The relative humidity is 50%, if air contains about

Options

A. 2.55 g of water vapour at `40^@C`
B. 25.5 g of water vapour at `40^@C`
C. 2.55 kg of water vapour at `40^@C`
D. 25.5 kg of water vapour at `40^@C`

Answer

To solve the question regarding relative humidity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Relative Humidity**:
Relative humidity (RH) is defined as the amount of water vapor present in the air compared to the maximum amount of water vapor that air can hold at a specific temperature, expressed as a percentage.

2. **Formula for Relative Humidity**:
\[ \text{Relative Humidity (RH)} = \left( \frac{\text{Actual Water Vapor Pressure}}{\text{Saturation Vapor Pressure}} \right) \times 100\% \]
In this case, we know RH is 50%.

3. **Interpret the Given Information**:
If the relative humidity is 50%, it means that the air contains half of the maximum amount of water vapor it can hold at that temperature.

4. **Determine the Saturation Vapor Pressure**:
Let’s denote the saturation vapor pressure (the maximum amount of water vapor the air can hold at the given temperature) as \( P_s \). Since RH is 50%, we can express the actual water vapor pressure \( P_a \) as:
\[ P_a = 0.5 \times P_s \]

5. **Use the Given Data**:
The problem states that at a certain temperature (40 degrees Celsius), the air contains 25.5 grams of water vapor. Since this amount corresponds to 50% relative humidity, we can deduce that:
\[ 25.5 \text{ grams} = 0.5 \times P_s \]

6. **Calculate the Saturation Amount**:
To find the saturation amount (the maximum amount of water vapor the air can hold at 40 degrees Celsius), we can rearrange the equation:
\[ P_s = 2 \times 25.5 \text{ grams} = 51 \text{ grams} \]

7. **Conclusion**:
Therefore, at 40 degrees Celsius, the air can hold a maximum of 51 grams of water vapor, and at 50% relative humidity, it contains 25.5 grams of water vapor.

### Final Answer:
The air contains 25.5 grams of water vapor at 40 degrees Celsius when the relative humidity is 50%.

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