Question

A plate is called a theoretical plate when

• A. The vapour and liquid leaving the plate are in equilibrium
• B. The vapour and liquid entering the plate are in equilibrium
• C. The vapour leaving the plate is in equilibrium with the liquid entering the plate
• D. The liquid leaving the plate is in equilibrium with the vapour entering the plate

Hint:

Theoretical plates are idealizations. Real plates in distillation columns do not achieve perfect equilibrium. The efficiency of a real plate is defined as the number of theoretical plates required to achieve the same separation as one real plate.

Answer 1

The Correct Option is A

Step 1: Understand the concept of a theoretical plate in distillation.
In distillation columns and other staged separation processes, a theoretical plate (or ideal stage) represents a hypothetical stage where the vapor and liquid streams leaving the stage are in thermodynamic equilibrium. This implies that there is sufficient contact time and perfect mixing between the vapor rising from the plate below and the liquid flowing down from the plate above, allowing them to reach equilibrium with respect to the components being separated. Step 2: Analyze the conditions for equilibrium on a theoretical plate.
For the vapor and liquid leaving a theoretical plate to be in equilibrium, the following must hold:
The temperature of the exiting vapor and the exiting liquid are the same.
For each component, the vapor and liquid phases are in thermodynamic equilibrium, meaning the relationship between their compositions is governed by vapor-liquid equilibrium (VLE) data at the plate's temperature and pressure. This is often represented by equilibrium relationships like Raoult's Law (for ideal solutions) or more complex VLE correlations for non-ideal systems. In essence, a theoretical plate achieves the maximum possible separation for a single stage because it assumes that the exiting streams have had enough contact to reach complete equilibrium. Step 3: Evaluate the given options based on the definition of a theoretical plate.
(1) The vapour and liquid leaving the plate are in equilibrium: This directly matches the definition of a theoretical plate. The ideal condition assumes that the vapor rising and the liquid descending achieve equilibrium on the plate before they leave. (2) The vapour and liquid entering the plate are in equilibrium: In a real or theoretical plate, the streams entering are generally not in equilibrium. The purpose of the plate is to bring them closer to equilibrium. If they were already in equilibrium, no further separation would occur on that stage. (3) The vapour leaving the plate is in equilibrium with the liquid entering the plate: The vapor leaving a plate has interacted with the liquid on that plate, which originated from the plate above. It is not necessarily in equilibrium with the liquid entering the plate from above, which has a different composition. (4) The liquid leaving the plate is in equilibrium with the vapour entering the plate: Similarly, the liquid leaving a plate has interacted with the vapor rising from the plate below. It is not necessarily in equilibrium with the vapor entering the plate from below, which has a different composition. Step 4: Conclude the correct condition for a theoretical plate.
The defining characteristic of a theoretical plate is that the vapor and liquid streams leaving the plate are in thermodynamic equilibrium with each other.