We wish to absorb two gas streams in an absorber. The main gas stream (stream A) is at \(15.0^{\circ} \mathrm{C}, 2.5 \mathrm{~atm}\), and has a flow rate of \(100.0 \mathrm{kmol} / \mathrm{h}\). Stream A is \(90.0 \mathrm{~mol} \%\) methane, \(6.0 \mathrm{~mol} \% \mathrm{n}\)-butane, and \(4.0 \mathrm{~mol} \% \mathrm{n}\)-pentane. The second gas stream (stream \(\mathrm{B}\) ) is at \(10.0^{\circ} \mathrm{C}, 2.5 \mathrm{~atm}\), and has a flow rate of 75.0 \(\mathrm{kmol} / \mathrm{h}\). Stream B is \(99.0 \mathrm{~mol} \%\) methane, \(0.9 \mathrm{~mol} \% \mathrm{n}\)-butane, and \(0.1 \mathrm{~mol} \% \mathrm{n}-\) pentane. Liquid solvent fed to the absorber is at \(15.0^{\circ} \mathrm{C}\) and \(2.5 \mathrm{~atm}\) and has a flow rate of \(200.0 \mathrm{kmol} / \mathrm{h}\). This stream is \(99.9 \mathrm{~mol} \% \mathrm{n}\)-decane and \(0.1 \mathrm{~mol} \% \mathrm{n}-\) pentane. Absorber pressure is \(2.5 \mathrm{~atm}\). We desire an outlet gas stream that is \(99.9 \mathrm{~mol} \%\) methane or slightly higher. Determine the total number of stages and the optimum feed stages for streams A and B required to just achieve the desired methane purity of outlet gas stream. (Use "on stage" for all feeds.) Report the following information:

a. Total number of stages required:_______________________________________

b. Feed stage location for the solvent::_______________________________________

c. Feed stage location for stream A::_______________________________________

d. Feed stage location for stream B::_______________________________________

e. Outlet mole fractions of gas stream leaving absorber::_______________________________________

f. Outlet mole fractions of liquid leaving absorber::_______________________________________ g. Outlet gas flow rate: \( \qquad \) \(\mathrm{kmol} / \mathrm{h}\):_______________________________________ h. Outlet liquid flow rate: \( \qquad \) \(\mathrm{kmol} / \mathrm{h}\):_______________________________________ i. Highest temperature in column: \( \qquad \) \({ }^{\circ} \mathrm{C}\) and stage on which it occurs::_______________________________________