Liquid Phase Esterification of Acetic Acid and Isobutanol into Isobutyl Acetate and Water

Question

The liquid-phase esterification of acetic acid (A) with isobutanol (B) to form isobutyl acetate (P) and water (W), using Amberlite IR-120 ion exchange resin as a catalyst, has been studied in a batch reactor, in which mass transfer effects are negligible.  The rate equation was found to be

r_A = K (C_A C_B - C_P C_W/ K_eq)/1 + K_B C_B + K_W C_W mol.A / g.cat-hr

At 333 K, k = 0.00384 L²/g.cat-mol-hr, Keq = 4, KB = 0.460 L/mol.B, and KW = 3.20 L/mol.W.  The initial concentrations of acetic acid and isobutanol are both 1.50 mol/L, and there is no water or isobutyl acetate initially.  What concentration of ion exchange resin (g/L) is required to reach a fractional conversion of acetic acid of 0.40 in 100 hr?

Summary

The question belongs to Chemical Engineering and it is about liquid phase esterification of acetic acid with isobutanol to form isobutyl acetate and water. The concentration of ion exchange resin required to reach the desired amount of reaction needs to be calculated.

Note: The solution is in handwritten format