A reaction $($irreversible$,$ in liquid phase$)$ represented broadly as A$+$B$->2$P takes place with an excess of B $.$ The rate law of this reaction at room temperature follows $-$ r$\_($A$)=$kC$\_($A$)^(1\mathrm{.}5)$ The conversion of reagent in a small test tube was $72\%$ after $90$min $.$ The initial concentration of reagent was $1\mathrm{.}2$mo$($l$)/($L$)($that of B was $5\mathrm{.}97$mo$($l$)/($L$)).$ Both reagents, and no product P initially, were dissolved in a solvent. Write the material balance to a batch reactor $($the lab test tube$)$ and determine the reaction rate constant. Note: $($dx$)/((1-$x$)^($n$))=(1)/(($n$-1)(1-$x$)^($n$-1))$