Surface reaction rate-controlling

For many heterogeneous reactions, the surface reaction rate is slow compared with rates of the adsorption processes (steps 2 and 4). The overall reaction rate may then be determined by setting = 0 in equation (82) for all species i thus 

For simplicity we shall neglect the reverse surface reaction and shall employ the phenomenological expression 

In view of equation (79), equations (87) provides N linear relations for the N quantities 9i. Since equation (87) can be rewritten as 

The substitution of equation (90) into equation (79) relates 9 to 6. This result may be substituted into equation (89) with i = 1 to show that 

Before utilizing equation (92) in equation (88), let us consider the equilibrium surface concentration of an adsorbed gas as predicted by equation (92). Suppose that N — 1 and no surface reaction occurs. Equation (92) then reduces to 

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Reaction A2 -t B R -I- S, with A2 dissociated upon adsorption and with surface reaction rate controlling ... 

As noted by Froment and Bischoff (1990, p. 209), the case of surface-reaction-rate control is not consistent with the existence of a sharp core boundary in the SCM, since this case implies that diffusional transport could be slow with respect to the reaction rate. 

Corresponding equations for the two special cases of gas-film mass-transfer control and surface-reaction-rate control may be obtained from these results (they may also be derived individually). The results for the latter case are of the same form as those for reaction-rate control in the SCM (see Table 9.1, for a sphere) with R0 replacing (constant) R (and (variable) R replacing rc in the development). The footnote in Example 9-2 does not apply here (explain why). 

A triatomic molecule undergoes the reaction, A3 B + C, in contact with a catalytic surface. It dissociates completely on adsorption. Write rate equations for the two cases (a) Surface reaction rate controlling, adsorptive equilibrium of all participants maintained (b) Rate of desorption of substance B controlling, surface reaction equilibrium maintained. 

Net desorption rate of B controlling. (1) Surface reaction rate controlling,. 

The growth rate is isotropic and linear (i.e., surface reaction rate controlled) and three-dimensional with time. If the growth were diffusion-limited, the growth rate would be not linear with time but parabolic. 

As a second example of surface-reaction-rate control, consider the slightly more complicated case of a bimolecular reaction occurring on the same sites, S, of a surface. Overall, A -I- B C -I- D, and the individual steps are... 

As an example of this procedure, the rate equation for R will now be derived for surface reaction rate controlling. This means that in (2.3.1-1), —> oo and since from (2.3.1-6) the rate must remain finite... 

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