Certain volume of a gas exerts on its walls some pressure at a particular temperature. It has been observed that by reducing the volume of the gas to half of its original value the pressure becomes twice that of its initial value at constant temperature. This happens because

Options

A. Mass of the gas increases with pressure
B. Speed of the gas molecules decreases
C. More number of gas molecules strike the surface per second
D. Gas molecules attract each other

Answer

To solve the question, we will analyze the relationship between pressure, volume, and the number of collisions of gas molecules with the walls of the container, using the ideal gas law and kinetic molecular theory.

### Step-by-Step Solution:

1. **Understanding the Initial Situation**:
- We have a certain volume of gas at a specific temperature, exerting a certain pressure on the walls of its container. According to the ideal gas law, pressure (P) is related to volume (V) and temperature (T) as follows:
\[ PV = nRT \]
- Here, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature.

2. **Reducing the Volume**:
- When the volume of the gas is reduced to half of its original value (let's denote the original volume as \( V_1 \) and the new volume as \( V_2 = \frac{V_1}{2} \)), we want to understand how this affects the pressure.
- According to Boyle's Law (which states that pressure is inversely proportional to volume at constant temperature), if the volume is halved, the pressure will double. This can be mathematically represented as:
\[ P_1 V_1 = P_2 V_2 \]
\[ P_2 = \frac{P_1 V_1}{V_2} = \frac{P_1 V_1}{\frac{V_1}{2}} = 2P_1 \]

3. **Reason for Increased Pressure**:
- The increase in pressure can be explained by the fact that the gas molecules are now confined to a smaller space. As a result, they will collide with the walls of the container more frequently.
- The number of collisions per unit time increases because the distance that the gas molecules have to travel to hit the walls is reduced. This leads to a higher force exerted on the walls, resulting in increased pressure.

4. **Conclusion**:
- The pressure of the gas becomes twice its initial value when the volume is halved at constant temperature due to an increase in the frequency of collisions of gas molecules with the walls of the container.

### Final Answer:
This happens because the number of gas molecules striking the surface per second increases when the volume is reduced, leading to an increase in pressure.