McCabe–Thiele analysis: what is the typical slope of the operating line in the stripping section (assume constant molal overflow)?

Introduction / Context:
In binary distillation with constant molal overflow, the rectifying and stripping sections have straight operating lines on the y–x diagram. Their slopes depend on internal flow ratios and inform the number of stages and feasibility.

Given Data / Assumptions:

• Constant molal overflow holds (enthalpy effects modest).
• Definitions: Rectifying slope = L/V above the feed; Stripping slope = L̄/V̄ below the feed.
• Typical column no side draws; total condenser and partial reboiler.

Concept / Approach:
In the stripping section, the internal vapor flow V̄ is commonly larger than the liquid flow L̄ (because of vapor generation in the reboiler), so L̄/V̄ is less than 1, giving an operating line with slope under unity. Only in unusual configurations (heavy reflux of bottoms, side draws) could the slope exceed 1.

Step-by-Step Solution:
Write stripping operating line: y = (L̄/V̄) x − (B/V̄) xB (form depends on definitions).Recognize slope = L̄/V̄.For typical designs, L̄ < V̄ → slope < 1.

Verification / Alternative check:
Worked examples commonly show rectifying slope near R/(R+1) (below 1) and stripping slope also below 1 under standard conditions.

Why Other Options Are Wrong:
0 or ∞: would imply no mass exchange or a vertical line; not representative of operating sections.> 1: contradicts the usual L̄/V̄ relationship in the stripping section.

Common Pitfalls:
Mixing rectifying and stripping definitions; forgetting side draw effects on internal flows.

Final Answer:
< 1