Sulphur dioxide may be converted to $S{O}_3,$ which has many uses including the production of $H_{2}S{O}_4$ and sulphonation of detergent. A gas stream having $20$ mole$\%S{O}_2,19$ mole $\%O_2,$ and $61$mole$\%N_2$ is to be passed through a reactor. The single pass conversion of $S{O}_2$ in the reactor is $55\%.$ To boost the overall conversion to $96\%,$ some of the exit gas from the reactor is recycled back and mixed with fresh to the reactor. The reaction taking place in the reactor is

$2S{O}_2+O_{2}2S{O}_3$

Taking the basis as $1500$kmo$\frac{l}{h}r$ of fresh feed $($FF$),$ calculate:

$1\mathrm{.}1$ The flow rate $(kmo\frac{l}{h}r)$ of the product stream $(P)$ and the composition $($mole$\%)$ of RP$,$ P $($RF$)?(17)$

$1\mathrm{.}2$ The flow rate $(kmo\frac{l}{h}r)$ of the recycle stream $(R)?(6)$

$1\mathrm{.}3$ The flow rate $(kmo\frac{l}{h}r)$ of the reactor feed stream $(RF)?(2)$