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By John B. Butt

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To explain these phenomena qualitatively it is necessary only to recognize that the number of active centers can be decreased by physically removing them from the system by sintering or rendering them inactive by having nonreacting molecules (poisons or coke) adsorbed on them, thereby preventing their further use by reacting molecules. Thus, from a fundamental viewpoint, a useful parameter for the interpretation of deactivation phenomena would be related to Nt, the number of active centers per unit mass of catalyst at any stage of deactivation.

Now from the equilibrium assumptions X2 = KXCAXX ;} (2-37) X3 — ^ 3 C&X An active center balance, therefore, becomes Xx + 2 Kx CAX2X + 2X3 CBX2X + 2X4 = *o from which v X l " -l±Vl-8(X1CA+X3CB)(2X4-Xo) 4 ( 1 ^+1^) (2"38) We select the positive root to make Xx positive. As before, we identify the activity a = (Xo-2X4)/X0 (2-39) Substituting back into Eq. (2-36) and letting Kx CA + K3 C B = K, we get Reaction rate = K2KxCA{-\+J\ + %KaXJ4K) (2-40) Equation (2-11) cannot be put in the form of Eq. (2-34) and is therefore nonseparable.

2-15) X2 = X1K1CA (2-55) whereupon the rate is k2KlCA(X0 — X4) \ + KxCA+K3CB (2-56) Similarly, the rate of the reaction of B to C is c _k2K[CB(Y0-Y4) I + K;C B +I^C C (2-57) At this point, it is convenient to define a^(X0-X4)/X0 (2-58) a2=(Y0-Y4)/Y0 (2-59) To describe this system we need to define an activity and a selectivity. Similar to the earlier definition of activity, we define the activity for this system in terms of the disappearance of A, leaving the selectivity to account for the distribution of reacted A into products B and C.

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