A liquid mixture of benzene and toluene contains $60\%$ benzene by mass. The mixture is to be partially evaporated to yield a vapor containing $85\%$ benzene and a residual liquid containing $20\%$ benzene by mass. The process is carried out continuously and at a steady state. No reactions occur in the separator. The feed enters the separator at a rate of $100k\frac{g}{h}.$

$($a$)$ Begin your analysis by drawing and labeling a flow sheet of the process and identifying all unknowns.

$($b$)$ How many independent balances may be written for the system?

$($c$)$ Solve for the liquid $(k\frac{g}{h})$ and vapor $(k\frac{g}{h})$ flow rates leaving the separator.