Fenske's equation for determining the minimum number of theoretical stages in distillation column holds good, when thea)relative volatility is reasonably constant.b)mixture (to be separated) shows negative deviation from ideality.c)mixture (to be separated) shows positive deviation from ideality.d)multicomponent distillation is involved.Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Introduction:
Fenske's equation is used to determine the minimum number of theoretical stages required in a distillation column. It is based on the assumption of constant relative volatility, which is the ratio of vapor pressures of the more volatile component to the less volatile component in a mixture. Fenske's equation holds good when the relative volatility is reasonably constant.

Explanation:
a) Relative volatility is reasonably constant:
When the relative volatility is reasonably constant, Fenske's equation can be used to accurately estimate the minimum number of theoretical stages required for separation. This assumption is valid for many binary mixtures where the components have similar boiling points and molecular weights.

b) Mixture shows negative deviation from ideality:
Negative deviation from ideality occurs when the intermolecular forces between the components of a mixture are stronger than the forces between the pure components. In such cases, the relative volatility may not remain constant throughout the distillation process. Therefore, Fenske's equation may not accurately predict the minimum number of theoretical stages required.

c) Mixture shows positive deviation from ideality:
Positive deviation from ideality occurs when the intermolecular forces between the components of a mixture are weaker than the forces between the pure components. Similar to negative deviation, the relative volatility may not remain constant in this case, and Fenske's equation may not provide accurate results.

d) Multicomponent distillation:
Fenske's equation is derived for binary mixtures and assumes that only two components are present in the mixture. When multicomponent distillation is involved, the assumptions of Fenske's equation may not hold true, as the relative volatility between each component can vary significantly. In such cases, more complex methods, such as the Fenske-Underwood-Gilliland method, should be used to determine the minimum number of theoretical stages.

Conclusion:
In conclusion, Fenske's equation for determining the minimum number of theoretical stages in a distillation column holds good when the relative volatility is reasonably constant. However, it may not provide accurate results when the mixture shows negative or positive deviation from ideality or when multicomponent distillation is involved. It is important to consider the specific characteristics of the mixture and use appropriate methods to determine the minimum number of stages for efficient separation.

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