Transport-controlled rates

The results in Figs. 19 and 20 clearly show that these reactions occur at a transport-controlled rate. For example, the concentration of Fc ce is zero at the interface [Figs. 

FIGURE 1.7 Effect of poisoning on mass the transport-controlled rate compared with the effect of poisoning on the true chemical rate. 

There are of course intermediate cases where the rate is of the order of the transport controlled rate, but somewhat less, and it is possible to treat these cases more delicately than by choosing one of the extremes (1-3,7,8). 

It has been shown that Cu and Ag dissolve at essentially the same transport-controlled rate in acidified ceric sulfate solution (37). The authors postulate that the larger enthalpy of this reaction facilitates desorption of the product ions. The equilibrium adsorption of silver salts on silver is dependent on the anion and is much less than a monolayer at low concentrations (38). 

A potential step experiment was carried out in a solution containing 0.05 M ferrocyanide ([FejCNje] ) dissolved in a solution containing a large excess of inert electrolyte. Care was taken to ensure that there was no stirring of the solution during the experiment. The potential was stepped from a value where there was no reaction to a potential at which the [FejCNje] was oxidised to [FejCNje] at a mass transport controlled rate, and the following currents were recorded ... 

There is nothing particularly special about the product except its feed rate, which is fairly low in comparison to some of the other novel oxygen scavengers. It exhibits passivation characteristics (forming magnetite in a way similar to hydrazine), coupled with good corrosion and iron transport control. 

In this section we consider experiments in which the current is controlled by the rate of electron transfer (i.e., reactions with sufficiently fast mass transport). The current-potential relationship for such reactions is different from those discussed (above) for mass transport-controlled reactions. 

Use equations to demonstrate how an increase of the stirring rate will effect the mass transport-controlled limiting current. 

Groundwater environments can be represented as a simple flow-through system. For the situation where chemical weathering of mineral grains is transport controlled, the weathering rate of a mineral should be directly dependent on the rate of throughput of water. For the situation where rates are controlled by surface... 

The effect of temperature on the rate of a typical heterogeneous reaction is shown in Figure 3.25. At low temperatures the reaction is chemically controlled and at high temperatures it is diffusion or mass transport controlled. 

The kinetics of tea extraction have been studied in detail 89 90 Rates for caffeine, theaflavin, and thearubigen extraction have been determined. It has been demonstrated that extraction is not a transport-controlled process. Temperature and time are the rate-limiting variables. 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

The fundamental concept of heat transport controlled moisture uptake [17] is shown in Eq. (22), where the rate of heat gained at the solid/vapor surface (W AH) is balanced exactly by the heat flow away from the surface (Q). The term All is the heat generated by unit mass of water condensed on the surface. The two most probable sources of heat generation are the heat of water condensation and the heat of dissolution. A comparison of the heat of water condensation (0.58 cal/mg water) with the heat of dissolution for a number of salts indicates that the heat of dissolution can be neglected with little error for many materials. 

If the rate of the reaction is not restricted by the kinetics of the surface reaction, the reaction is called reversible and its rate is transport controlled. By Faraday s law the current density i is proportional to the reacting ion (or molecule) flux N, ... 

Yet another way to detect mass transport problems is with a newly developed poisoning technique.24,26,49,50 This technique works for liquid-phase hydrogenations and possibly for other reactions that are poisoned by CS2. It takes advantage of the fact that CS2 poisons Pd and Pt linearly until all reaction stops. If mass transfer problems exist, the initial linear decrease in rate occurs at a slope less steep than the slope of the chemically controlled rate (Fig. 1.7). If no mass transport problems exist, the rate decreases linearly from the start with no change in slope. Therefore a plot of rate versus amount of CS2 reveals the existence or absence of mass transport problems 49... 

The diffusion layer theory, illustrated in Fig. 15B, is the most useful and best-known model for transport-controlled dissolution. The dissolution rate here is controlled by the rate of diffusion of solute molecules across a diffusion layer of thickness h, so that kT kR in Eq. (40), which simplifies to kx = kT. With increasing distance, x, from the surface of the solid, the concentration, c, decreases from cs at x = 0 to cb at x = h. In general, c is a nonlinear function of x, and the concentration gradient dddx becomes less steep as x increases. The hyrodynamics of the dissolution process has been fully discussed by Levich [104]. In a stirred solution, the flow velocity of the liquid dissolution medium increases from zero at x = 0 to the bulk value at x = h. 

Equation (43) describes the transport-controlled dissolution rate of a solid according to the diffusion layer theory in its simplest form. The mass transfer coefficient here is given by k, = kT = Dlh. 

The rate of agitation, stirring, or flow of solvent, if the dissolution is transport-controlled, but not when the dissolution is reaction-con-trolled. Increasing the agitation rate corresponds to an increased hydrodynamic flow rate and to an increased Reynolds number [104, 117] and results in a reduction in the thickness of the diffusion layer in Eqs. (43), (45), (46), (49), and (50) for transport control. Therefore, an increased agitation rate will increase the dissolution rate, if the dissolution is transport-controlled (Eqs. (41 16,49,51,52), but will have no effect if the dissolution is reaction-controlled. Turbulent flow (which occurs at Reynolds numbers exceeding 1000 to 2000 and which is a chaotic phenomenon) may cause irreproducible and/or unpredictable dissolution rates [104,117] and should therefore be avoided. 

The diffusivity, D, of the dissolved solute, if dissolution is transport-controlled (Eqs. 41-46,49,51,52). The dissolution rate of a reaction-controlled system will be independent of D. 

The viscosity (dynamic, 17, or kinematic, v) and density, p (Eq. 47), influence the dissolution rate if the dissolution is transport-controlled, but not if the dissolution is reaction-controlled. In transport-controlled dissolution, increasing 17 or v will decrease D (Eq. 53), will increase h (Eqs. 46 and 49) and will reduce J (Eqs. 51 and 52). These effects are complex. For example, if an additional solute (such as a macromolecule) is added to the dissolution medium to increase 17, it may also change p and D. The ratio of 17/p = v (Eq. 47) and D directly influence h and J in the rotating disc technique, while v directly influences the Reynolds number (and hence J) for transport-controlled dissolution in general [104]. 

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