Gas–liquid interfacial area in different setups: which vessel/operation has the highest surface area available for oxygen transfer under otherwise comparable conditions?

Introduction:
Oxygen transfer depends strongly on gas–liquid interfacial area. Sparging directly injects gas, creating many bubbles and vastly increasing interfacial area compared with relying only on the headspace or surface agitation. This question contrasts typical setups used in labs and industry.

Given Data / Assumptions:

• Sparging introduces bubbles throughout the liquid, maximizing area.
• Agitation improves dispersion and renews interfaces.
• Non-sparged systems rely on the top surface only, giving far less interfacial area.

Concept / Approach:
A sparged, agitated tank provides both bubble surface area and rapid surface renewal, resulting in the largest effective a in k_La. Shake flasks create waves and surface renewal but lack dispersed gas bubbles. Standing test tubes have minimal surface area relative to volume, and sealed bottles limit gas exchange to headspace diffusion.

Step-by-Step Solution:
Identify configurations with dispersed bubbles: sparged stirred tank.Recognize agitation at 400 rpm helps bubble breakup and dispersion.Select the sparged, agitated reactor as having the greatest interfacial area.

Verification / Alternative check:
Empirical k_La measurements are highest in sparged, well-agitated reactors versus surface-aerated vessels of similar scale.

Why Other Options Are Wrong:

• Shake flask: Greater area than static tubes but less than sparged tanks.
• Standing test tube: Very low interfacial area.
• Non-sparged stirred tank: No bubble area, only surface renewal.
• Sealed bottle: Essentially no oxygen transfer by sparging.

Common Pitfalls:
Overestimating the effect of headspace aeration compared with direct sparging and dispersion.

Final Answer:
A sparged stirred tank reactor agitated at 400 rpm