We wish to absorb ammonia from an air stream using water at $20C$ and a total pressure of $1$ atm $.$ The entering water stream is pure water. The entering vapor is $7-$mol$\%$ ammonia. We desire to recover $99\%$ ammonia in the water outlet stream. The total gas flow rate is $93,588\mathrm{.}4c\frac{c}{m}in.$ We want to use a solvent rate that is $1\mathrm{.}5$ times the minimum solvent rate. Assume that temperature is constant at $20C,$ water is nonvolatile, and air does not dissolve in water. Equilibrium data are given below:

Table: Partial Pressure of Ammonia over Ammonia$-$Water Solutions at $20C($Ref: Table $12-3,$ Wankat$)$

$\backslash$table$[[$NH Partial Pressure, $mmHg,gN\frac{H}{100}gH$ O$],[31\mathrm{.}7,5],[69\mathrm{.}6,10],[114,15],[166,20],[227,25]]$

a$)$ Determine marks$]$

b$)$ Determine the amount of water needed $[8$ marks$]$

c$)$ Determine the number of theoretical stages graphically $[20$ marks$].$

d$)$ Explain if Kremser equation to obtain N is applicable in this case $[4$ marks$].$