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Qwestrum Engineering360 · Chemical Engineering · Mass Transfer

Interphase Mass Transfer

The two-film theory adds gas-film and liquid-film resistances in series (through the Henry constant) to give an overall coefficient; the interface is assumed to be at equilibrium, so no resistance sits there and the two film fluxes must be equal.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Equilibriumattheinterface:yi=mxiEquilibrium at the interface: y_{i} = m x_{i} (ideal)
  • The phase with the smaller k dominates the resistance
  • Overall driving force must match the same flux N

Topic details

Introduction

This Treybal topic explains how a solute crosses from one phase to another in absorbers and strippers. You picture two stagnant films either side of the interface, assume equilibrium at the interface itself, and combine the individual film coefficients into overall coefficients K_G or K_L using the equilibrium (Henry’s-law) slope to convert between phases.

Key relations & formulas

NA=KG(pA,G−pA∗)=KL(CA∗−CA,L)N_{A} = K_{G} (p_{A},G - p_{A}*) = K_{L} (C_{A}* - C_{A},L)
(overall driving forces)
1KG=1kG+HkL\frac{1}{K_{G}} = \frac{1}{k_{G}} + \frac{H}{k_{L}}
(two-film resistance addition, H = Henry constant)
NA=Ky(y−y∗)=Kx(x∗−x)N_{A} = K_{y} (y - y*) = K_{x} (x* - x)
(mole-fraction driving force)

Notation and sign conventions

Relation 1 —
NA=KGN_{A} = K_{G}
NA=KG(pA,G−pA∗)=KL(CA∗−CA,L)N_{A} = K_{G} (p_{A},G - p_{A}*) = K_{L} (C_{A}* - C_{A},L)
(overall driving forces)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
1KG=1kG+HkL\frac{1}{K_{G}} = \frac{1}{k_{G}} + \frac{H}{k_{L}}
1KG=1kG+HkL\frac{1}{K_{G}} = \frac{1}{k_{G}} + \frac{H}{k_{L}}
(two-film resistance addition, H = Henry constant)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
NA=KyN_{A} = K_{y}
NA=Ky(y−y∗)=Kx(x∗−x)N_{A} = K_{y} (y - y*) = K_{x} (x* - x)
(mole-fraction driving force)
Write this relation with symbols exactly as in Mass Transfer Operations — Treybal before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

The two-film model localises all resistance to thin films on each side of the interface, where transport is by molecular diffusion. Because the interface is at equilibrium, the concentration there is fixed by the equilibrium relation, and the same flux must pass through both films at steady state. Adding resistances in series (with the Henry constant translating a liquid resistance into gas-side terms) gives the overall coefficient; whichever film has the larger resistance controls, so a highly soluble gas is liquid-film controlled only weakly and is usually gas-film controlled. Overall driving forces use hypothetical equilibrium compositions (y* or x*) so the same measured flux fits either coefficient.

Assumptions and validity limits

State assumptions explicitly before using any relation for interphase mass transfer — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Mass Transfer viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Mass Transfer papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to interphase mass transfer.
4. Use equation 1:
NA=KGN_{A} = K_{G}
.
5. Use equation 2:
1KG=1kG+HkL\frac{1}{K_{G}} = \frac{1}{k_{G}} + \frac{H}{k_{L}}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Interphase Mass Transfer appears in distillation, absorption, and drying. In Indian chemical curricula this topic is tested because it connects theory to diffusion and interphase transfer.
GATE and semester exams often combine interphase mass transfer with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use interphase mass transfer?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students place a resistance at the interface (there is none, by the equilibrium assumption), forget to include the Henry constant when adding film resistances, and mismatch the driving force with its coefficient (using K_G with a liquid-side ΔC). Confusing individual coefficients k with overall coefficients K is very common.

Quick revision checklist

Before attempting interphase mass transfer problems, confirm you can:
1.
Equilibriumattheinterface:yi=mxiEquilibrium at the interface: y_{i} = m x_{i}
(ideal)
2. The phase with the smaller k dominates the resistance
3. Overall driving force must match the same flux N
Revise the solved examples in Mass Transfer Operations — Treybal and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Overall gas-phase coefficient

Problem

k_G = 0.02, k_L = 0.005 (consistent units), Henry constant H = 2. Find K_G from 1/K_G = 1/k_G + H/k_L.

Solution

1/K_G = 1/0.02 + 2/0.005 = 50 + 400 = 450, so K_G = 2.22×10⁻³. The liquid film (400 of 450) dominates the resistance.

Conceptual check — Interphase Mass Transfer

Problem

In a Mass Transfer semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of interphase mass transfer." What should a complete answer include?

Exams & GATE

Draw concentration profiles — interface y_i, x_i in equilibrium.

📖 Standard books (India)

  • Mass Transfer Operations — Treybal

    Read: Syllabus unit

    Absorption, distillation, and extraction

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