Question

The McCabe-Thiele method for distillation is valid, when______

• A. Molal overflow is non-constant
• B. constant molal overflow (CMO) is assumed
• C. feed is always saturated liquid
• D. relative volatility varies with composition

Hint:

Remember that if the latent heats of vaporization of the two components are vastly different, the CMO assumption fails.
In such cases, the Ponchon-Savarit method is used because it incorporates enthalpy balances along with material balances.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the fundamental simplifying assumption under which the graphical McCabe-Thiele method for analyzing fractional distillation columns is valid.
This is a standard mass transfer topic in fractional distillation.

Step 2: Key Formula or Approach:
The McCabe-Thiele method uses straight operating lines for the rectifying and stripping sections.
For these lines to be straight on a \( y \)-\( x \) diagram, the liquid and vapor flow rates within each section must remain constant from stage to stage:
\[ L_{n} = L_{n+1} = L \quad \text{and} \quad V_{n} = V_{n+1} = V \]
This condition is known as Constant Molal Overflow (CMO).

Step 3: Detailed Explanation:

• Constant Molal Overflow (CMO): This assumption means that for every mole of high-boiling component that condenses in a stage, exactly one mole of low-boiling component is vaporized.
This holds true when:
1. The molal heats of vaporization of the components are approximately equal.
2. Sensible heat changes are negligible compared to latent heat.
3. Heat losses from the column to the surroundings are negligible.

• Significance of CMO: Under CMO, the operating lines in the rectifying and stripping sections are straight lines, which makes graphical stage-by-stage construction possible using only simple mass balances.

• Other Options:
If molal overflow is non-constant, more complex methods (such as the Ponchon-Savarit method, which includes enthalpy balances) must be used.
The feed does not have to be a saturated liquid; the McCabe-Thiele method can handle any feed thermal state (\( q \)-value).
The method assumes a constant relative volatility (\( \alpha \)) to generate a smooth, constant equilibrium curve.


Step 4: Final Answer:
The McCabe-Thiele method is valid when constant molal overflow (CMO) is assumed.