GATE Chemical Engineering Mass Transfer Syllabus

Mass Transfer syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mass Transfer in GATE Chemical Engineering, not a summary of it.

1. 1

   Fick’s laws, Molecular Diffusion, and Mass Transfer Coefficients

   3 topics

   • Fick’s Laws
   • Molecular Diffusion in Fluids
   • Mass Transfer Coefficients
2. 2

   Mass Transfer Theories

   3 topics

   • Film Theory
   • Penetration Theory
   • Surface Renewal Theory
3. 3

   Analogies in Momentum, Heat, and Mass Transfer

   1 topic

   • Analogies
4. 4

   Stage-wise and Continuous Contacting

   1 topic

   • Stage Efficiencies
5. 5

   HTU & NTU Concepts

   2 topics

   • HTU Concept
   • NTU Concept
6. 6

   Design and Operation of Equipment

   8 topics

   • Distillation
   • Absorption
   • Leaching
   • Liquid-Liquid Extraction
   • Drying
   • Humidification
   • Dehumidification
   • Adsorption
7. 7

   Membrane Separations

   4 topics

   • Micro-filtration
   • Ultra-filtration
   • Nano-filtration
   • Reverse Osmosis

Mass Transfer flashcards for GATE Chemical Engineering

19 of 54 cards from the Mass Transfer deck — real questions with worked answers.

1. State Fick's first law of diffusion for a binary mixture (molar flux relative to molar-average velocity).

   Fick's first law: $J_A = -D_{AB}\,\dfrac{dC_A}{dz}$, where $J_A$ is the diffusive molar flux of A, $D_{AB}$ is the diffusivity, and $\dfrac{dC_A}{dz}$ is the concentration gradient. The negative sign shows diffusion proceeds from high to low concentration.

2. What is Fick's second law of diffusion (unsteady-state, constant $D_{AB}$)?

   $$\frac{\partial C_A}{\partial t} = D_{AB}\,\frac{\partial^{2} C_A}{\partial z^{2}}$$ It describes how concentration varies with time and position during transient diffusion.

3. Write the total molar flux $N_A$ in terms of diffusion and bulk (convective) contributions for binary diffusion.

   $$N_A = -C\,D_{AB}\frac{dx_A}{dz} + x_A\,(N_A + N_B)$$ The first term is molecular diffusion; the second is the bulk-flow (convective) contribution.

4. Give the flux equation for steady-state diffusion of A through stagnant non-diffusing B (e.g. evaporation).

   $$N_A = \frac{D_{AB}\,P}{R T\, z\, p_{B,lm}}\,(p_{A1}-p_{A2})$$ where $p_{B,lm}$ is the log-mean of the partial pressures of B. Here $N_B = 0$.

5. Define the log-mean partial pressure $p_{B,lm}$ used in diffusion of A through stagnant B.

   $$p_{B,lm} = \frac{p_{B2}-p_{B1}}{\ln\!\left(\dfrac{p_{B2}}{p_{B1}}\right)}$$ It accounts for the variation of B's partial pressure across the diffusion path.

6. What is the flux relation for equimolar counter-diffusion (EMCD), and how does it compare to diffusion through stagnant B?

   For EMCD, $N_A = -N_B$, so the bulk term vanishes: $$N_A = \frac{D_{AB}}{R T\,z}(p_{A1}-p_{A2})$$ EMCD has no $p_{B,lm}$ factor, so the flux is lower than diffusion through stagnant B (where $p_{B,lm}<P$ enhances flux).

7. How does the gas-phase diffusivity $D_{AB}$ depend on temperature and pressure (Chapman–Enskog scaling)?

   $D_{AB} \propto \dfrac{T^{3/2}}{P}$. Diffusivity increases with temperature and decreases with total pressure for gases.

8. Compare typical magnitudes of diffusivity in gases, liquids, and solids.

   Gases: $D \sim 10^{-5}\ \text{m}^2/\text{s}$; liquids: $D \sim 10^{-9}\ \text{m}^2/\text{s}$; solids: $D \sim 10^{-12}\ \text{m}^2/\text{s}$ or smaller. Diffusion is fastest in gases and slowest in solids.

9. How does liquid diffusivity vary with temperature and viscosity (Stokes–Einstein relation)?

   $$D_{AB} = \frac{k_B T}{6\pi\mu r_A}$$ so $\dfrac{D_{AB}\,\mu}{T} \approx \text{constant}$. Liquid diffusivity increases with temperature and decreases with solvent viscosity.

10. Define the convective mass transfer coefficient $k_c$ (or $k_y$, $k_x$).

    It is the proportionality constant between flux and a concentration (or mole-fraction) driving force: $N_A = k_c\,(C_{A,s}-C_{A,\infty})$, or $N_A = k_y\,(y_{A,i}-y_A)$ for gases and $N_A = k_x\,(x_A - x_{A,i})$ for liquids.

11. What is the relationship between the individual gas-phase coefficient $k_y$ and the overall gas-phase coefficient $K_y$?

    $$\frac{1}{K_y} = \frac{1}{k_y} + \frac{m}{k_x}$$ where $m$ is the slope of the equilibrium line. It represents addition of gas-film and liquid-film resistances in series.

12. For the overall liquid-phase coefficient $K_x$, write the resistance-in-series relation.

    $$\frac{1}{K_x} = \frac{1}{k_x} + \frac{1}{m\,k_y}$$ where $m$ is the equilibrium-line slope.

13. What does it mean for a system to be 'gas-film controlled' vs 'liquid-film controlled'?

    Gas-film controlled: gas-phase resistance dominates ($1/k_y \gg m/k_x$), typical for very soluble gases (small $m$), so $K_y \approx k_y$. Liquid-film controlled: liquid resistance dominates, typical for sparingly soluble gases (large $m$), so $K_x \approx k_x$.

14. State the central assumption and key result of the Film (Two-Film / Whitman) theory.

    It assumes a stagnant film of thickness $\delta$ next to the interface across which all resistance lies, with steady molecular diffusion through it. Result: $k_c = \dfrac{D_{AB}}{\delta}$, so $k_c \propto D_{AB}^{1}$.

15. According to Film theory, how does the mass transfer coefficient depend on diffusivity?

    $k_c \propto D_{AB}^{1}$ (first power), since $k_c = D_{AB}/\delta$.

16. State the key idea and result of Higbie's Penetration theory.

    Each fluid element is exposed to the interface for a fixed contact (exposure) time $t_c$ during which unsteady diffusion occurs. Result: $$k_c = 2\sqrt{\frac{D_{AB}}{\pi t_c}}\quad\Rightarrow\quad k_c \propto D_{AB}^{1/2}$$

17. State the key assumption and result of Danckwerts' Surface Renewal theory.

    Fluid elements at the surface are randomly replaced by fresh fluid at a constant fractional renewal rate $s$ (not a fixed exposure time). Result: $$k_c = \sqrt{D_{AB}\,s}\quad\Rightarrow\quad k_c \propto D_{AB}^{1/2}$$

18. Contrast the dependence of $k_c$ on diffusivity predicted by Film, Penetration, and Surface Renewal theories.

    Film theory: $k_c \propto D_{AB}^{1}$. Penetration and Surface Renewal theories: $k_c \propto D_{AB}^{1/2}$. Experiments usually give an exponent between $0.5$ and $1$ (often $\sim 0.5$–$0.7$).

19. State the Reynolds analogy and its key assumption.

    Reynolds analogy relates momentum, heat, and mass transfer: $$\frac{f}{2} = St_H = St_M$$ where $St_M = \dfrac{k_c}{u}$. It assumes $Pr = Sc = 1$ (all diffusivities equal).

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