The diagram below represents the PFD for steady$-$state $2-$unit process involving three components, A$,$ B and C$,$ and no chemical reactions. Using a copy of the diagram, which is available on the last page of this examination paper, answer the following.

$($a$)$ Indicate on a copy of the above diagram, by means of dashed boxes, the systems and sub$-$systems about which balances can be taken. $[10\%]$

$($b$)$ State the maximum number of balances that can be taken for each system and subsystem.

$10\%$

$($c$)$ Using a degree$-$of$-$freedom analysis suggest a solution strategy in order to calculate a fully balanced PFD$.$

$[20\%]$

$($d$)$ Calculate the values of all of the unknowns in the above diagram using the strategy outlined in $($c$)$ above.

$50\%$

$($e$)$ If the molecular weights of A$,$ B and C are $32,64$ and $128$ respectively determine the molar flow rate and the composition in mole fractions of stream $4.$

$[10\%]$