$$ A flue gas desulphurization system is designed to treat a flue gas stream with a flow rate of $40,000\frac{m^3}{h}$ and an $S{O}_2$ concentration of $2000ppm.$ The system uses lime $($ CaO as the sorbent and achieves an $S{O}_2$ removal efficiency of $95\%.$ Determine the required stoichiometric ratio $(C\frac{a}{S})$ for the process. $[10$ marks$]$