Under the assumption that the temperature and amount of gas are kept unchanged, increase in volume will increase the mean free path of the gas atoms/molecules between collisions with the vessel walls and among themselves (more space to move).
As a consequence, the number of collisions with the vessel walls will be reduced. Each collision with the wall is registered as applied force to the wall and averaged force over the surface we measure as pressure.
The net result is that fewer collisions with the vessel wall (more space available in larger volume) result in less force applied to the same wall’s surface, and therefore there is less pressure.
Department of Physics