Distillation — Fenske’s equation for minimum number of theoretical stages (at total reflux) is valid under which condition?

Introduction:
Fenske’s equation provides the minimum number of equilibrium stages required for a specified key-component split at total reflux. It is a powerful shortcut for preliminary column design when its assumptions are met. Recognizing those assumptions ensures correct application to binary and pseudo-binary separations.

Given Data / Assumptions:

• Total reflux (no product withdrawal, maximum internal reflux).
• Constant or average relative volatility between the light and heavy key components.
• Constant molar overflow not required at total reflux but equilibrium behavior must be consistent.

Concept / Approach:

Under total reflux, the composition profile is governed by equilibrium alone. If the relative volatility α is reasonably constant from tray to tray, the separation factor per stage is constant, allowing the logarithmic form of the Fenske equation to predict stage count directly. Significant variation in α due to non-ideality or large temperature/composition swings undermines the equation’s accuracy and calls for rigorous methods (e.g., stage-by-stage simulation).

Step-by-Step Solution:

Verification / Alternative check:

Process simulators show good agreement between Fenske and rigorous calculations for near-ideal binaries with mild α variation; discrepancies grow as α varies strongly.

Why Other Options Are Wrong:

B/C point to deviations that often make α composition-dependent; D: Fenske can be extended to multicomponent using effective keys but the core assumption remains constant α; E: Feed condition is irrelevant at total reflux.

Common Pitfalls:

Applying Fenske away from total reflux or to strongly non-ideal systems without checking α variability.

Final Answer:

relative volatility is reasonably constant