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In a packed bed tower air is purified from methanol by using water. Tower has a cross sectional area of $0\mathrm{.}2m^2$ and system operates at $313\mathrm{.}1K$ and $101\mathrm{.}32$kPa. The inlet air contains $10$mol$\%$ methanol and at outlet the concentration of methanol drops to $2$mol$\%.$ The gas flow is $20$kgmol inert air$/$h$.$ The pure inlet flow is $50$kgmol water$/$h$.$ Film coefficients for the given flows in the tower are $k_x^{\text{'}}a=0\mathrm{.}07kgmo\frac{l}{s}.m^3.$mol frac and $k^{\text{'}}ya=0\mathrm{.}04$kgmo$\frac{l}{s}.m^3.$mol frac. Equilibrium data is given below. Calculate the tower height.

Equilibrium data for methanol$-$water system at $313\mathrm{.}1K$

$\backslash$table$[[\backslash$table$[[$Mole fraction Methanol$],[$in Liquid, $xA$