1069where fo 5 exp. (-2 *ao) is the conversion under given reaction conditions on an unpoisoned surface. This may be substituted into Equation 53:The factor 7 can be evaluated empirically by taking logarithms:This equation is remarkable in presenting one of the few theoretically justified log-log curves.Equation 57 shows that the effectiveness of the surface, at constant process period t, decreases with increasing conversion; i.e., more active catalysts are more quickly poisoned. 'Near the beginning of the process period, activity falls off in exact proportion to the decrease in reactant and linearly with increasing process period. Thus one would expect the poisoning deposit to build up in inverse proportion to the Concentration of reactant and to increase exponentially with time when conversion is low. Other mechanisms of poisoning will, of course, give different kinetic behavior.The case in which diffwion is rate controlling is not so easily treated since there is no analytical expression for X under these conditions. The limiting case, XO = constant, ie not of practical importance, since the large values of ( I for which i t holds are soon reduced by poisoning. For the experimental determination of rate constants, very fast reactions for which a is large may be studied best on almost completely poisoned surfaces, to which Equation 59 will apply. I n the converse problem, given the rate constants and specific surface area, a numerical integration of Equation 62 wilt serve in calculating the conversion to be expected.
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