Two container 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 same temperature, the water vapour in the container 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 relationship between the water vapor pressures in the two containers, A and B.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Volume of container A (V_A) is twice that of container B (V_B):
\[ V_A = 2V_B \]
- Amount of water in container A (m_A) is half that in container B (m_B):
\[ m_A = \frac{1}{2} m_B \]
- Both containers are at the same temperature (T_A = T_B).

2. **Understand the Concept of Vapor Pressure:**
- The vapor pressure of a liquid is determined by its temperature and is independent of the volume of the container or the amount of liquid present, as long as there is some liquid present to establish equilibrium.

3. **Apply the Concept of Vapor Pressure:**
- Since both containers are at the same temperature, the vapor pressure of water in both containers will be the same. This is because vapor pressure is a property of the liquid and depends only on temperature.

4. **Express the Vapor Pressure:**
- Let the vapor pressure in container A be P_A and in container B be P_B. Since the temperatures are the same:
\[ P_A = P_B \]

5. **Calculate the Ratio of Vapor Pressures:**
- Therefore, the ratio of the vapor pressures in the two containers is:
\[ \frac{P_A}{P_B} = 1 \]

### Final Answer:
The ratio of the water vapor pressures in container A and B is:
\[ P_A : P_B = 1 : 1 \]