Question $2[$ Question $2[8$ marks$]$

A pulse tracer test is carried out to determine the residence time distribution $($RTD$)$ of a reactor with a constant flow rate of $500m\frac{L}{m}in.$ The tracer concentration is $100$mol$\frac{e}{L}$ and $10mL$ is added at the start of the test $(t-=0).$ The tracer concentration is measured at the exit of the reactor and the values are summarized in the table below:

$\backslash$table$[[\backslash$table$[[$Time after tracer addition$/$outlet sampling$],[$time $($min$)]],\backslash$table$[[$Tracer concentration in$],[$outlet $($mole$/$L$)]]],[0,0],[1,0\mathrm{.}02],[2,0\mathrm{.}03],[3,0\mathrm{.}05],[4,0\mathrm{.}08],[5,0\mathrm{.}1],[6,0\mathrm{.}12],[7,0\mathrm{.}11],[8,0\mathrm{.}09],[9,0\mathrm{.}07],[10,0\mathrm{.}06]]$

a$)$ Calculate the RTD function, $E(),$ at each sampling time using the information provided. $($Do not plot the data to find the area under the curve!$)[4$ marks$]$

b$)$ What percentage of tracer spends between $7$ and $10$ minutes in the reactor? $[4$ marks$]$ A pulse tracer test is carried out to determine the residence time distribution $($RTD$)$ of a reactor with a constant flow rate of $500$mL $/$ min. The tracer concentration is $100$mole $/$ L and $10$mL is added at the start of the test $($t$-0).$ The tracer concentration is measured at the exit of the reactor and the values are summarized in the table below: a$)$ Calculate the RTD function, E$($t$),$ at each sampling time using the information provided. $($Do not plot the data to find the area under the curve!$)$ b$)$ What percentage of tracer spends between $7$ and $10$ minutes in the reactor?