If saturated vapours are compressed slowly (temperature remains constant) to half the initial volume, their pressure will be constant. give reason

Explanation

To solve the question, we need to understand the behavior of saturated vapors when they are compressed and how this relates to pressure and volume.

### Step-by-Step Solution:

1. **Understanding Saturated Vapors**:
- Saturated vapors are the vapor phase of a substance that is in equilibrium with its liquid phase at a given temperature. At this point, any additional vapor will condense into liquid.

2. **Applying the Ideal Gas Law**:
- The ideal gas law is represented as \( PV = nRT \). Here, \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.
- In this scenario, we are told that the temperature remains constant during the compression.

3. **Compression of Saturated Vapors**:
- When saturated vapors are compressed to half their initial volume, the volume \( V \) decreases.
- According to the ideal gas law, if the temperature \( T \) is constant and the volume \( V \) is halved, one might expect the pressure \( P \) to increase.

4. **Behavior of Saturated Vapors**:
- However, saturated vapors do not behave like ideal gases. When they are compressed, a portion of the vapor condenses into liquid, maintaining the pressure constant.
- This is because the system reaches a new equilibrium between the liquid and vapor phases, which stabilizes the pressure.

5. **Conclusion**:
- Thus, even though the volume is halved, the pressure remains constant as the vapor condenses into liquid, preventing any increase in pressure. This behavior is due to the unique properties of saturated vapors, which do not obey the ideal gas law under these conditions.

### Final Answer:
The pressure of saturated vapors remains constant when compressed to half the initial volume at constant temperature because the vapor condenses into liquid, maintaining equilibrium between the liquid and vapor phases. This behavior is characteristic of saturated vapors, which do not follow the ideal gas law.