Q11.1 Examine how the following parameters influence
(a) absorption flux,
(b) the absorption rate per unit volume, and
(c) the total rate of absorption (in say, moles/sec) in the different regimes of absorption with chemical reaction: Liquid holdup, liquid volume, interfacial area, interfacial area per unit volume, gas holdup, temperature, concentration of the liquid reagent, partial pressure of the gaseous solute, liquid phase mass transfer coefficient.

Q11.2 The following questions address some issues on gas-liquid reaction theory.

Q11.2.1 The diffusional sub-regime of the slow reaction regime is such that A_b is zero (or nearly so) because of reaction, but the later is still now fast enough to occur to a significant extent in the film. These seemingly contradictory requirements are often met in gas-liquid contactors because of the large ratio of bulk volume to film volume. Given that the value of the Hatta number needs to be about 0.1 or lower before any reaction in the film may be assumed to be insignificant, derive an upper limit for the ratio of the film volume (and hence the ratio of /) which ensures the existences of a diffusional sub regime. Assume first order kinetics.

Q11.2.2 Derive the film theory equation for the case where the above criterion is not met, that is reaction occurs to a significant extent in the film even with non-zero A_b. This situation could apply, for example, to certain cases of liquid-liquid contacting. Show that, for such cases, the mass transfer rate in the presence of chemical reaction is no longer linear in the concentration difference (driving force).

Q11.2.3 Solve the film theory differential equation for the pseudo-zero order reaction (i.e. a reaction that is zero order in the gaseous solute and independent of the liquid reagent concentration) taking place partly in the film, and wholly in the film. Note that, in the later case, the point at which flux becomes zero within the film has to be explicitly invoked in the derivation. Compare the variation of the enhancement factor in this region (slow to fast transition and fast reaction) as a function of  with the prediction of the general equation  .
Q11.2.4 How does it happen that, although based on entirely different physical premises the film and the penetration theory lead to almost identical results in practice so long as the diffusivities of the gas and liquid phase reactants are not far different ? On the basis of your answer (or otherwise) comment on how and to what extent the distribution assume for the surface ages would be expected to influence the prediction of the enhancement factor.

Q11.3 The following data pertain to the oxidation of cyclohexane by a mixture of oxygen and nitrogen. The data were obtained in stirred tank with the gas mixture being bubbled continuously through cyclohexane at 150°C and 12 bar (abs). The reaction is autocatalytic. The time course of the process is followed by measuring oxygen content in the leaving gases and the dissolved oxygen concentration as function of time. Quasi steady state conditions may be assumed for the mass transfer process.

Time (min)	28	31.5	37.5	47.4	50	53.4	57.4	9.0
O2 Flow Rate out Mol/s × 103	1.11	1.09	1.02	0.885	0.85	0.80	0.77	0.73
Diss. O2 concn. Mol.fr.×104	4	3.8	3.4	2.1	1.3	0.65	0.97	0.19

11.3.1 Assuming the volumetric mass transfer coefficient to be constant, and the regime of absorption to be slow (why is this reasonable assumption ?) dawn an overall mass balance for oxygen in the reactor. The actual kinetics is unknown. Assume the gas in the reactor to be well mixed and the solubility of oxygen to be given by Henry’s law. Hence, derive an equation between the molar exit flow rate of oxygen and the dissolved oxygen mole fraction to calculate the volumetric mass transfer coefficient and the Henry’s law coefficient H from a single plot of the above data.