Question $7(max10)$

The gas stream from a chemical reactor contains $25$mol$\%$ propane and is being stripped by direct superheated steam in a stripping tray tower to reduce the propane content to $0\mathrm{.}2$mol $\%.$ The temperature is held constant at $422K$ by internal heating in the tower at $2\mathrm{.}026{10}^5$ Pa pressure. A total of $11\mathrm{.}42kg$ mol of direct steam is used for $300$kgmol of total entering liquid. The vapour $-$ liquid equilibria can be represented by $y=2\mathrm{.}5x,$ where $y$ is mole fraction propane in the steam, and $x$ is mole fraction propane in the oil. Steam can be considered as an inert gas and will not condense.

$($a$)$ Plot the operating and equilibrium lines and determine the number of theoretical trays needed

$($b$)$ Using transfer units method, calculate the height of the tower