Kinetics of the Dissolution of Copper(II) Oxychloride in Diluted

The calculated time dependence of the H+ ion concentration is presented in Figure 5 by a full line. One can notice an improved agreement between compu...
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Ind. Eng. Chem. Res. 1999, 38, 4277-4283

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Kinetics of the Dissolution of Copper(II) Oxychloride in Diluted Aqueous Hydrochloric Acid Solutions at Different Temperatures Andrej Lubej,‡ Tine Koloini,† and Ciril Pohar*,† Department of Chemistry and Chemical Technology, University of Ljubljana, Asˇ kercˇ eva 5, 1000 Ljubljana, Slovenia, and Cinkarna Celje, Metallurgical and Chemical Industry, Kidriceva 26, 3000 Celje, Slovenia

The dissolution kinetics of copper(II) oxychloride in a diluted hydrochloric acid solution at different temperatures was studied. The progress of the dissolution was followed by tracking changes of pH of the solution. The kinetic parameters of the early stage of a dissolution reaction, the Arrhenius pre-exponential factor and the activation energy, were estimated. The values were 6.7 × 106 mol m-2 s-1 and 71 ( 10 kJ/mol, respectively, indicating the surface-controlled kinetics. The model in which the rate of dissolution was determined by the distance of the system from equilibrium was used to interpret the dissolution process. An agreement between the experimental and the calculated values of the H+ ion concentration as a function of time was obtained. Introduction Copper(II) oxychloride, Cu2Cl(OH)3 [1332-65-6] or dicopper chloride trihydroxide (IUPAC), is a sparingly soluble compound which is most often used as a fungicide. Its fungicidal efficiency is a result of its ability to produce Cu2+ ions when the solid material comes in contact with water. It is very important that the rate of forming Cu2+ ions from the solid material is fast enough to ensure the mortal concentration of Cu2+ ions before the fungal growth runs out of control. On the other hand, copper oxychloride is often used as a copper compound from which other copper fungicides with special properties are made. For example, calcium tricopper(II) chloride trihydroxide (CaCl2‚3Cu(OH)2) is produced from a suspension of copper oxychloride and a lime. In this process, also of considerable industrial importance, the rate of the overall reaction may rely on the dissolution kinetics of copper(II) oxychloride particles. To our knowledge, no data about this subject has been published yet. Therefore, in the present work the dissolution kinetics of copper(II) oxychloride was studied both experimentally and theoretically. The dissolution of an electrolyte crystal in an aqueous solution takes place in two steps: a reaction at the crystal surface and transport of the dissolved matter away from the crystal through the surrounding liquid. The surface reaction involves disintegration of the crystal lattice, hydration of the ions, and entry into the liquid. Before entry into the liquid, ions may diffuse over a distance in an ion adsorption layer on the crystal surface. The transport from the interface region into the bulk solution may take place by diffusion and/or convection.1,2 In addition to these processes, the kinetics of dissolution of the copper(II) oxychloride in a dilute acid solution seems to be influenced also by the neutralization reaction of OH- with H+ ions somewhere within the Nernst film surrounding a particle. Previous Work. The majority of studies of dissolution kinetics have pertained to sparingly soluble materi* Corresponding author. Phone: +386611760595. Fax: +386611254458. E-mail: [email protected]. † University of Ljubljana. ‡ Metallurgical and Chemical Industry.

als. In the experiments, usually a suspension of a particulate material and a solvent have been stirred under controlled operational conditions (steering rate, P, T, and degree of undersaturation), and the change of a chemical composition of a bulk solution as a function of time has been measured.3 In a stationary experiment the flow rate of the titrant that needed to maintain a constant solution composition is measured.1,4 From such experimental data, combined with a presumed dissolution mechanism, the kinetic and mechanistic information about a dissolution process have been inferred. It was recognized that these methods exhibit several deficiencies and limitations, such as an absence of welldefined hydrodynamics and a lack of control over surface morphology. To overcome these problems, other methods with more defined experimental conditions have been developed. For example, the rotating disk method,5 and channel flow cell methods,6 allow dissolution reactions to be studied in a well-defined mass-transport regime. Techniques capable of probing dissolution kinetics on the atomic level, such as the in situ atomic force microscope method, and a SECM (scanning electrochemical microscope) method3,7 allow the study of spatially resolved dissolution kinetics under conditions of welldefined local mass transport. Objectives of This Study. For industrial purposes it is often valuable in the absence of the exact knowledge of dissolution kinetic parameters and the pertinent mechanisms of the dissolution process to have operational data for those quantities available. Such data could be obtained directly in the plant under not welldefined, but constant, operational experimental conditions. The present paper discusses the results of the dissolution experiments where a powder consisting of copper(II) oxychloride particles was introduced into a diluted solution of hydrogen ions at different temperatures and initial hydrogen ion concentrations. Specifically, the kinetic parameters are determined and a simple dissolution model was proposed and applied to simulate the course of the dissolution process at various experimental conditions. A satisfactory agreement between the experiment and calculation was obtained.

10.1021/ie990139m CCC: $18.00 © 1999 American Chemical Society Published on Web 10/07/1999

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because the glass electrode behaved dynamically as a first-order system with a time constant τ of 10 s, the readings of the pH meter were corrected for the dynamic error11 by the relation

pH(ti) ) pH′(ti) +

pH′(ti+1) - pH′(ti-1) τ ti+1 - ti-1

(2)

Change of the particles surface area, due to the dissolution process, was neglected because the estimated decrease of mass of the solid phase was smaller than 6%. Because the ionic strengths in our experiments were below 0.001 M (pH < 6 and Cu2+ ion concentration ) 10-4 mol/dm-3), we assumed that the ionic activities are equal to their molar concentrations. Theory

Figure 1. Crystal size distribution diagram of the sample.

Experimental Section Pure copper(II) oxychloride was prepared by purging a 1 mol dm-3 solution of CuCl2 with oxygen in the presence of copper powder. Copper(II) chloride solution was prepared from Merck’s p.a. copper(II) chloride dihydrate and deionized water. p.a. copper powder was supplied by Fluka. After the reaction,

CuCl2 + 3Cu + 3/2O2 + 3H2O w 2[Cu2Cl(OH)3] (1) which was carried out at 70 °C, was completed, the excess copper was removed, then resultant dried, and finally pure Cu2Cl(OH)3 was obtained. The specific surface area of dried copper(II) oxychloride was found to be 0.9 m2/g (Stro¨hlein Area meter II) and with an average particle diameter of 7.53 µm (Malvern Mastersizer-S 1002). The solubility product of copper(II) oxychloride was recently determined by Lubej et al.8 For dissolution experiments 4.0 g of powder consisting of copper(II) oxychloride particles with the narrow size distribution (Figure 1) was suspended into 25 cm3 of ethanol and homogenized by means of an ultrasonic bath. The experiments were started by pouring this sample into 6.3 dm3 of freshly prepared diluted (about 0.001 mol dm-3) HCl solution. During the experiment, the system was stirred at a constant rate by using a Teflon-coated magnetic stirring bar, and the suspension was purged with nitrogen to prevent contamination with carbon dioxide from the air. Under these conditions it was assumed that around each of the particles a stagnant film9 of the solution was formed. The progress of the dissolution reaction was followed by measuring the pH as a function of time. The pH of the solution was measured with a Radiometer pH-meter type PH95 using a glass electrode and a reference calomel electrode with a double-junction KCl/KNO3 electrolytic bridge to avoid contamination of the sample with Cl- ions. The pH meter was standardized at each temperature using a Radiometer Phthalate buffer10 and a precision of (0.01 pH unit was achieved. The temperature of the solution was controlled within (0.1 °C by an IKA thermostat. Because of the rapid change of pH, and

Dissolution Model. In this section a short outline of the applied simplified solubility model for the powder dissolution experiments is given. The solubility process has been presumed to be a reaction-/diffusion-transport process. We assumed the dissolution mechanism in which released ions from the crystal surface diffuse through the stagnant film to the bulk solution

Cu2Cl(OH)3 f 2Cu2+ + Cl- + 3OH-(surface) 2Cu2+ + Cl- + 3OH-(surface) f 2Cu2+ + Cl- + 3OH-(stagnant film) f 2Cu2+ + Cl-(bulk solution) (3) This process involves the neutralization reaction of OHions with the H+ ions at the crystal surface or somewhere within the stagnant film:

3OH- + 3H+ S 3H2O

(4)

The H+ ions are supplied to the reaction point by diffusion from the bulk solution phase. In the absence of any detailed knowledge of the mechanism of dissolution of the copper(II) oxychloride, we initially assumed that the rate of dissolution was determined simply by the distance of the system from equilibrium:6

Rdis ) kA(Ksp - Ip)

(5)

This rate equation is supported by the finding of the relatively high, but constant, rate of mass transport in the early stage of the process. The process was assumed to be controlled in that period by a zero-order surface reaction (the second term in eq 5 was then of negligible value and could be omitted). As the ionic product had increased to the value which was comparable to the Ksp, the reaction rate began to decrease. Computer simulations of the dissolution process had shown that the main reason for the decreased reaction rate may be ascribed to the increased concentration of OH- ions in the adsorption layer. Simulation of the Dissolution Process. Numerical simulations of the dissolution process were performed using the model which will be introduced next. Because of the spherical geometry of the system under consideration, only one-dimensional radial flow of matter was examined. Through the stagnant film a diffusive transport of detached Cu2+, Cl-, and OH- ions from the surface of the particle to the bulk solution, and a transport

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Figure 2. The cell model of a solution. The particle is surrounded by a stagnant film and bulk of the solution.

of H+ ions in the opposite direction, were taken into account by applying the mass-balance equation. In the calculations, it was formally assumed that the neutralization reaction rate, although extremely fast and normally considered instantaneous, had a definite reaction rate defined by the expression

RH+ ) ROH- ) -kp(aH+aOH- - Kw)

(6)

The value of the constant kp is 1.4 × 108 m3/(mol s) at 25 °C.12 The detailed equations and the computational method are described below. Let us imagine the whole volume of a suspension to be divided into spherical cells with one spherical particle in the center of each cell. To each of the cells, an average volume of

V VFVp VN ) ) np m

(7)

was assigned. From this value the radius rN of an equivalent sphere was calculated

rN )

( ) 3VN 4π

1/3

Transport of Ions. Transport processes in electrolyte solutions are characterized by the coupling of the flows of the individual ionic species by an electric field. The field may be externally imposed or it may be created internally by differences in ionic mobilities.13 Therefore, the flux of each dissolved species, i, in a radial direction through the stagnant film must be expressed by the following transport equation:14

Ni ) -ziuiFCi

(9)

Using the Nernst-Einstein relation

Di ) RTui

(10)

and taking into account the assumption that the transport of all ions is electrically balanced, so that the condition

∑ziNi ) 0

(11)

is valid for every distance from the particle, eq 9 may be rewritten as

(8)

The volume which belongs to the single particle was further divided, according to Figure 2, into the three domains (1) volume of the spherical particle having radius r0 (r0 was taken as the radius of the particle with an average value of the surface area), (2) the volume of the spherical shell of the stagnant film of thickness δ ) rN-1 - r0, and (3) the volume of the spherical shell which was assigned to the bulk solution. The thickness of this shell was δN ) rN - rN-1. The stagnant film thickness δ was further divided into N - 1 close-spaced spherical shells to solve the dissolution problem by a numerical computation. The concentration of the bulk solution was determined from the amount of dissolved matter divided by the volume of the solution. According to film theory,9 it is assumed that the transport of ions through the stagnant film had been taking place by diffusion. Because of the small size of the particle, the thickness of the film is supposed to be one-half the particle diameter.

∂Ci ∂Φ - Di ∂r ∂r

∂Ci

∑ziDi ∂r ∂Ci - Di Ni ) ziDiCi 2 ∂r ∑zi DiCi

(12)

Computational Procedure. The concentration profile of all moving species in the stagnant film at a given time t could be obtained from the mass balance. The change of the number of moles of the ionic species i in a finite segment of length ∆r ) rn - rn-1, i.e., in a single shell (let it be the nth shell) of volume Vn ) 4πrn2∆r in unit time, could be stated in the form15

∆Ci ) Ni|n-1An-1 - Ni|nAn + Ri|nVn (13) ∆t in out reaction accumulation Vn

If ∆r and ∆t are allowed to approach zero, eq 13 becomes 2 ∂Ci 1 ∂(Nir ) )- 2 + Ri ∂t ∂r r

(14)

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which is the basic transport model for a radial flow of matter through a spherical stagnant film in which a reaction is taking place. The standard explicit method16 was used to obtain a numerical solution of the above stated partial differential equation. The flux of OH-, Cl-, and Cu2+ ions into the first shell at the film-particle interface (r ) r0), was assumed equal to the rate of the surface reaction. The flux of matter into the bulk solution was taken equal to the diffusive flux through the interface area at r ) rN-1. The values for the Ni and Ri were obtained from eqs 12 and 6, respectively. Ri were calculated only for the H+ and OH- ions. The boundary conditions were as follows: (a) At the particle surface,

NOH- ) Rdis

rN3 r2 rN3

NCl- ) 1/3Rdis

NCu2+ ) 2/3Rdis NH ) 0 +

}

r2 , for r ) r0, t > 0 rN3 r2

(15)

(Constants 1/3 and 2/3 in eq 15 come from stoichiometric coefficients, cf. eq 3.) (b) At the film boundary,

∆Ci 3r2 ) 3Ni, for r ) r0 + δ, t g 0 ∆t r

(16)

N

(The constant 3 comes from the spherical geometry of the system under consideration as a surface area divided by volume). The initial conditions depend on the value of the Rdis, i.e., on the experimental value of the dissolution rate at the beginning of the experiment. We also assumed that at the beginning of the experiment the concentration of every ionic specieswithin the film was equal to its concentration in the bulk solution. The choice of small enough increments ∆r and ∆t was crucial for obtaining the stable numerical solution. Results and Discussion Empirical Rate Constants. During the dissolution of copper(II) oxychloride in a diluted hydrogen chloride solution, the pH of the solution was measured. From the pH values, the hydrogen ion concentrations were determined using the relation CH+ ) 10-pH, assuming that the ion activities are equal to the concentrations. This assumption is supposed to be justified because the ionic strength was very low at all the experiments. Measurements of dissolution rates were performed for temperatures 15, 20, 30, 40, and 50 °C. The change of the hydrogen ion concentration as a function of time for different temperatures is presented in Figure 3a,b. One can see almost linear time dependence of the H+ ion concentration, down to the value of 0.1 mol/m3, and the large effect of temperature on the slope of the curves. The linear time dependence of the H+ ion concentration suggests a conclusion that the order of the reaction is zero in this concentration and temperature range. The rate constants were determined from the slopes of the curves and are presented in Table 1.

Figure 3. The time dependence of the H+ ion concentration at the dissolution of copper(II) oxychloride at different temperatures. (a) Circles, 15 °C; triangles, 30 °C; squares, 50 °C. (b) Circles, 20 °C; triangles, 40 °C. Table 1. Temperature Dependence of the Zero-Order Dissolution Rate Constants of Copper(II) Oxychloride (Values Were Determined at Experiments at Which 4.00 g of Dry Sample Was Dissolved in 6.3 dm3 of 0.5 × 10-3 M HCl) temperature, °C

-∆CH+/∆t, mol m-3 s-1

15 20 30 40 40 50

0.00160 0.00244 0.00613 0.0166 0.0169 0.0206

A plot of the logarithm of initial rate constants at various temperatures against the reciprocal of the absolute temperature (an Arrhenius plot) is shown in Figure 4. From this plot, the activation energy of 71 (1 ( 10) kJ/mol and the Arrhenius pre-exponential factor of 6.7 × 106 m-2 s-1 were estimated. This rather high value of the activation energy suggests that the surface kinetics is rate-determining at high undersaturations and not by diffusion to the bulk of the solution. This was supported by an observed independence of dissolu-

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Figure 4. Dependence of the natural logarithm of the dissolution rate constant vs the inverse of the absolute temperature. The line represents the least-squares fit of all the measured values, except the value at 50 °C.

Figure 5. The experimental (circles) and calculated (a) and (b) course of the H+ ion concentration at the temperature 20 °C and 0 -3, C0 ) the following initial compositions: CH + ) 0.0490 mol m Cl0 -3. See the text. 0.187 mol m-3, and CCu ) 0.069, mol m 2+

tion rates of the stirring speed in the range 200-700 rpm.1 Zero order of a chemical reaction implies that the reaction proceeds with the constant rate until one of the reactants has been depleted. From Figure 3 it is also evident that, at a certain small H+ ion concentration, the curves start to deviate from the linear behavior, indicating slowing down of the dissolution rate. However, no systematic study has been made of the influence of pH on the kinetics of the copper(II) oxychloride dissolution. Among many factors which may have influence on the kinetics of the dissolution are the change of the controlled dissolution mechanism, and/or most probably the significant reduction of the undersaturation near the surface of the particle.17 Results of the Computer Simulation. According to the presumed model for copper(II) oxychloride dissolution in acidic solutions, the dissolution rate should decrease with an increasing degree of saturation. Likewise, an increased concentration of Cu2+ and Cl- ions in a solution at the beginning of a dissolution experiment should reduce the dissolution rates of copper(II) oxychloride. To verify these assumptions, the experiments with an increased degree of saturation already at the beginning of dissolution were performed. Results from the experiment at 20 °C, using the solution with the following initial compositions: CH+ ) 0.0490 mol m-3, CCl- ) 0.187 mol m-3, and CCu2+ ) 0.069 mol m-3 (Ip ) 7.6 × 10-24 (mol6/m18) are shown in Figure 5. The circles represent experimental values of the concentra-

tion of H+ ions during the copper(II) oxychloride dissolution. One can notice a considerable reduction of the dissolution rate, in this case in comparison with the dissolution rate in pure acidic solutions. (Compare experimental curves in Figures 3 and 5). Lowering of the dissolution rate was predicted also by the computer simulations. Here, two different cases regarding the neutralization reaction were examined: (a) In the first case the neutralization reaction (eq 4) was assumed to happen instantaneously (i.e., RH+ ) ROH- f ∞. In the calculations the kp in eq 6 was taken to be 100 times bigger than the literature value). The time course of the hydrogen ion concentration found by the simulation is shown in Figure 5 as a dotted line. This line failed to match the experimental data. (b) In the second case, eq 6 with the finite neutralization rate12 was taken into account. The calculated time dependence of the H+ ion concentration is presented in Figure 5 by a full line. One can notice an improved agreement between computed and experimental results. Inspection of the concentration profiles of reacting ions across the diffusion film have revealed that the finite neutralization rate incorporates in the model the possibility of accumulation of the hydroxyl ions in the adlayer (Table 2). Such a case may occur, for instance, if the concentration of the H+ ions falls below the value at which the rate of neutralization becomes smaller than the rate of production of OH- ions by the disintegration reaction. The diffusion transport of ions to the bulk of

Table 2. Calculated Concentration Profile of the Constituent Ionic Species and the Ionic Product in the Diffusion Layer after 100 s of Dissolution for the Experiment Presented in Figure 5, Case b shell no.

[Cu2+], mol/m3

[OH-], mol/m3 × 103

[Cl-], mol/m3

Ip, mol6/m18 × 1018

Ip/Ksp

1 2 3 4 5 6 7 8 9 bulk solution

0.086 07 0.085 90 0.085 89 0.085 88 0.085 87 0.085 85 0.085 84 0.085 83 0.085 82 0.069 00

0.014 647 0.009 212 0.005 836 0.003 745 0.002 455 0.001 666 0.001 194 0.000 931 0.000 813 0.000 020

0.195 37 0.195 53 0.195 52 0.195 50 0.195 48 0.195 45 0.195 45 0.195 44 0.195 42 0.187 00

4.547 864 1.127 986 0.286 681 0.075 739 0.021 322 0.006 656 0.002 452 0.001 160 0.000 773 0.000 008

0.600 45 0.148 92 0.037 85 0.009 99 0.002 82 0.000 88 0.000 32 0.000 15 0.000 10 0.000 001

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the solution is then insufficient to prevent the local increase of the OH- ion concentration.18 The consequence is a large increase of the ionic product, and according to eq 5, a decrease of the dissolution rate. The results of the calculations have shown that transport of all other involved ions by the diffusion was always faster than the surface reaction. However, it has to be pointed out that the change of H+ concentration as a function of time is not sufficient for the exact mechanism of dissolution to be determined. For this purpose, the dissolution rate as a function of undersaturation has to be known. From the form of the saturation dependence of dissolution rate it is then possible to recognize a particular kinetic mechanism.19 In the absence of reliable experimental data for Cu2+ and Cl- ion concentrations in the solution, this method cannot be applied here. To reveal the exact mechanism of the dissolution of copper(II) oxychloride, further work is needed, applying other traditional and modern techniques of studying the dissolution kinetics.7 Conclusions The results obtained by this study are worthy, mainly from a practical point of view. For instance, data about the maximum possible rates of the dissolution of copper(II) oxychloride are very useful for the prediction of the rate of industrial production of calcium tricopper(II) chloride trihydroxide. As an example, by studying the process of conversion of copper(II) oxychloride into another product,18 it was found that the rate of dissolution of the copper(II) oxychloride was normally much faster than the process of conversion. The experiments presented here have shown that the surface kinetics is rate-determining at large undersaturations. From the computer simulation studies it may be concluded that the dissolution rate appreciably diminishes as the ionic product within the adlayer becomes comparable to the solubility product, although the bulk solution is not saturated. Acknowledgment The research was supported in part by the Ministry of Science and Technology of Slovenia, Grant No. J27508-0103. Nomenclature ai ) activity of species i A ) specific area of copper(II) oxychloride particles in suspension, m2 m-3 An ) sphere area at r ) rn, m2 Ci ) concentration of the ith ion in the stagnant film, mol m-3 Ci′ ) concentration of the ith ion in the bulk of the solution, mol m-3 Di ) self-diffusion coefficient of ith ion, m2 s-1 F ) Faraday constant, As mol-1 Ip ) ionic product of copper(II) oxychloride, defined as Ip ) [Cu2+]2[Cl-][OH-]3, mol6 m-18 k ) proportionality constant, m16 s-1 mol-5 kp ) rate constant of neutralization, m3 mol-1 s-1 Ksp ) solubility product constant of copper(II) oxychloride, mol6 m-18 Kw ) ionic product of water, mol2 m-6 m ) mass of the copper(II) oxychloride particles, kg Ni ) flux of species i, mol m-2 s-1

Ni|n ) flux of the ith ion through the sphere area at r ) rn, mol m-2 s-1 np ) number of the copper(II) oxychloride particles pH′(tm) ) measured pH value at the time of the mth measurement pH(tm) ) true pH value at the time of the mth measurement r ) radial distance from the center of a particle, m R ) gas constant, J mol-1 K-1 RH+ ) ROH- ) rate of neutralization, mol m-3 s-1 Rdis ) global rate of copper(II) oxychloride dissolution, mol m-3 s-1 rN ) radius of the sphere, m rn ) radius of the nth shell, m T ) temperature, K tm ) time, s ui ) mobility of the ith ion, m2 mol J-1 s-1 V ) the volume of the suspension of the copper(II) oxychloride, m-3 VN ) volume of a suspension, which is associated with a single particle, m-3 Vn ) volume of the nth shell, m3 Vp ) volume of the particle with the mean surface area, m3 zi ) valence of the ith ion Greek Symbols τ ) glass electrode response time, s δ ) thickness of the stagnant film around the particle, m Φ ) electric potential, V F ) density of the copper(II) oxychloride particle, kg m-3

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Received for review February 22, 1999 Revised manuscript received August 9, 1999 Accepted August 19, 1999 IE990139M