Two containers A and B are partly filled with water and closed. The volume of A is twice that of B and it contains half the amount of water in B. If both are at the same temperature, the water vapour in the containers will have pressure in the ratio of

Options

A. `1 : 2`
B. `1 : 1`
C. `2 : 1`
D. `4 : 1`

Answer

To solve the problem, we need to analyze the information given about the two containers A and B.

### Step-by-Step Solution:

1. **Understanding the Containers**:
- Container A has a volume that is twice that of container B.
- Let the volume of container B be \( V \). Then, the volume of container A is \( 2V \).
- Container A contains half the amount of water compared to container B.
- If container B has \( m \) grams of water, then container A has \( \frac{m}{2} \) grams of water.

2. **Vapor Pressure Concept**:
- The vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor are in equilibrium.
- Importantly, the vapor pressure of a substance depends only on the temperature and is independent of the amount of liquid present.

3. **Applying the Concept to Containers**:
- Since both containers are at the same temperature, the vapor pressure of water in both containers will be the same.
- Therefore, the vapor pressure in container A (let's denote it as \( P_A \)) will be equal to the vapor pressure in container B (denote it as \( P_B \)).

4. **Finding the Ratio of Vapor Pressures**:
- Since \( P_A = P_B \), we can express the ratio of the vapor pressures as:
\[ \frac{P_A}{P_B} = 1 \]

### Final Answer:
The ratio of the vapor pressures in the two containers A and B is \( 1:1 \).

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