Distillation design — Overall (column) efficiency: what is the correct definition? Choose the statement that correctly defines the overall efficiency of a distillation column in terms of plates (or trays).

Introduction:
Overall (column) efficiency is a lumped measure that connects the number of ideal (theoretical) equilibrium stages predicted by equilibrium calculations to the number of real, physical trays (or height of packing) required in an actual distillation column. This question checks whether you know the correct definition that engineers use when converting theoretical designs into hardware.

Given Data / Assumptions:

• A distillation column designed by McCabe–Thiele, Fenske–Underwood–Gilliland, or rigorous simulation yields an ideal plate count.
• Actual trays exhibit non-idealities (mixing, weeping, entrainment, finite mass transfer).
• We need a single factor to scale theoretical stages to actual trays.

Concept / Approach:
Overall efficiency, often denoted E_o, is defined as E_o = N_ideal / N_actual. Rearranged, the actual number of trays is N_actual = N_ideal / E_o. E_o consolidates all non-ideal effects into one multiplier for column-wide sizing. It is different from Murphree tray efficiency, which is defined per tray and can vary along the column, and different from point efficiency, which is local to the mass-transfer surface.

Step-by-Step Solution:
Identify the theoretical equilibrium stage count from design calculations (N_ideal).Recognize that real trays are less efficient → more trays are needed.Apply the definition E_o = N_ideal / N_actual.Conclude: overall efficiency equals the ratio of ideal plates to actual plates.

Verification / Alternative check:
O’Connell-type correlations provide empirical overall efficiencies based on system properties (e.g., viscosity), confirming the practical use of E_o = N_ideal / N_actual.

Why Other Options Are Wrong:

• (b) Inverts the definition.
• (c) Murphree efficiency is per tray and not generally identical to E_o.
• (d) Point efficiency can exceed or be less than other efficiencies; no universal ordering applies.
• (e) Efficiency is affected by hydraulics and contacting, not just volatility.

Common Pitfalls:
Confusing overall efficiency with Murphree or point efficiencies; forgetting that efficiencies can vary between rectifying and stripping sections.

Final Answer:
The ratio of number of ideal (theoretical) plates to actual plates