dissolution kinetics of metallic copper with cuso4–nacl–hcl

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    Dissolution kinetics of metallic copper with CuSO4 –NaCl–HCl

    Osvaldo Herrerosa,T, Roberto Quiroza , Ambrosio Restovic b, Joan Viñalsc

    a  Departamento Ingenierı́a Minas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile b Departamento de Quı́mica, Universidad de Antofagasta, Chile

    c Departamento de Ingenierı́a Quı́mica y Metalurgia, Universidad de Barcelona, Spain

    Received 4 May 2004; received in revised form 10 November 2004; accepted 21 November 2004

    Abstract

    A study was made on the dissolution kinetics of metallic copper flat packs using solutions of Cu(II) in a chloride medium

    which was obtained via reaction between copper sulfate and sodium chloride. The effect of stirring, chloride and Cu(II)

    concentrations, distribution of Cu(II) chlorocomplexes and temperature were investigated.

    The leaching data showed the reaction to be under chemical kinetics control, with an activation energy of 28 kJ/mol (7 kcal/ 

    mol). Leaching occurred at an apparent order of  1 with respect to the total chloride concentration and an apparent first order with respect to the total copper concentration. The Cu(II) ion was the main active species based on calculation of copper species

    distribution and the solution kinetics may be interpreted as rate= k [Cu

    2+

    ]. For ratios of  C Cl/ C Cu2+

    of less than about 8, a layer of CuCl(s)   formed which impeded the solubilization process.

    D  2005 Elsevier B.V. All rights reserved.

     Keywords:  Copper; Leaching; Chlorides; Chlorocomplexes

    1. Introduction

    Processes for the leaching of metallic copper in

    chloride media have been based primarily on the

    action of cupric copper in the presence of sodium

    chloride. Important references on this topic include

    the studies of  Lin et al. (1992) and Tolley et al. (1977),

    which report on the thermodynamics of the equili-

     brium involved as well as on kinetic data in the Cu/ 

    Cl system. Lin et al. report a copper leaching rate

    consistent with the following expression:

    rate ¼  k   Cu2þ 1=2

    Cl½ 2 ð1Þ

    The order of this in reference to [Cu2+] is 0.5, which is

    in agreement with that reported by   Tolley et al.

    (1977), who leached copper beads with CuCl2   in a

    stirred reactor.

    The study carried out by   Herreros et al. (1999)

    on the dissolution of copper flat packs by aqueous

    Cl2/Cl media (0.5102 –1.9102 M Cl2, 0.5–1.4

    M Cltot ), reported that the most significant effects

    0304-386X/$ - see front matter  D   2005 Elsevier B.V. All rights reserved.

    doi:10.1016/j.hydromet.2004.11.010

    T  Corresponding author.

     E-mail address:   [email protected] (O. Herreros).

    Hydrometallurgy 77 (2005) 183–190

    www.elsevier.com/locate/hydromet 

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    were those related to the concentrations of chlorine

    and chloride, and that the aqueous chlorine was the

    reagent that made possible the dissolution of the

    copper, with chloride contributing a negative effect.

    The chloride inhibited the dissolution, probably due

    to the formation of a superficial layer of CuCl.

    When working with excess chlorine, however, the

    dissolution of this solid CuCl was increased. In this

    case the kinetic control was affected by the transfer 

    of mass in the film, with activation energy of 18 kJ/ 

    mol (4.3 kcal/mol). The apparent order of reaction

    with respect to chlorine was 1.0 and   0.17 for thechloride.

    On the other hand, the literature describes a process

    for copper recovery from bronze scrap in which

    leaching is obtained using 0.28 M CuCl2  and 4.8 M

     NaCl at a temperature of 75   8C (Langer et al., 1977).

    The CLEAR process, dating from the 1970s (Copper 

    Leach, Electrolysis and Regeneration) also uses cupric

    chloride together with a solution of 4.4 M NaCl and 2.4

    M KCl, although in this case, the objective was the

    leaching of chalcopyrite (Atwood and Livingston,

    1980).In contrast with results from the preceding brief 

    literature review, the objective of the present research

    was to study the dissolution of metallic copper with

    cupric chlorocomplexes generated in situ by reacting

    copper sulfate with sodium chloride in a hydro-

    chloric acid medium, and then determining if the

    CuCl+ complex is the main active species in the

    leaching of the metallic copper by having a

    sufficiently oxidative potential for obtaining the

    solubilization. This kinetic study may be applicable

    in the leaching of copper precipitates, which in Chile

    have varying degrees of surface oxidation, as well as

    in treatment of discarded cathodes from the electro-

    winning process.

    Our study determined the effects of the stirring,

    temperature, as well as the concentrations of total

    Cu(II), total chloride, and copper chlorocomplexes for 

     postulating the possible controlling stage or stages of 

    the dissolution, and modeling a kinetic expression for 

    the leaching rate.

    1.1. Criteria for the application of kinetic models

    It is broadly recognized in the literature that in the

    case of dissolution of pure species without formation

    of insoluble products in surface layers, the only

    controlling steps can be the mass transfer through

    the fluid film and the specific chemical reaction

    (Levenspiel, 1979; Sohn and Wadsworth, 1986). In

    the case of leaching of Cu with Cu(II) in a Cl

    medium, competition may exist between a   bsolid Q 

    intermediate formed on the surface of the metallic

    copper, probably CuCl, which would tend to dissolve,whereupon the leaching reagent would advance to the

    reaction surface.

    A diagram of the possible steps is presented as Fig.

    1. The reactions of this process would be

    Cu þ Cu2þ þ 2Cl ¼ 2CuClðsÞ   ð2Þ

    Cu þ CuClþ þ Cl ¼ 2CuClðsÞ   ð3Þ

    2CuClðsÞ þ 2Cl ¼ 2CuCl2   ð4Þ

    Cu + CuCl+ + Cl- CuCl+ 

    Cu2+

    Cu + Cu2+ + 2Cl-   2 CuCl

    CuCl + Cl- CuCl2- 

    Cu0 CuCl Cu2+ orCuCl+ 

    2 CuCl

    Fig. 1. Scheme of the possible steps in the leaching of metallic copper with Cu(II) in chloride media.

    O. Herreros et al. / Hydrometallurgy 77 (2005) 183–190184

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    The overall reaction from combining Eqs. 3 and 4 is:

    Cu þ CuClþ þ 3Cl ¼ 2CuCl2   ð5Þ

    Following data from tables of standar d potentials

    (Software HSC Chemistry; Duby, 1977), the equili-

     brium of Cu(II)–Cu(I) in chloride solutions is shown as

    Cu2þ þ Cl þ e ¼ CuCl   E 0 ¼ 0:538V   ð6Þ

    and the Cu(I)–Cu(0) reduction as:

    CuCl þ e ¼ Cu  þ Cl  E 0 ¼ 0:137V   ð7Þ

    Using these data, the solution of copper by cupric

    chloride may be written as:

    Cu þ Cu2þ þ 2Cl ¼ 2CuCl   ð8Þ

    Reaction (8) has   E cel=0.401 V and free energy of 

    formation=38.7 kJ/mol (9.25 kcal/mol).The cuprous chloride is only slightly soluble under 

    these standard conditions, but its solubility increases

    with increase in the chloride concentration due to the

    successive formation of CuCl2 and CuCl3

    2 ion

    complexes. Also, the solubility increases with temper-

    ature (Jackson, 1986).

    1.2. Kinetic model utilized 

    The geometry of the particles used to carry out the

     present leaching experiments was of small flat-packs,

    and the conversion model used is described below

    (Levenspiel, 1979; Sohn and Wadsworth, 1986):

    a ¼  2bk r 

    qBe0C AO½

    nt    ð9Þ

    or also

    a ¼  k expt    ð10Þ

    and

    k exp  ¼  2bk r 

    qBe0C AO½

    n ð11Þ

    where   a=fraction reacted,   k exp=experimental rate

    constant (min1),   t =time (min),   b=stoichiometric

    factor (mol solid dissolved/mol leaching reagent),

    qB=molar density of solid (mol solid dm3), [C AO]=

    molar concentration of leaching species in the bulk 

    solution,   n=reaction order,   k r =rate constant (cm

    min1, for  n=1) and   e0=flat pack thickness (cm).

    1.3. Distribution of chloride species

    When chloride ion and cupric ion share an aqueous

    system, the composition of the result ing solution   is

    governed by the following equilibria (Duby, 1977):

    Cu2þ þ Cl ¼ CuClþ  K 1  ¼  100:46 ð12Þ

    CuClþ þ Cl ¼ CuCl2 Aqð Þ   K 2  ¼  100:27 ð13Þ

    CuCl2 Aqð Þ þ Cl ¼ CuCl3   K 3  ¼  10

    2:48 ð14Þ

    CuCl3   þ Cl ¼ CuCl24   K 4  ¼  10

    2:30 ð15Þ

    For determination of the different species of the

    copper chlorocomplexes in the initial solution, the

    following material balance is used:

    C Cl  ¼   Cl½ þ   CuClþ½ þ 2 CuCl2 Aqð Þ

     þ 3 CuCl3

    þ 4 CuCl24

      ð16Þ

    and

    C Cl  ¼  C  NaCl þ C HCl   ð17Þ

    C Cu  ¼   Cu2þ

     þ   CuClþ½ þ   CuCl2 Aqð Þ

     þ   CuCl3

    þ   CuCl24

      ð18Þ

    where   C Cl   ,   C  NaCl,   C HCl   and   C Cu   are total concen-

    trations (mol/L), and [i] are concentrations of the

    different species. If   C Cl   and   C Cu   are known, the

    concentrations of the remaining species are defined if 

    it is assumed that the activity coefficients are near unity.

    According to values for the formation of chlor-

    ocomplexes, the predominant species in this Cu2+/Cl

    system are Cu2+, CuCl+ and CuCl2(Aq).

    2. Materials and experimental procedure

    2.1. Materials

    Metallic copper of about 99.99% purity was used in

    all experimentation. Copper flat packs of about 11mm and 0.105 mm in thickness cut from electrolytic

    copper sheets were used in the kinetic experiments. The

    O. Herreros et al. / Hydrometallurgy 77 (2005) 183–190   185

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    reagents, copper sulfate pentahydrate, sodium chloride

    and hydrochloric acid, were of analytical grade.

    2.2. Reactor 

    A conventional leaching apparatus was used,

    consisting of a 1200-cm3 triple-neck spherical glass

    reactor submerged in a thermostatic bath, and fitted

    with motor-driven stirring using a Teflon-coated

    agitator (propeller of 5 cm diameter). The solution

     potential was continuously measured with a platinum

    electrode and a AgCl/Ag (KClsat ) reference electrode,

    connected to a high impedance potentiometer. Tem-

     perature was also continuously monitored and the

     progress of reaction, copper concentrations and the pH were measured by removing samples for measure-

    ment at specified times. The reactor was operated

    under closed conditions.

    2.3. Leaching reagent 

    The experiments were designed so that the

    concentration of both the total chloride as well as

    total cupric ion could be determined initially.

    The solutions used in each experiment were

    obtained by the following methods: a given volume

    of distilled water was placed in the reactor, followed

     by given masses of copper sulfate pentahydrate and

    sodium chloride, and the pH was adjusted with

    concentrated HCl to the desired value. The system

    was then made up to 1000 cm3, and the initial

    concentration of copper and pH were determined.

    The kinetic experiments were initiated once the

    solution was prepared. Here 2 g of copper flat packs

    was added at  t =0, and the progress of the leaching was

    determined by taking 5-ml samples of the liquid for 

    copper analysis using atomic absorption spectrometry

    (AA). Selected samples of attacked copper in the dif-ferent conditions were examined by SEM/EDS in order 

    to detect possible layers of solid reaction products.

    3. Results and discussion

    3.1. Effect of stirring 

    The effect of stirring on the dissolution kinetics of 

    the copper flat packs was carried out fixing the initial

    concentration of   C Cu   at 1.38101 (M),   C Cl   at 

    1.43 (M) and temperature of 24   8C. Under these

    experimental conditions and according to the dis-

    tribution of species (Eqs. (13)–(19)), it was foundthat [Cl]=1.3 M, [Cu2+ ]=0.019 M, [CuCl+]=0.070

    M, [CuCl2]=0.049 M, [CuCl3]=2.1 104 M and

    [CuCl4]=1.4 106 M.

    The experiment al results are presented graphi-

    cally in   Fig. 2. In   Fig. 2   it is seen that the fraction

    reacted,   a, increases as the stirring increases,

     becoming essentially constant at stirrings above

    350 rpm, which ensure full particle suspension.

    This suggests that chemical or electrochemical

    reaction control dominates at high agitations levels.

     No formation of CuCl(s)   was observed in this set of experiments.

    3.2. Effect of total copper concentration

    Leaching experiments were carried out by varying

    the initial copper concentration in the system to

    determine the effect produced by this reactant on the

    dissolution kinetics of the copper flat packs in order to

    subsequently determine the apparent order of reaction

    (350 rpm, 24   8C,   C Cl=1.43 M). The calculated

    distribution of species for these experimental con-

    ditions is shown in Table 1.

    Fig. 3   presents the experimental leaching results

    in graphical form.   Fig. 3   shows that the exper-

    imental data fit the flat packs model well for up to

    15–20 min of leaching. By linear regression of   a

    0.1 

    0.2 

    0.3 0.4 

    0.5 

    0.6 

    0.7 

    0 20 40 60 80

    Time (min)

       F  r  a  c   t   i  o  n  r  e  a  c   t  e   d

    180 rpm 300 rpm

    350 rpm 400 rpm

    Fig. 2. Dissolution of copper flat packs over time as a function of 

    the stirring speed (24   8C,  C Cu=1.38101 M,  C Cl=1.43 M).

    O. Herreros et al. / Hydrometallurgy 77 (2005) 183–190186

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    vs.   t , the   experimental rate constant,   k exp, is

    obtained.   Fig. 4   illustrates the rate constant in

    relation to the total copper concentration, Cu2+,

    CuCl+ and CuCl2. It can be seen that the reaction

    rate increases in proportion to the total copper concentration. However, when the concentration of 

    chloride is maintained constant, an increase in the

    total copper concentration brings an almost propor-

    tional increase in concentrations of the various Cu

    species present. At this stage, the active species

    responsible for the dissolution of the copper cannot 

     be clearly resolved from this effect.

    3.3. Effect of total chloride concentration

    Leaching experiments were carried out varying the

    initial chloride concentration of the system to deter-mine the effect produced by this reactant on the

    dissolution kinetics of copper flat packs and to

    determine the apparent order of reaction (350 rpm,

    24   8C,   C Cu=3.39102 M).The calculated distribu-

    tion of species f or these experimental conditions is

    shown in Table 2.

    The experimental r esults of  the leaching are shown

    in graphic form in   Fig. 5.   Fig. 5   shows that the

    experimental leaching data fit the flat-packs model

    well up to a time of 15–20 min. Over longer time

     periods, lowering of the total Cu2+ concentration, as

    consequence of the reaction progress, produces

    curvature of the plots. No formation of a CuCl layer 

    was observed in this set of experiments. The experi-

    ment rate constant (k exp ) was obtained by considering

    only the straight portion of the curve of linear 

    regression of   a   vs.   t .

    Fig. 6   shows the dependence of   k exp   on the

    concentrations of Cl and   C Cl. The apparent order 

    of the reaction for both   C Cl   and free chloride was

    1.1, based on the linear regression data of   Fig. 6.This dependency may be due to the fact that the

    chloride ion shows a real (chemical or electro-

    chemical) order of about   1, although this order may only be apparent, i.e., increase in the chloride

    concentration may decrease the concentrations of 

    active oxidants.

    Table 1

    Calculated distribution of species as a function of the total copper 

    concentration

    Cl total(M)

    Cu total(M)

    Cl

    (M)Cu2+

    (M)CuCl+

    (M)CuCl2(M)

    1.43 0.0352 1.386 0.0044 0.0176 0.013

    1.43 0.0442 1.375 0.0056 0.0222 0.016

    1.43 0.0641 1.351 0.0083 0.0323 0.024

    1.43 0.0820 1.329 0.0108 0.0415 0.030

    0

    0.2

    0.4

    0.6

    0.8

    1

    0 4020 60 80

    Time (min)

       F  r  a  c   t   i  o  n  r  e  a

      c   t  e   d

    0.035 M 0.044 M 0.064 M 0.082 M

    Fig. 3. Fraction reacted vs. time, as a function of total copper 

    concentration (350 RPM, 24   8C,  C Cl=1.43M).

    0

    0.005

    0.01

    0.015

    0.02

    0.025

    0.03

    0.035

    0.04

    0.045

    0 0.040.02 0.06 0.08 0.1

    Copper species concentration (mole/L)

       K  e  x  p   (   1   /  m   i  n   )

    Cu tot Cu2+ CuCl+

    CuCl2

    Fig. 4. Dependence of the   k exp   on the concentrations of Cu2+,

    CuCl+, CuCl2  and  C Cu.(350 rpm, 24   8C,  C Cl=1.43 M).

    Table 2

    Calculated distribution of species as a function of total chloride

    Cl total

    (M)

    Cu total

    (M)

    Cl

    (M)

    Cu2+

    (M)

    CuCl+

    (M)

    CuCl2(M)

    0.56 0.034 0.53 0.0115 0.0175 0.0049

    0.74 0.034 0.71 0.0089 0.0182 0.0068

    0.91 0.034 0.87 0.0073 0.0182 0.0084

    1.43 0.034 1.39 0.0043 0.0171 0.0126

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    Fig. 7 shows the approximately proportional depend-

    ence of the rate constant on the calculated Cu2+

    concentration; the fact that the curve passes practi-

    cally through the origin strongly suggests that Cu2+

    may be the active species in the copper leaching.

    On the other hand, similar plots of rate constant 

    with respect to the calculated CuCl+ and CuCl2concentrations do not show significant correlation.

    Thus, the effect of chloride concentration on the

    leaching kinetics should be only apparent, sincevariation of [Cl] markedly varies the distribution of 

    calculated Cu(II) species. Among these, the only one

    that shows a significant effect is Cu2+, which propor-

    tionally increases the reaction rate. Increases in the

    concentrations of the other species do not lead to

    significant changes in the reaction rate which lead tothe conclusion that the Cu2+ is the main active species

    under these conditions. The rate for the investigated

    interval is:

    rate ¼  k   C Cu

    1 þ 100:46 Cl½ þ 100:46100:27 Cl½ 2  ð19Þ

    3.4. Effect of temperature

    Experimental results of the effect of temperature

    on the dissolution kinetics of copper flat packs are presented in   Fig. 8.   The experimental constants

     based on the data of   Fig. 8  were obtained by linear 

    regression. An Arrhenius plot is presented in  Fig. 9.

    An activation energy of 28 kJ/mol (aprox. 7 kcal/ 

    0

    0.05

    0.1

    0.15

    0.2

    0.250.3

    0.35

    0.4

    0.45

    0.5

    0 4020 60 80

    Time (min)

       F  r  a  c   t   i  o  n  r  e  a

      c   t  e   d

     0.56 M  0.74 M  0.91 M  1.43 M

    Fig. 5. Fraction reacted vs. time, as a function of  C Cl (350 rpm, 24

    8C,  C Cu  3.4102 M).

    1.8

    1.9

    2

    2.1

    2.2

    2.3

    2.4

    -0.2 -0.1 0 0.1 0.2 0.

    - log [i] (mole/L)

      -   l  o  g   K   (  m   i  n  -   1   )

     Cl total Cl-

    Fig. 6. Dependence of  k exp on the  C Cl and Cl concentrations (350

    rpm, 24   8C,  C Cu=3.4102 M).

    0

    0.002

    0.004

    0.0060.008

    0.01

    0.012

    0.014

    0.016

    0 0.0040.002 0.006 0.008 0.01 0.012

    Cu2+ concentration (M) 

       K  e  x  p   (   1   /  m   i  n   )

    Fig. 7. Dependence of   k exp   as a function of the calculated Cu2+

    concentration (350 rpm, 24   8C,  C Cu=3.39102 M).

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0 2010 30 40

    Time (min)

       F  r  a  c   t   i  o  n

      r  e  a  c   t  e   d

     

    9°C   15°C   24°C   37°C  47°C

    Fig. 8. Fraction reacted vs. time as a function of temperature: (350

    rpm,  C Cu  1.37101 M,  C Cl  1.43 M).

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    mol) was obtained, which is indicative of chemical

    or electrochemical reaction control.

    4. Surface study

    Copper surfaces attacked with different concen-

    trations of Cu(II) and chloride were studied by

    scanning electron microscopy (SEM) coupled by

    energy dispersive microanalysis (EDS). Samples

    were carbon coated. Observation was performed by

    secondary electron signal and EDS spectra were

    recorded at 20 kV. For ratios   C Cl/ C CuN8, no

    formation of CuCl(s)   on the copper was found.   Fig.

    10   is an example of corrosion texture observed for this concentration ratio.

    However, for ratios   C Cl/ C Cub8, formation of 

    CuCl(s)  was found on the surface.  Fig. 11   shows the

    surface of metallic copper attacked for 5 min by NaCl

    0.56M, HCl 0.06 M and total Cu of 0.08 M. Here, a

    continuous layer of tetrahedric crystals of CuCl is

    observed. The attack was rapid at 0.08 M Cu but the

    concentration of the Cl is not very high, and thus, the

    dissolution of the CuCl is slow in this case.  Fig. 12

    shows t he corresponding EDS spectrum of CuCl from

    Fig. 11.

    Based on the kinetics results, the species distribu-

    tion calculations and the surface studies, it is

    0

    1

    2

    3

    4

    5

    6

    7

    3 3.83.4 4.2

    1000/T (1/K)

      -   l  n   K  e  x  p

       (  m   i  n  -   1   )

    Fig. 9. Arrhenius plot of the experimental rate constants (350 rpm,

    C Cu  1.37101 M,  C Cl  1.43 M).

    Fig. 10. SEM image of metallic copper attacked by NaCl 1.43 M,

    HCl 0.06 M and total Cu of 0.034 M.

    Fig. 11. SEM image of metallic copper attacked by NaCl=0.56 M,

    HCl 0.06 M and total Cu of 0.08 M.

    X-RAY:Live:Real:

    0  –  20 keV

    keV 10.6 >

    15s Preset:  Remaining:20s

    85s25% Dead

    100s

    < .4 5.480FS= 1K 33 ctsch 284=MEM1:CL 0.62 CU 0.08 5MIN

    C

    C

    C

    C

    u

    u

    u

    l

    Fig. 12. EDS spectrum of the CuCl.

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    suggested that the dissolution of copper with Cu(II) in

    chloride media occurs in the following steps:

    CuðsÞ þ Cu2þ

    ðaqÞ ¼  2Cuþ

    ðadsÞ   ð20Þ

    CuþðadsÞ þ 2ClðaqÞ  ¼  CuCl

    2   ð21Þ

    With a high Cl/Cu(II) ratio, reaction (20) would be a

    slow and overall controlling process. In contrast, at 

    low Cl/Cu(II) ratios, reaction (21) would not occur,

    forming CuCl(s)   in accordance with:

    CuþðadsÞ þ ClðaqÞ  ¼  CuClðsÞ   ð22Þ

    inhibiting the reaction. If the chloride concentration

    reached zero, there would be no attack on the metalliccopper as experimentally shown when exposing the

    copper flat packs to solutions of Cu2+ in the absence

    of chloride. It is thus clear that chloride is necessary in

    the leaching process, although high concentrations of 

    the chloride decrease the reaction rate. Species

    distribution calculations suggest that this is due to

    decreasing the concentration of the active Cu2+

    species.

    5. Conclusions

    (1) The dissolution of metallic copper using solu-

    tions of Cu(II) in Cl media is relatively

    insensitive to stirring when the particles are well

    suspended. The activation energy of the process

    is 28 kJ/mol (7 kcal/mol) which suggests

    chemical-type control.

    (2) The leaching rate of copper has an apparent 

    order of   1 with respect to the total chlorideconcentration and an apparent order of unity (1)

    with respect to the copper concentration.

    (3) The correlation of rate constants with thecalculated distribution of copper species in

    solution indicates that the Cu(II) ion is the main

    active species. Within the interval studied, the

    equation for the rate is:

    rate ¼  k   C Cu

    1 þ 100:46 Cl½ þ 100:46100:27 Cl½ 2

    (4) For total chloride/total copper ratios of approx-

    imately less than 8, a layer of cuprous chloride is

    formed on the copper surface, which inhibits the

    leaching process.

    Acknowledgements

    The authors thank the National Fund for Scientific

    and Technological Research (FONDECYT) for sup-

     port of the present study (FONDECYT project no.

    1030046). The support of the   bServeis Cientı́fico-

    Tècnics de la Universitat de Barcelona Q  in the surface

    studies is also gratefully acknowledged.

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