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Relative Volatility
Measures how much more volatile one component is than another in a mixture, the key parameter that determines how easily a mixture can be distilled.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| alpha_AB | Relative volatility of A to B | |
| y_A, y_B | Vapor-phase mole fractions of A and B | |
| x_A, x_B | Liquid-phase mole fractions of A and B |
What it means
Relative volatility is a key parameter in distillation that indicates how easily two components can be separated. It is defined as the ratio of the equilibrium vapour‑liquid distribution of component A to that of component B: α_AB = (y_A / x_A) / (y_B / x_B), where x and y are mole fractions in liquid and vapour, respectively. For ideal mixtures, α is approximately constant and equal to the ratio of vapour pressures (P_A_sat / P_B_sat). A value of α > 1 means that component A is more volatile and will concentrate in the vapour. The larger the α, the easier the separation, requiring fewer theoretical stages. When α approaches 1, separation becomes difficult and may require azeotropic or extractive distillation. Relative volatility is used in the Fenske equation to estimate the minimum number of stages, and in the McCabe‑Thiele method for binary systems. Understanding α is essential for distillation column design and for selecting the most suitable separation process.
Worked example
Relative Volatility – Two Examples
Real‑World| Parameter | Value |
|---|---|
| y_A | 0.6 |
| x_A | 0.4 |
| y_B | 0.4 |
| x_B | 0.6 |
| Parameter | Value |
|---|---|
| y_A | 0.7 |
| x_A | 0.5 |
| y_B | 0.3 |
| x_B | 0.5 |
Common mistakes
- Compositions: y_A and x_A are mole fractions in vapour and liquid phases, respectively.
- Relative volatility α: For ideal systems, α is constant; for non‑ideal, it varies with composition.
- α > 1: Means A is more volatile than B; the separation by distillation is easier.
- Temperature dependence: α often changes with temperature; use average or local values.
- Ratio of K‑values: α = K_A / K_B, where K_i = y_i/x_i.
Applications
Relative volatility, α_AB = (y_A/x_A) / (y_B/x_B), quantifies the difference in volatility between two components. It is a key parameter in distillation, as it determines the ease of separation. When α > 1, component A is more volatile and tends to concentrate in the vapour phase. Engineers use α to assess the feasibility of a distillation separation, to estimate the number of stages required, and to select between alternatives like pressure‑swing distillation or extractive distillation. For mixtures with α close to 1, difficult separations require many stages or high reflux. By understanding relative volatility, engineers can design economical and energy‑efficient distillation processes.
- Distillation column design – estimation of minimum number of stages
- Feasibility studies for separation of azeotropic or close‑boiling mixtures
- Selection of entrainers for extractive or azeotropic distillation
- Process simulation and optimisation of distillation sequences
- Understanding of vapour‑liquid equilibrium behaviour