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Gases exert pressure against anything around them, because of something called Brownian motion: every particle is moving in a random direction with a speed based on temperature. These particles rebound millions of times a second off each otehr and off container walls, changing direction and speed as they do. But for something to change direction, a force must be applied. This force acts on everything, the gas and the container.

That "anything" includes other parts of the gas volume. Now, if they don't fill up all of the available space, there is zero pressure exerted on one side, while there is nonzero positive pressure exerted on all others. The net result is pressure towards the empty volume.

This pulls/pushes the gas into the empty volume, filling it up. When there is enough gas in that space to counteract the pressure form the rest of the gas - which will be when the entire volume has the same number of molecules per volume unit - the pressures in all directions are balanced, and the gas in general stops moving.

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