Problem Statement$\backslash$

Your boss at Storrs Chemical has asked you to determine how long it will take to convert $90\%$ of A to R in a $1\mathrm{.}0$ m$3$ rigid $($constant$-$volume$)$ batch reactor. The reactor originally contains $700$ moles of A and $1400$ moles of B$.$ You know the stoichiometry of the reaction is A $($g$)+2$B $($g$)->2$R $($g$).$Unfortunately, your boss does not supply you with further kinetic information, only the experimental results below and the information that the rate law follows the form$-$rA$=$kCAmCBn where m and n are both integers equal to $0,1,$ or $2($they may or may not have the same value$).$ Your final report should include the final kinetics $($orders$,$ rate constant, activation energy, and pre$-$exponential factor$)$ for the reaction, the time to reach $90\%$ conversion of A in a constant$-$volume batch reactor at $25\backslash \backslash \backslash \backslash$deg C$,$ and final amounts and partial pressures of each species in the reactor. Please note that these experiments use an approach called the Excess Reactant Approach so you can find the order in each reactant.$\backslash$

$\backslash$

Experiment #$1($constant$-$volume batch reactor$)$:$\backslash$

T $=400\backslash \backslash \backslash \backslash$deg C CA$0=1\mathrm{.}0$ mol$/$L CB$0=0\mathrm{.}01$ mol$/$L$\backslash$

t $($min$)\backslash$

$[$B$]($mol$/$L$)\backslash$

$10\backslash$

$0\mathrm{.}0079\backslash$

$20\backslash$

$0\mathrm{.}0062\backslash$

$30\backslash$

$0\mathrm{.}0049\backslash$

$40\backslash$

$0\mathrm{.}0038\backslash$

$50\backslash$

$0\mathrm{.}003\backslash$

$60\backslash$

$0\mathrm{.}0024\backslash$

$70\backslash$

$0\mathrm{.}0019\backslash$

$80\backslash$

$0\mathrm{.}0015\backslash$

$90\backslash$

$0\mathrm{.}0012\backslash$

$100\backslash$

$0\mathrm{.}0009\backslash$

$110\backslash$

$0\mathrm{.}0007\backslash$

$120\backslash$

$0\mathrm{.}0006\backslash$

$\backslash$

$\backslash$

Experiment #$2($constant$-$volume batch reactor$)$:$\backslash$

T $=750\backslash \backslash \backslash \backslash$deg C CA$0=0\mathrm{.}05$ mol$/$L CB$0=2\mathrm{.}0$ mol$/$L$\backslash$

t $($min$)\backslash$

$[$A$]($mol$/$L$)\backslash$

$10\backslash$

$0\mathrm{.}02483\backslash$

$20\backslash$

$0\mathrm{.}01233\backslash$

$30\backslash$

$0\mathrm{.}00612\backslash$

$40\backslash$

$0\mathrm{.}00304\backslash$

$50\backslash$

$0\mathrm{.}00151\backslash$

$60\backslash$

$0\mathrm{.}00075\backslash$

$70\backslash$

$0\mathrm{.}00037\backslash$

$80\backslash$

$0\mathrm{.}00018\backslash$

$90\backslash$

$0\mathrm{.}00009\backslash$

$100\backslash$

$0\mathrm{.}00005\backslash$

$110\backslash$

$0\mathrm{.}00002\backslash$

$120\backslash$

$0\mathrm{.}00001$