Propylene oxide $(C_3{H}_{6}O)$ is produced by the partial oxidation of propane $(C_3{H}_8).$ The fresh feed to the entire process is an equimolar stream of propane and oxygen. The reactor effluent stream is split into recycle stream and product stream. The ratio of the flow rate of recycle stream to product stream is $5\mathrm{.}0.$ A total of $100$ mol of product leaves the system. The mole fraction of propane in the product stream is $0\mathrm{.}20.$ How much propane enters the system in the fresh feed? What is the single$-$pass conversion of propane?

$C_3{H}_8+O_2{C}_3{H}_{6}O+H_{2}O$