Temperature sensitivity of liquid versus gas mass transfer: Compared with gases, how does temperature typically affect liquid-phase mass transfer coefficients?

Introduction / Context:
Mass transfer coefficients depend on diffusivity and viscosity, both of which vary with temperature. The sensitivity differs markedly between liquids and gases and is essential when evaluating temperature control in extraction, absorption, and mixing operations.

Given Data / Assumptions:

• Physical (nonreactive) mass transfer.
• Ordinary pressure ranges.
• Representative liquids and gases with typical property–temperature trends.

Concept / Approach:
In liquids, molecular diffusivity generally increases strongly with temperature (often following an Arrhenius-type relation) while viscosity decreases, both changes increasing mass transfer coefficients markedly. In gases, diffusivity rises with approximately T^1.5 / P and viscosity also rises with temperature, yielding a comparatively milder net effect on k. Therefore, liquid-phase mass transfer is usually more temperature-sensitive than gas-phase mass transfer.

Step-by-Step Solution:
Recognize k ∝ D * f(Sc, Re) and D_liquid increases sharply with T; μ_liquid decreases with T.For gases, D_gas increases with T but μ_gas also increases, partly offsetting gains in convective transport.Conclude: liquids show stronger dependence; choose option (a).

Verification / Alternative check:
Empirical correlations (e.g., film theory, penetration theory) show liquid-side k_L scaling strongly with D_L and ν_L; temperature exponents are larger for liquids.

Why Other Options Are Wrong:
(b) Opposite of observed behavior; (c) ignores clear property variations; (d) is unnecessary because a correct specific statement exists.

Common Pitfalls:

• Assuming constant properties over wide temperature ranges in design calculations.
• Neglecting solubility changes with temperature which also affect driving forces.

Final Answer:
Affected more by temperature than that for gases