In order to perform the kinetic analysis of the hydrolysis reaction of acetic anhydride an experiment in a laboratory$-$scale discrete reaction vessel, isothermally at $23C$ it was realized and the change of the acetic anhydride concentration over time was obtained. Acetic the initial concentrations of anhydride $($A$)$ and water $(B)$ are $1mo\frac{l}{L}$ and $55mo\frac{l}{L},$ respectively.

The stoichiometric equation shows the kinetic model of the reaction given below and the velocity constant at $23C.$ find it using the differential method. $($Note: $C>>C4$ can be taken$)$

$(CH,CO)2O+H2O2CH,\frac{C}{O}OH$

$\backslash$table$[[t,$min,,$5,10,15,20,25,30,35,40,45,50],[$a$,$ mol$/$L$,,0\mathrm{.}49,0\mathrm{.}26,0\mathrm{.}14,0\mathrm{.}072,0\mathrm{.}04,0\mathrm{.}025,0\mathrm{.}018,0\mathrm{.}011,0\mathrm{.}007,0\mathrm{.}004],[,,,,,,,,,,,],[,,,,,,,,,,,]]$