Benzene is produced using hydrodealkylation process. During the hydrodealkylation of toluene $($C$6$H$5$CH$3),$ both benzene $($C$6$H$6)$ and methane $($CH$4)$ are produced. C$6$H$5$CH$3+$ H$2$ C$6$H$6+$ CH$4100$ kmol$/$h of pure liquid toluene is fed along with $200$ kmol$/$h of pure hydrogen gas. These streams are combined with recycle streams and fed to a reactor. In the reactor, $50\%$ of the toluene fed to the reactor is consumed. The effluent from the reactor enters a vaporliquid separator. All of the hydrogen and methane gas leave the separator in the vapor stream; all of the liquids toluene and benzene leave the separator in the liquid stream. The liquid stream then enters a second separator in which all of the benzene leaves in one stream and all of the toluene leaves in the other stream. The benzene stream leaves the process as a product stream. The toluene stream is completely recycled by mixing it with the toluene in fresh fed to the process. The vapor stream from the separator is split into two equal streams. One of these streams is recycled and combined with the hydrogen fresh feed stream, and the other stream is sent to another process unit for further processing. Determine the following: $($a$)$ The molar flow rate of benzene produced. $(100$ kmol$/$h$)($b$)$ The composition of first separator vapor stream. $(50$ mol$\%$ CH$4$ and $50$ mol$\%$ H$2)($c$)$ The toluene is actually fed to the reactor. $(200$ kmol$/$h$)($d$)$ The component molar flow rate of the vapor stream fed to the reactor. $($H$2=300$ kmol$/$h$,$ CH$4=100$ kmol$/$h$)$