McCabe–Thiele method — Which of the following is <em>not</em> a valid simplifying assumption used for continuous binary distillation when calculating the number of ideal stages by the McCabe–Thiele graphical method?

Introduction:The McCabe–Thiele method estimates the number of equilibrium stages for binary distillation. It relies on simplifying assumptions that linearise operating lines and make the graphical construction practical.

Given Data / Assumptions:

• Binary system, single feed, steady operation.
• Negligible heat losses to surroundings.
• Focus on typical textbook assumptions.

Concept / Approach:Key assumptions for constant molar overflow include: negligible sensible heat effects (so L and V are constant section-wise), equal or nearly equal molar latent heats, and negligible heats of mixing. Reflux is typically assumed saturated liquid at the column top (q = 1 for total condenser), which simplifies operating lines. Stating that reflux is not saturated contradicts the standard simplifying basis.

Step-by-Step Solution:List standard assumptions: constant L and V, equal latent heats, zero heat of mixing, saturated reflux from a total condenser.Identify the exception: “reflux is not saturated” is inconsistent with the simplifying basis.Therefore, option (b) is not a valid assumption.

Verification / Alternative check:When reflux is subcooled or partially condensed (q ≠ 1), additional enthalpy balances are needed and the simple linear operating lines change, complicating the McCabe–Thiele plot.

Why Other Options Are Wrong:

• (a), (c), and (d) are the classic assumptions enabling constant molar overflow and linear operating lines.

Common Pitfalls:Assuming the method applies unchanged when heats of mixing or non-idealities are large; forgetting that partial condensers or superheated vapor overhead alter the q-line and operating lines.

Final Answer:Reflux is not a saturated liquid.