Nernst believes that the chemical process occurring at the interface is always much faster than at least one transfer process, so the reaction rate is controlled by the mass transfer process. In the simplest case, the reaction between a single reactant ion and a solid is very fast, almost at equilibrium, so that the reactant concentration c 1 at the interface is always too small to be noticeable. Thus the rate at which the reaction occurs is determined by the rate at which the reactants reach the interface. If the system is stirred sufficiently, a uniform concentration of the solution phase material c, through the thickness of the sheet Fixed δ c presence of a concentration gradient of the c. Let the solid surface area be A. According to Fick's law, the number of solute molecules dN transferred from the solution body to the solid surface in time dt is proportional to the concentration gradient dc∕dy perpendicular to the surface:
dN=-DA(dc∕dy)dt (1)
The scale factor D is the diffusion coefficient and the dimension is (length) 2 / time. If the volume of the solution in contact with the solid is V, then
-dc∕dt=(DA∕V)(dc∕dy) (2)
Nernst assumes that the concentration gradient is linear and can be expressed by (c-c 1 ) ∕δ, then
-dc∕dt=DA(c-c 1 )∕Vδ (3)
And the first order rate constant k is
k=DA∕Vδ (4)
The rate constant k T per unit area per unit volume can be determined experimentally, and the subscript T indicates that the rate constant is responsible for the mass transfer control reaction. If the diffusion coefficient is known, the thickness δ of the diffusion through the liquid layer can be obtained from the following relationship
k T =DA∕Vδ (5)
For many reactions occurring in aqueous solution, the value of δ at 20 ° C is about 3 × 10 -3 cm . The fact that many of the chemically different reactions are approximately the same is consistent with the assumption that the diffusion process controls the rate. However, this order of magnitude of the delta value means that the diffusion layer has a thickness of about 50,000 molecules and thus is physically impossible. It appears that the solid is unlikely to exert a significant influence on such a large amount of water molecules other than it, and it can only be assumed that the diffusion layer is similar to the liquid film held by the surface when the liquid flows through the solid surface.
The effect of temperature on the k T value can be used to support Nernst's view of heterogeneous reactions. If the value of δ is independent of temperature, then dk T /dT should be equal to the rate at which the diffusion coefficient changes with temperature. The activation energy of diffusion at 25 °C usually depends on the solute and solvent between 12-27kJ∕mol, so the critical energy critical increase E A of the mass transfer control process should be within this range, about 17kJ∕mol, practical It is often found that it is true. The critical energy increment of the heterogeneous reaction is equivalent to the activation energy of the homogeneous reaction, which can be determined by the Arrhenius equation.
E A =RT 2 (dlnk∕dT)
When the homogeneous reaction is studied by the absolute reaction rate theory, the experimentally determined activation energy can be analyzed by the free energy and the entropy of the transition state, and in the case of the heterogeneous reaction, the heat of adsorption is also involved. So the two situations are different, or strictly speaking they should be different. However, in the hydrometallurgical literature, this distinction is often ignored in the past.
Increasing the agitation rate reduces the thickness of the aqueous layer attached to the solid surface, thereby reducing the delta value and increasing the reaction rate. For a specific agitation rate δ value depends on the scale and geometry of the system. If the reaction solid is a suspended powder, it is necessary to consider the relative motion between the particles and the fluid, which is strongly influenced by turbulence, and the addition of baffles can cause turbulence.
For dense solids, the rate of reaction increases with power rate a (several revolutions per minute), where a is less than or equal to one. For a simple system, the delta value is inversely proportional to the agitation rate (r∕min), ie a = 1, about 3 x 10 -3 cm.
Consider a number of solids, each of which is insoluble in a pure solvent, but forms a soluble product in the presence of a solute and then dissolves. If the rate of dissolution is only controlled by the mass transfer rate of the solute to the solid surface, it will dissolve evenly under the same experimental conditions. This is the case, for example, in the dissolution of mercury , cadmium , zinc , copper , silver , iron , nickel and cobalt in an aqueous solution of iodine . Iodine acts as an oxidant and provides a metal anion ligand.
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