A kinetic model for batch leaching of various metals with different lixiviants has been developed. Overall material balances for reactants and products at the solid/liquid interface were formulated with various types of heterogeneous reactions in place at the interface. The solutions to these mass balances have been identified analytically as well as numerically using a Runge-Kutta method.

For a dissolution reaction of metals in aqueous solutions, the overall reaction process usually consists of 1) transport of reactants from the bulk solution to the solid/liquid interface; 2) adsorption of reactants to the surface; 3) chemical reaction at the solid surface; 4) desorption of soluble products of the reaction; and 5) transport of soluble products back to the bulk solution. It is generally agreed that one or a combination of these steps can be rate limiting. It is very important to identify the rate limiting step for the overall reaction process, which in turn helps the optimization of the process as well as the design of the leaching process resulting in the most economical process.

Kinetic Model

Generally, the dissolution of a metal in solutions can be represented by the following stoichiometric reaction:

<M> + a(A) + b(B) → c(P) + d(D)

An example of such a reaction could be the leaching of copper metal in aerated acidic solutions:

<Cu> + ½(O2)aq + 2(H+)aq → (Cu++)aq + (H2O)aq

The Runge-Kutta method is used in this study in obtaining the solutions for half and second order reactions.

In order to demonstrate the applicability of the model, a hypothetical reaction system is considered. It is assumed that b=0.5, n = 10 6 and the values of k1, km1 as well as km2 were varied within the reasonable range. Initial conditions are also assumed as: CAb=0.1 mole/l and kept constant, CAs = CAb/ Cps = Cpb = 0. The computation results are shown in sections that follow.

The bulk concentration of the dissolved metal product, Cpb was calculated as a function of time by solving the differential equation group, Equation 3 numerically with the conditions specified above. Three different types of heterogeneous chemical reaction order, namely half, first and second order were considered in this study.

It is obvious from these results that for irreversible chemical reactions, the product concentration always has a linear relationship with time regardless of chemical reaction order. The product concentration, Cpb is very dependent upon k1 and km1, however. It is also seen that as the order of the heterogeneous chemical reaction increases, the overall rate decreases.

It is well known that the maximum overall rate of dissolution in aqueous solution could be identified with the rate of mass transfer. Therefore, when the observed rate of dissolution is far less than the rate expected for mass transfer rate, the reaction could be assumed to be either a mixed or a chemically controlled reaction.

It should also be noted that when the ratio, k1/km1 is 0.01, regardless of the order of reaction, the heterogenous chemical reaction at the solid/liquid interface will be the limiting step for the overall reaction. Corollary to this analysis is that chemical reaction at the surface of the solid becomes the limiting step, as long as the rate of mass transfer is at least 100 times greater than the rate of heterogeneous chemical reaction for all orders of chemical reaction.

When the dissolution of a metal is irreversible and can be described by a mixed controlling mechanism, the rate expression could be determined by combination of mass transfer of the limiting reactant and the heterogeneous chemical reaction.

For irreversible reaction systems, mass transfer of products has no significant effect on the overall rate. Under the conditions studied in this investigation, when the heterogeneous chemical reaction has a half or a first order with respect to the limiting reactant concentration, the overall rate is determined by mass transfer if the rate of chemical reaction is about 100 times larger than that of mass transfer. However, for second order reactions, chemical reaction controlling or mixed controlling is most likely.

Dissolution Behavior of Cobalt in Iodine Iodide Solutions

The dissolution kinetics of cobalt in iodine/iodide solutions was investigated using a rotating disc technique. Variables studied here included temperature, rotating speed, concentration of lixiviants, and pH of the solution.

The overall dissolution reaction was found to be limited by mass transfer of triiodide through the diffusion boundary layer with Arrhenius activation energy of less than 16.2 kj/mol (4 kcal/mol) over the temperature range, 2-42°C. The pH of the solution had little effect as long as the pH of the solution was less than 8. However, when the pH of the solution became greater than 8, the dissolution rate decreased dramatically due to passivation. The rate of dissolution was in good agreement with the dissolution model developed by the authors earlier.

Theoretical Approach

There are a number of reactions involved in the leaching of cobalt metal in iodide/iodine solutions. These are given below:

The thermodynamic data used in the above calculations were taken from the Handbook of Chemistry and Physics. It is noted that the equilibrium constants given by the above equations are very large at 25°C. It is generally accepted that a reaction with a large equilibrium constant is considered to be irreversible. It can be noted that tri-iodide is a more dominating species than iodide and hence

Leaching solutions were prepared by dissolving known amounts of reagent-grade chemicals in distilled water. A 500 ml of leaching solution was placed in a 1000 ml glass reactor which was placed in a water bath. Leaching experiments began as soon as the cobalt disc was in contact with the solution, five ml-samples of solution were withdrawn for analysis at regular time intervals.

The dissolution of cobalt was found to be related to the rotating speed of the disc.

It is apparent that the dissolution of cobalt increased with the increase of the rotating speed. It should be noticed that the concentration of cobalt is in fact nonlinear to the leaching time. This is because the concentration of the reactant, triiodide changes during the dissolution period.

The concentration of triiodide is not related to the rate constant k. However, the dissolution of cobalt should be proportional to the initial concentration of triiodide. It can be seen that the higher the concentration of iodine, the more the dissolution of cobalt proceeded.

The effect of pH of the solution on the dissolution of cobalt was investigated by changing the pH of the solution. The pH of the solution was adjusted with sulfuric acid for low pH or ammonia for high pH.

However, the rate dramatically decreased when pH was greater than 8. The dissolution of cobalt is kinetically negligible at pH greater than 10. This is because cobalt may be passivated at high pH. At low pH(< 7.5), there is no passivation expected, and the hydrogen ion does not participate in the dissolution reaction.

The dissolution of cobalt in iodide/iodine solution is controlled by the mass transfer step of triiodide through the boundary layer. The leaching behavior of the cobalt disc in this study can be described in terms of an equation:
[Co] = [I3-]° (1 – e-kt)