A gas$-$phase reaction, $A2B,$ is conducted at $300K($constant$)$ in a variable$-$volume reactor equipped with a piston to maintain a constant pressure of $150$kPa. Initially, $8$mol of A are present in the reactor. The reaction is second$-$order with respect to $A,$ with the following rate expression:

$(-r_A)=k{c}_A^2$;$k=0\mathrm{.}075Lmo{l}^{-1}mi{n}^{-1}$

Determine the time of reaction, $t,$ if $f_A,$ the fractional conversion of $A,$ is $0\mathrm{.}80.$ State any assumption$($s$)$ made. Solve this in excel.