Feed thermal condition in distillation: what is the value of the “q” line slope parameter for a SATURATED LIQUID feed entering a distillation column?

Introduction / Context:
In McCabe–Thiele analysis, the feed condition is represented by a “q-line” whose slope depends on the fraction of the feed that must be vaporized to reach saturated vapor at column pressure. Correctly identifying q is crucial for locating the intersection with operating lines and determining the number of stages.

Given Data / Assumptions:

• Saturated liquid feed at the column pressure.
• Binary or pseudobinary system representation.
• Constant molar overflow assumptions apply for graphical analysis.

Concept / Approach:

By definition, q is the fraction of the feed that is liquid after an adiabatic flash to column conditions. For a saturated liquid, the entire feed is liquid (no vapor fraction), so q = 1. The q-line in x–y space then has slope q/(q − 1) → infinite (vertical line), but in the common slope definition for enthalpy-free form, we report simply q = 1 for the thermal condition identifier.

Step-by-Step Solution:

Verification / Alternative check:

Other canonical cases: saturated vapor → q = 0; subcooled liquid → q > 1; superheated vapor → q < 0; part-liquid/part-vapor → 0 < q < 1.

Why Other Options Are Wrong:

0, <1, and >1 correspond to different feed enthalpy states, not saturated liquid.

Common Pitfalls:

Confusing q with the slope of the q-line directly; mixing sign conventions among textbooks.

Final Answer:

1