Sulfur dioxide may be converted to SO$3,$ which has many uses. A gas stream that has a

composition of $10\%$ SO$2,9\%$ O$2,$ and $81\%$ N$2$ is to be passed through two reactor stages. The

reaction conversion of the SO$2$ to SO$3$ in the first stage is $0\mathrm{.}75$ and in the second stage is $0\mathrm{.}65.$ In

order to boost the overall conversion to $0\mathrm{.}95,$ some of the exit gas from the second reactor is

recycled back and mixed with the inlet gas to the second reactor. If $100$ moles are in the feed to

the entire system, how many moles are in the recycle stream?

I need help with a diagram and a degree of freedom analysis $($unknown species, relation equations$)$