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Topic Guide

Mass Transfer
GATE CH Guide

Syllabus breakdown, weightage, essential formulas, and a study plan for the Mass Transfer section of GATE Chemical Engineering, with five in-depth guides on distillation, absorption, drying, evaporation, and diffusion.

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Overview

Mass Transfer is the GATE Chemical Engineering syllabus's largest applied section, covering how species move between phases, the physics behind distillation, absorption, drying, adsorption, and extraction. It builds directly on vapor-liquid equilibrium concepts, so a solid grip on the Antoine equation and Raoult's law pays off across nearly every subtopic here.

The section starts with diffusion (Fick's law) as the microscopic driving force, then scales up to phase-equilibrium relationships (Antoine equation, Raoult's law, dew/bubble point) that determine how far a separation can go. From there it branches into equipment-specific applications: distillation (McCabe-Thiele), absorption/stripping (HTU-NTU), humidification and drying (psychrometry), adsorption (Langmuir/Freundlich isotherms), and liquid-liquid extraction.

GATE draws numericals from across this whole span, dew/bubble point calculations from the Antoine equation (GATE 2025 Q47), drying-time problems using constant- and falling-rate periods, and adsorption-isotherm numericals. ChemeGate's Antoine Equation Calculator solves log₁₀(P*) = A − B/(C+T) for vapor pressure and dew point directly, including the worked GATE 2025 Q47 solution.

Real GATE CH PYQ Frequency (2024–2026)

2024	2025	2026	3-Yr Avg
4	6	6	5.3

Computed directly from 16 real questions tagged to this topic across our GATE CH 2024–2026 archive, averaging 5.3 questions/year. Browse the underlying 16 questions for this topic in the PYQ archive, or see the full topic weightage comparison across all topics.

GATE Weightage

Mass Transfer typically contributes 4–6 questions (about 9–13 marks) to the GATE CH paper, the single largest concentration of marks in the core subjects, split across VLE/distillation, absorption, and humidification/drying/adsorption.

Sub-area	Approx. Marks
VLE, Antoine equation & distillation	~3–4
Diffusion & mass transfer coefficients	~2–3
Humidification, drying & psychrometry	~2–3
Absorption, adsorption & extraction	~2–3

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

Diffusion fundamentals

Fick's first law and molecular diffusion in gases and liquids, including diffusion through a stagnant film and estimation of diffusivity.

Vapor-liquid equilibrium

Raoult's law, relative volatility, and the Antoine equation for pure-component vapor pressure, the basis for dew point and bubble point calculations in mixtures.

Distillation

The McCabe-Thiele graphical method for binary distillation, the Fenske-Underwood-Gilliland shortcut method, reflux ratio, and flash distillation.

Absorption & stripping

The HTU-NTU method for packed-tower design, operating-line vs. equilibrium-line construction, and the minimum liquid-to-gas ratio.

Humidification & drying

The psychrometric chart, wet-bulb and dry-bulb temperature, and the constant-rate and falling-rate periods that govern drying time.

Adsorption

Langmuir and Freundlich isotherms describing equilibrium loading on a solid adsorbent, and breakthrough-curve behavior in fixed-bed adsorption columns.

Liquid-liquid extraction

Distribution coefficients, single- and multi-stage extraction calculations, and ternary phase diagrams for partially miscible systems.

Mass transfer coefficients

Film theory and the two-film model, plus overall mass transfer coefficients (Ky, Kx) that combine gas- and liquid-phase resistances.

Essential Formulas

Full formula reference →

$N_A = -D_{AB}\dfrac{dC_A}{dz}$

Fick's first law of molecular diffusion (add bulk-flow term for diffusion through a stagnant film)

$\log_{10}(P^{*}) = A - \dfrac{B}{C+T}$

Antoine equation for pure-component vapor pressure (T in °C, constants from Perry's Handbook)

$p_A = x_A P_A^{*}$

Raoult's law, partial pressure of component A over an ideal liquid mixture

$\alpha = \dfrac{y_A/x_A}{y_B/x_B}$

Relative volatility, the key parameter driving distillation separability

$\sum x_i P_i^{*} = P$

Bubble point condition for a liquid mixture at total pressure P

$\sum \dfrac{y_i P}{P_i^{*}} = 1$

Dew point condition for a vapor mixture at total pressure P

$N_A = K_y(y_A - y_A^{*}) = K_x(x_A^{*} - x_A)$

Two-film theory, flux written in terms of overall gas- or liquid-phase driving force

$\dfrac{1}{K_y} = \dfrac{1}{k_y} + \dfrac{m}{k_x}$

Overall mass transfer coefficient combining individual gas- and liquid-film resistances (m = local slope of equilibrium line)

$q = \dfrac{q_{max} K C}{1 + K C}$

Langmuir adsorption isotherm, monolayer equilibrium loading q vs. fluid concentration C

$q = K C^{1/n}$

Freundlich adsorption isotherm, empirical power-law equilibrium relationship

$t_c = \dfrac{(W_1 - W_c) L_s}{A R_c}$

Constant-rate drying time, from initial moisture W1 down to critical moisture Wc

$t_f = \dfrac{L_s}{A R_c} W_c \ln\!\left(\dfrac{W_c}{W_2}\right)$

Falling-rate drying time (linear falling-rate assumption), from Wc down to final moisture W2

$H = \dfrac{18}{29}\cdot\dfrac{p_w}{P - p_w}$

Humidity (kg water vapor per kg dry air) from water vapor partial pressure pw and total pressure P

$F = C - P + 2$

Gibbs phase rule, degrees of freedom F for C components and P phases, used to check VLE problem consistency

Visual Reference

No resistance in the well-mixed bulk phases (flat), all of it packed into the two thin films — and a real composition jump at the interface itself, set by the local equilibrium slope m = (yi − y*)/(xi − x).

Granules of activated charcoal, a porous adsorbent material — Activated charcoal — a real adsorbent, its enormous internal surface area is exactly what the Langmuir/Freundlich isotherms in this guide's formula table describe. Mubychemcom, CC0, via Wikimedia Commons.

Derivations & Physical Insight

Building the Overall Mass Transfer Coefficient from Two Films

Two-film theory models the resistance to interphase mass transfer as two stagnant films, one on the gas side, one on the liquid side, with bulk turbulence assumed to eliminate any resistance beyond them. At the interface itself, the gas and liquid compositions are assumed to be in local equilibrium (no resistance there), so the flux through each film must be equal at steady state:

Because the interface compositions (y_i, x_i) aren't directly measurable, it's more useful to express flux in terms of an overall driving force referenced to one bulk phase, using an overall coefficient. Substituting the individual-film flux equations and the local equilibrium slope m = (y_i − y*)/(x_i − x) at the interface gives the standard resistances-in-series form:

N_A = k_y(y - y_i) = k_x(x_i - x)

\dfrac{1}{K_y} = \dfrac{1}{k_y} + \dfrac{m}{k_x}

Why the McCabe-Thiele Operating Line Is Linear

McCabe-Thiele analysis reduces a full stage-by-stage distillation design to two straight lines on a y-x diagram. The rectifying-section operating line comes directly from a mass balance around the top of the column down to any stage n, using constant molar overflow (equal molar latent heats assumption, so L and V are constant tray-to-tray):

Because L, V, and the distillate composition x_D are all constant under this assumption, y_n is a linear function of x_(n+1), that's the entire justification for why the operating "line" is straight rather than curved, and why the method works graphically instead of requiring a full energy balance at every stage.

y_{n+1} = \dfrac{L}{V}x_n + \dfrac{D}{V}x_D = \dfrac{R}{R+1}x_n + \dfrac{x_D}{R+1}

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

Relative Volatility from Antoine-Derived Vapor Pressures

Problem: At 85°C, benzene has a vapor pressure of 875 mmHg and toluene has a vapor pressure of 345 mmHg. Find the relative volatility of benzene with respect to toluene, assuming an ideal (Raoult's law) mixture.

Given: P*_benzene = 875 mmHg, P*_toluene = 345 mmHg at T = 85°C.

\alpha_{B,T} = \dfrac{P^{*}_{B}}{P^{*}_{T}} = \dfrac{875}{345}

Answer: α ≈ 2.54

2-mark · NAT

Minimum Reflux Ratio Estimate for a Binary Distillation

Problem: A saturated liquid feed with x_F = 0.5 is to be separated with a relative volatility α = 2.5 (constant). Estimate the minimum reflux ratio using the Fenske-Underwood shortcut for a binary system with a q-line at q = 1 (saturated liquid feed).

Given: x_F = 0.5, α = 2.5, saturated liquid feed (q = 1), so the q-line is vertical at x = x_F.

y^{*} = \dfrac{\alpha x_F}{1+(\alpha-1)x_F} = \dfrac{2.5\times 0.5}{1+1.5\times 0.5} = \dfrac{1.25}{1.75}

R_{min} = \dfrac{x_D - y^{*}}{y^{*} - x_F}\ \text{(read graphically once } x_D \text{ is fixed; here we report the pinch composition)}

Answer: y* (pinch vapor composition) ≈ 0.714, used with the chosen x_D to read R_min off the q-line intersection.

Topic-wise PYQ Frequency

High

Antoine equation, dew point & bubble point

A GATE staple, GATE 2025 Q47 asked exactly this: dew point temperature from a given humidity using the Antoine equation.

High

Distillation (McCabe-Thiele, relative volatility)

Frequently tested, both as graphical-method conceptual questions and reflux-ratio numericals.

Medium

Diffusion & Fick's law

Common as a direct numerical on flux through a stagnant film or diffusivity estimation.

Medium

Humidification & drying

Drying-time numericals (constant-rate and falling-rate periods) appear regularly, in the style of GATE 2025 Q40.

Medium

Adsorption (Langmuir/Freundlich)

Isotherm-fitting or equilibrium-loading numericals show up periodically, in the style of GATE 2025 Q65.

Medium

Absorption & stripping

HTU-NTU and minimum liquid-rate problems are less frequent than distillation but still recurring.

Low

Liquid-liquid extraction

Occasional conceptual or single-stage numerical question.

Recommended Study Order

1
1. Diffusion fundamentals (Fick's law)
The microscopic basis for every later topic in this section, understand flux and driving force before scaling up to equipment.
2
2. Vapor-liquid equilibrium & the Antoine equation
The highest-yield subtopic and a prerequisite for distillation, practice dew point and bubble point calculations until they're fast and automatic.
3
3. Distillation (McCabe-Thiele)
Builds directly on VLE concepts and carries some of the heaviest weightage in this section.
4
4. Mass transfer coefficients & two-film theory
Needed before absorption/stripping design, since both use overall coefficients built from individual film resistances.
5
5. Absorption & stripping
A direct application of the two-film theory and operating-line/equilibrium-line construction from distillation.
6
6. Humidification & drying
A self-contained, numerically distinct topic, study once VLE fundamentals are solid, since humidity calculations reuse vapor-pressure concepts.
7
7. Adsorption
Isotherm equations (Langmuir, Freundlich) are quick to learn and pair well with the equilibrium-relationship intuition built earlier.
8
8. Liquid-liquid extraction
Lowest PYQ frequency, cover last with a focus on distribution coefficients and basic stage calculations.

Common Pitfalls

✗ Using the Antoine equation with temperature in the wrong unit (K instead of °C, or vice versa) for the given constants.

✓ Always check whether the Antoine constants A, B, C were fitted for T in °C or K before substituting, mixing them produces a vapor pressure off by orders of magnitude.

✗ Confusing dew point and bubble point conditions, or applying the wrong summation (Σx·P* vs. Σy·P/P*).

✓ Bubble point: liquid mostly present, solve Σ(x_i·P*_i) = P. Dew point: vapor mostly present, solve Σ(y_i·P/P*_i) = 1.

✗ Assuming the falling-rate drying period is always linear.

✓ The linear falling-rate assumption is a simplification, check whether the problem specifies it, since real falling-rate curves can be nonlinear and need graphical integration.

✗ Mixing up individual film coefficients (ky, kx) with overall coefficients (Ky, Kx) in two-film theory calculations.

✓ Overall coefficients combine both film resistances via 1/Ky = 1/ky + m/kx, only use individual coefficients when finding the interface composition directly.

Put It Into Practice

Compute vapor pressure and dew point interactively with the Antoine equation, then check your approach against the worked GATE 2025 Q47 solution and other solved previous-year questions.

Open the Antoine Equation Calculator →Take a Practice Test →

Go Deeper

Keep Exploring

Mass Transfer
GATE CH Guide

Overview

Real GATE CH PYQ Frequency (2024–2026)

GATE Weightage

Key Subtopics

Essential Formulas

Visual Reference

Derivations & Physical Insight

Building the Overall Mass Transfer Coefficient from Two Films

Why the McCabe-Thiele Operating Line Is Linear

Worked Practice Problems

Relative Volatility from Antoine-Derived Vapor Pressures

Minimum Reflux Ratio Estimate for a Binary Distillation

Topic-wise PYQ Frequency

Recommended Study Order

Common Pitfalls

Put It Into Practice

Mass Transfer In Depth

Diffusion & Mass Transfer Coefficients

Distillation

Absorption, Stripping & Extraction

Drying & Humidification

Evaporation & Crystallization

Related

Antoine Equation

GATE CH Formula Sheet

GATE Practice Tests by Year

Mass TransferGATE CH Guide

Overview

Real GATE CH PYQ Frequency (2024–2026)

GATE Weightage

Key Subtopics

Essential Formulas

Visual Reference

Derivations & Physical Insight

Building the Overall Mass Transfer Coefficient from Two Films

Why the McCabe-Thiele Operating Line Is Linear

Worked Practice Problems

Relative Volatility from Antoine-Derived Vapor Pressures

Minimum Reflux Ratio Estimate for a Binary Distillation

Topic-wise PYQ Frequency

Recommended Study Order

Common Pitfalls

Put It Into Practice

Mass Transfer In Depth

Diffusion & Mass Transfer Coefficients

Distillation

Absorption, Stripping & Extraction

Drying & Humidification

Evaporation & Crystallization

Related

Antoine Equation

GATE CH Formula Sheet

GATE Practice Tests by Year

Mass Transfer
GATE CH Guide