Derivation of McCabe - Thiele Method

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The McCabe-Thiele method is essential for determining the minimum number of separation stages in distillation for two-component mixtures with similar enthalpy of vaporization. This method relies on the constant molar overflow condition, where one mole of vapor condenses for every mole of liquid vaporized on each stage of the column. The discussion highlights a need for a derivation of this method based on general energy and mass balances for a stationary column operation. References such as "Mass Transfer Operations" by Treybel and "Chemical Engineers' Handbook" by Perry et al. are suggested for further reading. Understanding this derivation is crucial for applying the McCabe-Thiele method effectively in distillation processes.
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Derivation of McCabe - Thiele method from general energy and mass balance around a tray at stationary state column operation
McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization.

If components have similar enthalpy of vaporization ,than on every stage of the column for one mole of vapor that condenses there is one mole of liquid which is vaporized and this ensures constant molar overflow condition which is essence of McCabe - Thiele method.

However, I can't find derivation of this method from general energy and mass balances written around a tray with condition that column operates stationary. If someone can provide it, it would be nice.
 
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Dario56 said:
Summary:: Derivation of McCabe - Thiele method from general energy and mass balance around a tray at stationary state column operation

McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization.

If components have similar enthalpy of vaporization ,than on every stage of the column for one mole of vapor that condenses there is one mole of liquid which is vaporized and this ensures constant molar overflow condition which is essence of McCabe - Thiele method.

However, I can't find derivation of this method from general energy and mass balances written around a tray with condition that column operates stationary. If someone can provide it, it would be nice.
See Mass Transfer Operations by Treybel or Chemical Engineers' Handbook by Perry et al
 
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