1 grade lead (UMMC, Verkhnaya Pyshma, Russian Federation). Chemically pure reagents were used to prepare the electrolyte. A Pt-PtRh thermocouple was used to control the melt temperature.

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The cell was placed into a solid tile, which was heated to a desired temperature in a resistance furnace. The temperature was maintained with accuracy of ±1°C by the Varta temperature regulator. The EMF value was recorded using the APPA-109 multimeter with an input resistance of ∼10 Mohm. The set equilibrium potential was registered when the value remained constant during 60 minutes (±0.1 mV). The compositions of the metal alloys and electrolyte were controlled before and after the experiment by the atomic-absorption method. No changes were detected in the compositions of alloys and electrolyte.

Figure 2 presents the results of the studied alloys potentials measuring at different temperatures. The EMF polytherms are seen to be linear, which indicates that the alloy and the melt are in equilibrium.

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Table II provides the results of EMF measurements of the Pb-SbBi ternary system at 773 K and the values of dE/dT temperature coefficient.

The lead activity in the Pb-SbBi alloys was calculated using the experimental data and known thermodynamic expressions²¹ as follows:

where

a_Pb is the lead activity;

F is the Faraday constant, 96495 C/mol;

E is the potential, mV;

R is the gas constant, 8.314 J/(mol·K);

T is the temperature, K.

The activity coefficient was calculated according to the following formula:

where

f_Pb is the activity coefficient;

x_Pb is the Pb mole fraction.

Table III presents the calculation results of Pb activity and activity coefficients in the Pb-SbBi_i,j system. The Pb activity coefficient f_Pb in the Pb-SbBi_i,j alloys becomes smaller as a Pb mole fraction decreases and becomes larger as the temperature increases. The Pb activity coefficient approaches to unity in the alloys with Pb mole fraction exceeding 0.7. A decrease in lead concentration (Pb-SbBi system) results in negative deviations from the Raoult's law. In cases when lead concentration in the alloy is less than 0.15 mole fraction, the lead activity decreases more than by 30–40% at all temperatures studied.

The following equations were used to calculate the Pb partial thermodynamic functions:

where

Δ is the partial Gibbs energy, J/mol;

Δ is the partial enthalpy, J/mol;

Δ is the partial entropy, J/(K·mol).

The excess thermodynamic functions of lead mixing were calculated as follows:

where

Δ is the excess partial Gibbs energy, J/mol;

Δ is the partial excess entropy, J/(K·mol).

Table IV demonstrates the calculated values of Pb thermodynamic functions in the Pb-SbBi_i,j alloy.

Table IV. Pb partial functions in liquid Pb-SbBi_i,j alloys at 773 K.

Alloy (A) PbxSb0.25^*(1-x)Bi0.75^*(1-x)

Pb mole fraction, xPb	Δ, kJ/mol	Δ, kJ/mol	Δ, kJ/mol	Δ, J/(K·mol)	Δ, J/(K·mol)
0.03	−24.945	−4.231	−2.157	26.051	2.639
0.07	−19.698	−3.785	−1.961	20.455	2.305
0.12	−16.825	−3.273	−1.731	16.981	1.929
0.15	−14.604	−2.988	−1.602	15.823	1.724
0.52	−4.520	−0.697	−0.457	5.696	0.252
0.61	−3.432	−0.419	−0.293	5.210	0.119
0.70	−2.212	−0.223	−0.168	3.666	0.042
0.87	−0.899	−0.033	−0.030	2.123	−0.002
Alloy (B) PbxSb0.5*(1-x)Bi0.5*(1-x)
0.17	−6.930	−3.007	−1.502	14.859	1.815
0.24	−6.009	−2.392	−1.234	11.771	1.377
0.35	−4.273	−1.601	−0.873	9.262	0.841
0.45	−3.347	−1.051	−0.606	6.561	0.494
0.54	−2.234	−0.673	−0.412	4.052	0.278
0.64	−1.559	−0.371	−0.245	2.509	0.124
Alloy (C) PbxSb0.75*(1-x)Bi0.25*(1-x)
0.15	−6.533	−3.311	−1.551	16.209	2.244
0.32	−3.978	−1.857	−0.950	10.613	1.103
0.33	−3.905	−1.788	−0.920	10.227	1.051
0.51	−2.271	−0.812	−0.469	6.175	0.379
0.52	−2.163	−0.772	−0.448	5.982	0.354
0.69	−1.333	−0.267	−0.178	3.087	0.078

According to the classification of metal alloys on the basis of measuring their thermodynamic functions suggested by G. Kaptay,^22–23 the Pb-SbBi pseudo-binary system belongs to the "B –" type, i.e. the values of the excess partial enthalpy and the partial excess entropy are small and are close to zero.

The Pb activity coefficients of the first Pb-SbBi_i,j alloy homogeneous component, which were calculated using experimental data, are well described by the Margules equation²¹ limited to a second term of the expansion in power series (1-N_Pb) with the coefficients presented as the Taylor expansion²⁴ with respect to reciprocal temperature limited to the second term of the expansion of the following form.

The equation is true for all studied temperatures and alloy compositions.

The SbBi_i,j activity coefficients were calculated using the Gibbs-Duhem equation:

The analytical integration of Eq. 11 considering Eqs. 9 and 10 results in the analogous equation, which coefficients are expressed in terms of Pb coefficients:

The parameters of the temperature and concentration dependences of the Pb-SbBi components activity coefficients were calculated via the system of nonlinear equations using the Newton method (Microsoft Excel 2007). The parameters values are α₀ = 0,07, α₁ = −203; β₀ = −0,42, β₁ = −75.

The mean-squared deviations of the lnf values and 95% confidence interval are s_{n − 3} = ±0.065 and Δ_0.95 = ±0.029, respectively. The values of Gibbs energy are ±450 and ±195 J/mol at the medium temperature of the experiment, respectively.

Table V shows the activity coefficients of the second component, calculated using Eq. 12, and the SbBi activity in the PbxSb0.25^*(1-x)Bi0.75^*(1-x) system.

The SbBi component demonstrates negative deviations from the ideal behavior in the PbxSb0.25^*(1-x)Bi0.75^*(1-x) liquid alloy. The SbBi_(0.25-0.75) activity coefficient is less than unity (f_Bi < 1) throughout the studied temperature and concentration range. Figure 3 illustrates the Pb-SbBi_i,j system components activity at 723, 773, 823 and 873 K.

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The composition dependences of Pb and SbBi_i,j activities values elucidates that the deviation from the ideal behavior is nonsymmetrical.

The following equations were used to evaluate relative partial molar values and SbBi_i,j excess thermodynamic functions in the Pb-Sb-Bi system (see Table VI):

Table VI. SbBi_(0.25-0.75) partial functions in the PbxSb0.25^*(1-x)Bi0.75^*(1-x) liquid alloys at 773 K.

Pb mole fraction, xPb	Δ, kJ/mol	Δ , kJ/mol	Δ, kJ/mol	Δ, J/(K·mol)	Δ, J/(K·mol)
0.03	−0.201	−0.005	−0.002	0.257	0.004
0.07	−0.495	−0.028	−0.012	0.624	0.022
0.12	−0.904	−0.082	−0.036	1.123	0.061
0.15	−1.171	−0.127	−0.056	1.444	0.093
0.52	−5.942	−1.147	−0.621	6.820	0.768
0.61	−7.636	−1.584	−0.834	8.768	0.940
0.70	−9.692	−1.953	−1.071	11.094	1.084
0.87	−15.746	−2.631	−1.574	18.187	1.225

The integral molar and excess characteristics of the Pb-SbBi_i,j system components mixing were calculated as follows:

Table VII provides the values of thermodynamic functions, calculated according to Equations 17–21.

The values of partial and integral Gibbs energies of the Pb-SbBi_i,j system become more negative as the temperature increases. The excess integral Gibbs energy has the greatest negative deviation from ideality at the Pb concentration of 0.55 mole fractions (Fig. 4), the entropy maximum positive values (Table VII) are located within the same Pb concentration interval.

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The functions of integral enthalpy have negative values, which are smaller than that in the Pb-Bi binary systems,¹² but larger than that in the Pb-Sb systems¹⁰ in absolute magnitude. The extremum of the Pb-SbBi_i,j system integral enthalpy is observed at x_Pb = 0.55 mole fraction (Fig. 5). The functions of integral entropy of the ternary system have positive values, which are close to the values of integral entropy of the Pb-Bi binary system^12–14 and are larger than that of the Pb-Sb binary system.^8,10

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The entropy impact on the deviation from the ideal behavior decreases in a minor way as the Sb concentration in the alloy increases and reaches 40–50% at the extreme values of excess Gibbs energy. It has been previously shown that the entropy impact is 14% at x_Pb = 0.18 molar fractions and is 39% at x_Pb = 0.88 molar fractions at 773 K in the Pb-Bi alloys,¹² while in the Pb-Sb systems¹⁰ the entropy impact is 46–48% in the wide Sb concertation interval.

The analysis of the Pb-SbBi_i,j system thermodynamic functions demonstrates that the liquid alloys under study have insignificant negative deviations from ideality and cannot be subsumed as regular solutions.

• (1)  
  The equilibrium potentials of the Pb-SbBi_i,j alloys in the KCl-PbCl₂ melt were measured in the temperature interval of 723–893 K for a wide compositional range. The thermodynamic functions were calculated for the metal Pb-SbBi_i,j system using the EMF method.
• (2)  
  The Pb-SbBi_i,j system demonstrates small negative deviations from the law of ideal mixtures with the asymmetric thermodynamic functions behavior. The extremum was observed solely at x_Pb = 0.55 molar fractions.
• (3)  
  The Pb-SbBi_i,j system is not a regular solution, because the excess entropy influences greatly the deviations from ideality and the values of excess Gibbs energy significantly differ from those of the heat of mixing.