Oxygen reacts irreversibly in aqueous sodium sulfate solutions according to the following reaction kinetics:

where k₂ is a second-order rate constant. The reaction is catalyzed by cobalt ions in solution. Thus, k₂ depends on the sodium sulfite concentration as well as on the concentration of cobalt. For 0.8 mol/L sodium sulfite solutions at 30°C, based on data in Sherwood et al. we obtain  where is incm³/mol s and is the cobalt concentration in mol/cm³. The physical solubility of O² in 0.8 mol/L sodium sulfite is 0.58 × 10^-6 mol/cm³ atm and the diffusivity is 1.2 × 10^-5 cm²/s.

(a) Estimate the rate of absorption of pure O₂ at 1 atm in 0.8 mol/L sodium sulfite in a single-sphere absorber as illustrated in Example 13.3 if the solution contains no cobalt. The sphere radius is R = 2 cm and the flow rate of the liquid is 1.0 cm³/s.

(b) Estimate the rate of absorption for the same conditions in (a) if the solution contains a cobalt concentration of 0.6 × 10^-7 mol/cm³. Verify that the reaction regime is fast pseudo-first-order.

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Ro = k(Co)