Tray efficiencies in distillation: which of the following can exceed 100% under certain conditions?

Introduction / Context:
Tray or plate efficiencies quantify how closely actual mass transfer on a tray approaches ideal equilibrium behavior. Several efficiency definitions are used, including point, Murphree, and overall (column) efficiencies.

Given Data / Assumptions:

• Binary distillation framework.
• Definitions based on vapor composition change across a tray and the corresponding equilibrium compositions.

Concept / Approach:
The Murphree vapor-phase efficiency compares the actual change in vapor composition across a tray to the change that would occur if the exiting vapor reached equilibrium with the exiting liquid. Because composition profiles can “overshoot” the local equilibrium point due to hydraulics and contact patterns, the Murphree efficiency can mathematically exceed 100%.

Step-by-Step Solution:
1) Define E_M = (y_out − y_in) / (y_eq,liquid_out − y_in).2) If y_out lies beyond y_eq,liquid_out due to non-ideal contacting, the numerator exceeds the denominator.3) Hence E_M > 1 (i.e., > 100%) is possible even though it does not imply super-equilibrium mass transfer.

Verification / Alternative check:
Point efficiencies reflect local transfer and remain ≤ 100% by definition. Overall efficiencies average performance across many trays and hydraulic regimes and are also ≤ 100% in standard interpretations.

Why Other Options Are Wrong:
Overall plate efficiency is an averaged measure and does not exceed 100%.Point efficiency is defined locally relative to equilibrium and stays ≤ 100%.Therefore “None of these” is incorrect.

Common Pitfalls:
Interpreting E_M > 100% as physical violation; confusing Murphree with overall efficiency used for shortcut design.

Final Answer:
Murphree plate efficiency