The X-ray fluorometer (XRF), X-supreme 600 oxford instruments was used for the elemental analysis of the ore. The mineralogical analysis of the ore was done using ARL X’TRA X-ray Diffractometer, Thermoscientific with the serial number 197492086 and Empyrean by PanAnalytical model with CuKα (1.54 Å) radiation generated and 40 mA and 45 kV. This unit comprises of a single compact cabinet. The cabinet houses a high speed, high precision Goniometer; high efficiency generator (X-ray) and an automatic sample loading facility.

The petrographic slides of galena ore were prepared using Epoxy and Lakeside 70 media according to the method of Hutchison [27] .

FTIR analysis was carried out using Buck Scientific M530 Infrared Spectrophotometer. SEM analysis was carried out using Q250 by FEI model from the Netherlands.

The results of the elemental composition of galena by X-ray fluorescence technique showed that the galena mineral exist mainly as PbS with metals such as Na, Mg, Al, Ca, Fe and Zn occurring as minor elements, and K, Cr, and Sr as traces. The elemental analysis gave Pb (60.01%), S (14.66%), Fe (4.32%), Na (3.78%), Si (7.69%), Mg (1.21%), Al (1.94%), P (1.37%), Cl (1.19%), K (0.09%), Ca (1.99%), Cr (0.01%), Mn (0.49%), Zn (1.22%), and Sr (0.04%).

The analysis of galena by X-ray diffraction gives a better description in terms of the mineral phases present in the ore. Table 2 present the results of the X-ray diffractogram of the ore and shows that the ore exist mainly as lead sulphide (PbS).

The galena ore gave three major peaks at 2.96, 3.42, and 2.09 Å, respectively as shown in Figure 1. All these supported the results of the elemental analysis by XRF.

The FTIR spectra of galena ore is shown in Figure 2. The spectrum of the ore exhibit absorption bands at 3821 cm⁻¹, 3652 cm⁻¹, 3353 cm⁻¹, 2958 cm⁻¹, and 2564 cm⁻¹. These are attributed to O-H stretching. The band at 1410 cm⁻¹ is attributed to O-H bending. The bands at 3519 cm⁻¹, 3353 cm⁻¹ and 2564 cm⁻¹ are attributed to N-H stretching. The band at 2564 cm⁻¹ which is attributed to S-H

JCPDS File No.: Joint Committee on Power Diffraction Standards File Number.

stretching confirms the presence of sulphur in the ore. The band at 1634 cm⁻¹ is attributed to Si-O and Al-O stretching while the band at 1634 cm⁻¹ is also attributed to Al-O-H stretching.

The FTIR result is in agreement with XRF and XRD results which confirmed the presence of the minerals detected.

The scanning electron micrograph (SEM) of galena ore was obtained with magnifications of 240×, 520×, 1000×, and 1500× respectively as shown in Figure 3.

The average cell diameter of the ore ranges from 8 to 62 µm while the average cell density ranges from 0.0042 to 1.13 cells/mm. The results indicate that the ore particles are very cohesive, forming an aggregate mass that appeared to have been formed by several flaky particles stacked together in form of agglomerates [28] . The particles have irregular shapes with rough edges, and are highly crystalline due to the high level of purity of the ore.

The results of the effect of HNO₃ concentration on galena dissolution are illustrated in Figure 4. The result shows that the fraction of galena dissolved increases with increasing acid concentration. The yield of lead obtained with 12 M HNO₃ is slightly lower than that obtained with 10 M HNO₃, and this could be attributed to a change in the rate determining step due to the significant quantity of elemental sulphur produced [14] .

In all cases, unreacted acid remained in the leach solution and the free acid increased with increasing initial acid concentration, since the use of more concentrated acid did not increase the dissolution of galena or decrease the leaching time for maximum dissolution. Therefore, 10 M HNO₃ was used for further investigation.

The results on the effect of stirring rate on galena dissolution in 10 M HNO₃ over the range of 90 - 720 rpm at 363 K are presented in Figure 5.

Figure 5 shows that the amount of galena dissolved is dependent on the stirring speed over the range 90 - 540 rpm. Above 540 rpm, the stirring speed no

longer has any observable effect on the solid dissolution. Hence dissolution reached a steady rate at 540 rpm, and a stirring speed of 540 rpm was retained for further experiments. Increase in stirring speed causes a decrease in the thickness of the film layer, therefore, causing an increase in the dissolution rate [29] .

The effect of temperature on galena dissolution has been investigated over the temperature range 303 - 363 K in 10 M HNO₃ solution at a stirring rate of 540 rpm using 75 µm particle diameter and solid/liquid ratio of 20 g/L. These results are presented in Figure 6.

As seen in Figure 6, galena dissolution increases with increasing temperature. This is as a result of high kinetic energy available for the reacting molecules [29] . For instance, at 363 K, the amount of galena dissolved within 150 min was 85.2%.

The influence of particle diameter on galena dissolution in HNO₃ was investigated for five different sized fractions. The results are summarized in Figure 7.

The results from Figure 7 showed that the smaller the galena particle size, the higher was the fraction of galena dissolved. This is attributed to larger specific surface area provided by the smaller particles for contact with the acid molecules [29] . This observation was also supported by Aydogan et al. [13] and Dutrizac and MacDonald [30] .

The results on the effect of solid/liquid ratio on galena dissolution in 10 M HNO₃ were investigated in the range 0.02 to 0.045 g/ml at a temperature of 363 K.

Figure 8 shows the effect of solid/liquid ratio on galena dissolution in 10 M HNO₃. Decreasing the solid/liquid ratio is accompanied with increase in the equilibrium percentage of the ore dissolved. For instance, by varying the solid/liquid ratio from 0.045 to 0.02 g/ml, the percentage of galena dissolved increased from 47% to 84% at 363 K. This could be attributed to the decrease in the fluid reactant per unit weight of the solid [29] . Accordingly, an optimum solid/liquid ratio of 0.02 g/ml has been retained for subsequent studies.

For this study, three shrinking core models were tested for better understanding

of the dissolution of galena in HNO₃ media. The kinetic models as previously utilized by some authors such as Aydogan et al. [13] [18] , Baba and Adekola [31] , Habashi [32] , Khalique et al. [33] , Leao [34] and Merwe [21] include:

1 − ( 1 − X ) 1 / 3 = b k s C A ρ s r o t = k 2 t (2)

1 + 2 ( 1 − X ) − 3 ( 1 − X ) 2 / 3 = 6 b D e C A ρ s r o 2 t = k 3 t (3)

1 − ( 1 − X ) 1 / 3 + ( y / 6 ) [ ( 1 − X ) 1 / 3 + 1 − 2 ( 1 − X ) 2 / 3 ] = k 4 t (4)

where X is the fraction of galena dissolved at time t, b the stoichiometric coefficient of the reagent in the leaching reaction, k s the kinetic constant, C A the concentration of nitric acid (HNO₃), ρ s the density of the solid, r o the initial radius of the solid, and k₂ the rate constant from Equation (2). D ϵ is the effective diffusion coefficient, k₃ and k₄ are the rate constants for Equations ((3) and (4)) respectively, y is taken to be 1 for heterogeneous systems.

Equation (2) is applicable to a chemical reaction controlled process at the interface; Equation (3) is a diffusion-controlled process through the product layer and Equation (4) is a mixed controlled process (a combination of surface reaction and diffusion). Of all the three models tested, all the studied data were found only to fit the relation in Equation (3) with a perfect correlation of about 0.99. The analysis of the plots of other kinetic curves, however, gave lower correlation coefficients. Hence, the linearization of Figures 4-8 was made. To this end, the relation: 1 + 2 ( 1 − X ) − 3 ( 1 − X ) 2 / 3 = k 1 t , gave an average correlation coefficient of 0.994 and this is shown in Figure 9.

From Figure 9, the experimental rate constant k₁, was calculated from the slope of the straight line at various HNO₃ concentrations and the plots of Ink₁ versus In[HNO₃] are shown in Figure 10.

From Figure 10, the slope of the resulting plot gave 0.93. This shows that the order of reaction with respect to H⁺ ion concentration is 0.93 with correlation coefficient of 0.990.

Similarly, the apparent rate constant k₅ was calculated from the slope of the straight line at various stirring rates (w) as shown in Figure 11 and the plots of Ink₅ versus Inw are shown in Figure 12.

Furthermore, the data in Figure 6 at different temperatures were linearized by Equation (3). This is shown in Figure 13. The data in Figure 7 and Figure 8 were also linearized by means of Equation (3) as shown in Figure 15 and Figure 16 respectively.

From Figure 13, the apparent rate constants, k₃ and other tested constants, k₂ and k₄ were calculated from the slopes of the straight lines. The values of these rate constants with their equivalent correlation coefficients are summarized in Table 3.

By using the rate constants derived from the slopes in Figure 13, the Arrhenius diagram in Figure 14 was plotted from which the activation energy of 27.01 KJ mol was calculated, which supports the proposed diffusion controlled mechanism. The Arrhenius constant for the process was estimated to be 26.71 s⁻¹ with a correlation coefficient of 0.985. In some instances and as reported by Olanipekun [35] , the rate controlling mechanism of the heterogeneous dissolution

process could either be predicted from plots of the kinetic equations or from the activation energy.

In general and as demonstrated by Aydogan et al. [18] , it has been accepted that a diffusion-controlled process is characterized by a slight dependence on temperature, while the chemically controlled process is strongly dependent on temperature. The reason being that diffusion coefficient, D, is linearly dependent on temperature formulated as: k = A e − E a / R T , where A is the Arrhenius constant, E_a is the activation energy, R is the Boltzmann constant and T is the absolute temperature. The activation energy calculated for this study appears to be the lowest compared to other reported works as summarized in Table 4. The galena ore obtained from Abakaliki can therefore be said to be kinetically

more favorable to leaching by HNO₃ compared to other galena types.

According to Olanipekun [35] , the rate controlling mechanism of heterogeneous dissolution process is often predicted from the plots of the kinetic equations, rather than the activation energy. Therefore, in order to determine the rate determining step for the present study, the kinetic curves in Figure 7 were also linearized by means of Equation (3). The values of the rate constants, k₄, were plotted against the reciprocal of the particle radii (1/r_o), yielding a linear relationship with a correlation coefficient of 0.995 (Figure 19). It is worthy of note that the plot of the rate constants as a function of the square of particle radii (1/r_o)² did not give a linear relationship. This indicates that the surface chemical reaction was the rate controlling step during the dissolution. Hence, the diffusion of the H⁺ ion was at higher rate because of the high transport number in aqueous solution [22] .

From the effects of the solid/liquid ratio (Figure 17) and particle diameters (Figure 18) on galena dissolution in 10 M HNO₃ solution, the apparent rate constants, k₆ and k₇ were evaluated, respectively.

The solid/liquid ratio and initial particle size (d_p) were found to be inversely proportional to 1.99 power (S/L)^−1.99 and 0.94 power ( d p − 0.94 ), respectively. Hence, the proposed model equation for galena dissolution by 10 M HNO₃ solution at 90˚C is consistent with the following relation:

1 + 2 ( 1 − X ) − 3 ( 1 − X ) 2 / 3 = k o C HNO 3 0.93 ( d p ) − 0.94 ( ρ S L ) − 1.99 ( w ) 0.79 e ( − 27012 / R T ) t

where ρ is the ore density (Baba and Adekola, 2011). k_o is a reaction constant, which can be determined from the fraction of galena ore dissolved, X at a given time, t. The parameter, X is determined experimentally. For instance, at 90˚C, the value of X = 0.845 (84.5% dissolution); k_o is calculated to be 3.54 × 10⁸. The value of k_o, however, is found to vary depending on the leaching systems/conditions [13] [37] .

The scanning electron micrograph (SEM) of galena leached with 10 M HNO₃

was obtained with magnifications of 150×, 500× and 1000× respectively as shown in Figure 20. The average cell diameter ranges from 26 µm to 104 µm while the average cell density ranges from 0.0938 cell/mm to 0.156 cell/mm. The results above indicate an increase in the diameter of the particles and a corresponding decrease in density as the particle volume automatically increases and therefore decreases the specific gravity [28] . The micrographs of the leaching residues show a progressive increase in the roughness of the solid and also an increase in the amount of elemental sulphur covering the particle surfaces [38] . The particles have irregular shapes and may be poorly crystalline due to acid attack.

The analysis of galena leached with 10 M HNO₃ at 90˚C by X-ray diffraction gives a description of the mineral phases present in the residue. Table 5 present the results of the X-ray diffractogram of the residue with important compounds identified. The result showed two major and one minor peaks at 4.51, 2.26, and 1.51 Å, respectively. The XRD data revealed the presence of gahnite and anglesite as shown in Figure 21. The XRD result agrees with the SEM result of the residue. In summary, the overall dissolution reaction of galena in HNO₃ solution can be described by the following stoichiometry:

PbS ( s ) ( galena ) + 2 H ( aq ) + ⇄ Pb ( aq ) 2 + + H 2 S ( g ) ( ≅ 85 % releasedintosolution )