Continuous Binary Distillation

$1.)$ Consider a distillation column with $18$ physical trays that operate at $50\%$ efficiency. Answer the following:

$($a$)$ If the column has a total reboiler and total condenser, how many equilibrium stages are present?

$($b$)$ If the column has a partial reboiler and partial condenser, how many equilibrium stages are present?

$2.)$ Consider a distillation column with a minimum reflux ratio $R_{\text{m}\text{i}\text{n}}=2\mathrm{.}5$ that is operated at twice the mimumum

reflux ratio. If the distillate flow rate is $100$kmo$\frac{l}{h}r,$ what is the vapor flow rate entering the condenser?

$3.)$ Consider a distillation column with a total condenser. if the distillate light key composition is $x_D=0\mathrm{.}75$ and

the relative volatility is $=2,$ what is the composition of the liquid leaving the first equilibrium stage?