Distillation design – what does the Fenske equation determine? In binary or multicomponent distillation at total reflux, the Fenske equation is used to compute which design parameter?

Introduction / Context:
Short-cut distillation methods separate the tasks of stage count and reflux determination. The Fenske–Underwood–Gilliland framework starts with Fenske for stage count at total reflux, Underwood for minimum reflux ratio, and Gilliland (or modern alternatives) for finite reflux design. Recognizing which equation does what avoids common exam and design errors.

Given Data / Assumptions:

• Total reflux (no distillate or bottoms withdrawal).
• Constant relative volatility assumption for each key pair.
• Sharp split specified by key components.

Concept / Approach:
The Fenske equation relates the composition targets of light and heavy key components to the minimum theoretical stage number at total reflux. Because all vapor is condensed and returned, separation is maximized per stage without finite reflux penalties. Column height depends on plate efficiency and spacing, not directly from Fenske. Optimum or minimum reflux arises from Underwood and economic trade-offs, not Fenske.

Step-by-Step Solution:

Verification / Alternative check:
Design texts present Fenske for N_min, Underwood for R_min, and Gilliland for N vs R design point; this triad is standard in column synthesis.

Why Other Options Are Wrong:

• Maximum plates: Not a defined concept; total reflux gives minimum required plates.
• Column height: Requires tray efficiency/packing data, not Fenske alone.
• Optimum reflux: Determined by economics and correlations, not Fenske.

Common Pitfalls:
Using Fenske at finite reflux; it strictly applies at total reflux conditions.

Final Answer:
minimum number of theoretical plates