Investigation_of_Leaching_Kinetics_of_Copper

Investigation of Leaching Kinetics of Copper from Malachite Ore in Ammonium Nitrate SolutionsAHMET EKMEKYAPAR,EVRIM AKTAS¸,ASIM KU NKU L,and NIZAMETTIN DEMIRKIRANThe production of metallic copper from low-grade copper ores is generally carried out byhydrometallurgical methods.Leaching is thefirst prerequisite of any hydrometallurgical pro-cess.Solutions containing ammonia may allow for selective leaching of the copper from the ore.In this study,the leaching kinetics of malachite,which is an oxidized copper ore,in ammoniumnitrate solutions was examined.The effects of some experimental parameters on the leachingprocess were investigated,and a kinetic model to represent the effects of these parameters on theleaching rate was developed.It was determined that the leaching rate increased with increasingsolution concentration,temperature,and agitation speed,as well as decreasing particle size.Itwas found that the leaching reaction followed the mixed kinetic controlled model,whichincludes two different leaching processes including the surface chemical reaction(303K to323K[30°C to50°C])and diffusion through a porous product layer(323K to343K[50°C to70°C]).The activation energies of these sequential steps were determined to be95.10and29.50kJ/mol,respectively.DOI:10.1007/s11663-012-9670-2ÓThe Minerals,Metals&Materials Society and ASM International2012I.INTRODUCTIONI N the literature,oxide and sulfide copper ores mainly are known as azurite,malachite,tenorite, chrysocolla,brochantite,enargite,chalcopyrite,chalco-cite,covellite,and bornite.[1]The production of metallic copper from these ores is carried out by pyrometallur-gical and hydrometallurgical methods.[2]Pyrometallur-gical methods are generally applied to the relatively high-grade sulfide copper ores.Increasingly,the low-grade copper ores and secondary sources containing copper are being used for the production of copper because of depletion of high-grade copper ores at the present time.[3]Pyrometallurgical methods are not normally suitable for the processing of low-grade ores. Instead,hydrometallurgical methods are usually pre-ferred for the recovery of copper from these kinds of ores.Leaching is the term applied to the process of recovering a metal from the metal source by a solvent or lixiviant,and it is typically thefirst step of any hydrometallurgical process.[4]In the leaching process, strong acids,such as HCl,HNO3,and H2SO4,are commonly used as the leaching reagents.[5]Sulfuric acid is the preferred lixiviant in the leaching of the oxidized copper ores,such as azurite,malachite,tenorite,and chrysocolla.[2,6]However,during the leaching of ores,other metals in ore matrix are also dissolved along with the copper.These undesired impurities cause some problems in further processing of the leaching solution, such as the electrowinning of copper.[7]In addition,the impurities in the ore can cause a high consumption of acid.For these reasons,the use of solutions more basic than sulfuric acid can be attractive in the leaching of oxidized copper ores.For example,ammoniacal leach-ing systems have some advantages over acid leaching systems.In the ammoniacal leaching system,the disso-lution of ore can be carried out at mildly acidic or basic conditions.Second,ammonia can be recovered by evaporation.Furthermore,some metals,which pass into the solution during the leaching process,precipitate because of the higher pH of solutions containing ammonia.Ammonia also forms stable complexes with copper ions,which can lead to an increase in the leaching rate from the ore.Thus,ammonia allows for selective extraction of the copper from ore,leaving the undesired components in the residue.[7–9]As a result,at the end of the leaching process,a high purity solution can be obtained for the electrolytic recovery of copper. The leaching and kinetics of malachite,which is an oxidized copper ore,in ammonia-containing solutions has been investigated by various researchers.Oudenne and Olson[10]studied the leaching kinetics of malachite in ammonium carbonate solutions.They reported that the leaching of malachite took place in two stages.At thefirst stage,the dissolution of malachite proceeded rapidly.Then,the dissolution rate decreased because the surface was coated from the formation of a needle-structured intermediate product,which is most likely Cu(OH)2.Subsequently,malachite and the intermediate product dissolved concurrently.The second stage of leaching begun when essentially all the malachite wasAHMET EKMEKYAPAR and ASIM KU NKU L,Professors,and N_IZAMETT_IN DEM_IRKIRAN,Assistant Professor,are with the Chemical Engineering Department,Faculty of Engineering,Inonu University,Malatya44280,Turkey.Contact e-mail:nizamettin. demirkiran@.tr EVR_IM AKTAS,Chemical Engineer,is with the Malatya Sugar Factory,Malatya44080,Turkey.Manuscript submitted September22,2011.dissolved and only the remaining intermediate phase remained leached.It was determined that the activation energies of these two stages were64and75kJ/mol, respectively.Ku nku l et al.[11]examined the dissolution of malachite in ammonia solutions.They stated that the leaching process was controlled by diffusion through the surface product layer.The activation energy of this process was found to be22kJ/mol.A kinetic study was performed by Yartas¸ıand C opur[12]on the dissolution of malachite in ammonium chloride solutions.This study also showed that the leaching rate was controlled by diffusion through the product layer.Ekmekyapar et al.[7]investigated the dissolution kinetics of malachite in ammonium chloride solutions.They determined that the leaching rate was controlled by the mixed kinetic model.A semiempirical mathematical model was also suggested to represent the reaction kinetics.The activa-tion energy for the malachite leaching reaction was calculated to be71kJ/mol.A study was performed by Arzutug et al.[2]with water saturated by ammonia gas chosen as lixiviant.They determined that the leaching rate of malachite in ammonia-saturated water increased with decreasing particle size and solid-to-liquid ratio and increasing reaction temperature,ammonia concen-tration,and agitation speed.The rate of dissolutionfit a homogeneous pseudo–second-order kinetic model with activation energy of85kJ/mol.The dissolution kinetics of malachite in ammonia/ammonium carbonate solu-tions was examined by Bingo l et al.[13]In this study,the effects of leaching time,ammonium hydroxide,and ammonium carbonate concentration,solution pH, ammonia/ammonium ratio,agitation speed,solid-to-liquid ratio,particle size,and reaction temperature on the dissolution of malachite were investigated.They found that the leaching process was controlled by the interface transfer and diffusion across the product layer. Recently,Lui et al.[14]investigated the dissolution kinet-ics of low-grade complex copper ore,composed of mainly malachite,chrysocolla,and bornite,in ammonia–ammonium chloride solutions.In this study,the effects of various parameters on the dissolution of copper ore were examined,and it was determined that the leaching process was controlled by diffusion through the surface product layer around the shrinking unreacted core. The use of ammoniacal systems in the leaching of ores mostly seems to be feasible chemically.Ammonium nitrate was chosen as lixiviant in the current study,and the leaching and kinetics of malachite were investigated in detail.The use of ammonium nitrate solutions has some advantages over other ammoniacal systems.One of the most important characteristics of leaching in ammonium nitrate solutions is that the pH is essentially constant during the leaching process.In addition, ammonium nitrate provides ammonium ions,which contributes the hydronium ions required for the disso-lution of the ore.Ammonia produced by a reaction with the ammonium ion forms stable complexes with Cu2+ ions,which leads to an increase in the dissolution rate of the copper minerals.Because ammonium nitrate solu-tions have mildly acidic character(pH5.1to5.5,in the current study),ferric ions(Fe3+)passing into the solution during the leaching process precipitate in the form of Fe(OH)3.Thus,a high-purity solution can be obtained.The aim of this study is to investigate and discuss the leaching kinetics and dissolution parameters of mala-chite in ammonium nitrate solutions.II.MATERIALS AND METHODSAn oxidized copper ore sample(malachite)used in this study was provided from the mine in Ovacık, Tunceli,Turkey.The ore sample was crushed,ground, and then sieved using standard test sieves to obtain desired particle size fractions.The mineralogical analysis of the ore sample was performed using a Rigaku RadB-DMAX II model X-ray diffractometer(Rigaku Corpo-ration,The Woodlands,TX).The result of the X-ray analysis given in Figure1indicates that the sample contains mainly malachite(CuCO3Cu(OH)2),quartz (SiO2),and smithsonite(ZnCO3).Malachite mineral in the ore matrix has a monoclinic crystal structure.The chemical analysis result of the sample is given in Table I. The leaching experiments were carried out in a750-mL cylindrical glass reactor equipped with a mechanical agitator,a reaction temperature control unit,and a condenser to avoid loss of solution from evaporation. The experimental procedure was initiated by adding 500mL of an ammonium nitrate solution into the glass reactor and bringing it to the desired reaction temper-ature.A given amount of solid sample was then added to the solution.The dissolution process was carried out for various reaction times.Aliquots of5mL were withdrawn at regular intervals during the reaction and were immediatelyfiltered.The amount of dissolved copper in the solution was determined complexometri-cally using ethylenediaminetetraacetic acid solutionas Fig.1—X-ray diffraction pattern for oxidized copper(malachite)ore used in the study.titrant and murexide as indicator.The conversion fraction of malachite was calculated as follows:x=mass of copper passing to the solution/mass of copper in the ore sample.The leaching rate of malachite was determined as a function of time by changing the ammonium nitrate concentration,particle size,agitation speed,and reac-tion temperature.In the experiments,while the effect of one parameter was investigated,the values of other parameters shown with an asterisk in Table II were kept constant.The leaching data obtained were plotted as a function of conversion fraction x vs reaction time t.III.RESULTS AND DISCUSSIONA.Leaching ReactionsAmmonium nitrate is the salt of a strong acid(HNO3) and a weak base(NH3),and it has a weakly acidic character.Ammonium nitrate ionizes in aqueous medium according to the following reaction:NH4NO3!NHþ4þNOÀ3½1 The ammonium ion is hydrolyzedNHþ4þH2O)NH3þH3Oþ½2 Ammonia and hydronium ion formed by the hydrolysis reaction play an important role in the leaching process. The ammonium ion provides the protons(hydronium ion)required for the dissolution of basic malachite ore, whereas the ammonia produced forms stable complexes with copper(II)ions passing dissolved from the ore.The formation of these complexes leads an increase in the leaching rate of malachite ore.The copper in the malachite ore is in the form of CuCO3Cu(OH)2.When malachite ore is added into ammonium nitrate solution,the reactions occurring during the leaching process are expected to beCuCO3Cu OHðÞ2þ2H3Oþ!Cu2þþCO2þ3H2OþCu OHðÞ2½3Cu OHðÞ2þ2H3Oþ!Cu2þþ4H2O½4 Copper ions passing into the solution form copperamine complexes with ammonia,and thus,no precipi-tation of copper occurs from the solution.The forma-tion reactions of the copper amine complexes arewritten as follows:Cu2þþ2NH3)Cu NH3ðÞ2þ2½5Cu NH3ðÞ2þ2þ2NH3)Cu NH3ðÞ2þ4½6 It is reported that the Cu(NH3)22+formed during theleaching reaction is an intermediate species,and itconverts to the stable complex of Cu(NH3)42+.[2,7]Consequently,the overall leaching reaction can bewritten as follows:CuCO3Cu OHðÞ2þ4NH4NO3!2Cu2þþ4NH3þ4NOÀ3þCO2þ3H2O½7B.Effects of Ammonium Nitrate ConcentrationTo investigate the effect of ammonium nitrate con-centration on the leaching rate,the experiments werecarried out using from2to5mol/L of ammoniumnitrate.In these experiments,the reaction temperature,solid-to-liquid ratio,particle size,and agitation speedwere kept at313K(40°C),2g solid/0.5L solution,62.4l m,and400rpm,respectively.The results obtainedfrom these experiments were plotted in Figure2.Thisfigure shows that the leaching rate increases with anincrease in lixiviant concentration.After150minutes ofleaching,the copper extraction from the ore was62.9pct,70.6pct,82.3pct,and87.8pct at2,3,4,and5mol/L ofconcentration,respectively.It is clear from these resultsthat the extents of copper extraction from the oreincreased with increasing lixiviant concentration.C.Effect of Particle SizeThe effect of particle size on the leaching of copperfrom the malachite ore was examined by using fractionsof the ore with average particle size of136,120,93,71.5,and62.4l m.In these experiments,the values of otherparameters were kept constant at4mol/L,313K(40°C),2g solid/0.5L solution,and400rpm.Figure3shows the effect of particle size on the leaching rate.Itcan be observed from thisfigure that the dissolution rateincreases with decreasing particle size.D.Effect of Stirring SpeedThe effect of the agitation speed on the leaching of themalachite ore was studied by testing agitation speeds ofTable I.Chemical Analysis of Malachite Ore Used in the StudyComponent SiO2ZnO CuO Fe2O3Al2O3Ignition LossOther Oxides (Na,Ca,K,Mg,Oxides)Value,pct50.4115.2310.558.43 1.8112.40 1.17 Table II.Leaching Parameters and the Ranges Used in theLeaching ExperimentsParameter ValueConcentration(mol/L)2,3,4*,5Temperature[K(°C)]303(30),313(40)*,323(50),333(60),343(70)Agitation speed(rpm)200,300,400*,500Average particle size(l m)136,120,93,71.5,62.4**These parameters were kept constant.200,300,400,and 500rpm while the values of the solution concentration,reaction temperature,solid-to-liquid ratio,and particle size were kept constant at 4mol/L,313K (40°C),2g solid/0.5L solution,and 62.4l m,respectively.The results are given in Figure 4.After 150minutes of leaching,the extent of leaching of copper from the ore increased from 72pct to 89.8pct when the agitation speed increased from 200to 500rpm.The experimental findings indicate that the agitation speed is a major factor in the leaching of the malachite ore.E.Effect of Reaction TemperatureTo determine the effect of the reaction temperature on copper extraction from the malachite ore,the experi-ments were carried out at five different temperatures in the range of 303K to 343K (30°C to 70°C).While conducting these experiments,the values of other experimental parameters were kept constant at 4mol/L,2g solid/0.5L solution,62.4l m,and 400rpm.From the results plotted in Figure 5,the leaching rate increases considerably with higher reaction tempera-tures.The reaction temperature has a significant effect on the extent of copper extraction from malachite ore.At a temperature of 303K (30°C),55pct of copper was extracted after 150minutes of leaching,whereas at a temperature of 343K (70°C),98pct of copper was extracted only after 75minutes of leaching.F.Kinetic StudyIncreasing attention is being paid to the study of the chemical kinetics of nonhomogeneous systems.In the classic homogeneous systems,the usual rate laws of first-and second-order kinetics are often sufficient to explain and analyze the experimental data.[15]Leaching is a central unit operation in the hydrometallurgical treatment of ores,and the reactions occurring during the leaching process are typically heterogeneous.Thus,leaching reactions do not often obey simple first-and second-order kinetics.A kinetic analysis of these kinds of reactions is generally performed by noncatalytic heterogeneous reaction models.A kinetic analysis of leaching reactions is required for the effective design of leaching reactors for use in a hydrometallurgical plant.[15,16]The leaching reaction of mineral particles by a reagent (a solid–fluid reaction)can be represented by the followingreaction:Fig.2—Effect of ammonium nitrate concentration on leaching of malachiteore.Fig.3—Effect of particle size on leaching of malachiteore.Fig.4—Effect of agitation speed on leaching of malachite ore.A fluidðÞþbBðsolidÞ!fluid and=or solid products½8 where A,B,and b represent thefluid reactant,the solid undergoing leaching,and stoichiometric coefficient, respectively.The kinetic of leaching reactions is often described by the shrinking core model.According to the shrinking core model,it is thought that the reaction between solid andfluid reactants takes place on the outer surface of solid.The solid reactant is initially surrounded by afluidfilm through which mass transfer occurs between the solid and the bulkfluid.As the reaction proceeds,the unreacted core of the solid shrinks toward the center of the solid,and a porous product layer forms around the unreacted core.However,it is assumed that the initial outside radius of the solid does not change while the leaching reaction continues.[5,17–19]The leaching rate of solid is governed by physical and chemical factors.The governing factors are the rate of transport offluid reactant to and products from the particle surface(i.e.,diffusion through thefluidfilm),the rate of diffusion offluid reactant and products through the porous product layer that forms on the unreacted core of solid(i.e.,diffusion through the product layer), and the rate of the reaction at the surface of unreacted core(i.e.,surface chemical reaction).Each of these phenomena affects the rate of the overall leaching reaction.One or more of these factors might control the rate of reaction.[16]For each step mentioned,the integrated rate equations derived from the shrinking core model are given in the literature.[17,18,20]These rate equations can be written as follows:If the leaching rate is controlled by the diffusion through the liquidfilm,then the integrated rate equation isx¼k l t½9 If the reaction rate is controlled by the diffusion through the ash or product layer,then the integrated rate expression is1À3ð1ÀxÞ2=3þ2ð1ÀxÞ¼k d t½10 If the leaching rate is controlled by the surface chemical reaction,then the integrated rate equation is1Àð1ÀxÞ1=3¼k r t½11 where x is the conversion fraction of solid particle,k l is the apparent rate constant for diffusion through the fluidfilm,k d is the apparent rate constant for diffusion through the product layer,k r is the apparent rate constant for the surface chemical reaction,and t is the reaction time.To determine the kinetic parameters and rate-control-ling step of the leaching of malachite in ammonium nitrate solutions,the data obtained in the leaching experiments were analyzed based on the shrinking core model using the rate expression given in Eqs.[9]through [11].By applying the rate expression in Eqs.[9]through [11]to the experimental data obtained,the apparent rate constants were calculated.To obtain the apparent rate constants of each step,the left side of Eqs.[9]through [11]was plotted vs the reaction time for each parameter, and the slopes of the straight lines passing through the origin were equalling the rate constants.For each experimental parameter,the apparent rate constant values obtained from the plots and the correlation coefficients are provided in Table III.As can be observed from the data in Table III,the low regression coefficients were obtained for thefilm diffusion and the chemical reaction models,indicating that neither of these pro-cesses represent the rate-controlling step.From Table III, the largest regression coefficients were obtained for the diffusion through the product layer model,indicating that the diffusion through the product layer acts as the rate-controlling step in this leaching system.This obser-vation is supported by the experimental observations and findings as shown in Figure6,which is plot of1–3(1–x)2/3+2(1–x)vs time for different particle sizes. However,if the leaching reaction is controlled by diffusion through the product layer,then the leaching rate should not be sensitive to the reaction temperature. However,as shown in Figure5,the leaching reaction of malachite was quite sensitive to temperature.Therefore, to define the rate-determining step of this process,the mixed kinetic models were tested using the experimental data.These kinds of kinetic models have been described in the literature.[7,13,17,21,22]Among the mixed kinetic models tested,it was found that the following model could be more suitable to represent the kinetics of the dissolution of malachite in ammonium nitrate solutions.1À2ð1ÀxÞ1=3þð1ÀxÞ2=3¼k m t½12 where k m is the apparent rate constant for the mixed kinetic model.To test the validity of the model in Eq.[12],the left side of Eq.[12]vs time was plotted for thesolution Fig.5—Effect of reaction temperature on leaching of malachite ore.concentration,agitation speed,particle size,and tem-perature.The graphs obtained are given in Figures 7through 10.The apparent rate constants calculated from the slopes of the straight lines in Figures 7through 10and their correlation coefficients are given in Table IV .From the results shown in Figures 7through 10and in Table IV demonstrate that the kinetic model in Eq.[12]is appropriate to explain this leaching process.To determine the effects of the reaction parameters on the reaction rate constant,the following mathematical model can be suggested:k m ¼k o :C ðÞc :PS ðÞp :SS ðÞr :exp ÀE a =R T ðÞ½13where C ,PS ,SS ,E a ,R,and T represent the concen-tration,particle size,stirring speed,activation energy,Table III.The Apparent Rate Constants,k l ,k r ,and k d for Kinetic Models and Correlation Coefficient Values ParameterDiffusion Through theLiquid FilmXSurface Chemical Reaction1–(1–x )1/3Diffusion Through theProduct Layer1–3(1–x )2/3+2(1–x )k l (min À1)R 2k r (min À1)R 2k d (min À1)R 2Concentration (mol/L)20.00500.6270.00210.7880.00130.99630.00570.5760.00250.7860.00170.99640.00670.5720.00320.8340.00260.99850.00740.4220.00380.7900.00340.990Temperature [K (°C)]303(30)0.00430.7220.00170.8400.00090.995313(40)0.00670.5720.00320.8340.00260.998323(50)0.00930.3900.00560.8730.00570.992333(60)0.01200.3320.00730.8510.00760.986343(70)0.01670.2850.01030.8270.01070.980Stirring speed (rpm)2000.00580.6300.00260.8200.00170.9973000.00620.5750.00290.8000.00210.9914000.00670.5720.00320.8340.00260.9985000.00730.4730.00380.8170.00380.993Particle size (l m)1360.00490.7520.00210.8740.00120.9961200.00530.6940.00230.8470.00140.99793.00.00570.0570.00250.8600.00170.99771.50.00620.6520.00290.8500.00210.99862.40.00670.5720.00320.8340.00260.998Fig.6—Plot of 1–3(1–x )2/3+2(1–x )vs time for different particlesizes.Fig.7—Plot of 1–2(1–x )1/3+(1–x )2/3vs t for different lixiviant concentrations.universal gas constant,and temperature,respectively.The constants c,p,and r are the reaction order for relating parameters,and k o is the frequency or preex-ponential factor.Combining Eqs.[12]and [13],the following equation is obtained:1À21Àx ðÞ1=3þ1Àx ðÞ2=3¼k o :C ðÞc :PS ðÞp :SS ðÞr :exp ÀE a =R T ðÞ:t½14The constants c,p,and r were estimated from the apparent rate constant values given in Table IV .The plots of ln(k m )vs ln(C ),ln(k m )vs ln(PS ),and ln(k m )vs ln(SS )were constructed using the values given in Table IV for each parameter.The slopes of the straight lines in the graphs obtained assign the reaction order for each parameter.The values of the constants c,p,and r were determined to be 0.80,–1.04,and 1.02,respectively.The activation energy of this leaching process was estimated from the Arrhenius equation.The Arrhenius plot of the reaction is shown in Figure 11.As can be observed from this figure,two straight lines were obtained.This situation indicates that the leaching reaction is controlled by two different leaching processes.A shift in the activation energy at 323K (50°C)is probably a result of the change in the reaction mech-anism.The lines in Figure 11show the variations between 303K to 323K (30°C to 50°C)the first zone (surface reaction)and 323K to 343K (50°C to 70°C)the second zone (product layer diffusion).At tempera-tures below 323K (50°C)(i.e.,the first zone),the activation energy and the preexponential factor were calculated to be 95.10kJ/mol and 7.799109s À1,respectively.At temperatures above 323K (50°C)(i.e.,the second zone),these values were determined to be 29.50kJ/mol and 5.3s À1,respectively.In the literature,it is stated that the diffusion controlled heterogeneous reactions are slightly depen-dent on temperature,while chemically controlled pro-cesses are strongly dependent on temperature.The activation energy of a diffusion controlled process is usually below 40kJ/mol,while for a chemically con-trolled reaction this value is usually greater than 40kJ/mol.[23,24]Therefore,the value of the activationenergyFig.8—Plot of 1–2(1–x )1/3+(1–x )2/3vs t for different particlesizes.Fig.9—Plot of 1–2(1–x )1/3+(1–x )2/3vs t for different agitationspeeds.Fig.10—Plot of 1–2(1–x )1/3+(1–x )2/3vs t for different temper-atures.of a leaching reaction may be used to predict the rate controlling step of the process.According to the activation energies values determined in this study,the rate of process is controlled by the surface chemical reaction in the first zone (i.e.,less than 323K [50°C])and by the diffusion through the product layer in the second zone (i.e.,greater than 323K [50°C]).As aresult,the kinetic expressions including the reaction parameters used in this leaching process can be written for the two regions as follows:1À21Àx ðÞ1=3þ1Àx ðÞ2=3¼7:79Â109C ðÞ0:80PS ðÞÀ1:04SS ðÞ1:02exp 11438=T ðÞ:t½15(for 303K to 323K [30°C to 50°C])1À21Àx ðÞ1=3þ1Àx ðÞ2=3¼5:3C ðÞ0:80PS ðÞÀ1:04SS ðÞ1:02exp 3558=T ðÞ:t ½16(for 323K to 343K (50°C to 70°C))G.Analysis of Leach ResidueTo determine the mineralogy of dissolved malachite ore,the X-ray diffraction (XRD)analysis of the solid residue obtained after leaching process was performed.The result of XRD analysis relating to leach residue is given in Figure 12.It can be observed from Figure 12that the peaks of CuCO 3Cu(OH)2(malachite)and ZnCO 3(smithsonite)disappear while quartz and Fe remain in the leach residue.This result shows that malachite ore can be leached by using ammonium nitrate solutions.The resulting leach solution contains copper and zinc amine complexes.IV.CONCLUSIONSIn this study,the leaching kinetics of malachite ore was studied using ammonium nitrate solutions as the lixiviant.The effects of several experimental parametersTable IV.The Apparent Rate Constant,k m ,for MixedKinetic Model and Correlation Coefficient ValuesParameterMixed Kinetic Model 1–2(1–x )1/3+(1–x )2/3k m (min À1)R 2Concentration (mol/L)20.00050.99830.00080.99840.00110.99750.00160.999Temperature (K (°C))303(30)0.00030.992313(40)0.00110.997323(50)0.00310.994333(60)0.00410.996343(70)0.00590.998Stirring speed,rpm 2000.00060.9973000.00090.9974000.00110.9975000.00150.999Particle size,l m 1360.00050.9921200.00060.99593.00.00070.99771.50.00090.99862.40.00110.997Fig.11—Arrhenius plot for leachingprocess.Fig.12—X-ray diffraction pattern of the solid residue resulting from leaching of malachite ore.。