A column packed with gas-phase activated carbon is initially filled with clean air. At \(t=0\), a feed gas containing \(y=0.05 \mathrm{wt} \%\) toluene in air is started. This feed continues until \(\mathrm{t}=\) 100.0 hours at which time a feed that is \(\mathrm{y}=0.15 \mathrm{wt} \%\) toluene is introduced and continued throughout the remainder of the operation. The superficial velocity is always \(20.0 \mathrm{~cm} / \mathrm{s}\). Find the minimum column length required to have a single shock wave exit the column. Data: Equilibrium: \(\mathrm{q}=2000 \mathrm{y} /(1+2200 \mathrm{y})\) (Basmadjian, 1997), \(\mathrm{q}=\mathrm{kg}\) toluene \(/ \mathrm{kg}\) carbon and \(\mathrm{y}=\mathrm{wt}\) frac, which is essentially \(\mathrm{kg}\) toluene \(/ \mathrm{kg}\) air. \(\mathrm{T}=298 \mathrm{~K}, \mathrm{P}_{\text {tot }}=50.0 \mathrm{kPa}\). Assume gas has density of pure air, which acts as an ideal gas, \(\mathrm{MW}_{\text {air }}=28.9 \mathrm{~g} / \mathrm{mol}, \mathrm{R}=0.008314\) \(\left(\mathrm{m}^{3} \mathrm{kPa}\right) /(\mathrm{mol} \mathrm{K}), \mathrm{K}_{\mathrm{d}}=1.0, \varepsilon_{\mathrm{e}}=0.40, \varepsilon_{\mathrm{p}}=0.65, ho_{\mathrm{s}}=1500 \mathrm{~kg} / \mathrm{m}^{3}\). Watch your units.