Question

Why does changing the volume of a container change the pressure of the gas in it?
Changing the volume reduces the number of molecules so they hit the walls of the container less often.
Changing the volume reduces the force with which the molecules hit the walls of the container.
Changing the volume increases the speed of the molecules so they hit the walls of the container more often.
Changing the volume increases the area that the molecules collide with so the force is spread over a larger area.

Answer 1

None of the four statements is correct as written.

Correct explanation (kinetic-theory/ideal-gas view):
- Pressure is the force per unit area from molecules colliding with the walls. That force comes from the momentum change (impulse) delivered in each collision and how often collisions occur.
- For a fixed amount of gas at constant temperature, reducing the volume does not change the number of molecules or their average speed, but it shortens the distance they travel between wall hits. So they hit the walls more often — more impulses per second per unit area — and pressure increases (Boyle’s law, pV = constant at constant T).
- If temperature changes (e.g., adiabatic compression), the molecules’ speeds (and per-collision momentum change) also change, which additionally affects pressure. The general kinetic-theory formula is p = (1/3) ρ v_rms^2 (or pV = NkT).

Why each given choice is wrong:
1) Changing the volume does not by itself reduce the number of molecules (unless molecules are removed).
2) The force per collision is set by molecular speeds (temperature); at constant T it does not decrease when volume changes.
3) Molecular speed only increases if temperature increases — volume change alone doesn’t necessarily do that.
4) The pressure change is not primarily caused by spreading the same force over a larger wall area; often the wall area does not change (e.g., a piston), and pressure depends on collision rate and impulse, not just wall area.