Use of slurry adsorbents has received some industrial attention because it allows for countercurrent movement of the solid and fluid phases. Your manager wants you to design a slurry adsorbent system for removing methane from a hydrogen gas stream. The actual separation process is a complex combination of adsorption and absorption, but total equilibrium can be represented by a simple equation. At \(5.0^{\circ} \mathrm{C}\), equilibrium can be represented as

\section*{Weight fraction \(\mathrm{CH}_{4}\) in gas \(=1.2 \times\) (weight fraction \(\mathrm{CH}_{4}\) in slurry)}

At \(5.0^{\circ} \mathrm{C}\), no hydrogen could be detected in the slurry, and heat of sorption was negligible. We wish to separate a gas feed at \(5.0^{\circ} \mathrm{C}\) that contains 100.0 \(\mathrm{lb} / \mathrm{h}\) of hydrogen and \(30.0 \mathrm{lb} / \mathrm{h}\) of methane. An outlet gas concentration of \(5.0 \mathrm{wt} \%\) methane is desired. Entering slurry contains no methane and flows at a rate of \(120.0 \mathrm{lb} / \mathrm{h}\). Find the number of equilibrium stages required for this separation and the mass fraction of methane leaving in the slurry.