ANS:B - number of plates is infinity.

At minimum reflux ratio for a given separation, the number of plates is infinity. Explanation:

1. Minimum Reflux Ratio:
   • The reflux ratio in a distillation column refers to the ratio of the liquid reflux (returned liquid) to the distillate (product) flow rate.
   • The minimum reflux ratio represents the minimum amount of reflux required to achieve a desired separation between the components in the feed mixture.
   • At the minimum reflux ratio, the distillation column operates at the least reflux possible while still maintaining the desired separation efficiency.
2. Number of Plates:
   • The number of theoretical plates in a distillation column refers to the number of equilibrium stages required for the separation of components in the feed mixture.
   • At minimum reflux ratio, the number of theoretical plates required for the separation is theoretically infinite.
   • This is because the minimum reflux ratio provides the minimum amount of liquid necessary to maintain the required vapor-liquid equilibrium conditions across the column, allowing for an infinite number of theoretical plates to achieve the desired separation.
3. Efficiency of Separation:
   • At minimum reflux ratio, the separation is theoretically the most efficient because it represents the minimum amount of reflux required for the separation.
   • However, achieving this efficiency may require an infinite number of theoretical plates, which is practically unattainable.

In summary, at minimum reflux ratio for a given separation, the number of plates required for the separation is theoretically infinite, and the separation is theoretically the most efficient. However, achieving this efficiency may not be practical due to the impracticality of having an infinite number of theoretical plates.