A single$-$effect evaporator is used to concentrate $7k\frac{g}{s}$ of a solution at $21C$ from $10\%$ to $50\%$ solids. Saturated steam is available at $200$kPa and evaporation takes place at $50$kPa. If the overall heat transfer coefficient is $3kJ{s}^{-}{m}^2{?}^{2}C{C}^{-1}$ and the condensate leaves the heating space at $80C.$ Take the specific heat capacity of the $10\%$ solution as $3\mathrm{.}1kJk{g}^{-1}-C^{-4},$ the specific heat capacity of the $50\%$ solution as $3\mathrm{.}5kJk{g}^{-1}{C}^{-1}$ and the specific heat capacity of water as $4\mathrm{.}2k{g}^{-1}{C}^{-1}.$ Calculate:

$($i$)$ the amount of steam used to carry out the process;

$($ii$)$ the steam economy of the evaporator

$($iii$)$ the heating surface area of the above

How would a double effect evaporator improve the efficiency of the operation?

A rectification column is fed with $100kg-$molhr$-1$ of a mixture of $50$mol$\%$ Benzene and $50$mol$\%$ toluene at $110$kPa absolute pressure. The feed is liquid at its boiling point. The distillate is to contain $90$mol$\%$ benzene and the bottoms, $90$mol$\%$ toluene. The actual reflux ratio should be threetimes $(3$X$)$ the minimum, Rmin. Using the McCabe$-$Thiele method, calculate:

$($i$)$ the distillate and bottoms flow rates of this operation;

$($ii$)$ the number of trays required to effect the mass transfer at a tray efficiency of $60\%$ :

$($iii$)$ the location of the feed tray.

$[$the V$-$L diagram of the Benzene$-$Toluene System is attached$]$