(Solved): The catalytic cracking reaction \( \mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}+\mathrm{D} \) is ta ...

The catalytic cracking reaction \( \mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}+\mathrm{D} \) is taking place in a fluidized bed reactor. At reaction conditions, the reaction is irreversible and is second order in \( \mathrm{A} \). The reactor can be approximated as a CSTR. The reactor contains \( 100,000 \mathrm{~kg} \) of catalyst. The feed to the reactor in pure A with a rate of \( 200,000 \mathrm{~mol} / \mathrm{min} \). The concentration of \( \mathrm{A} \) in the feed is \( 15.8 \mathrm{~mol} / \mathrm{m}_{3} \). When the reactor is started up with "fresh" catalyst, the fractional conversion of \( \mathrm{A} \) is \( 71 \% \). However, the catalyst deactivated with continued operation until the conversion had declined to \( 47 \% \). The form of the rate equation does not change as the catalyst deactivates. 1. What is the value of the rate constant of the reaction with "fresh" catalyst? 2. By what percentage does the rate constant decrease once the catalyst becomes deactivate?