Argon and methane are absorbed from nitrogen into liquid ammonia at 252.3 \(\mathrm{K}\) and \(175.0 \mathrm{~atm}\) in an ammonia plant. Feed rate of gas is \(100.0 \mathrm{kmol} / \mathrm{h}\). Feed gas contains \(0.020 \mathrm{~mol} \% \mathrm{Ar}\) and \(0.130 \mathrm{~mol} \%\) methane. Outlet gas contains \(0.0008 \mathrm{~mol} \%\) methane. Entering liquid ammonia is pure. Operate with L/V = 26.0. Assume \(\mathrm{L}\) and \(\mathrm{V}\) flow rates are constant. Equilibrium data: partial pressure methane atm \(=3600.0 \times\) (methane mole fraction in liquid); partial pressure argon \(\mathrm{atm}=7700.0 \times\) (argon mole fraction in liquid) (Alesandrini et al., 1972).

a. Find the outlet mole fraction of methane in the liquid.

b. Find the number of equilibrium stages required.

c. Find the outlet mole fraction of argon in the gas.