Rate of Heterogeneous Reactions

Mass Transfer. The reaction rate of heterogeneous reactions may be controlled by the rates of diffusion of the reacting species, rather than the chemical kinetics. 

At low temperatures (T<1320 °C) and small particles, combustion regime (I) prevails [11,74,75]. Regime (I) is controlled by chemical kinetics intraparticle (reaction control), see Figure 55. The oxygen content is constant at any radius inside the particle since the rate of diffusion is fast compared to the rate of heterogeneous reaction. The particle then burns with reducing density and a constant diameter, see Figure 55. 

The rates of heterogeneous reactions do not usually follow rate laws of homogeneous reactions instead, they involve multisteps and are controlled by the... 

In general, the influence of temperature on the rate of heterogeneous reactions is very great. At one time a view was current that heterogeneous reactions as a whole had temperature coefficients of a much smaller order than homogeneous reactions. This must have been to some extent a preconceived idea based upon the diffusion theory, because there is no experimental ground for such a belief. 

The rate of calcite dissolution is known to depend on the hydrodynamic conditions of the environment and on the rate of heterogeneous reaction at the mineral surface. Numerous laboratory studies demonstrate transport and surface-controlled aspects of calcite reactions in aqueous solutions, but until recently, no study has been comprehensive enough to enable comparison of kinetic results among differing hydro-chemical systems. 

The Rate of Heterogeneous Reactions. A heterogeneous reaction takes place at the surfaces (the interfaces) of the reacting phases, and it can be made to go faster by increasing the extent of the surfaces. Thus finely divided zinc reacts more rapidly with acid than does coarse zinc, and the rate of burning of a perchlorate propellant is increased by grinding the potassium perchlorate to a finer crystalline powder. 

Discuss the effects of four different factors upon the rate of heterogeneous reaction. 

Figure 2. Effect of gas volume thickness on the fraction of the rate of heterogeneous reaction in total conversion and on the time of 10% oxygen conversion (1000 K, 1 atm., CH4 02 =...

The effect of the gas volume thickness on the contribution of the surface reaction to the overall kinetics is presented in Fig.2. At L = 10 nm the time of 10% conversion characterizing the rate of reaction is 10 times less than in the case of a homogeneous gas reaction and the fraction of the rate of heterogeneous reaction Ws in the total conversion rate Wtot is nearly 1. At increasing thickness of the gas volmne the fraction of the heterogeneous reaction and the rate of overall process both decline. However, even at L = 1 cm, the reaction occurring in the gas volume still experiences the influence of the surface taking part in the radical reactions. 

One can also evaluate the relative change in rate of heterogeneous reaction at the substrate by measuring concentration of the reaction product at the tip. In this setup, the tip is positioned at fixed distance from the substrate, and the time dependence of concentration is measured. This simpler approach is based on the proportionality between the heterogeneous reaction rate and the product concentration. It is most useful when the substrate flux cannot be measured directly (e.g., the substrate reaction is not an electrochemical process) [30,31]. 

It has been shown that the rate of heterogeneous reactions depends upon the rate at which the reacting components of a mixture can diffuse up to the surface of the catalyst, become activated, and react. Still another factor is involved, however, and this is the rate at which the product can... 

Nemst29 considered that the equilibrium at the interface of two phases was established very rapidly, instantaneoudy compared to the rate of diffusion. The diffusion equation is similar in form to that of a monomolecu-lav reaction and it is, hence, probable that measurement of the rate of heterogeneous reactions which appear to be nionomolecular is really measurement of the rate of diffusion. Thus, heterogeneous reactions are determined as to rate by die velocity at which the reacting molecules can diffuse to the catalyst surface and penetrate or partly displace the adsorbed film. In the light of Langmuir s discoveries this view must be modified since not all of the surface may be active. The rate is then fixed by the rate of movement of reactants to active portions only of the catalyst and by the proportion of active surface present. 

The principles that govern electrochemistry at semiconductor electrodes can also be applied to redox processes in particle systems. In this case, one considers the rates of the oxidation and reduction half-reactions that occur on the particle, usually in terms of the current, as a function of particle potential. One can use current-potential curves to estimate the nature and rates of heterogeneous reactions on surfaces. This approach applies not only to semiconductor particles, but also to metal particles that behave as catalysts and to surfaces undergoing corrosion. 

When the mole fraction of species A is not small compared to 1, the diffusive flux in this transport equation will not be correct. If the diffusive flux plays an important role in the rate of heterogeneous reaction, equation 1.59 will not lead to a correct representation for the rate of reaction. 

It is established that for a higher D value of a surface, the rates of heterogeneous reactions increase because of the higher number of active sites available. In diffusion-controlled reactions, the initial rate is directly dependent on D and the steady-state rate on a parameter derived from it. It was fotmd recently for silica, commonly used in solid-supported reactions, that the value of D, originally 1.8-2.3, increases up to 2.8 by sonication.12 If this observation can be generalized, the higher reactivity of sonicated solids should be explained by the transformation of a reaction in a two-dimensional space to a process occurring in a volume. 

In the case of heterogeneous systems (Table 4) almost all of the characteristics of ultrasound are utilized for mass and heat transfer, surface activation, phase mixing, etc. Generally speaking enhancement in the rates of heterogeneous reactions are a complex result of mixtures of any or all of these. 

One of the factors limiting the rate of heterogeneous reactions such as (9), (10) and (11) is the availability of the second reactant at the surface. For a trace species like HCl, this may be determined by the solubility of the species in sulfuric acid. Measurements of the effective Henry s law constant for HCl in sulfuric acid solutions between 50 wt.% and 60 wt.% [24] have been made. Because the solubility is low, the range of temperatures and compositions over which the Knudsen cell experiment could be performed is limited. However, extrapolation to room temperature measurements [28] looks reasonable, and the agreement with the results of other groups [29,30] is good. 

Gaseous mixtures and dissolved particles can mix and collide freely therefore, reactions involving them can occur rapidly. In heterogeneous reactions, the reaction rate depends on the area of contact of the reaction substances. Heterogeneous reactions involve reactants in two different phases. These reactions can occur only when the two phases are in contact. Thus, the surface area of a solid reactant is an important factor in determining rate. An increase in surface area increases the rate of heterogeneous reactions. 

Figure 5.5. The influences of fluid flow rate and temperature T on the rate of heterogeneous reactions at the surface of solid particles. It is assumed that the mass transfer coefficient is proportional to the square root of the fluid flow rate see eqs, (4.24) and (4.25). The horizontal parts of the curves indicate the situation when chemical kinetics are rate determining, the steepest parts when mass transfer is rate detemining.

In the above derivation a power-law kinetic expression was assumed for the intrinsic chemical reaction. For the systems where large concentration differences occur between the bulk fluid and the interior of the porous solid, the Langmuir-Hinshelwood type rate expression should be used because this provides a better description of the rate of heterogeneous reactions. 

Althou the rate of heterogeneous reactions is usually expressed according to the Langmuir-Hinshelwood mechanisms (Walker et al. (18)), a simpler power law expression is recommended for most of the char-gas reactions. This is to reduce the mathemati- cal complexity in reactor modelling and the number of parameters needed to be determined by experimentation. Accordingly, the rate e q>ression for a volumetric reaction can be described in the following forms ... 

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