A \(50.0 \mathrm{~cm}\) long column is packed with a strong acid cation-exchange resin \(\left(\mathrm{c}_{\mathrm{RT}}=2.2 \mathrm{eq} / \mathrm{L}\right.\), \(\varepsilon_{\mathrm{e}}=0.42\) ). Fluid superficial velocity is \(25.0 \mathrm{~cm} / \mathrm{min}\). Cations are not excluded. Anions are excluded. Anderson (1997) lists \(\mathrm{K}_{\mathrm{H}-\mathrm{Li}}=1.3 \& \mathrm{~K}_{\mathrm{K}-\mathrm{Li}}=2.9\). Dechow (1989) lists \(\mathrm{K}_{\mathrm{H}-\mathrm{Li}}=\) 1.26 and \(\mathrm{K}_{\mathrm{K}-\mathrm{Li}}=2.63\).

a. If resin is initially in \(\mathrm{H}^{+}\)form in equilibrium with a \(0.10 \mathrm{eq} / \mathrm{L}\) solution of \(\mathrm{HCl}\) and an aqueous feed that is \(0.10 \mathrm{eq} / \mathrm{L} \mathrm{KCl}\) is fed to the column, calculate times that \(\mathrm{K}^{+}\)shock wave exits for both sets of equilibrium parameters.

b. If resin is initially in equilibrium with a \(1.0 \mathrm{eq} / \mathrm{L}\) solution of \(\mathrm{HCl}\) and an aqueous feed that is \(1.0 \mathrm{eq} / \mathrm{L} \mathrm{KCl}\) is fed to the column, calculate times that \(\mathrm{K}^{+}\)shock wave exits for both sets of equilibrium parameters.

c. If resin is initially in equilibrium with a \(1.0 \mathrm{eq} / \mathrm{L}\) solution of \(\mathrm{HCl}\) and \(\mathrm{KCl}\left(\mathrm{x}_{\mathrm{H}}=0.8\right.\), \(\left.\mathrm{x}_{\mathrm{K}}=0.2\right)\) and an aqueous feed that is \(1.0 \mathrm{eq} / \mathrm{L}\) solution of \(\mathrm{HCl}\) and \(\mathrm{KCl}\left(\mathrm{x}_{\mathrm{H}}=0.15, \mathrm{x}_{\mathrm{K}}\right.\) \(=0.85)\) is fed to the column, calculate times that \(\mathrm{K}^{+}\)shock wave exits for both sets of equilibrium parameters.

d. Discuss your results.