We are exchanging \(\mathrm{Ag}^{+}\)and \(\mathrm{K}^{+}\)on a strong acid resin with \(8 \%\) divinylbenzene (DVB). Total resin capacity is \(\mathrm{c}_{\mathrm{RT}}=2.0 \mathrm{eq} / \mathrm{L}\), and ionic concentration of feed solution is \(\mathrm{c}_{\mathrm{T}}=1.20\) eq/L, all of which is \(\mathrm{Ag}^{+}\). Column is initially at a solution concentration of \(\mathrm{c}_{\mathrm{T}}=0.20 \mathrm{eq} / \mathrm{L}\), all of which is \(\mathrm{K}^{+}\).

a. How long does it take for the total ion wave to break through?

b. At what time does \(\mathrm{Ag}^{+}\)shock wave break through?

c. After \(\mathrm{Ag}^{+}\)shock wave breaks through, regenerate column with pure \(\mathrm{K}^{+}\)solution with \(\mathrm{c}_{\mathrm{T}}=1.20 \mathrm{eq} / \mathrm{L}\). Predict shape of ensuing diffuse wave. (Reset \(\mathrm{t}=0\) when start \(\mathrm{K}^{+}\) regeneration solution.)

Data: \(\varepsilon_{\mathrm{e}}=0.40, \varepsilon_{\mathrm{p}}=0.0, \mathrm{~K}_{\mathrm{E}}=1.0, \mathrm{v}_{\text {super }}=3.0 \mathrm{~cm} / \mathrm{min}, \mathrm{L}=50.0 \mathrm{~cm}\).