Air containing $1\mathrm{.}7\%$ by volume $S{O}_2$ is scrubbed with pure water in a packed column of $1\mathrm{.}2m^2$ in cross sectional area and $3\mathrm{.}2m$ in packed height. Entering gas and liquid flow rates are, respectively, $0\mathrm{.}062$ and $2\mathrm{.}2$kmo$\frac{l}{s}.$ If the outlet mole fraction of $S{O}_2$ in the gas is $0\mathrm{.}005$ and column temperature is near$-$ambient with $KS{O}_2=40,$ calculate:

a$)N_{OG}($number of overall gas$-$phase transfer units$)$ for absorption of $S{O}_2(3$ marks, A&A $1\mathrm{.}4)$

b$)H_{OG}($height of an overall transfer unit based on the gas phase$)$ in meters $(2$ marks, A&A $1\mathrm{.}4)$

c$)$ Kya $($volumetric mass$-$transfer coefficient for the gas phase based on a mole$-$fraction driving force$)$ for $S{O}_2$ in kmol$/$m$^3$ s