10 litres of an air sample with relative humidity 0.6 is compressed to 5 litres at same temperature. What is the partial pressure of the water vapour in the compressed air, if the pressure of saturated water vapour at that temperature is 2.4 K Pa 

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
We have:
- Initial volume of air sample (V1) = 10 liters
- Compressed volume of air sample (V2) = 5 liters
- Relative humidity (RH) = 0.6
- Saturated vapor pressure at the given temperature (P_sat) = 2.4 kPa

### Step 2: Calculate the partial pressure of water vapor in the original air sample
The relative humidity is defined as the ratio of the partial pressure of the water vapor (P_water) to the saturated vapor pressure (P_sat), expressed as a percentage:

\[ RH = \frac{P_{water}}{P_{sat}} \times 100 \]

Rearranging this formula to find the partial pressure of water vapor gives us:

\[ P_{water} = RH \times \frac{P_{sat}}{100} \]

Substituting the values we have:

\[ P_{water} = 0.6 \times \frac{2.4 \, \text{kPa}}{100} = 0.6 \times 2.4 = 1.44 \, \text{kPa} \]

### Step 3: Analyze the effect of compression on the partial pressure
When the volume is reduced from 10 liters to 5 liters at constant temperature, the pressure of the gas will increase. According to Boyle's Law, if the volume is halved, the pressure will double (assuming temperature remains constant).

Thus, the new partial pressure (P'_water) after compression can be calculated as:

\[ P'_{water} = 2 \times P_{water} = 2 \times 1.44 \, \text{kPa} = 2.88 \, \text{kPa} \]

### Step 4: Compare with the saturated vapor pressure
Since the saturated vapor pressure at the given temperature is 2.4 kPa, we need to check if the new partial pressure exceeds this value.

Since \( P'_{water} = 2.88 \, \text{kPa} \) is greater than \( P_{sat} = 2.4 \, \text{kPa} \), this indicates that the air is now saturated with water vapor.

### Step 5: Conclusion
In this case, when the air is compressed, the partial pressure of the water vapor cannot exceed the saturated vapor pressure. Therefore, the partial pressure of water vapor in the compressed air is equal to the saturated vapor pressure:

\[ P_{water} = P_{sat} = 2.4 \, \text{kPa} \]

### Final Answer
The partial pressure of the water vapor in the compressed air is **2.4 kPa**.

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