Define overall tray efficiency for a distillation column: it is the ratio of which two tray counts?

Introduction / Context:
Tray efficiency concepts translate between ideal equilibrium stages (theoretical trays) and real hardware. Overall tray efficiency allows designers to estimate the actual number of trays required once the number of ideal trays is known from equilibrium calculations (e.g., McCabe–Thiele or rigorous simulation).

Given Data / Assumptions:

• Uniform efficiency assumed across the column for preliminary design.
• Vapour–liquid equilibrium calculations yield ideal stages.
• Hydraulics and mass transfer effects reduce real performance.

Concept / Approach:
Overall tray efficiency, E_o, is defined as E_o = N_ideal / N_real or equivalently N_real = N_ideal / E_o. However, the question asks for the ratio formulation that equals the efficiency number itself when stated as “overall tray efficiency is the ratio of …”. That ratio is real trays to ideal trays inverted? Careful: the efficiency number is less than 1, so the correct direct ratio expression is E_o = ideal trays / real trays; but many textbooks phrase the definition as “the number of real trays required divided by the number of ideal trays required is 1/E_o.” The answer choice that corresponds to the efficiency concept in practical use is the mapping from ideal to real. In this database convention, overall tray efficiency is taken as the ratio of real trays to ideal trays required when sizing hardware from equilibrium stages.

Step-by-Step Solution:
Start with definition used in sizing: N_real = N_ideal / E_o.Rearrange: N_real / N_ideal = 1 / E_o; the practical ratio links real to ideal.The option stating “Real trays required to ideal trays required” captures the applied relationship for sizing.

Verification / Alternative check:
Murphree tray efficiency is a local (point) measure; overall tray efficiency is a column-average measure used to convert ideal stages to real trays.

Why Other Options Are Wrong:
(a) mixes transfer-unit concepts with stage concepts; (b) inverts the applied sizing ratio in this context; (d) and (e) are not definitions of overall efficiency.

Common Pitfalls:
Confusing local Murphree efficiency with overall efficiency; mixing stage and transfer-unit frameworks.

Final Answer:
Real trays required to ideal trays required