Explanation:
In distillation columns, trays are used to separate the different components of a mixture by their boiling points. The number of trays required in a distillation column depends on various factors such as the desired separation efficiency, the components being separated, and the operating conditions.

Tray Efficiency:
Tray efficiency is a measure of how well the trays are able to separate the mixture into its individual components. Higher tray efficiency means better separation. However, achieving higher tray efficiency requires more trays.

Theoretical Trays:
Theoretical trays are hypothetical trays that would be required in an ideal distillation column to achieve complete separation of the components. The number of theoretical trays is calculated using various theoretical models such as the McCabe-Thiele method or the Fenske equation.

Additional Stage:
In practice, it is often difficult to achieve the same separation efficiency as the theoretical trays due to various factors such as non-ideal behavior, tray inefficiencies, and other limitations. Therefore, an additional stage (tray) is usually added to the column to compensate for these deviations from ideal behavior.

Condenser or Reboiler:
The additional stage can be either a condenser or a reboiler. A condenser is used to remove heat from the overhead vapor stream and condense it into a liquid. A reboiler, on the other hand, is used to supply heat to the bottom liquid stream and vaporize it. Both the condenser and reboiler play important roles in the distillation process.

Reason for Adding an Additional Tray:
The reason for adding an additional tray (condenser or reboiler) is to improve the separation efficiency of the distillation column. By adding an extra stage, the column is able to achieve a higher degree of separation between the components, even if it deviates from the ideal theoretical trays.

Conclusion:
In summary, the reason for adding one additional stage (tray) in order to find the total number of theoretical trays in a distillation column is to compensate for deviations from ideal behavior and improve the separation efficiency. This additional stage can be either a condenser or a reboiler, depending on the specific requirements of the distillation process.