According to the kinetic theory of gases, the pressure of a gas is due to

Options

A. change of kinetic energy of molecules as they strike the wall.
B. change of momentum of molecules as they strike the wall.
C. average kinetic energy of the molecules.
D. force of repulsion between the molecules.

Answer

**Step-by-Step Solution:**

1. **Understanding Gas Pressure**: The pressure of a gas is a result of the collisions of gas molecules with the walls of its container. When gas molecules move randomly, they collide with the walls, exerting force on them.

2. **Momentum Change During Collision**: When a gas molecule strikes the wall, it experiences a change in momentum. If we denote the mass of the molecule as \( m \) and its velocity before the collision as \( v \), the momentum before the collision is \( mv \).

3. **Calculating Change in Momentum**: Upon colliding elastically with the wall, the molecule reverses its direction. Thus, its velocity after the collision is \( -v \). The momentum after the collision is \( m(-v) = -mv \). Therefore, the change in momentum (\( \Delta p \)) can be calculated as:
\[ \Delta p = \text{Final momentum} - \text{Initial momentum} = -mv - mv = -2mv \]
Since we are interested in the magnitude, we can express this as \( 2mv \).

4. **Force Exerted on the Wall**: According to Newton's second law, the force exerted by the molecule on the wall is related to the change in momentum over time. If \( n \) is the number of collisions per second, the total force \( F \) exerted on the wall by one molecule can be expressed as:
\[ F = \frac{\Delta p}{\Delta t} = \frac{2mv}{\Delta t} \]
where \( \Delta t \) is the time interval during which the molecule collides with the wall.

5. **Pressure Definition**: Pressure (\( P \)) is defined as force per unit area. Therefore, if \( A \) is the area of the wall, the pressure exerted by the gas can be expressed as:
\[ P = \frac{F}{A} \]
Substituting the expression for force, we can see that the pressure is directly related to the change in momentum of the gas molecules as they strike the wall.

6. **Conclusion**: Thus, according to the kinetic theory of gases, the pressure of a gas is due to the change in momentum of the gas molecules as they collide with the walls of the container.

**Final Answer**: The pressure of a gas is due to the change of momentum of molecules as they strike the wall.

---