Question

What is the dimension of liquid – phase mass-transfer coefficient “kS”?

(a) LT^-1

(b) LT

(c) L^-1T^-1

(d) L^-1T

The question was posed to me during an interview for a job.

Origin of the question is External Mass Transfer topic in section Heterogenous Reactions of Bioprocess Engineering

Answer 1

The correct answer is:

(c) L⁻¹T⁻¹

Explanation: The mass-transfer coefficient kSk_SkS​ (liquid-phase) is typically associated with the rate of mass transfer in the liquid phase in processes like absorption, diffusion, or reaction. Its units are derived from the relationship between mass transfer rate and the driving force (concentration gradient).

• The driving force is typically the concentration difference (unit: mass per volume, e.g., kg/m³).

• The mass transfer rate is the amount of mass transferred per unit time (unit: mass/time, e.g., kg/s).

• Therefore, kSk_SkS​ can be understood as a proportionality constant between the mass flux and the concentration gradient, which leads to the following dimensions:

• Concentration gradient: L−3\text{L}^{-3}L−3

• Mass flux: M⋅T−1\text{M} \cdot \text{T}^{-1}M⋅T−1

Hence, the dimension of kSk_SkS​ is L−1T−1\text{L}^{-1} \text{T}^{-1}L−1T−1, representing the reciprocal of length and time, which aligns with choice (c).