we suddenly injected $Ag$ of non$-$reactive tracer into the liquid feed stream of a continuous

steady state flow reactor at time $t=0$ and show the measured concentration of the

tracer in the output stream over time, $c_f(t).$

$($a$)(1$ point$)$ how much tracer did we inject into the reactor? ie$.$ what is $A?$

$($b$)(1$ point$)$ write an expression for the residence time distribution, $E(t).$

$($c$)(1$ point$)$ what are the units of $E(t)?$

$($d$)(1$ point$)$ write $($but do not evaluate$)$ a determined integral for the mean residence

time, $\frac{?}{\text{b}\text{a}\text{r}}(t)[min].$

$($e$)(2$ points$)$ now, we wish to carry out a first$-$order reaction AlongrightarrowR taking place

in non$-$coalescing droplets of oil in the feed $($at the same

$u{?}_{(}()()0))$ to this reactor. the

concentration of $A$ in the oil droplets in the feed is $C_{A0}=0\mathrm{.}25mo\frac{l}{L},$ and the rate

constant is $k=0\mathrm{.}8mi{n}^{-1}.$ write $($but do not evaluate$)$ a determined integral for

the average concentration of $A$ in the oil droplets of the exit stream, $\frac{?}{\text{b}\text{a}\text{r}}(c{)}_A[mo\frac{l}{L}].$