Why does compressing a gas raise its pressure?

Gas pressure comes from moving particles colliding with container walls. Many collisions produce an average force over each area of wall. Pressure is this force per area, not simply the number of particles shown in a picture.

The model keeps the amount of gas and its temperature fixed while a piston changes the available volume. In a smaller volume, particles reach the walls more frequently per wall area. This raises pressure even though there are no extra particles. The twelve symbols continue to represent the same much larger population.

Fixed temperature also means unchanged average kinetic energy, the energy associated with particle motion. The higher pressure does not require the particles to gain a higher average kinetic energy. The short motion arrows are illustrative, not identical paths followed by all the particles.

For this ideal gas, pressure and volume change inversely: halving the volume doubles the pressure. The initial 2-liter state has a pressure of 100 kilopascals; the 1-liter state has 200, and the 4-liter state has 50. This comparison assumes the gas has reached the stated temperature after compression. Real gases and rapid uncooled compression can require a more detailed account.