Q$2$: A liquid$-$phase decomposition reaction of A has been conducted in a BMR$,$ and the data obtained under steady$-$state conditions are shown in the table below. Using this data, find the rate expression for the reaction. Then, using the expression you found, calculate the operation time required to achieve $75\%$ conversion in the piston flow reactor when the inlet concentration is $0\mathrm{.}8mo\frac{l}{L}.$

$A$ Products

$\backslash$table$[[$Inlet concentration of A$,$mol$/$L$,$Outlet concetration of A$,$mol$/$L$,$Operation time, s$],[0\mathrm{.}48,0\mathrm{.}2,560],[0\mathrm{.}48,0\mathrm{.}28,200],[0\mathrm{.}48,0\mathrm{.}42,24],[1\mathrm{.}00,0\mathrm{.}37,360],[1\mathrm{.}00,0\mathrm{.}56,110],[2\mathrm{.}00,0\mathrm{.}61,300],[2\mathrm{.}00,0\mathrm{.}92,100]]$

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