Gas–liquid equilibrium — Henry’s law relates which pair of oxygen variables in bioprocessing at constant temperature?

Introduction:
Henry’s law provides the equilibrium relationship between a gas’s partial pressure and its dissolved concentration in a liquid at a given temperature. For oxygen in water or broth, this sets the upper bound on the dissolved oxygen concentration achievable at equilibrium with a given headspace or bubble partial pressure.

Given Data / Assumptions:

• Isothermal conditions (Henry’s constant depends strongly on temperature).
• Ideal dilute gas–liquid solution behavior for oxygen.
• No chemical reaction consuming oxygen during the equilibrium statement.

Concept / Approach:
Henry’s law: C* = H * p_O2 (using a suitable convention), where C* is the saturation (equilibrium) concentration in the liquid phase and p_O2 is the oxygen partial pressure in the contacting gas. This is distinct from dynamic mass transfer, which introduces k_La and driving forces (C* − C). Henry’s law alone is an equilibrium relation, not a rate expression.

Step-by-Step Solution:
State relationship: C* is proportional to p_O2 with proportionality H at fixed T.Recognize that OTR depends on k_La and driving force, not directly on Henry’s law alone.Select the option that pairs p_O2 with saturation concentration C*.

Verification / Alternative check:
Increasing headspace oxygen fraction or total pressure increases p_O2 and thus C*, as predicted by Henry’s law and confirmed by DO probe readings at equilibrium after long aeration at low k_La.

Why Other Options Are Wrong:

• Options (b), (c), (d), and (e) involve rate parameters or hydrodynamics; Henry’s law is not a rate law.

Common Pitfalls:
Confusing equilibrium (C*) with actual DO (C) during transfer; forgetting that temperature changes Henry’s constant substantially.

Final Answer:
The partial pressure of oxygen and the saturation concentration of oxygen dissolved in the liquid