Problem $(2)$: Consider semi$-$spherical bawl of radius $R$ in which liquid $A$ is evaporating into gas $B.$ We imagine there is some device that maintains the liquid level at $z=h..$ Right at the liquid$-$gas interface, the gas$-$phase concentration of $A,$ expressed as mole fraction, is $x_h.$ This is taken to be the gas$-$phase

concentration of A corresponding to equilibrium with the liquid at the interface. That is$,x_h$ is the vapor pressure of A divided by the total pressure, provided that A and $B$ form an ideal gas mixture and that the solubility of gas B in liquid is negligible. A stream of gas mixture $A-B$ of concentration $x_H$ flows slowly past the top of the bawl, to maintain the mole fraction of $A$ at $x_H$ for $Z=H.$ The entire system is kept at constant temperature and pressure. Gases A and B are assumed to be ideal. Derive the following expression relating variation of concentration of A with $z$ :

$\frac{log(\frac{1-x_A}{1-x_{A1}})}{log(\frac{1-x_{A1}}{1-x_{A2}})}=\frac{log[(\frac{2R-z}{z})(\frac{z_1}{2R-Z_1})]}{log[(\frac{2R-z_1}{Z_1})(\frac{Z_2}{2R-z_2})]}.$