A tray$-$tower with $N$ equilibrium stages is employed for stripping ammonia from a wastewater

stream by means of countercurrent air at atmospheric pressure and $80F.$ In this process,

ammonia $($solute$)$ is transferred from water to air. Thus, this process is opposite to the gas$-$

absorption discussed in the class and is known as "gas$-$stripping".

$($a$)$ Using the figure below and following an analysis like the one discussed in the class, derive

the following form of KREMSER's equation applicable for stripping:

$x_{N+1}=\frac{1-S^{N+1}}{1-S}{x}_1$

In the above equation, $S$ is the stripping factor and is defined as $S=\frac{K{V}^{\text{'}}}{L^{\text{'}}}$ and $K=\frac{Y_i}{x_i}$

$($Note that, both for "absorption" and "stripping", the numbering of stages follows the convention that

stage $1$ is the stage onto which fresh "solute$-$receiving phase" is admitted$)$

$($b$)$ A tower with six equilibrium stages is used for stripping ammonia from wastewater using

pure air. Calculate the concentration of ammonia in the exit water if the inlet liquid

concentration is $0\mathrm{.}1$mol$\%$ ammonia in water, the inlet air is free of ammonia, and $1\mathrm{.}43$mol

of air per mol of water are fed to the tower. K for ammonia at this temperature is $1\mathrm{.}414.$