Question

In distillation column design, the McCabe-Thiele procedure is inadequate and Ponchon-Savarit procedure is needed when:

• A. saturated feed is not used
• B. an azeotrope forms
• C. the latent heats of vaporization of the more and less volatile components are greatly different
• D. a total condenser is used

Hint:

Distillation design choice criteria: - Equal latent heats (\(\lambda_A = \lambda_B\)) \(\rightarrow\) Constant Molar Overflow holds \(\rightarrow\) Use the simpler McCabe-Thiele Method (straight operating lines). - Unequal latent heats (\(\lambda_A \neq \lambda_B\)) \(\rightarrow\) Variable Molar Overflow \(\rightarrow\) Must use the comprehensive Ponchon-Savarit Method (incorporates complete enthalpy balances).

Answer 1

The Correct Option is C

Concept: The McCabe-Thiele method and the Ponchon-Savarit method are two classic graphical techniques used to determine the number of theoretical stages required for a binary distillation separation. The McCabe-Thiele method relies strictly on the simplifying assumption of Constant Molar Overflow (CMO) in each section of the column. This assumption dictates that the molar flow rates of liquid and vapor remain perfectly constant from one stage to the next within the rectifying or stripping sections ($L_{n} = L_{n+1}$ and $V_{n} = V_{n+1}$). The key physical requirements needed for the Constant Molar Overflow (CMO) assumption to hold valid are:
• The molar latent heats of vaporization ($\lambda$) of the two components must be equal ($\lambda_A \approx \lambda_B$).
• Sensible heat changes ($\Delta C_p \Delta T$) across stages are negligible compared to latent heat changes.
• Heat losses from the column shell to the surrounding environment are negligible.
• The heat of mixing upon blending components is completely negligible.

Step 1: Analyzing what happens when latent heats differ significantly.
If the molar latent heat of vaporization of the more volatile component ($\lambda_A$) is significantly different from that of the less volatile component ($\lambda_B$), the condensation of one mole of the less volatile vapor component will not release the exact amount of thermal energy required to vaporize exactly one mole of the more volatile liquid component. For instance, if component B has a much higher molar latent heat, its condensation will release enough energy to vaporize more than one mole of component A. This imbalance causes the total molar flow rates of vapor ($V$) and liquid ($L$) to fluctuate significantly from stage to stage throughout the column: \[ V_n \neq V_{n+1} \quad \text{and} \quad L_n \neq L_{n+1} \] Because the molar flow rates vary from stage to stage, the operating lines on a McCabe-Thiele diagram become curved instead of straight lines, making the standard McCabe-Thiele stepping procedure mathematically inaccurate and inadequate.

Step 2: Identifying the role of the Ponchon-Savarit method.
To properly design a distillation column under these conditions, one must use the more rigorous Ponchon-Savarit method. The Ponchon-Savarit method does not assume constant molar overflow. Instead, it incorporates complete, simultaneous material balances and enthalpy (energy) balances at every stage using an enthalpy-concentration ($H-x-y$) diagram. Therefore, when the latent heats of vaporization of the components are significantly different, the McCabe-Thiele procedure is inadequate, and the Ponchon-Savarit procedure is required.