A strong acid resin is exchanging \(\mathrm{Ni}^{+2}\) and \(\mathrm{H}^{+}\). The column is \(100.0 \mathrm{~cm}\) long and is initially at \(\mathrm{c}_{\mathrm{T}}=0.10\) eq/L with \(\mathrm{x}_{\mathrm{Ni}}=0.20\). At \(\mathrm{t}=0\), a feed with \(\mathrm{c}_{\mathrm{T}}=5.1 \mathrm{eq} / \mathrm{L}\) and \(\mathrm{x}_{\mathrm{Ni}}=0.20\) is input. \(\mathrm{v}_{\text {super }}=15.0 \mathrm{~cm} / \mathrm{min}\). Use ion movement theory to predict outlet concentration profile. Data: \(\mathrm{c}_{\mathrm{RT}}=2.1, \varepsilon_{\mathrm{e}}=0.40, \mathrm{~K}_{\mathrm{DE}}=1.0\), and equilibrium data are in Table 20-5.

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TABLE 20-5. Approximate ion-exchange equilibrium constants Strong-Acid Sulfonated with 8% DVB lon B = Li+ (reference ion) Strong-Base Trimethylamine with 8% DVB Ion B = CI (reference ion) Ion A KAB Ion D KDB lon A KAB lon D KDB Li+ 1.0 Mg++ 3.3 F 0.1 SO 0.15 H+ 1.3 Zn++ 3.5 CH3COO 0.2 CO3 0.03 Na+ 2.0 Co++ 3.7 HCO3- 0.4 HPO 0.01 NH 2.6 Cu++ 3.8 Bro 1.0 10 K+ 2.9 Cd++ 3.9 CI 1.0 Cs+ 3.3 Ni++ 3.9 CN 1.3 W3 Ag+ 8.5 Mn 4.1 NO 1.3 Ca++ 5.2 HSO 1.6 Sr++ 6.5 Br 3 Pb++ 9.9 NO 4 Bat ++ 11.5 | 8