SO$3$ is being produced by the reaction of sulphur dioxide with oxygen in a series of two reactors $($with the product stream from the first reactor being fed to the second reactor$).$ The first reactor achieves a single$-$pass conversion of SO$2$ of $70\%.$ The single$-$pass conversion of SO$2$ is the second reactor is $60\%.$The feed to the first reactor consists of $15$ mole$\%$ SO$2,$ with the remainder dry air. To boost the

overall conversion of SO$2$ to $90\%,$ a portion of the product stream from the second reactor is recycled back to mix with the stream entering the second reactor. Calculate the ratio of the moles of recycle stream to the moles of SO$2$ fed to the process