Chapter $4$: Q$6.(14$ pts$)$ You are a manager of a process engineering group and you have asked one of your young

process engineers to determine the conversion in a CSTR$,$ for a liquid reaction system that is expected to be irreversible

with first order kinetics $AB.$ The feed is only pure $A.$ The value of the rate constant is $1h{r}^{-1}.$

a$)$ The engineer has determined that, at steady$-$state, with a space time of $1$ hour, the conversion will be $50\%.$ Confirm

this result. Remember to show your work and units.

b$)$ It turns out that the rate constant and irreversible assumption is only true for low conversions. An experimental

CSTR$,$ with a space time of $1$ hour results in a conversion of only $25\%.$ Assuming that the first$-$order rate constant

is correct, but that the reaction is reversible, what is the value of the reaction equilibrium constant. $K_c?$ Remember

to show your work and units.