Derive (15-44). Use this equation to solve the following problem. Sulfate ion is to be removed from 60 L of water by exchanging it with chloride ion on 1 L of a strong-base resin with relative molar selectivities as listed in Table 15.6 and an ion-exchange capacity of 1.2 eq/L of resin. The water to be treated has a sulfate-ion concentration of 0.018eq/L and a chloride-ion concentration of 0.002eq/L. Following the attainment of equilibrium ion exchange, the treated water will be removed and the resin will be regenerated with 30 L of 10 wt% aqueous NaCl.

(a) Write the ion-exchange reaction.

(b) Determine the value of K_SO^{2 –}₄, Cl^–.

(c) Calculate equilibrium concentrations c_SO^{2 –}₄, c,_Cl– , q _SO^{2 –}₄, and q_Cl– in eqL for the initial ion-exchange step.

(d) Calculate the concentration of C1^– in eq/L for the regenerating solution.

(e) Calculate c_SO^{2 –}₄, c_Cl–, q _SO^{2 –}₄, and q_Cl- upon reaching equilibrium in the regeneration step.

(f) Are the separations sufficiently selective?

Table 15.6 Approximate Relative Molar Selectivities for Anions with Strong-Base Resins ( I) 0.65 , 0.4 NO, 4 3 CH3COO- 0.2 Br 1.6 0.1 HSO, NO, F- ( I) so? co ? 0.05-0.07 1.3 0.15 CN- 1.3 CI- 1.0 0.03 3 1.0 0.01