Reaction rates of heavy metal ions at goethite: relaxation experiments and modeling

In the present paper we extend our theory that calculates the fastest reaction step observable in suspensions containing charged microcrystals and heavy metal cations. The calculation requires the solution of the nonlinear Poisson–Boltzmann equation for nonsymmetric electrolytes plus the Nernst–Planck equation for transport of ions in electric fields. We find that the diffusional transport of ions to and from the surface is the rate-limiting process for our experimentally observed maximum rates. At low pH and low metal ion concentration the diffusion of metal ions is the rate-limiting step, whereas for high pH and high metal ion concentration the diffusion of the solvated protons controls the overall relaxation rate. The validity of this theory is checked for the reactions of Pb2+ and Cd2+ with goethite by means of pressure jump relaxation experiments over a wide range of temperature and pH. In all cases we observe fast processes (relaxation in the range of 103s−1) in quantitative agreement with the theory, followed by slower processes, most probably caused by diffusion into the interior of the porous microcrystals.