A decay process occurs in a completely mixed batch reactor $($CMBR$)$ with a reaction rate constant $0\mathrm{.}1mg-1*L*min-1.$ The volume of the batch reactor is $2000L$ and influent concentration of the pollutant is $400m\frac{g}{L}.$

a$.$ Determine the order of the reaction and show your work.

b$.$ Starting from the fundamental mass balance equation, derive an equation which will give the effluent concentration at any reaction time $\text{'}t\text{'}.$

c$.$ Determine the required residence time $($in min $)$ of the batch reactor to reach a concentration of $100m\frac{g}{L}.$