Individual & Overall Mass Transfer Coefficients

Convert two resistances into one practical coefficient you can use in a design equation.

Core toolsDesign equationsGas–liquid
⏱️ About 20 min

A plant datasheet often gives an overall coefficient—how do you relate it back to gas- and liquid-side films?

💡
The big idea: Overall coefficients package two-film resistances into a single coefficient by choosing a basis (gas or liquid) and converting the other-side driving force using equilibrium (Henry’s law).
🎯 By the end, you'll be able to
  • Define individual coefficients k_G and k_L
  • Define overall coefficients K_G and K_L
  • Apply 1/K_L = 1/k_L + 1/(H k_G)
  • Compute K_L from k_L, k_G, and H
📎 Helpful to know first

Individual film coefficients

The individual mass-transfer coefficients describe transport through one film using a driving force in that phase.

Typical forms are: gas-side coefficient kG using partial-pressure driving force, and liquid-side coefficient kL using concentration (or mole-fraction) driving force.

🔑 Why we introduce overall coefficients

In experiments or design, it is often hard to know the interfacial values (pA,i, xA,i). Overall coefficients eliminate the interfacial unknowns by combining the two resistances in series.

\[ \frac{1}{K_L}=\frac{1}{k_L}+\frac{1}{H\,k_G} \]
Overall liquid-phase coefficient (liquid basis). H converts gas-side driving force to the liquid basis.

What H is doing in the formula

The two resistances must be expressed on the same basis before adding them. Henry’s law provides the conversion between gas and liquid equilibrium at the interface.

Large H (poor solubility) typically makes the gas-side resistance smaller on a liquid basis because 1/(H k_G) decreases as H increases.

⚠️ Unit consistency is not optional

Make sure H and kG are defined so that H·kG has units consistent with kL on the chosen basis. Different textbooks use different definitions (pressure vs concentration, mole fraction vs molarity).

📝 Worked example: Compute the overall liquid-phase coefficient K_L using the resistance-in-series relation. Given: k_L = 3.0×10⁻⁵ m/s, k_G = 0.015 mol/(m²·s·atm), H = 1.64×10³ atm/(mole fraction). Use 1/K_L = 1/k_L + 1/(H k_G).
  1. Compute 1/k_L = 1/(3.0×10⁻⁵) = 33,333.3333 s/m.
  2. Compute H·k_G = (1.64×10³)·(0.015) = 24.6.
  3. Compute 1/(H·k_G) = 1/24.6 = 0.0406504065.
  4. Add resistances: 1/K_L = 33,333.3333 + 0.0406504065 = 33,333.37398.
  5. Invert: K_L = 1/(33,333.37398) = 2.99999634×10⁻⁵ m/s.
✓ K_L = 3.00×10⁻⁵ m/s (to 3 sig figs).
✏️ Practice: Compute K_L from: k_L = 1.5×10⁻⁵ m/s, k_G = 0.008 mol/(m²·s·atm), H = 1.64×10³ atm/(mole fraction). Use 1/K_L = 1/k_L + 1/(H k_G).
m/s
Solution
  1. 1/k_L = 1/(1.5×10⁻⁵) = 66,666.6666667.
  2. H·k_G = (1.64×10³)·(0.008) = 13.12.
  3. 1/(H·k_G) = 1/13.12 = 0.0762195121951.
  4. 1/K_L = 66,666.6666667 + 0.0762195121951 = 66,666.7428862.
  5. K_L = 1/66,666.7428862 = 1.4999982851×10⁻⁵.

Analogous overall gas-phase coefficient

You can also define an overall coefficient on the gas basis, KG, by converting the liquid-side driving force to the gas basis using equilibrium.

Which overall coefficient you use depends on which phase’s bulk concentration you can measure or specify most naturally in your problem.

Check your understanding

1. What is the main purpose of introducing an overall mass-transfer coefficient (K)?
Overall coefficients fold resistances in series into one coefficient on a chosen basis, removing the interfacial unknowns from the rate expression.
2. In 1/K_L = 1/k_L + 1/(H k_G), which term represents the gas-film resistance expressed on a liquid basis?
1/(H k_G) is the gas-side resistance converted to a liquid-phase driving-force basis using Henry’s law.
3. If 1/k_L is much larger than 1/(H k_G), then K_L is approximately:
If the liquid-side resistance dominates, the overall coefficient on a liquid basis is essentially the liquid-side coefficient.
🔎 Related lessons
Two-Film Theory
✅ Key takeaways
  • k_G and k_L describe transport across individual gas and liquid films.
  • K_G or K_L combine both films into one coefficient on a chosen basis.
  • On a liquid basis, resistances add: 1/K_L = 1/k_L + 1/(H k_G).
  • If one resistance dominates, the overall coefficient is essentially the individual coefficient for that phase.
➡️ The conversion factor linking gas and liquid driving forces is equilibrium at the interface—next we make Henry’s law concrete and compute interfacial equilibrium compositions.
Want to test yourself on this? Try the Chemical Aptitude test →