The state of matter where particles are far apart and move randomly and quickly is the:

In a gas, particles have kinetic energy enough to completely overcome intermolecular forces. This results in particles being far apart with large empty spaces between them, moving randomly and quickly in all directions. Gas particles are widely spaced and have no regular arrangement. In contrast, solid particles are tightly packed in a fixed lattice, and liquid particles are close together but can slide past each other. Due to high kinetic energy, gas particles move freely at high speeds and frequently collide with each other and the walls of their container.